**Meet the editor**

Dr. Moumita Mukherjee completed higher-education from Presidency College, Calcutta, India and University of Calcutta, India. She received M.Sc. degree in Physics with specialization in Electronics and Communication and Ph.D. (Tech) in Radio Physics and Electronics from University of Calcutta, India. She worked as a Senior Research Fellow (SRF) of Defence Research and Devel-

opment Organization (DRDO), Ministry of Defence, Govt. of India, under Visva Bharati University, India, Advanced Technology Centre, Jadavpur University, India and Centre for Millimeter-wave Semiconductor Devices & Systems (CMSDS), India. She is presently working as a 'DRDO- Research Associate' at CMSDS, IRPE, University of Calcutta. Her research interest is focused on the modeling/simulation and fabrication of Millimeter and Sub-millimeter (Terahertz) wave high power homo-junction/hetero-junction devices based on wide-band-gap semiconductors, photo-irradiation effects on the high power Terahertz IMPATT oscillators, nano-scale THz devices and Microwave photonics. She published more than 85 peer-reviewed research papers on semiconductor devices in reputed International refereed journals and reviewed IEEE-Proceedings. She is the author of a book on "Fundamentals of Engineering Physics", a number of international book-chapters and worked as a Chief Editor and editor in a number of reputed international journals and publications in India and abroad.

Contents

**Preface IX** 

**Part 1 Silicon Carbide: Theory, Crystal Growth, Defects,** 

Kun Xue, Li-Sha Niu and Hui-Ji Shi

**the Other Diamond Synthetics 53**  Shigeto R. Nishitani, Kensuke Togase, Yosuke Yamamoto, Hiroyasu Fujiwara and

**in the SiCx Layers (x = 0.03–1.4)** 

Chapter 2 **SiC Cage Like Based Materials 23** 

Chapter 3 **Metastable Solvent Epitaxy of SiC,** 

Chapter 4 **The Formation of Silicon Carbide** 

Lina Ning and Xiaobo Hu

Philippe Colomban

Chapter 7 **SiC, from Amorphous to Nanosized Materials,** 

Chapter 8 **Micropipe Reactions in Bulk SiC Growth 187**  M. Yu. Gutkin, T. S. Argunova,

V. G. Kohn, A. G. Sheinerman and J. H. Je

Patrice Mélinon

Tadaaki Kaneko

Chapter 5 **SiC as Base of Composite** 

J.M. Molina

Chapter 1 **Mechanical Properties of Amorphous Silicon Carbide 3** 

**Characterization, Surface and Interface Properties 1** 

**Formed by Multiple Implantation of C Ions in Si 69** 

Kair Kh. Nussupov and Nurzhan B. Beisenkhanov

**Materials for Thermal Management 115** 

Chapter 6 **Bulk Growth and Characterization of SiC Single Crystal 141** 

**the Exemple of SiC Fibres Issued of Polymer Precursors 161** 

### Contents

#### **Preface** XIII


X Contents


Chapter 10 **Creation of Ordered Layers on Semiconductor Surfaces: An ab Initio Molecular Dynamics Study of the SiC(001)-3×2 and SiC(100)-c(2×2) Surfaces 231**  Yanli Zhang and Mark E. Tuckerman

Contents VII

Chapter 19 **Silicon Carbide Filled Polymer Composite for** 

Chapter 21 **Compilation on Synthesis, Characterization and** 

Chapter 20 **Comparative Assessment of**

Nor Zaihar Yahaya

**Erosive Environment Application: A Comparative** 

Sandhyarani Biswas, Amar Patnaik and Pradeep Kumar

**Si Schottky Diode Family in DC-DC Converter 469** 

**Properties of Silicon and Boron Carbonitride Films 487**  P. Hoffmann, N. Fainer, M. Kosinova, O. Baake and W. Ensinger

**Analysis of Experimental and FE Simulation Results 453** 

	- **Part 2 Silicon Carbide: Electronic Devices and Applications 335**

VI Contents

Chapter 9 **Thermal Oxidation of Silicon Carbide (SiC) – Experimentally Observed Facts 207** Sanjeev Kumar Gupta and Jamil Akhtar

Yanli Zhang and Mark E. Tuckerman

Karly M. Pitman, Angela K. Speck,

**Silicon Carbide Technology 283**  Zhongchang Wang, Susumu Tsukimoto, Mitsuhiro Saito and Yuichi Ikuhara

**with High Pressure Method 309**

**Prospects and Challenges 337** 

Chapter 15 **Recent Developments on Silicon Carbide** 

Amel Laref and Slimane Laref

**SiC Device Insulation: Review of** 

**Abrasive Water Jet Machining 431**  Ahsan Ali Khan and Mohammad Yeakub Ali

Chapter 17 **Dielectrics for High Temperature** 

Zarel Valdez-Nava

Chapter 18 **Application of Silicon Carbide in** 

**Electronic Devices and Applications 335** 

Mariana Amorim Fraga, Rodrigo Sávio Pessoa, Homero Santiago Maciel and Marcos Massi

**New Polymeric and Ceramic Materials 409**  Sombel Diaham, Marie-Laure Locatelli and

Chapter 16 **Opto-Electronic Study of SiC Polytypes: Simulation** 

**Thin Films for Piezoresistive Sensors Applications 369** 

**with Semi-Empirical Tight-Binding Approach 389** 

Chapter 11 **Optical Properties and Applications** 

Chapter 12 **Introducing Ohmic Contacts into** 

Chapter 13 **SiC-Based Composites Sintered** 

Chapter 14 **SiC Devices on Different Polytypes:** 

Moumita Mukherjee

Piotr Klimczyk

**Part 2 Silicon Carbide:** 

Chapter 10 **Creation of Ordered Layers on Semiconductor Surfaces: An ab Initio Molecular Dynamics Study of the SiC(001)-3×2 and SiC(100)-c(2×2) Surfaces 231**

**of Silicon Carbide in Astrophysics 257** 

Anne M. Hofmeister and Adrian B. Corman

Chapter 21 **Compilation on Synthesis, Characterization and Properties of Silicon and Boron Carbonitride Films 487**  P. Hoffmann, N. Fainer, M. Kosinova, O. Baake and W. Ensinger

Preface

broadband and efficient power generation.

benefits when considering the overall system performance.

**Silicon Carbide** (SiC) and its polytypes have been a part of human civilization for a long time; the technical interest of this hard and stable compound has been realized in 1885 and 1892 by *Cowless* and *Acheson* for grinding and cutting purpose, leading to its manufacture on a large scale. The fundamental physical limitations of Si operation at higher temperature and power are the strongest motivations for switching to wide bandgap (WBG) semiconductors such as SiC for these applications. The high output power density of WBG transistors allows the fabrication of smaller size devices with the same output power. Higher impedance, due to the smaller size, allows easier and lower loss matching in amplifiers. The operation at high voltage, due to its high breakdown electric field, not only reduces the need for voltage conversion, but also provides the potential to obtain high efficiency, which is a critical parameter for amplifiers. The wide bandgap enables it to operate at elevated temperatures. These attractive features in power amplifier enabled by the superior properties make these devices promising candidates for microwave power applications. Especially military systems such as electrically steered antennas (ESA) could benefit from more compact,

Another application area is robust front end electronics such as low noise amplifiers (LNAs) and mixers. A higher value of saturation velocity in SiC will allow higher current and hence higher power from the devices. Heat removal is a critical issue in microwave power transistors. The thermal conductivity of SiC is substantially higher than that of GaAs and Si. The large bandgap and high temperature stability of SiC and GaN also makes them possible to operate devices at very high temperatures. At temperatures above 300 0C, SiC has much lower intrinsic carrier concentrations than Si and GaAs. This implies that devices designed for high temperatures and powers should be fabricated from WBG semiconductors, to avoid effects of thermally generated carriers. When the ambient temperature is high, the thermal management to cool down crucial hot sections introduces additional overhead that can have a negative impact relative to the desired

The potential of using SiC in semiconductor electronics has been already recognized half a century ago. Despite its well-known properties, it has taken a few decades to overcome the exceptional technological difficulties of getting SiC material to reach

device quality and travel the road from basic research to commercialization.

### Preface

**Silicon Carbide** (SiC) and its polytypes have been a part of human civilization for a long time; the technical interest of this hard and stable compound has been realized in 1885 and 1892 by *Cowless* and *Acheson* for grinding and cutting purpose, leading to its manufacture on a large scale. The fundamental physical limitations of Si operation at higher temperature and power are the strongest motivations for switching to wide bandgap (WBG) semiconductors such as SiC for these applications. The high output power density of WBG transistors allows the fabrication of smaller size devices with the same output power. Higher impedance, due to the smaller size, allows easier and lower loss matching in amplifiers. The operation at high voltage, due to its high breakdown electric field, not only reduces the need for voltage conversion, but also provides the potential to obtain high efficiency, which is a critical parameter for amplifiers. The wide bandgap enables it to operate at elevated temperatures. These attractive features in power amplifier enabled by the superior properties make these devices promising candidates for microwave power applications. Especially military systems such as electrically steered antennas (ESA) could benefit from more compact, broadband and efficient power generation.

Another application area is robust front end electronics such as low noise amplifiers (LNAs) and mixers. A higher value of saturation velocity in SiC will allow higher current and hence higher power from the devices. Heat removal is a critical issue in microwave power transistors. The thermal conductivity of SiC is substantially higher than that of GaAs and Si. The large bandgap and high temperature stability of SiC and GaN also makes them possible to operate devices at very high temperatures. At temperatures above 300 0C, SiC has much lower intrinsic carrier concentrations than Si and GaAs. This implies that devices designed for high temperatures and powers should be fabricated from WBG semiconductors, to avoid effects of thermally generated carriers. When the ambient temperature is high, the thermal management to cool down crucial hot sections introduces additional overhead that can have a negative impact relative to the desired benefits when considering the overall system performance.

The potential of using SiC in semiconductor electronics has been already recognized half a century ago. Despite its well-known properties, it has taken a few decades to overcome the exceptional technological difficulties of getting SiC material to reach device quality and travel the road from basic research to commercialization.

SiC exists in a large number of cubic (C), hexagonal (H) and rhombohedral (R) polytype structures. It varies in the literature between 150 and 250 different ones. For microwave and high temperature applications the 4H is the most suitable and popular polytype. Its carrier mobility is higher than in the 6H-SiC polytype, which is also commercially available. SiC as a material is thus most suited for applications in which high-temperature, high-power, and high-frequency devices are needed. To that end, this book is a good compendium of advances made since the early 1990s at numerous reputable international institutions by top authorities in the field.

Sequence of chapters is arranged to cover a wide array of activities in a fairly coherent and effective manner. In 21 chapters of the book, special emphasis has been placed on the "materials" aspects and developments thereof. To that end, about 70% of the book addresses the theory, crystal growth, defects, surface and interface properties, characterization, and processing issues pertaining to SiC. The remaining 30% of the book covers the electronic device aspects of this material. Overall, this book will be valuable as a reference for SiC researchers for years to come.

This book prestigiously covers our current understanding of SiC as a semiconductor material in electronics. Its physical properties make it more promising for highpowered devices than silicon. The volume is devoted to the material and covers methods of epitaxial and bulk growth. Identification and characterization of defects is discussed in detail. The contributions help the reader to develop a deeper understanding of defects by combining theoretical and experimental approaches. Apart from applications in power electronics, sensors, and NEMS, SiC has recently gained new interest as a substrate material for the manufacture of controlled graphene. SiC and graphene research is oriented towards end markets and has high impact on areas of rapidly growing interest like electric vehicles.

> **Dr. Moumita Mukherjee, Scientist-B, Senior Asst. Professor**  Centre for Millimeter-wave Semiconductor Devices and Systems (CMSDS), Institute of Radio Physics and Electronics, University of Calcutta, India

## **Part 1**

**Silicon Carbide: Theory, Crystal Growth, Defects, Characterization, Surface and Interface Properties** 

**1** 

 *China* 

**Silicon Carbide** 

*Beijing Institute of Technology* 

*Tsinghua University, Beijing,* 

Kun Xue1, Li-Sha Niu2 and Hui-Ji Shi2

*1State Key Laboratory of Explosion Science and Technology,* 

*2School of Aerospace, FML, Department of Engineering Mechanics,* 

Excellent physical and chemical properties make silicon carbide (SiC) a prominent candidate for a variety of applications, including high-temperature, high-power, and high-frequency and optoelectronic devices, structural component in fusion reactors, cladding material for gas-cooled fission reactors, and an inert matrix for the transmutation of Pu(Katoh, Y. et al., 2007; Snead, L. L. et al., 2007). Different poly-types of SiC such as 3C, 6H of which 6H have been researched the most. There has been a considerable interest in fabricating 3C-SiC/6H-SiC hetero p-n junction devices in recent years. Ion implantation is a critical technique to selectively introduce dopants for production of Si-based devices, since conventional methods, such as thermal diffusion of dopants, require extremely high temperatures for application to SiC. There is, however, a great challenge with ion implantation because it inevitably produces defects and lattice disorder, which not only deteriorate the transport properties of electrons and holes, but also inhibit electrical activation of the implanted dopants(Benyagoub, A., 2008; Bolse, W., 1999; Jiang, W. et al., 2009; Katoh, Y. et al., 2006). Meanwhile the swelling and mechanical properties of SiC subjected to desplacive neutron irradiation are of importance in nuclear applications. In such irradiations the most dramatic material and microstructural changes occur during irradiation at low temperatures. Specifically, at temperatures under 100C volumetric swelling due to point defect induced strain has been seen to reach 3% for neutron irradiation doses of ~0.1-0.5. At these low temperatures, amorphization of the SiC is also possible, which would lead to a substantial volumetric expansion of ~15%, along with decreases in mechanical properties such as hardness and modulus(Snead, L. L. et al., 1992; Snead, L. L. et al., 1998; Snead, L. L., 2004;

Intensive experimental and theoretical efforts have been devoted to the dose and temperature dependence of the properties of irradiation-amorphized SiC (a-SiC)(Weber, W. J. et al., 1997). Heera *et al*. (Heera, V. et al., 1997) found that the amorphization of SiC induced by 2 MeV Si+ implantation is accompanied by a dramatic and homogeneous volume swelling until a critical dose level dependent on the temperature. Afterwards the volume tends to saturate and the density of *a*-SiC is about 12% less than that of the crystalline

**1. Introduction** 

Weber, W. J. et al., 1998).

**Mechanical Properties of Amorphous** 

### **Mechanical Properties of Amorphous Silicon Carbide**

Kun Xue1, Li-Sha Niu2 and Hui-Ji Shi2

*1State Key Laboratory of Explosion Science and Technology, Beijing Institute of Technology 2School of Aerospace, FML, Department of Engineering Mechanics, Tsinghua University, Beijing, China* 

#### **1. Introduction**

Excellent physical and chemical properties make silicon carbide (SiC) a prominent candidate for a variety of applications, including high-temperature, high-power, and high-frequency and optoelectronic devices, structural component in fusion reactors, cladding material for gas-cooled fission reactors, and an inert matrix for the transmutation of Pu(Katoh, Y. et al., 2007; Snead, L. L. et al., 2007). Different poly-types of SiC such as 3C, 6H of which 6H have been researched the most. There has been a considerable interest in fabricating 3C-SiC/6H-SiC hetero p-n junction devices in recent years. Ion implantation is a critical technique to selectively introduce dopants for production of Si-based devices, since conventional methods, such as thermal diffusion of dopants, require extremely high temperatures for application to SiC. There is, however, a great challenge with ion implantation because it inevitably produces defects and lattice disorder, which not only deteriorate the transport properties of electrons and holes, but also inhibit electrical activation of the implanted dopants(Benyagoub, A., 2008; Bolse, W., 1999; Jiang, W. et al., 2009; Katoh, Y. et al., 2006). Meanwhile the swelling and mechanical properties of SiC subjected to desplacive neutron irradiation are of importance in nuclear applications. In such irradiations the most dramatic material and microstructural changes occur during irradiation at low temperatures. Specifically, at temperatures under 100C volumetric swelling due to point defect induced strain has been seen to reach 3% for neutron irradiation doses of ~0.1-0.5. At these low temperatures, amorphization of the SiC is also possible, which would lead to a substantial volumetric expansion of ~15%, along with decreases in mechanical properties such as hardness and modulus(Snead, L. L. et al., 1992; Snead, L. L. et al., 1998; Snead, L. L., 2004; Weber, W. J. et al., 1998).

Intensive experimental and theoretical efforts have been devoted to the dose and temperature dependence of the properties of irradiation-amorphized SiC (a-SiC)(Weber, W. J. et al., 1997). Heera *et al*. (Heera, V. et al., 1997) found that the amorphization of SiC induced by 2 MeV Si+ implantation is accompanied by a dramatic and homogeneous volume swelling until a critical dose level dependent on the temperature. Afterwards the volume tends to saturate and the density of *a*-SiC is about 12% less than that of the crystalline

Mechanical Properties of Amorphous Silicon Carbide 5

suppresses the cavity nucleation, leading to increased ductility and toughness without

Because amorphous materials lack a topologically ordered network, analysis of deformations and defects presents a formidable challenge. Conventional computational techniques used for crystalline solids, such as the modulus of slip vector(Rodriuez de la Fuente, O. et al., 2002), centrosymmetry, and local crystalline order, fail to identify the deformation defects in disordered materials. Various models have been proposed to describe defects in such structures. The prevailing theory of plasticity in metallic glasses involves localized flow events in shear transformation zones (STZ)(Shi, Y. & Falk, M. L., 2005). An STZ is a small cluster of atoms that can rearranges under applied stress to produce a unit of plastic deformation. It is worth noting that most of these theories are based on the observations of metallic glasses. Whereas covalently bonded amorphous solids differs from their metallic counterparts due to their directed stereochemical bonds in forms of welldefined coordination polyhedral, e.g. [SiX4]or [CX4] tetrahedra in SiC. Thanks to the short range order retained in the amorphous covalent materials, plastic deformation tends to be more pronounced localized than in the case of metallic glasses(Szlufarska, I. et al., 2007). Moreover for amorphous alloys like *a*-SiC, the degree of chemical order has been always under the debates, although the consensus from these recent experimental studies of *a*-SiC seems to be in favor of the existence of C-C homonuclear bonds(Bolse, W., 1998; Ishimaru, M. et al., 2002; Ishimaru, M. et al., 2006; Snead, L. L. & Zinkle, S. J., 2002). The presence of dual disorder, namely chemical and topological disorder, in *a*-SiC definitely complicates the

compromising its strength(Mo, Y. & Szlufarska, I., 2007).

analysis of amorphous structure and the underlying atomic mechanisms.

**2. Amorphization mechanism of irradiation-amorphized SiC** 

identify.

switch of the fracture .

In general a truly atomistic model of plastic flow in amorphous covalent materials is still lacking. Instead of starting with complete *a*-SiC where widespread inhomogenities frozen into the entire material, we rather begin with a perfect 3C-SiC, then proceed to gradually increase the concentration of damage until a complete amorphous state is reached. Being a link between perfect crystalline and complete amorphous SiC, partially disordered SiC presents a favorable prototype to discern the role of isolated or clustered defects in the evolution of atomic mechanism, where the deformation defects are comparatively readily to

In this chapter, we first outline the studies concerning the c-a transition of irradiationamorphized SiC, laying the basis for the analysis of SiC amorphous. Then a complete topological description of simulated SiC structures ranging from c-a is presented in both the short – and medium-range with a special focus on the correlation between chemical disorder and the topology of *a*-SiC. Simulated tensile testing and nanoindentation are carried out on the varying *a*-SiC to examine the variations of mechanical response with varying concentration of defects. The correlation between some key mechanical properties of *a*-SiC, such as Young's modulus, strength, hardness, and the microstructure are quantified by virtue of chemical disorder, an characteristics underpinning the c-a transition. A crossover of atomic mechanisms from c-a are also discussed. This crossover is also embodied in the

With regard to the characterization of the varying disordered microstructures of *a*-SiC, the mechanisms controlling the c-a transformation have been of particular interest. By simulating the accumulation of irradiation damages due to the low energy recoils, Malerba

material. The experimental values of the elastic modulus and hardness of a-SiC estimated from measurements of surface and buried amorphous layers show a large degree of variability. In general, the hardness and elastic modulus in *a*-SiC are observed to decrease 20%-60% and 25%-40%, respectively. Weber *et al*.(Weber, W. J. et al., 1998) performed nanoindentation experiments with Berkovich indenter on the Ar+ beam induced *a*-SiC. The results suggest that the elastic modulus decreases ~24%, from 550 to 418 GPa. Snead *et al*.(Snead, L. L. et al., 1992) reported that the elastic modulus in SiC, irradiated with C+ at low temperatures, decrease from 400 GPa in the virgin region to about 275 GPa in the amorphized region; whereas the hardness was observed to decrease from 41 to 32 GPa. The mechanical properties of a-SiC irradiated by neutron have also been investigated(Snead, L. L. et al., 1998). A density decrease of 10.8% from the crystalline to amorphous (c-a) state is revealed along with a decrease in hardness from 38.7 to 21.0 GPa and a decrease in elastic modulus from 528 to 292 GPa.

The varying amorphous nature of a-SiC depending on the damage accumulation could justify the wide range of experimental measurements of mechanical properties of a-SiC. Thus of particular fundamental and technological interest has been developing the models capable of describing the various physical properties of SiC as a function of microstructural changes, specifically from c-a. Gao and Weber(Gao, F. & Weber, W. J., 2004) investigated the changes in elastic constants, the bulk and elastic moduli of SiC as a function of damage accumulation due to cascade overlap using molecular dynamics (MD) simulation. The results indicate a rapid decrease of these properties with increasing dose but the changes begin to saturate at doses greater than 0.1 MD-dpa. Given that fully amorphous state is reached at a dose of about 0.28 MD-dpa, they suggested that point defects and small cluster may contribute more significantly to the changes of elastic constants than the topological disorder associated with amorphization.

Although the inherent correlation between the mechanical properties and the disordered microstructures of *a*-SiC has been widely accepted, there still lacks a comprehensive description of this correlation given the intricate nature of a-SiC. Thus based on detailed examinations of an extensive series of simulated *a*-SiC models with varying concentration of defects, this chapter first attempts to characterize the structure of *a*-SiC with a range of underpinning parameters, whereby substantiates the correlation between the amorphous structure of SiC and a variety of mechanical properties. MD simulations are used to simulate the mechanical responses of varied disordered SiC microstructures subject to two typical loadings, namely axial tension and nanoindentaion, which are critical for measures of strength and ductility of bulk *a*-SiC and hardness of *a*-SiC film. The role of these simulations is not necessarily to reproduce exact experimental behaviors, but rather to identify possible atomistic mechanisms associated with a variety of disordered SiC structures, especially from c-a.

Amorphous materials often exhibit unique deformation mechanisms distinct from their crystalline counterparts. The coexistence of brittle grains and soft amorphous grain boundaries (GBs) consisting in nanocrystalline SiC (nc-SiC) results in unusual deformation mechanisms. In the simulation of nanoindentation(Szlufarska, I. et al., 2005), as the indenter depth increases, the deformation dominated by the crystallization of disordered GBs which "screen" the crystalline grains from deformation switches to the deformation dominated by disordering of crystalline grains. Plastic flow along grain boundaries can also effectively

material. The experimental values of the elastic modulus and hardness of a-SiC estimated from measurements of surface and buried amorphous layers show a large degree of variability. In general, the hardness and elastic modulus in *a*-SiC are observed to decrease 20%-60% and 25%-40%, respectively. Weber *et al*.(Weber, W. J. et al., 1998) performed nanoindentation experiments with Berkovich indenter on the Ar+ beam induced *a*-SiC. The results suggest that the elastic modulus decreases ~24%, from 550 to 418 GPa. Snead *et al*.(Snead, L. L. et al., 1992) reported that the elastic modulus in SiC, irradiated with C+ at low temperatures, decrease from 400 GPa in the virgin region to about 275 GPa in the amorphized region; whereas the hardness was observed to decrease from 41 to 32 GPa. The mechanical properties of a-SiC irradiated by neutron have also been investigated(Snead, L. L. et al., 1998). A density decrease of 10.8% from the crystalline to amorphous (c-a) state is revealed along with a decrease in hardness from 38.7 to 21.0 GPa and a decrease in elastic

The varying amorphous nature of a-SiC depending on the damage accumulation could justify the wide range of experimental measurements of mechanical properties of a-SiC. Thus of particular fundamental and technological interest has been developing the models capable of describing the various physical properties of SiC as a function of microstructural changes, specifically from c-a. Gao and Weber(Gao, F. & Weber, W. J., 2004) investigated the changes in elastic constants, the bulk and elastic moduli of SiC as a function of damage accumulation due to cascade overlap using molecular dynamics (MD) simulation. The results indicate a rapid decrease of these properties with increasing dose but the changes begin to saturate at doses greater than 0.1 MD-dpa. Given that fully amorphous state is reached at a dose of about 0.28 MD-dpa, they suggested that point defects and small cluster may contribute more significantly to the changes of elastic constants than the topological

Although the inherent correlation between the mechanical properties and the disordered microstructures of *a*-SiC has been widely accepted, there still lacks a comprehensive description of this correlation given the intricate nature of a-SiC. Thus based on detailed examinations of an extensive series of simulated *a*-SiC models with varying concentration of defects, this chapter first attempts to characterize the structure of *a*-SiC with a range of underpinning parameters, whereby substantiates the correlation between the amorphous structure of SiC and a variety of mechanical properties. MD simulations are used to simulate the mechanical responses of varied disordered SiC microstructures subject to two typical loadings, namely axial tension and nanoindentaion, which are critical for measures of strength and ductility of bulk *a*-SiC and hardness of *a*-SiC film. The role of these simulations is not necessarily to reproduce exact experimental behaviors, but rather to identify possible atomistic mechanisms associated with a variety of disordered SiC structures, especially from

Amorphous materials often exhibit unique deformation mechanisms distinct from their crystalline counterparts. The coexistence of brittle grains and soft amorphous grain boundaries (GBs) consisting in nanocrystalline SiC (nc-SiC) results in unusual deformation mechanisms. In the simulation of nanoindentation(Szlufarska, I. et al., 2005), as the indenter depth increases, the deformation dominated by the crystallization of disordered GBs which "screen" the crystalline grains from deformation switches to the deformation dominated by disordering of crystalline grains. Plastic flow along grain boundaries can also effectively

modulus from 528 to 292 GPa.

disorder associated with amorphization.

c-a.

suppresses the cavity nucleation, leading to increased ductility and toughness without compromising its strength(Mo, Y. & Szlufarska, I., 2007).

Because amorphous materials lack a topologically ordered network, analysis of deformations and defects presents a formidable challenge. Conventional computational techniques used for crystalline solids, such as the modulus of slip vector(Rodriuez de la Fuente, O. et al., 2002), centrosymmetry, and local crystalline order, fail to identify the deformation defects in disordered materials. Various models have been proposed to describe defects in such structures. The prevailing theory of plasticity in metallic glasses involves localized flow events in shear transformation zones (STZ)(Shi, Y. & Falk, M. L., 2005). An STZ is a small cluster of atoms that can rearranges under applied stress to produce a unit of plastic deformation. It is worth noting that most of these theories are based on the observations of metallic glasses. Whereas covalently bonded amorphous solids differs from their metallic counterparts due to their directed stereochemical bonds in forms of welldefined coordination polyhedral, e.g. [SiX4]or [CX4] tetrahedra in SiC. Thanks to the short range order retained in the amorphous covalent materials, plastic deformation tends to be more pronounced localized than in the case of metallic glasses(Szlufarska, I. et al., 2007). Moreover for amorphous alloys like *a*-SiC, the degree of chemical order has been always under the debates, although the consensus from these recent experimental studies of *a*-SiC seems to be in favor of the existence of C-C homonuclear bonds(Bolse, W., 1998; Ishimaru, M. et al., 2002; Ishimaru, M. et al., 2006; Snead, L. L. & Zinkle, S. J., 2002). The presence of dual disorder, namely chemical and topological disorder, in *a*-SiC definitely complicates the analysis of amorphous structure and the underlying atomic mechanisms.

In general a truly atomistic model of plastic flow in amorphous covalent materials is still lacking. Instead of starting with complete *a*-SiC where widespread inhomogenities frozen into the entire material, we rather begin with a perfect 3C-SiC, then proceed to gradually increase the concentration of damage until a complete amorphous state is reached. Being a link between perfect crystalline and complete amorphous SiC, partially disordered SiC presents a favorable prototype to discern the role of isolated or clustered defects in the evolution of atomic mechanism, where the deformation defects are comparatively readily to identify.

In this chapter, we first outline the studies concerning the c-a transition of irradiationamorphized SiC, laying the basis for the analysis of SiC amorphous. Then a complete topological description of simulated SiC structures ranging from c-a is presented in both the short – and medium-range with a special focus on the correlation between chemical disorder and the topology of *a*-SiC. Simulated tensile testing and nanoindentation are carried out on the varying *a*-SiC to examine the variations of mechanical response with varying concentration of defects. The correlation between some key mechanical properties of *a*-SiC, such as Young's modulus, strength, hardness, and the microstructure are quantified by virtue of chemical disorder, an characteristics underpinning the c-a transition. A crossover of atomic mechanisms from c-a are also discussed. This crossover is also embodied in the switch of the fracture .

#### **2. Amorphization mechanism of irradiation-amorphized SiC**

With regard to the characterization of the varying disordered microstructures of *a*-SiC, the mechanisms controlling the c-a transformation have been of particular interest. By simulating the accumulation of irradiation damages due to the low energy recoils, Malerba

Mechanical Properties of Amorphous Silicon Carbide 7

on the immediate coordination of a much larger number of atoms, hierarchical parameters signifying SRO and MRO seem to be more appropriate to describe the c-a transition and varying microstructures of *a*-SiC. The c-a transition is accordingly described in terms of the variations in the chemical disorder *χ* and other topological parameters. The correlation

Considerable investigations, including experimental and MD simulation studies, indicate a strong correlation between chemical and topological disorder. The x-ray absorption and Ramann spectroscropy performed by Bolse(Bolse, W., 1998) on Na+ irradiated SiC clearly showed that a large fraction of the [SiC4] tetrahedra is destroyed only after the removal of chemical order. The inspection of MD simulated melt-quenched *a*-SiC Has also revealed that chemical disorder determines the short- and medium-range topological order in *a*-SiC(Xue, K. et al., 2008). Therein an extended tetrahedron model only dependent on the composition and chemical disorder *χ* was developed to predict the probabilities of various local coordination tetrahedra, namely, Si-Si4-*n*C*n* and C-Si4-*n*C*n* (*n* = 0-4), reflecting the local spatial

0.0 100. 100. N 1.896 N 3.217 -6.39279 0.045 99.9 99.6 1.662 1.862 2.185 3.213 -6.32738 0.133 99.5 98.9 1.661 1.867 2.191 3.148 -6.21825 0.24 98.4 97.8 1.648 1.872 2.225 3.087 -6.10155 0.39 96.1 95.1 1.646 1.877 2.258 3.063 -5.99751 0.422 96.3 92.1 1.635 1.880 2.28 3.058 -5.9726 0.54 96.2 84.1 1.610 1.885 2.337 3.053 -5.88191 0.7 94.2 83.5 1.585 1.904 2.379 3.049 -5.81427 Table 1. Structural characteristics and potential energies of chemical disordered SiC with varying *χ*. Notations: X4 (X = C or Si), the percentage of four-fold coordinated X atoms; *l*X-Y (X, Y = C or Si), the average bond length of X-Y bond. In our calculations the cut-off distances of the C-C, Si-C, and C-C interactions are 1.75 Å, 2.0 Å and 2.5 Å, respectively.

The inspection of MD simulated irradiation-induced *a*-SiC has investigated the changes of topological order as a function of chemical disorder and suggested that some threshold chemical disorder should be one requirement for amorphization(Xue, K. & Niu, L.-S., 2009; Yuan, X. & Hobbs, L. W., 2002). Herein interatomic interactions were modeled using the 1994 Tersoff potential improved by Tang and Yip(Tang, M. & Yip, S., 1995; Tersoff, J., 1994). Devanathan et al.(Devanathan, R. et al., 2007) compared the structures of modeled meltquenched *a*-SiC obtained from three different potentials, namely Tersoff, Brenner, and ionic potentials, with the results of a tight-binding MD (TBMD) simulation and an *ab initio* study. They found that the structural features of *a*-SiC given by Tersoff potential appear to be in better agreement with *ab initio* and TBMD results. In order to explore the role of chemical disorder in the changes of SiC topology, varying chemical disorder ranging from 0 to 0.7 are imposed on a set of 3C-SiC perfect crystal models by swapping pairs of random sites.

Density (×103 Kg/m3)

Potential Energy (eV/atom)

between them would be clarified in the next section.

**3. Characterization of the structures of** *a***-SiC** 

(*χ*) C4 Si4 *l*C-C *l*Si-C *l*Si-Si

distribution of homonuclear bonds.

and Perlado(Malerba, L. & Perlado, J. M., 2001) argued that both Frenkel pairs and antisite defects play significant roles in the amorphization process and that the coalescence and growth of defect clusters account for the amorphization of SiC. Antisite defects were found to be less numerous than Frenkel defects, whose accumulation has been instead primarily supposed to trigger amorphization. However Frenkel pairs have strong correlation with antisites. The MD simulation of the disordering and amorphization processes in SiC irradiated with Si and Au ions reveals much higher concentration of antisites in complete amorphous areas where are supposed to comprise large amount of Frenkel pairs than other disordered domains(Gao, F. & Weber, W. J., 2001). Furthermore where is significant overlap of antisite coordination shells, where there are a significant number of Frenkel pairs that are accommodated. If completely excluding antisites, Frenkel defects would become extremely unstable, leading to difficulties of amorphization. Rong *et al*.(Rong, Z. et al., 2007) simulated the recovery of point defects created by a single cascade during the thermo annealing via dynamic lattice MD technique. The results suggest that a large number of irradiation induced Frenkel pairs are formed in metastable configurations, and majority of close pairs would recombine during the annealing at 200 K and 300 K. Contrasting with the dramatic annihilation of Frenkel defects upon annealing, the number of antisite largely remains constant even increases somewhat due to the recombination of interstitials from one sublattice with vacancies on the other. Therefore the role of antisite in the amorphization of SiC is of equal essence.

Basically both Frenkel and antisite defects could give rise to dual disorder, namely topological and chemical disorder. Homonuclear bonds (C-C, Si-Si) are likely to form when antisite or Frenkel defects are introduced, producing a certain degree of chemical disorder. The homonuclear bond ratio *R*hnb, defined for SiC as the ratio of number of homonuclear bonds to twice the number of heteronuclear bonds, provides a full homonuclear bond analysis. Chemical disorder *χ*(Tersoff, J., 1994), defined as the ratio of C-C bonds to C-Si bonds, *N*C-C/*N*Si-C, is not a full homonuclear bond analysis and is specified only for C atoms. The argument for using *χ* instead of *R*hnb derives mostly from the practical uncertainty of enumerating Si-Si bonds in amorphous structures for which Si atoms have no clearly defined first coordination shell. In practice, *χ* is quite a good approximation to *R*hnb and the deviation is proportional to the coordination number difference between Si and C.

The topological disorder of *a*-SiC manifests itself in variations of the short- and mediumrange. Short-range order (SRO), as its name implies, concerns structural order involving nearest-neighbour coordination shell. This is easiest to discuss in the case of covalently bonded amorphous solids since the presence of their directed stereochemical bonds simplifies the description considerably. For example, in the case of SiC, SRD is defined in terms of well defined local coordination tetrahedra. The parameters which are sufficient to describe topological SRO in stereochemical systems are the (coordination) number, *Nij*, of nearest neighbors of type *j* around an origin atom of type *i*, the nearest-neighbour bond length *Rij*, the bond angle subtended at atom *i*, *θjik* (when the atom of type k is different from j). The connectivity of polyhedral dictates the type and extent of medium-range order (MRO). Shortest-path ring(Rino, J. P. et al., 2004), defined as a shortest path consisting of nearest-neighboring atoms, and local cluster primitive ring(Yuan, X. & Hobbs, L. W., 2002) are among often used means to characterize the MRO. Because Frenkel pairs and anitisites have overlapping effects on the amorphization of SiC, and exclusively focusing on the formal Frenkel pairs and antisite configuration themselves has ignored the multiplier effects

and Perlado(Malerba, L. & Perlado, J. M., 2001) argued that both Frenkel pairs and antisite defects play significant roles in the amorphization process and that the coalescence and growth of defect clusters account for the amorphization of SiC. Antisite defects were found to be less numerous than Frenkel defects, whose accumulation has been instead primarily supposed to trigger amorphization. However Frenkel pairs have strong correlation with antisites. The MD simulation of the disordering and amorphization processes in SiC irradiated with Si and Au ions reveals much higher concentration of antisites in complete amorphous areas where are supposed to comprise large amount of Frenkel pairs than other disordered domains(Gao, F. & Weber, W. J., 2001). Furthermore where is significant overlap of antisite coordination shells, where there are a significant number of Frenkel pairs that are accommodated. If completely excluding antisites, Frenkel defects would become extremely unstable, leading to difficulties of amorphization. Rong *et al*.(Rong, Z. et al., 2007) simulated the recovery of point defects created by a single cascade during the thermo annealing via dynamic lattice MD technique. The results suggest that a large number of irradiation induced Frenkel pairs are formed in metastable configurations, and majority of close pairs would recombine during the annealing at 200 K and 300 K. Contrasting with the dramatic annihilation of Frenkel defects upon annealing, the number of antisite largely remains constant even increases somewhat due to the recombination of interstitials from one sublattice with vacancies on the other. Therefore the role of antisite in the amorphization of

Basically both Frenkel and antisite defects could give rise to dual disorder, namely topological and chemical disorder. Homonuclear bonds (C-C, Si-Si) are likely to form when antisite or Frenkel defects are introduced, producing a certain degree of chemical disorder. The homonuclear bond ratio *R*hnb, defined for SiC as the ratio of number of homonuclear bonds to twice the number of heteronuclear bonds, provides a full homonuclear bond analysis. Chemical disorder *χ*(Tersoff, J., 1994), defined as the ratio of C-C bonds to C-Si bonds, *N*C-C/*N*Si-C, is not a full homonuclear bond analysis and is specified only for C atoms. The argument for using *χ* instead of *R*hnb derives mostly from the practical uncertainty of enumerating Si-Si bonds in amorphous structures for which Si atoms have no clearly defined first coordination shell. In practice, *χ* is quite a good approximation to *R*hnb and the

deviation is proportional to the coordination number difference between Si and C.

The topological disorder of *a*-SiC manifests itself in variations of the short- and mediumrange. Short-range order (SRO), as its name implies, concerns structural order involving nearest-neighbour coordination shell. This is easiest to discuss in the case of covalently bonded amorphous solids since the presence of their directed stereochemical bonds simplifies the description considerably. For example, in the case of SiC, SRD is defined in terms of well defined local coordination tetrahedra. The parameters which are sufficient to describe topological SRO in stereochemical systems are the (coordination) number, *Nij*, of nearest neighbors of type *j* around an origin atom of type *i*, the nearest-neighbour bond length *Rij*, the bond angle subtended at atom *i*, *θjik* (when the atom of type k is different from j). The connectivity of polyhedral dictates the type and extent of medium-range order (MRO). Shortest-path ring(Rino, J. P. et al., 2004), defined as a shortest path consisting of nearest-neighboring atoms, and local cluster primitive ring(Yuan, X. & Hobbs, L. W., 2002) are among often used means to characterize the MRO. Because Frenkel pairs and anitisites have overlapping effects on the amorphization of SiC, and exclusively focusing on the formal Frenkel pairs and antisite configuration themselves has ignored the multiplier effects

SiC is of equal essence.

on the immediate coordination of a much larger number of atoms, hierarchical parameters signifying SRO and MRO seem to be more appropriate to describe the c-a transition and varying microstructures of *a*-SiC. The c-a transition is accordingly described in terms of the variations in the chemical disorder *χ* and other topological parameters. The correlation between them would be clarified in the next section.

#### **3. Characterization of the structures of** *a***-SiC**

Considerable investigations, including experimental and MD simulation studies, indicate a strong correlation between chemical and topological disorder. The x-ray absorption and Ramann spectroscropy performed by Bolse(Bolse, W., 1998) on Na+ irradiated SiC clearly showed that a large fraction of the [SiC4] tetrahedra is destroyed only after the removal of chemical order. The inspection of MD simulated melt-quenched *a*-SiC Has also revealed that chemical disorder determines the short- and medium-range topological order in *a*-SiC(Xue, K. et al., 2008). Therein an extended tetrahedron model only dependent on the composition and chemical disorder *χ* was developed to predict the probabilities of various local coordination tetrahedra, namely, Si-Si4-*n*C*n* and C-Si4-*n*C*n* (*n* = 0-4), reflecting the local spatial distribution of homonuclear bonds.


Table 1. Structural characteristics and potential energies of chemical disordered SiC with varying *χ*. Notations: X4 (X = C or Si), the percentage of four-fold coordinated X atoms; *l*X-Y (X, Y = C or Si), the average bond length of X-Y bond. In our calculations the cut-off distances of the C-C, Si-C, and C-C interactions are 1.75 Å, 2.0 Å and 2.5 Å, respectively.

The inspection of MD simulated irradiation-induced *a*-SiC has investigated the changes of topological order as a function of chemical disorder and suggested that some threshold chemical disorder should be one requirement for amorphization(Xue, K. & Niu, L.-S., 2009; Yuan, X. & Hobbs, L. W., 2002). Herein interatomic interactions were modeled using the 1994 Tersoff potential improved by Tang and Yip(Tang, M. & Yip, S., 1995; Tersoff, J., 1994). Devanathan et al.(Devanathan, R. et al., 2007) compared the structures of modeled meltquenched *a*-SiC obtained from three different potentials, namely Tersoff, Brenner, and ionic potentials, with the results of a tight-binding MD (TBMD) simulation and an *ab initio* study. They found that the structural features of *a*-SiC given by Tersoff potential appear to be in better agreement with *ab initio* and TBMD results. In order to explore the role of chemical disorder in the changes of SiC topology, varying chemical disorder ranging from 0 to 0.7 are imposed on a set of 3C-SiC perfect crystal models by swapping pairs of random sites.

Mechanical Properties of Amorphous Silicon Carbide 9

elastic constants and elastic modulus show expected softening behavior under irradiation for the dose range of interest. Fig. 2 shows their typical results with regard to the variations of elastic modulus, E and bulk modulus B. These elastic properties decrease rapidly at doses less than 0.1 MD-dpa, and the decrease becomes smaller at the high dose levels. On account of the dose dependence of the formation and coalescence of point defects and small clusters, they concluded that point defects and small clusters contribute much greater than

Fig. 2. variation of elastic modulus, *E*, and bulk modulus, *B*, as a function of dose(Rino, J. P.

Point defects, small clusters and topological disorder as forms of defect accumulation could somehow indicate the dependence of mechanical properties of *a*-SiC on the disordered microstructure. However it is difficult to enumerate these damages due to the ambiguous definitions of their complicated configurations. Bearing in mind that chemical disorder *χ* is of essence to trigger the c-a transition as elucidated in Sec.3, chemical disorder *χ* is able to distinguish varying disordered SiC structures. Thus formulating the correlation between a variety of mechanical properties and chemical disorder *χ* provide a favorable alternative to

(a) (b) Fig. 3. (a) stress vs strain curves for *a*-SiC samples with varying chemical disorder at a strain rate of 108s-1 (Xue, K. & Niu, L.-S., 2009); (b) stress vs strain curves for 3C-SiC, nc-SiC and melt-quenched *a*-SiC with an extension rate of 100 m/s(Ivashchenko, V. I. et al., 2007)

topological disorder to the degradation of elastic properties of *a*-SiC.

quantify the microstructure dependence of mechanical properties.

et al., 2004)

**4.2 Tensile mechanical response of** *a***-SiC** 

The SRO and MRO of all SiC assemblies with varying imposed chemical disorder are examined in terms of a variety of parameters, such as coordination number, pair correlation functions *gαβ*(r) and local cluster primitive ring statistics. Table 1 summaries the variations of some important SRO indicators of *a*-SiC with varying *χ*. The number of four-fold coordinated C and Si atoms declines with increasing *χ* especially for the case of Si atom, which is in accordance with the argument in Sec. 2 that more interstitials (vacancies) are accommodated in the areas abundant in antisites. Another feature worth noting is the significant lengthening of C-C bond and the shortening of Si-Si and Si-C bonds, the trend being more pronounced for small *χ*.

The two body structural correlations of the amorphous materials are analyzed by pair correlations functions *gαβ*(*r*). The evolution of MRO can be traced in terms of the local cluster primitive (LC) ring content, defined as a closed circuit passing through a given atom of the network which cannot be decomposed into two smaller circuits. The LCs haven been shown to uniquely characterize the topologies of all compact crystalline silica, Si3N4 and SiC polymorphs(Hobbs, L. W. et al., 1999). In the case of crystalline *α*- or *β*-SiC, the LCs comprises 12 6-rings (as in Si).

Fig. 1. (a) Total pair correlation function *gαβ*(*r*) and (b) distribution of local cluster ring number at Si sites for *a*-SiC samples with varying chemical disorder(Xue, K. & Niu, L.-S., 2009).

Fig. 1(a) shows the *gαβ*(*r*) for the SiC assemblies with increasing *χ*. The C-Si peak substantially declines as *χ* increases accompanying the enhancement of the C-C and Si-Si peaks. Any appreciable changes of *gαβ*(*r*) could barely be identified after *χ* ~ 0.5, in a sense meaning the saturation of short-range disordering. Fig. 1(b) demonstrates that the majority of the LCs for *χ* < 0.24 consist of 12 6-SiC as in 3C-SiC, significant changes of LCs contents occur within the range of 0.24 < *χ* < 0.54, and afterwards the changes tend to saturate. The chemical disorder dependences of SRO and MRO depict the same picture: perfect topological order in 3C-SiC structure is energetically stable until chemical disorder reaches beyond the *χ* = 0.24 – 0.42 range; for *χ* ≥ 0.54, topological perfection appears impossible to maintain and a stable amorphous structure is achieved.

#### **4. Tensile testing simulation of** *a***-SiC**

#### **4.1 Variations in elastic properties of SiC from crystalline to amorphous**

Gao and Weber(Gao, F. & Weber, W. J., 2004) calculated the changes of elastic constants, *C*11, *C*12, *C*44, the bulk modulus, *B*, and averaged elastic modulus, *E* as a function of dose for cascade-amorphized SiC by imposing moderate strain (<1%) along the MD cell axes. All

The SRO and MRO of all SiC assemblies with varying imposed chemical disorder are examined in terms of a variety of parameters, such as coordination number, pair correlation functions *gαβ*(r) and local cluster primitive ring statistics. Table 1 summaries the variations of some important SRO indicators of *a*-SiC with varying *χ*. The number of four-fold coordinated C and Si atoms declines with increasing *χ* especially for the case of Si atom, which is in accordance with the argument in Sec. 2 that more interstitials (vacancies) are accommodated in the areas abundant in antisites. Another feature worth noting is the significant lengthening of C-C bond and the shortening of Si-Si and Si-C bonds, the trend

The two body structural correlations of the amorphous materials are analyzed by pair correlations functions *gαβ*(*r*). The evolution of MRO can be traced in terms of the local cluster primitive (LC) ring content, defined as a closed circuit passing through a given atom of the network which cannot be decomposed into two smaller circuits. The LCs haven been shown to uniquely characterize the topologies of all compact crystalline silica, Si3N4 and SiC polymorphs(Hobbs, L. W. et al., 1999). In the case of crystalline *α*- or *β*-SiC, the LCs

Fig. 1. (a) Total pair correlation function *gαβ*(*r*) and (b) distribution of local cluster ring number at Si sites for *a*-SiC samples with varying chemical disorder(Xue, K. & Niu, L.-S., 2009).

Fig. 1(a) shows the *gαβ*(*r*) for the SiC assemblies with increasing *χ*. The C-Si peak substantially declines as *χ* increases accompanying the enhancement of the C-C and Si-Si peaks. Any appreciable changes of *gαβ*(*r*) could barely be identified after *χ* ~ 0.5, in a sense meaning the saturation of short-range disordering. Fig. 1(b) demonstrates that the majority of the LCs for *χ* < 0.24 consist of 12 6-SiC as in 3C-SiC, significant changes of LCs contents occur within the range of 0.24 < *χ* < 0.54, and afterwards the changes tend to saturate. The chemical disorder dependences of SRO and MRO depict the same picture: perfect topological order in 3C-SiC structure is energetically stable until chemical disorder reaches beyond the *χ* = 0.24 – 0.42 range; for *χ* ≥ 0.54, topological perfection appears impossible to

Gao and Weber(Gao, F. & Weber, W. J., 2004) calculated the changes of elastic constants, *C*11, *C*12, *C*44, the bulk modulus, *B*, and averaged elastic modulus, *E* as a function of dose for cascade-amorphized SiC by imposing moderate strain (<1%) along the MD cell axes. All

maintain and a stable amorphous structure is achieved.

**4.1 Variations in elastic properties of SiC from crystalline to amorphous** 

**4. Tensile testing simulation of** *a***-SiC** 

being more pronounced for small *χ*.

comprises 12 6-rings (as in Si).

elastic constants and elastic modulus show expected softening behavior under irradiation for the dose range of interest. Fig. 2 shows their typical results with regard to the variations of elastic modulus, E and bulk modulus B. These elastic properties decrease rapidly at doses less than 0.1 MD-dpa, and the decrease becomes smaller at the high dose levels. On account of the dose dependence of the formation and coalescence of point defects and small clusters, they concluded that point defects and small clusters contribute much greater than topological disorder to the degradation of elastic properties of *a*-SiC.

Fig. 2. variation of elastic modulus, *E*, and bulk modulus, *B*, as a function of dose(Rino, J. P. et al., 2004)

#### **4.2 Tensile mechanical response of** *a***-SiC**

Point defects, small clusters and topological disorder as forms of defect accumulation could somehow indicate the dependence of mechanical properties of *a*-SiC on the disordered microstructure. However it is difficult to enumerate these damages due to the ambiguous definitions of their complicated configurations. Bearing in mind that chemical disorder *χ* is of essence to trigger the c-a transition as elucidated in Sec.3, chemical disorder *χ* is able to distinguish varying disordered SiC structures. Thus formulating the correlation between a variety of mechanical properties and chemical disorder *χ* provide a favorable alternative to quantify the microstructure dependence of mechanical properties.

Fig. 3. (a) stress vs strain curves for *a*-SiC samples with varying chemical disorder at a strain rate of 108s-1 (Xue, K. & Niu, L.-S., 2009); (b) stress vs strain curves for 3C-SiC, nc-SiC and melt-quenched *a*-SiC with an extension rate of 100 m/s(Ivashchenko, V. I. et al., 2007)

Mechanical Properties of Amorphous Silicon Carbide 11

In order to gain further insights into the chemical disorder dependece of Young's modulus and strength, the knowledge of the deformation mechanims of varying disordered structures is necessary. Young's modulus of the covalent network is closely related with the ability of the topological network to homogeneously elastic deform to accomadate the small strain. Despite of the presence of moderate chemical disorder *χ*, the almost intact conection of fundamental tetrahedral units, as well as their relative orientation, ensure the homogeneously collective deformation of these units at small *χ*. Thus no appreciable decrease of Young's modulus could be detected for the SiC assembly with *χ* = 0.045. As *χ* increases, the topological order gradually decays, resulting in the reduced stiffness of the network and The ensuing decrease of Young's modulus until a complete amorphous state is reached. Actually the linear elastic region of mechanical response of *a*-SiC gradually

Although a handfull of homonuclear bonds introduced by a negligeable chemcial disorder (*χ* = 0.045) barely affect the topological order and the Young's modulus, they account for a substantial decline of strength. Due to the atom size difference, the C-C bonds in the undeformed system have been stretched with a bond length increase of ~7% contrasting to the contraction of Si-C and Si-Si bonds. With the strain processes, these stretched C-C bonds are expected to break prior Si-C and Si-Si bonds. The premature breakage of C-C bonds disconnects the neighboring tetrahedral network where the stress builds up. More decohesions of atomic bonds therein conversely take place due to the localized stress. As a results, Localized softened clusters around the initial chemical disorderd sites are formed, where atomic rearrangements dominate the confined plastic flow. Fig. 5 (a) illustrates the atomic slipping occurring in these softened regions. With the inceased *χ*, the enhanced topological disorder gives rise to the prevalence of softening regions. Thus the localized

plastic flow evolves into percolating flow through the entire system [Fig. 5(b)].

Fig. 5. Atomic configurations for (a) the *χ* = 0.045 and (b) the *χ* = 0.39 assemblies at *ε* = 0.27. Atoms are colored according to their motion relative to the homogeneous deformation. Blue atoms have moved towards right relative to what would be expected if the deformation had been homogeneous and elastic; red atoms have moved towards left. The scale indicates how

the atoms have moved (in angstroms)(Xue, K. & Niu, L.-S., 2009).

**4.4 Deformation mechanims** 

diminishes with the increasing *χ*.

Simulated axial tensile testing is carried out on a set of SiC assemblies with varying chemical disorder *χ*, representing a range of disordered structures from crystalline to complete amorphous. The full stress-strain dependences for different SiC assemblies with varying *χ* are shown in Fig. 3. The stress-strain curve for 3C-SiC features a linear elastic stage ending up with an abrupt drop of the stress, while the presence of negligible chemical disorder *χ* (*χ*=0.045) gives rise to a noticeable deviation beyond *ε* ≈ 0.13 from what would be expected from extrapolation of the linear elastic region. Meanwhile an appreciable softening of the material after the stress reaches *σ*max can be observed, evidenced by the weak decrease of the stress before the rupture. This plasticlike behavior becomes increasingly evident with increasing *χ*, pronounced plastic flow plateau covering a major part of the whole mechanical response. Such plasticelike behavior is reproduced in the tension of simulated melt-quenched *a*-SiC with a drastic reduction in the number of tetrahedrally coordinated atoms(Ivashchenko, V. I. et al., 2007).

#### **4.3 Mechanical properties of** *a***-SiC as a function of chemical disorder** *χ*

The chemical disorder dependence of the mechanical response of *a*-SiC is likewise embodied in the variations of the Young's modulus and strength of *a*-SiC with varying chemical disorder [Fig. 4]. Young's modulus and strength generally exhibit monotonic decrease with increasing *χ* while in distinct manners until *χ* reaches 0.54, afterwards tend to saturate regardless of the further increase of *χ*. Young's modulus *EY* shows negative linear dependence on *χ* within the range of 0 < *χ* < 0.54 as follows:

$$E\_Y = 0.9994E\_{Y\_0} - 0.316 \times \mathcal{X} \times E\_{Y\_0} \tag{1}$$

where *EY*0 is Young's modulus along the [100] direction of 3C-SiC (~413 GPa). Young's modulus of complete *a*-SiC is around ~321.4 GPa, agreeing well with the value calculated for the melt-quenched *a*-SiC which stands at ~327 GPa(Ivashchenko, V. I. et al., 2007). In contrast with the consistent reduction of *EY* with increasing *χ* before *χ* < 0.54, a dramatic decrease of 23.2% for strength occurs at *χ* = 0.045, decreasing from ~90.8 GPa (*χ* = 0) to ~69.7 GPa (*χ* = 0.045). Whereas strength almost linearly declines afterwards with increasing *χ* as the following relation until *χ* =0.54,

$$S = 0.745S\_0 - 0.328 \times \chi \times S\_0 \tag{2}$$

where *S*<sup>0</sup> is the strength of 3C-SiC (~90.8 GPa). When *χ* is beyond 0.54, a complete amorphous state is reached, Young's modulus and strength tend to be constant, which is in line with the saturation of Elastic moduli of *a*-SiC at high doses(Gao, F. & Weber, W. J., 2004).

Fig. 4. Variations of Young's modulus and strength as a function of chemical disorder(Xue, K. & Niu, L.-S., 2009)

#### **4.4 Deformation mechanims**

10 Silicon Carbide – Materials, Processing and Applications in Electronic Devices

Simulated axial tensile testing is carried out on a set of SiC assemblies with varying chemical disorder *χ*, representing a range of disordered structures from crystalline to complete amorphous. The full stress-strain dependences for different SiC assemblies with varying *χ* are shown in Fig. 3. The stress-strain curve for 3C-SiC features a linear elastic stage ending up with an abrupt drop of the stress, while the presence of negligible chemical disorder *χ* (*χ*=0.045) gives rise to a noticeable deviation beyond *ε* ≈ 0.13 from what would be expected from extrapolation of the linear elastic region. Meanwhile an appreciable softening of the material after the stress reaches *σ*max can be observed, evidenced by the weak decrease of the stress before the rupture. This plasticlike behavior becomes increasingly evident with increasing *χ*, pronounced plastic flow plateau covering a major part of the whole mechanical response. Such plasticelike behavior is reproduced in the tension of simulated melt-quenched *a*-SiC with a drastic reduction in the

The chemical disorder dependence of the mechanical response of *a*-SiC is likewise embodied in the variations of the Young's modulus and strength of *a*-SiC with varying chemical disorder [Fig. 4]. Young's modulus and strength generally exhibit monotonic decrease with increasing *χ* while in distinct manners until *χ* reaches 0.54, afterwards tend to saturate regardless of the further increase of *χ*. Young's modulus *EY* shows negative linear

where *EY*0 is Young's modulus along the [100] direction of 3C-SiC (~413 GPa). Young's modulus of complete *a*-SiC is around ~321.4 GPa, agreeing well with the value calculated for the melt-quenched *a*-SiC which stands at ~327 GPa(Ivashchenko, V. I. et al., 2007). In contrast with the consistent reduction of *EY* with increasing *χ* before *χ* < 0.54, a dramatic decrease of 23.2% for strength occurs at *χ* = 0.045, decreasing from ~90.8 GPa (*χ* = 0) to ~69.7 GPa (*χ* = 0.045). Whereas strength almost linearly declines afterwards with increasing *χ* as

where *S*<sup>0</sup> is the strength of 3C-SiC (~90.8 GPa). When *χ* is beyond 0.54, a complete amorphous state is reached, Young's modulus and strength tend to be constant, which is in line with the

Fig. 4. Variations of Young's modulus and strength as a function of chemical disorder(Xue,

saturation of Elastic moduli of *a*-SiC at high doses(Gao, F. & Weber, W. J., 2004).

0 0 0.9994 0.316 *EE E YY Y* = −× χ× (1)

0 0 *SS S* = −× 0.745 0.328 χ × (2)

number of tetrahedrally coordinated atoms(Ivashchenko, V. I. et al., 2007).

dependence on *χ* within the range of 0 < *χ* < 0.54 as follows:

the following relation until *χ* =0.54,

K. & Niu, L.-S., 2009)

**4.3 Mechanical properties of** *a***-SiC as a function of chemical disorder** *χ*

In order to gain further insights into the chemical disorder dependece of Young's modulus and strength, the knowledge of the deformation mechanims of varying disordered structures is necessary. Young's modulus of the covalent network is closely related with the ability of the topological network to homogeneously elastic deform to accomadate the small strain. Despite of the presence of moderate chemical disorder *χ*, the almost intact conection of fundamental tetrahedral units, as well as their relative orientation, ensure the homogeneously collective deformation of these units at small *χ*. Thus no appreciable decrease of Young's modulus could be detected for the SiC assembly with *χ* = 0.045. As *χ* increases, the topological order gradually decays, resulting in the reduced stiffness of the network and The ensuing decrease of Young's modulus until a complete amorphous state is reached. Actually the linear elastic region of mechanical response of *a*-SiC gradually diminishes with the increasing *χ*.

Although a handfull of homonuclear bonds introduced by a negligeable chemcial disorder (*χ* = 0.045) barely affect the topological order and the Young's modulus, they account for a substantial decline of strength. Due to the atom size difference, the C-C bonds in the undeformed system have been stretched with a bond length increase of ~7% contrasting to the contraction of Si-C and Si-Si bonds. With the strain processes, these stretched C-C bonds are expected to break prior Si-C and Si-Si bonds. The premature breakage of C-C bonds disconnects the neighboring tetrahedral network where the stress builds up. More decohesions of atomic bonds therein conversely take place due to the localized stress. As a results, Localized softened clusters around the initial chemical disorderd sites are formed, where atomic rearrangements dominate the confined plastic flow. Fig. 5 (a) illustrates the atomic slipping occurring in these softened regions. With the inceased *χ*, the enhanced topological disorder gives rise to the prevalence of softening regions. Thus the localized plastic flow evolves into percolating flow through the entire system [Fig. 5(b)].

Fig. 5. Atomic configurations for (a) the *χ* = 0.045 and (b) the *χ* = 0.39 assemblies at *ε* = 0.27. Atoms are colored according to their motion relative to the homogeneous deformation. Blue atoms have moved towards right relative to what would be expected if the deformation had been homogeneous and elastic; red atoms have moved towards left. The scale indicates how the atoms have moved (in angstroms)(Xue, K. & Niu, L.-S., 2009).

Mechanical Properties of Amorphous Silicon Carbide 13

Nanoindentation is a widely used technique for probing mechanical properties and stability, especially of surfaces and thin films. From the shape of load-indenter displacement (*P*-*h*) curves, one can extract information about elastic moduli or hardness. Atomistic computer simulations have been found very helpful in unraveling the processes underlying the nanoindentation responses. For example, MD simulations of indentation of 3C-SiC have shown that the *p-h* curve [Fig.7(b)] is correlated with the nucleation and coalescence of

Amorphous materials lack a long-range order of topological network and hence there is no clear notion of dislocations. Thus understanding atomistic processes during nanoindentation in amorphous materials presents a great challenge. A few atomistic simulations have been performed to tackle this problem. Szlufarska *et al*.(Szlufarska, I. et al., 2007) undertook the difficult task of simulating nanoindentation of melt-quenched *a*-SiC with a diamond indenter. The simulation reveals a noticeable localization of damage in the vicinity of the indenter, however the localization is less pronounced than in the case of 3C-SiC. As shown in Fig. 7(a), the *P*-*h* curve for *a*-SiC exhibits irregular, discrete load drops similar to 3C-SiC [Fig. 7(b)]. Here, the load drops correspond to braking of the local arrangements of atoms, in analogy to the slipping of atomic layers in 3C-SiC. Simulations also show that, even at indentation depth *h* smaller than those at which the material yields plastically, the material's response is not entirely elastic. Instead, the amorphous structure, which is metastable by nature, supports a small inelastic flow related to relaxation of atoms

Fig. 7. Load-displacement (*P*-*h*) responses for (a) *a*-SiC and (b) 3C-SiC(Szlufarska, I. et al.,

As aforementioned imposing increasing chemical disorder *χ* on 3C-SiC is able to produce a series of disordered SiC structures ranging from perfect crystalline to complete amorphous, providing favorable prototypes to observe the dependence of hardness on the damage accumulation. More importantly, this means could allow us to identify possible atomistic mechanisms in the early stages of plastic deformation as a function of microstructure. A set of disordered SiC assemblies with varying chemical disorder *χ* are established as the substrates in the means introduced in Sec.2. The Geometrical setup of the indenter and the substrate is detailed in ref(Xue, K. & Niu, L.-S., 2010). In the case of 3C-SiC, the *x*, *y*, *z* directions correspond to the [110] ,[001] and[110] crystallographic directions, respectively.

**5. Nanoindentation simulations of** *a***-SiC** 

dislocations under an indenter(Szlufarska, I. et al., 2005).

**5.1 P-h curves of** *a***-SiC** 

through short migration distances.

2007)

#### **4.5 Fracture modes**

When the disorder SiC undergoes c-a transition with the increasing chemical disorder *χ*, the main deformation mechanism evolves from elastic deformation to localized atomic rearrangement, and then to percolating plastic flow. This crossover is also manifested itself in the switch of the fracture mechanism. At a slight chemical disorder (*χ* =0.045), localized softened clusters are embedded in the rigid topological ordered lattice which strongly supresses the nucleation of nanocavities inside the disordered clusters. Thus the failure of ligaments between softened clusters rather than the percolation of nanocavities leads to the final brittle fracture, which is supported by the sudden drop of cavity density at ε ~0.3 [Fig.6]. Increased chemical disorder substantially alters the atomistic picture of fracture mechanisms. In the fully amorphous system (*χ* = 0.54), extensive plastic flow nucleates a large number of nanocavites, their coalescence and percolation through the system leading to the final fracture. This argument is consistent with the slow decline of cavity desity after *ε* ~0.23 for the *χ* = 0.54 assembly [Fig. 6]. For *a*-SiC with moderate chemical disorder (0 < *χ* < 0.54), we can expect a competition of brittle and ductile fracture mechanism, dominated by lattice instability and coalescence of nanocavities, respectively.

Fig. 6. Cavity densities as a function of strain (a) for different *a*-SiC samples with varying chemical disorder at a strain rate of 108 s-1 and (b) for the *χ* = 0.54 ensemble at different strain rates(Xue, K. & Niu, L.-S., 2009).

Recently special efforts have been made to reveal the possible crossover of fracture modes during c-a transition. Glassy materials are considered up to now as the archetype of pure brittle materials, the brittle fracture of which proceeds solely by decohesion of atomic bonds at the crack tip. However, AFM and high scanning electron microscopy (SEM) studies have generated considerable controversy about the nature of fracture mechanism in brittle amorphous solids(Celarie, F. et al., 2003). Xi *et al*.(Xi, X. K. et al., 2005) found a dimple structure at the fracture surface of Mg-based bulk metallic glass by high resolution SEM, indicating that the fracture in brittle metallic glassy materials might also proceed through the softening mechanism but at nanometer scale. Chen *et al*.(Chen, Y.-C. et al., 2007) further investigates the interaction of voids in silica glass by means of multimillion-to-billion-atom MD simulation, unveiling the mechanism of nanocavities nucleation. These findings are in line with the ductile fracture observed in *a*-SiC with *χ* ≥ 0.54 mediated by coalescence of cavities similar to metal materials, although taking place at different length scales.

#### **5. Nanoindentation simulations of** *a***-SiC**

#### **5.1 P-h curves of** *a***-SiC**

12 Silicon Carbide – Materials, Processing and Applications in Electronic Devices

When the disorder SiC undergoes c-a transition with the increasing chemical disorder *χ*, the main deformation mechanism evolves from elastic deformation to localized atomic rearrangement, and then to percolating plastic flow. This crossover is also manifested itself in the switch of the fracture mechanism. At a slight chemical disorder (*χ* =0.045), localized softened clusters are embedded in the rigid topological ordered lattice which strongly supresses the nucleation of nanocavities inside the disordered clusters. Thus the failure of ligaments between softened clusters rather than the percolation of nanocavities leads to the final brittle fracture, which is supported by the sudden drop of cavity density at ε ~0.3 [Fig.6]. Increased chemical disorder substantially alters the atomistic picture of fracture mechanisms. In the fully amorphous system (*χ* = 0.54), extensive plastic flow nucleates a large number of nanocavites, their coalescence and percolation through the system leading to the final fracture. This argument is consistent with the slow decline of cavity desity after *ε* ~0.23 for the *χ* = 0.54 assembly [Fig. 6]. For *a*-SiC with moderate chemical disorder (0 < *χ* < 0.54), we can expect a competition of brittle and ductile fracture mechanism, dominated by

0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35

Fig. 6. Cavity densities as a function of strain (a) for different *a*-SiC samples with varying chemical disorder at a strain rate of 108 s-1 and (b) for the *χ* = 0.54 ensemble at different strain

Recently special efforts have been made to reveal the possible crossover of fracture modes during c-a transition. Glassy materials are considered up to now as the archetype of pure brittle materials, the brittle fracture of which proceeds solely by decohesion of atomic bonds at the crack tip. However, AFM and high scanning electron microscopy (SEM) studies have generated considerable controversy about the nature of fracture mechanism in brittle amorphous solids(Celarie, F. et al., 2003). Xi *et al*.(Xi, X. K. et al., 2005) found a dimple structure at the fracture surface of Mg-based bulk metallic glass by high resolution SEM, indicating that the fracture in brittle metallic glassy materials might also proceed through the softening mechanism but at nanometer scale. Chen *et al*.(Chen, Y.-C. et al., 2007) further investigates the interaction of voids in silica glass by means of multimillion-to-billion-atom MD simulation, unveiling the mechanism of nanocavities nucleation. These findings are in line with the ductile fracture observed in *a*-SiC with *χ* ≥ 0.54 mediated by coalescence of

cavities similar to metal materials, although taking place at different length scales.

χ= 0.54

Strain

χ= 0.045

lattice instability and coalescence of nanocavities, respectively.

χ= 0.39

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8

Cavity density (1/nm3

rates(Xue, K. & Niu, L.-S., 2009).

)

**4.5 Fracture modes** 

Nanoindentation is a widely used technique for probing mechanical properties and stability, especially of surfaces and thin films. From the shape of load-indenter displacement (*P*-*h*) curves, one can extract information about elastic moduli or hardness. Atomistic computer simulations have been found very helpful in unraveling the processes underlying the nanoindentation responses. For example, MD simulations of indentation of 3C-SiC have shown that the *p-h* curve [Fig.7(b)] is correlated with the nucleation and coalescence of dislocations under an indenter(Szlufarska, I. et al., 2005).

Amorphous materials lack a long-range order of topological network and hence there is no clear notion of dislocations. Thus understanding atomistic processes during nanoindentation in amorphous materials presents a great challenge. A few atomistic simulations have been performed to tackle this problem. Szlufarska *et al*.(Szlufarska, I. et al., 2007) undertook the difficult task of simulating nanoindentation of melt-quenched *a*-SiC with a diamond indenter. The simulation reveals a noticeable localization of damage in the vicinity of the indenter, however the localization is less pronounced than in the case of 3C-SiC. As shown in Fig. 7(a), the *P*-*h* curve for *a*-SiC exhibits irregular, discrete load drops similar to 3C-SiC [Fig. 7(b)]. Here, the load drops correspond to braking of the local arrangements of atoms, in analogy to the slipping of atomic layers in 3C-SiC. Simulations also show that, even at indentation depth *h* smaller than those at which the material yields plastically, the material's response is not entirely elastic. Instead, the amorphous structure, which is metastable by nature, supports a small inelastic flow related to relaxation of atoms through short migration distances.

Fig. 7. Load-displacement (*P*-*h*) responses for (a) *a*-SiC and (b) 3C-SiC(Szlufarska, I. et al., 2007)

As aforementioned imposing increasing chemical disorder *χ* on 3C-SiC is able to produce a series of disordered SiC structures ranging from perfect crystalline to complete amorphous, providing favorable prototypes to observe the dependence of hardness on the damage accumulation. More importantly, this means could allow us to identify possible atomistic mechanisms in the early stages of plastic deformation as a function of microstructure. A set of disordered SiC assemblies with varying chemical disorder *χ* are established as the substrates in the means introduced in Sec.2. The Geometrical setup of the indenter and the substrate is detailed in ref(Xue, K. & Niu, L.-S., 2010). In the case of 3C-SiC, the *x*, *y*, *z* directions correspond to the [110] ,[001] and[110] crystallographic directions, respectively.

Mechanical Properties of Amorphous Silicon Carbide 15

The hardness (*H*) is usually defined as equal to the peak force applied during indentation divided by the projected contact area. The calculated values of hardness here are estimated by yield strength. For 3C-SiC and *a*-SiC with low or moderate chemical disorder (χ ≤ 0.16), yield strength is taken as the pressure of the first peak maximum signifying the onset of structural instability. However, the monotonically ascent *p*-*h* curve for the *χ* = 0.22 assembly displays a kink rather than distinguishable load peaks, so the pressure at the kink is picked up as the measure of calculated hardness. It's worth noting that the contact pressure deprived from nanoindentation simulations is usually several times greater than the experimental hardness(Mulliah, D. et al., 2006; Noreyan, A. et al., 2005). One major reason is the fact that the indenter size used in the MD simulations is always smaller by two or three orders of magnitude than the indenter used in experiments. According to a relation between contact pressure (*p*) and the indenter size at the onset of the nucleation of dislocation(Liu, X. M., 2008), we can readily convert the calculated yield

Fig. 9. Calculated hardness of disordered SiC with increasing chemical disorder(Xue, K. &

The calculated hardness values for different SiC assemblies are plotted in Fig. 9. A remarkable reduction of hardness can be observed for the *χ* = 0.077 assembly. For the complete *a*-SiC assembly with *χ* = 0.22, the hardness value is ~50% less than in 3C-SiC which agrees with the reduction of hardness in *a*-SiC observed in the experiments(Khakani, M. A.

The distinctive characteristics of the *p-h* curves of SiC from c-a could be understood in light of the corresponding atomistic mechanisms, which entail the detailed analysis of the evolution of the associated microstructures with the increasing indent depth *h*. The shortest path ring distribution has been widely used to identify the subsurface defects during the nanoindentation(Szlufarska, I. et al., 2004). The presence of nonthreefold rings marks the

occurrence of structural deformation, most likely the presence of dislocations.

**5.2 Hardness** 

Niu, L.-S., 2010)

E. & al, e., 1994).

**5.3 Atomistic mechanisms** 

strength into the equivalent hardness.

Fig. 8. Pressure-depth (*p*-*h*) response: (a) comparison of loading curves for 3C-SiC and *a*-SiC with varying chemical disorder. (b) Loading and unloading curves from *h* = 4.1 Å (red) for 3C-SiC. (c) Loading and unloading curves from *h* = 1.06 Å (blue) and *h* = 3.27 Å (red) for the *χ* = 0.008 assembly. (d) Loading and unloading curves from *h* = 1.61 Å (blue) and *h* = 3.12 Å (red) for the *χ* = 0.077 assembly. (e) Loading curves for the *χ* = 0.16 and the *χ* = 0.22 assemblies(Xue, K. & Niu, L.-S., 2010).

Fig.8 shows the computed *p*-*h* curves for varying SiC assemblies. Here the pressure (*p*) defined as the load *P* divided by actual contact is plotted as a function of depth *h*. For (110) surface of 3C-SiC, *p*-*h* curve displays a linear elastic region followed by a series of sudden load drops occurring at depths equally spaced by ~3 Å, resembling the simulated *P*-*h* curve of 3C-SiC modeled using an interatomic potential developed by Vashishta *et al*.(Szlufarska, I. et al., 2005)*.* The *p-h* curves of the *χ* = 0.008 assembly is similar to the case of 3C-SiC featuring roughly equally spaced peaks after the yield. Whereas the position of the first peak at which the maximum pressure is achieved is significantly deferred accompanying noticeable broadening of peaks. The alteration becomes increasingly pronounced with increasing *χ*. For the *χ* = 0.077 assembly, pressure peaks enveloping numerous small serrations are considerably broadened with a much larger separation of ~6 Å. Meanwhile the intensity (peak pressure) and magnitude (the amount of load drop) of peaks are substantially reduced. Given that the disordered atoms just account for ~3.5% and ~5% of total atoms for the *χ* = 0.008 and *χ* = 0.077 assembly, respectively, the changes of the *p-h* response seem striking. The defined peak structures of the *p-h* curves evolves into irregularly spaced fluctuations for the *χ* = 0.16 assembly and small oscillations in the *χ* = 0.22 assembly. These substantial changes of the *p-h* response with increasing *χ* suggest a crossover of underlying atomistic mechanisms, as we will discuss later.

#### **5.2 Hardness**

14 Silicon Carbide – Materials, Processing and Applications in Electronic Devices

Fig. 8. Pressure-depth (*p*-*h*) response: (a) comparison of loading curves for 3C-SiC and *a*-SiC with varying chemical disorder. (b) Loading and unloading curves from *h* = 4.1 Å (red) for 3C-SiC. (c) Loading and unloading curves from *h* = 1.06 Å (blue) and *h* = 3.27 Å (red) for the *χ* = 0.008 assembly. (d) Loading and unloading curves from *h* = 1.61 Å (blue) and *h* = 3.12 Å

Fig.8 shows the computed *p*-*h* curves for varying SiC assemblies. Here the pressure (*p*) defined as the load *P* divided by actual contact is plotted as a function of depth *h*. For (110) surface of 3C-SiC, *p*-*h* curve displays a linear elastic region followed by a series of sudden load drops occurring at depths equally spaced by ~3 Å, resembling the simulated *P*-*h* curve of 3C-SiC modeled using an interatomic potential developed by Vashishta *et al*.(Szlufarska, I. et al., 2005)*.* The *p-h* curves of the *χ* = 0.008 assembly is similar to the case of 3C-SiC featuring roughly equally spaced peaks after the yield. Whereas the position of the first peak at which the maximum pressure is achieved is significantly deferred accompanying noticeable broadening of peaks. The alteration becomes increasingly pronounced with increasing *χ*. For the *χ* = 0.077 assembly, pressure peaks enveloping numerous small serrations are considerably broadened with a much larger separation of ~6 Å. Meanwhile the intensity (peak pressure) and magnitude (the amount of load drop) of peaks are substantially reduced. Given that the disordered atoms just account for ~3.5% and ~5% of total atoms for the *χ* = 0.008 and *χ* = 0.077 assembly, respectively, the changes of the *p-h* response seem striking. The defined peak structures of the *p-h* curves evolves into irregularly spaced fluctuations for the *χ* = 0.16 assembly and small oscillations in the *χ* = 0.22 assembly. These substantial changes of the *p-h* response with increasing *χ* suggest a

(red) for the *χ* = 0.077 assembly. (e) Loading curves for the *χ* = 0.16 and the *χ* = 0.22

crossover of underlying atomistic mechanisms, as we will discuss later.

assemblies(Xue, K. & Niu, L.-S., 2010).

The hardness (*H*) is usually defined as equal to the peak force applied during indentation divided by the projected contact area. The calculated values of hardness here are estimated by yield strength. For 3C-SiC and *a*-SiC with low or moderate chemical disorder (χ ≤ 0.16), yield strength is taken as the pressure of the first peak maximum signifying the onset of structural instability. However, the monotonically ascent *p*-*h* curve for the *χ* = 0.22 assembly displays a kink rather than distinguishable load peaks, so the pressure at the kink is picked up as the measure of calculated hardness. It's worth noting that the contact pressure deprived from nanoindentation simulations is usually several times greater than the experimental hardness(Mulliah, D. et al., 2006; Noreyan, A. et al., 2005). One major reason is the fact that the indenter size used in the MD simulations is always smaller by two or three orders of magnitude than the indenter used in experiments. According to a relation between contact pressure (*p*) and the indenter size at the onset of the nucleation of dislocation(Liu, X. M., 2008), we can readily convert the calculated yield strength into the equivalent hardness.

Fig. 9. Calculated hardness of disordered SiC with increasing chemical disorder(Xue, K. & Niu, L.-S., 2010)

The calculated hardness values for different SiC assemblies are plotted in Fig. 9. A remarkable reduction of hardness can be observed for the *χ* = 0.077 assembly. For the complete *a*-SiC assembly with *χ* = 0.22, the hardness value is ~50% less than in 3C-SiC which agrees with the reduction of hardness in *a*-SiC observed in the experiments(Khakani, M. A. E. & al, e., 1994).

#### **5.3 Atomistic mechanisms**

The distinctive characteristics of the *p-h* curves of SiC from c-a could be understood in light of the corresponding atomistic mechanisms, which entail the detailed analysis of the evolution of the associated microstructures with the increasing indent depth *h*. The shortest path ring distribution has been widely used to identify the subsurface defects during the nanoindentation(Szlufarska, I. et al., 2004). The presence of nonthreefold rings marks the occurrence of structural deformation, most likely the presence of dislocations.

Mechanical Properties of Amorphous Silicon Carbide 17

11(a)], more energy being dissipated in the atomic rearrangement of disordered clusters rather than the bending of atomic layers. As the result the onset of plastic yield occurs at much deeper depth than 3C-SiC. The slipping of atomic layers upon the critical strain is alike arrested by these embedded disordered clusters [Fig.11(b)], evidenced by the prematurely terminated dislocation propagating a relatively shorter distance compared with ones in perfect lattice [Fig.11(c)]. Further penetration of the indenter motivates the pinned dislocation which resumes propagation again as seen in Fig. 10(d). These intermittent slipping of atomic layers accounts for a slower release of accumulated stress, corresponding to the broadened and serrated peaks in the *χ* = 0.008 assembly. A second breaking of atomic layers triggers a following dislocation located in (111) plane with a separation of several atomic layers below the first sliding plane [Fig.11(d)]. Afterwards the bending of atomic layers overlaps with the unfolding of the previous incomplete slip. Therefore the accumulation of stress offsets partial release of load, leading to less pronounced load drop

Fig. 11. The (110) projections of indentation damages for the *χ* = 0.008 assembly before (a) and after (b) the first slip of atomic layers. The pink and light blue atoms refer to the chemical disordered atoms. (c) and (d) illustrate the (110) projections of the *χ* = 0.008 assembly beneath the indenter after the first slip and the second slip of atomic layers,

With increased chemical disorder (*χ* = 0.077), extended disordered clusters penetrating the atomic layers contribute to the substantial decay of the elastic resistance of the network. The atomic rearrangement confined in these softened regions emerges as a major energy dissipation mode complementary to the bending and slipping of atomic layers. The release of stress through localized plastic flow accounts for the remarkable reduction of hardness for the *χ* = 0.077 assembly. Moreover, as the continuous atomic layers are dissolved into discrete but coupled fragments cemented by disordered clusters, the discrete motions of atomic layer fragments become prevalent, which are correlated but inconsistent, for the topological environment varies from one fragment to another. Therefore one load drop in the *p-h* curve of the *χ* = 0.077 assembly envelops a number of correlated but uncooperative

after the first peak.

respectively.(Xue, K. & Niu, L.-S., 2010)

Fig. 10. (110) projections of indentation damages in 3C-SiC composed by disordered atoms with non-threefold rings at different depths. (a) *h* = 3.08 Å, (b) *h* = 5.5 Å, (c) *h* = 6.05 Å. (d) shows the (111) slip plane along which the slip of atomic layers occur at *h* = 6.05 Å. (e) and (f) illustrate the (110) projections of 3C-SiC structure beneath the indenter after the first slip and the second slip of atomic layers, respectively. A stack fault along the red line (e) exists in (111) plane, which is terminated with a Shockley partial dislocation along the [110] direction with Burgers vector 1/6[112]. A second outburst of dislocations occurs on next (111) plane just below the first (111) plane (f).(Xue, K. & Niu, L.-S., 2010)

The atomistic mechanisms of 3C-SiC during indentations have been elaborated in quite a few of publications(Chen, H.-P. et al., 2007; Szlufarska, I. et al., 2004, 2005; Xue, K. & Niu, L.-S., 2010). Herein some basic deformation mechanisms related to the nanoindentation of 3C-SiC (110) surface with the cuboidal indenter are to be laid out in order to how the atomistic deformation determines the mechanical response, namely *p-h* curves. Basically the series of equally spaced sudden load drops can be attributed to the dissipation of accumulated stress by subsequent breaking of atomic layers of the substrate whose separation in the indentation (*z*) direction (here that is [110] crystallographic direction). Fig. 10 (a)-(d) demonstrates the atomic configurations which contain only nonthreefold rings before and after the onset of plastic yield. Fig. 10 (b) and (c) clearly shows the bending and slipping in (111) plane of sequent atomic layers under the indenter, corresponding to the accumulation and release of the load, respectively. The first dislocation emits from the corners of the indenter after the slip and resides in the (111) plane [Fig.10 (e)]. The following dislocation arising from the second slip of atomic layers initiates on the next below (111) plane [Fig. 10(f)]. Two stack faults existing on the neighboring {111} planes can be identified after the second load drop [Fig.01(f)], forming a thin layer of hexagonal (wurtzite) structure in the face-centered cubic (zinc-blende) structure of crystalline grains. Similar type of defect has been observed in the indentation of nc-SiC(Szlufarska, I. et al., 2005).

A negligible degree of chemical disorder (*χ* = 0.008) just disorders ~3.5% of total atoms, barely affecting the topological order. Whereas these small fraction of defects prone to cluster effectively hinders the symmetrical bending of atomic layers under the indenter [Fig.

Fig. 10. (110) projections of indentation damages in 3C-SiC composed by disordered atoms with non-threefold rings at different depths. (a) *h* = 3.08 Å, (b) *h* = 5.5 Å, (c) *h* = 6.05 Å. (d) shows the (111) slip plane along which the slip of atomic layers occur at *h* = 6.05 Å. (e) and (f) illustrate the (110) projections of 3C-SiC structure beneath the indenter after the first slip and the second slip of atomic layers, respectively. A stack fault along the red line (e) exists in (111) plane, which is terminated with a Shockley partial dislocation along the [110] direction with Burgers vector 1/6[112]. A second outburst of dislocations occurs on next (111) plane

The atomistic mechanisms of 3C-SiC during indentations have been elaborated in quite a few of publications(Chen, H.-P. et al., 2007; Szlufarska, I. et al., 2004, 2005; Xue, K. & Niu, L.-S., 2010). Herein some basic deformation mechanisms related to the nanoindentation of 3C-SiC (110) surface with the cuboidal indenter are to be laid out in order to how the atomistic deformation determines the mechanical response, namely *p-h* curves. Basically the series of equally spaced sudden load drops can be attributed to the dissipation of accumulated stress by subsequent breaking of atomic layers of the substrate whose separation in the indentation (*z*) direction (here that is [110] crystallographic direction). Fig. 10 (a)-(d) demonstrates the atomic configurations which contain only nonthreefold rings before and after the onset of plastic yield. Fig. 10 (b) and (c) clearly shows the bending and slipping in (111) plane of sequent atomic layers under the indenter, corresponding to the accumulation and release of the load, respectively. The first dislocation emits from the corners of the indenter after the slip and resides in the (111) plane [Fig.10 (e)]. The following dislocation arising from the second slip of atomic layers initiates on the next below (111) plane [Fig. 10(f)]. Two stack faults existing on the neighboring {111} planes can be identified after the second load drop [Fig.01(f)], forming a thin layer of hexagonal (wurtzite) structure in the face-centered cubic (zinc-blende) structure of crystalline grains. Similar type of defect

just below the first (111) plane (f).(Xue, K. & Niu, L.-S., 2010)

has been observed in the indentation of nc-SiC(Szlufarska, I. et al., 2005).

A negligible degree of chemical disorder (*χ* = 0.008) just disorders ~3.5% of total atoms, barely affecting the topological order. Whereas these small fraction of defects prone to cluster effectively hinders the symmetrical bending of atomic layers under the indenter [Fig. 11(a)], more energy being dissipated in the atomic rearrangement of disordered clusters rather than the bending of atomic layers. As the result the onset of plastic yield occurs at much deeper depth than 3C-SiC. The slipping of atomic layers upon the critical strain is alike arrested by these embedded disordered clusters [Fig.11(b)], evidenced by the prematurely terminated dislocation propagating a relatively shorter distance compared with ones in perfect lattice [Fig.11(c)]. Further penetration of the indenter motivates the pinned dislocation which resumes propagation again as seen in Fig. 10(d). These intermittent slipping of atomic layers accounts for a slower release of accumulated stress, corresponding to the broadened and serrated peaks in the *χ* = 0.008 assembly. A second breaking of atomic layers triggers a following dislocation located in (111) plane with a separation of several atomic layers below the first sliding plane [Fig.11(d)]. Afterwards the bending of atomic layers overlaps with the unfolding of the previous incomplete slip. Therefore the accumulation of stress offsets partial release of load, leading to less pronounced load drop after the first peak.

Fig. 11. The (110) projections of indentation damages for the *χ* = 0.008 assembly before (a) and after (b) the first slip of atomic layers. The pink and light blue atoms refer to the chemical disordered atoms. (c) and (d) illustrate the (110) projections of the *χ* = 0.008 assembly beneath the indenter after the first slip and the second slip of atomic layers, respectively.(Xue, K. & Niu, L.-S., 2010)

With increased chemical disorder (*χ* = 0.077), extended disordered clusters penetrating the atomic layers contribute to the substantial decay of the elastic resistance of the network. The atomic rearrangement confined in these softened regions emerges as a major energy dissipation mode complementary to the bending and slipping of atomic layers. The release of stress through localized plastic flow accounts for the remarkable reduction of hardness for the *χ* = 0.077 assembly. Moreover, as the continuous atomic layers are dissolved into discrete but coupled fragments cemented by disordered clusters, the discrete motions of atomic layer fragments become prevalent, which are correlated but inconsistent, for the topological environment varies from one fragment to another. Therefore one load drop in the *p-h* curve of the *χ* = 0.077 assembly envelops a number of correlated but uncooperative

Mechanical Properties of Amorphous Silicon Carbide 19

amorphization. Although increased chemical disorder could simultaneously produce interstitials, vacancies and interstitial/vacancy clusters, the concentration of these defects is far from the level observed in the irradiation experiments. The current model only involving chemical disorder should be accordingly modified to take into consideration the concentrations of other defects while eliminating the overlapping effects arising from these

Chemical disorder *χ*, a measure of the likelihood of forming homonuclear bonds in SiC controls the c-a transition occurring in the irradiation induced amorphization of SiC. A chemical disorder based model is proposed to describe the variations of different mechanical properties of SiC during the c-a transition as a function of microstructures. Elasticity and stiffness related mechanical properties of disordered SiC depend on the chemical disorder in distinct manners, which can be attributed to the different evolution stages of topological order with increasing chemical disorder. MD simulations reveal the atomistic mechanisms of varying *a*-SiC in response to tension and nanoindentation. A crossover of atomistic mechanism with damage accumulation is found in both cases, which is responsible for the evolution of mechanical responses when SiC varies from crystalline to fully amorphous. This crossover also manifests itself in the switch of fracture mode varying

from brittle fracture to nano-ductile failure due to the coalescence of nanocavities.

The authors are grateful for funding from National Basic Research Program of China No. 2010CB631005 and State Key Laboratory of Explosion Science and Technology No. QNKT10-

Benyagoub, A. (2008). Irradiation Effects Induced in Silicon Carbide by Low and High

Bolse, W. (1998). Formation and Development of Disordered Networks in Si-Based Ceramics

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*Materials and Atoms*, Vol. 148, No. 1-4, pp. 83-92, 0168-583X

Energy Ions. *Nuclear Instruments and Methods in Physics Research B*, Vol. 266, No., pp.

under Ion Bombardment. *Nuclear Instruments and Methods in Physics Research Section B: Beam Interactions with Materials and Atoms*, Vol. 141, No. 1-4, pp. 133-39, 0168-

*Nuclear Instruments and Methods in Physics Research Section B: Beam Interactions with* 

Glass Breaks Like Metal, but at the Nanometer Scale. *Physical Review Letters*, Vol. 90,

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two major defects.

**8. Acknowledgment** 

10 and No. ZDKT09-02.

583X

063514,

2766-71, 0168-583X

No. 7, pp. 075504,

**9. References** 

**7. Summary** 

slips of atomic layer fragments. Furthermore, the spacing between two load peaks is also no longer correlated with the separation of atomic layers in *z* directions.

Further increase of chemical disorder produces a percolating disordered zone through the network. The proportion of disordered atoms in the *χ* = 0.16 assembly exceeds 17%. Then the *a*-SiC can be considered as a mixture of two coexisting phases: hard crystalline fragments and soft amorphous regions. Henceforth the discrete motion of a fragment are decoupled from those of the neighboring fragments, giving rise to the irregular fluctuations in the *p*-*h* curve for the *χ* = 0.16 assembly. Both uncorrelated deformation of atomic layer fragments and enhanced plastic flow in amorphous regions contribute to the significant reduction of hardness in *χ* = 0.16 assembly. Nevertheless, the localized plastic flow plays a dominant role in the *χ* = 0.22 assembly, since there are no distinguishable peaks rather than small oscillations detected in the *p*-*h* curve for the *χ* = 0.22 assembly.

#### **6. Discussion**

This chemical disorder based model make an initiative to quantify the correlation between mechanical properties and irradiation-amorphized SiC, while gaining valuable insights for understanding the variations of mechanical responses from the perspective of atomistic mechanisms. However we should be aware of the limitations in the conclusion drawn. The main assumption of this model is that chemical disorder underpins the changes of topological order and then determines the c-a transition of SiC. This assumption is justified by the investigation into the topological structures of a range of SiC with varying imposed level of chemical disorder. Whereas the current experimental observation could just support the existence of C-C and Si-Si homonuclear bonds, rather than provide the accurate degree of chemical disorder. Also it is agreed that the total amorphization is attained at critical threshold in deposited nuclear energy loss which is a function of ion energy and temperature(Benyagoub, A., 2008; Bolse, W., 1998). Whether the experimental measured threshold of deposited nuclear energy loss corresponds to the simulated chemical disorder is still an open question.

Incapable of describing the configuration of the defects also limits the ability of chemical order *χ* to characterize the structure of *a*-SiC, especially in the case involving moderate *χ*. For example, two *a*-SiC assemblies with identical chemical disorder may well feature distinct configurations of defects, say, one having dispersed isolated chemical disordered defects while the defects in another network tend to cluster. It is impossible to distinguish them only via chemical disorder *χ*. Actually, SiC exhibits different amorphization behavior in response to ion beam irradiation depending on the ion energy and ion mass. The irradiation with ions of medium mass (such as C, Si, etc) having energies of a few hundreds keV primarily produce interstitials, vacancies, antisite and small defect cluster(Gao, F. & Weber, W. J., 2001). The growth and coalescence of these point defects and small clusters correspond to partial or total amorphization. In contrast, heavy impinging ion (such as Au, etc) creates, within its displacement cascade, an amorphous zone surrounded by a defective crystalline region which in turn becomes amorphous after subsequent ion impacts, either directly by defect accumulation or indirectly by the growing of already existing amorphous zones. Therefore the c-a transition process for 3C-SiC undergoes different path depending on ion mass. Complementary to chemical disorder, additional parameter(s) containing the information about the defects configuration are necessary to describe the c-a transition.

Another issue concerning the chemical disorder based model is that it somehow underestimates the effects of Frenkel pair and vacancy clusters on the irradiation induced amorphization. Although increased chemical disorder could simultaneously produce interstitials, vacancies and interstitial/vacancy clusters, the concentration of these defects is far from the level observed in the irradiation experiments. The current model only involving chemical disorder should be accordingly modified to take into consideration the concentrations of other defects while eliminating the overlapping effects arising from these two major defects.

#### **7. Summary**

18 Silicon Carbide – Materials, Processing and Applications in Electronic Devices

slips of atomic layer fragments. Furthermore, the spacing between two load peaks is also no

Further increase of chemical disorder produces a percolating disordered zone through the network. The proportion of disordered atoms in the *χ* = 0.16 assembly exceeds 17%. Then the *a*-SiC can be considered as a mixture of two coexisting phases: hard crystalline fragments and soft amorphous regions. Henceforth the discrete motion of a fragment are decoupled from those of the neighboring fragments, giving rise to the irregular fluctuations in the *p*-*h* curve for the *χ* = 0.16 assembly. Both uncorrelated deformation of atomic layer fragments and enhanced plastic flow in amorphous regions contribute to the significant reduction of hardness in *χ* = 0.16 assembly. Nevertheless, the localized plastic flow plays a dominant role in the *χ* = 0.22 assembly, since there are no distinguishable peaks rather than

This chemical disorder based model make an initiative to quantify the correlation between mechanical properties and irradiation-amorphized SiC, while gaining valuable insights for understanding the variations of mechanical responses from the perspective of atomistic mechanisms. However we should be aware of the limitations in the conclusion drawn. The main assumption of this model is that chemical disorder underpins the changes of topological order and then determines the c-a transition of SiC. This assumption is justified by the investigation into the topological structures of a range of SiC with varying imposed level of chemical disorder. Whereas the current experimental observation could just support the existence of C-C and Si-Si homonuclear bonds, rather than provide the accurate degree of chemical disorder. Also it is agreed that the total amorphization is attained at critical threshold in deposited nuclear energy loss which is a function of ion energy and temperature(Benyagoub, A., 2008; Bolse, W., 1998). Whether the experimental measured threshold of deposited nuclear energy loss corresponds to the simulated chemical disorder

Incapable of describing the configuration of the defects also limits the ability of chemical order *χ* to characterize the structure of *a*-SiC, especially in the case involving moderate *χ*. For example, two *a*-SiC assemblies with identical chemical disorder may well feature distinct configurations of defects, say, one having dispersed isolated chemical disordered defects while the defects in another network tend to cluster. It is impossible to distinguish them only via chemical disorder *χ*. Actually, SiC exhibits different amorphization behavior in response to ion beam irradiation depending on the ion energy and ion mass. The irradiation with ions of medium mass (such as C, Si, etc) having energies of a few hundreds keV primarily produce interstitials, vacancies, antisite and small defect cluster(Gao, F. & Weber, W. J., 2001). The growth and coalescence of these point defects and small clusters correspond to partial or total amorphization. In contrast, heavy impinging ion (such as Au, etc) creates, within its displacement cascade, an amorphous zone surrounded by a defective crystalline region which in turn becomes amorphous after subsequent ion impacts, either directly by defect accumulation or indirectly by the growing of already existing amorphous zones. Therefore the c-a transition process for 3C-SiC undergoes different path depending on ion mass. Complementary to chemical disorder, additional parameter(s) containing the information about the defects configuration are necessary to describe the c-a transition. Another issue concerning the chemical disorder based model is that it somehow underestimates the effects of Frenkel pair and vacancy clusters on the irradiation induced

longer correlated with the separation of atomic layers in *z* directions.

small oscillations detected in the *p*-*h* curve for the *χ* = 0.22 assembly.

**6. Discussion** 

is still an open question.

Chemical disorder *χ*, a measure of the likelihood of forming homonuclear bonds in SiC controls the c-a transition occurring in the irradiation induced amorphization of SiC. A chemical disorder based model is proposed to describe the variations of different mechanical properties of SiC during the c-a transition as a function of microstructures. Elasticity and stiffness related mechanical properties of disordered SiC depend on the chemical disorder in distinct manners, which can be attributed to the different evolution stages of topological order with increasing chemical disorder. MD simulations reveal the atomistic mechanisms of varying *a*-SiC in response to tension and nanoindentation. A crossover of atomistic mechanism with damage accumulation is found in both cases, which is responsible for the evolution of mechanical responses when SiC varies from crystalline to fully amorphous. This crossover also manifests itself in the switch of fracture mode varying from brittle fracture to nano-ductile failure due to the coalescence of nanocavities.

#### **8. Acknowledgment**

The authors are grateful for funding from National Basic Research Program of China No. 2010CB631005 and State Key Laboratory of Explosion Science and Technology No. QNKT10- 10 and No. ZDKT09-02.

#### **9. References**


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**0**

**2**

*France*

Patrice Mélinon

*University of Lyon and CNRS*

**SiC Cage Like Based Materials**

SiC is a compound of silicon and carbon with a chemical formula SiC. Silicon carbide(SiC) as a material is the most promising for applications in which high-temperature, high-power, and high-frequency devices, catalyst support, high irradiation environments are needed. Naturally occurring SiC is found only in poor quantities that explains the considerable effort made in the industrial SiC engineering. At a first glad, silicon and carbide are close but a careful inspection reveals different properties leading to brothers at odds behavior. In well ordered stoichiometric compounds SiC adopts a tetrahedral bonding like observed in common semiconductors (zincblende and wurtzite are the most populars). The difference of electronegativities induces a ionicity which is not enough to promote NaCl or CsCl structures but enough to induce multipolar effects. These multipolar effects are responsible to the huge number of polytypes. This polytypism has numerous applications including quantum confinement effects and graphene engineering. In this chapter, special emphasis has been placed on the non stoichiometric compounds. Silicon architectures are based from sp3 or more dense packing while carbon architectures cover a large spread of hybridization from sp to sp3, the sp<sup>2</sup> graphite-like being the stable structure in standard conditions. When we gather silicon and carbon together one of the basic issue is: what is the winner? When silicon and carbon have the same concentration (called stoichiometric compound), the answer is trivial: "the sp3" lattice since both the elements share this hybridization in bulk phase. In rich silicon phases, the sp<sup>3</sup> hybridization is also a natural way. However, a mystery remains when rich carbon compounds are synthesized. Silicon sp<sup>2</sup> lattice is definitively unstable while carbon adopts this structure. One of the solution is the cage-like structure (the fullerenes belongs to this family) where the hybridization is intermediate between sp2 and sp3. Other exotic structures like buckydiamonds are also possible. Special architectures can be built from the elemental SiC cage-like bricks, most of them are not yet synthesized, few are experimentally reported in low quantity. However, these structures are promising as long the electronic structure is quite different from standard phase and offer new areas of research in fuel cells (catalysis and gas storage), superconductivity, thermoelectric, optical and electronic devices. . .Moreover, the cage like structure permits endohedrally doping opening the way of heavily doped semiconductors strain free. Assembling elemental bricks lead to zeolite-like structures. We

review the properties of some of these structures and their potential applications.

**1. Introduction**


### **SiC Cage Like Based Materials**

### Patrice Mélinon

*University of Lyon and CNRS France*

#### **1. Introduction**

22 Silicon Carbide – Materials, Processing and Applications in Electronic Devices

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Amorphized Silicon Carbide. *Nuclear Instruments and Methods in Physics Research Section B: Beam Interactions with Materials and Atoms*, Vol. 191, No. 1-4, pp. 74-82, SiC is a compound of silicon and carbon with a chemical formula SiC. Silicon carbide(SiC) as a material is the most promising for applications in which high-temperature, high-power, and high-frequency devices, catalyst support, high irradiation environments are needed. Naturally occurring SiC is found only in poor quantities that explains the considerable effort made in the industrial SiC engineering. At a first glad, silicon and carbide are close but a careful inspection reveals different properties leading to brothers at odds behavior. In well ordered stoichiometric compounds SiC adopts a tetrahedral bonding like observed in common semiconductors (zincblende and wurtzite are the most populars). The difference of electronegativities induces a ionicity which is not enough to promote NaCl or CsCl structures but enough to induce multipolar effects. These multipolar effects are responsible to the huge number of polytypes. This polytypism has numerous applications including quantum confinement effects and graphene engineering. In this chapter, special emphasis has been placed on the non stoichiometric compounds. Silicon architectures are based from sp3 or more dense packing while carbon architectures cover a large spread of hybridization from sp to sp3, the sp<sup>2</sup> graphite-like being the stable structure in standard conditions. When we gather silicon and carbon together one of the basic issue is: what is the winner? When silicon and carbon have the same concentration (called stoichiometric compound), the answer is trivial: "the sp3" lattice since both the elements share this hybridization in bulk phase. In rich silicon phases, the sp<sup>3</sup> hybridization is also a natural way. However, a mystery remains when rich carbon compounds are synthesized. Silicon sp<sup>2</sup> lattice is definitively unstable while carbon adopts this structure. One of the solution is the cage-like structure (the fullerenes belongs to this family) where the hybridization is intermediate between sp2 and sp3. Other exotic structures like buckydiamonds are also possible. Special architectures can be built from the elemental SiC cage-like bricks, most of them are not yet synthesized, few are experimentally reported in low quantity. However, these structures are promising as long the electronic structure is quite different from standard phase and offer new areas of research in fuel cells (catalysis and gas storage), superconductivity, thermoelectric, optical and electronic devices. . .Moreover, the cage like structure permits endohedrally doping opening the way of heavily doped semiconductors strain free. Assembling elemental bricks lead to zeolite-like structures. We review the properties of some of these structures and their potential applications.

**1.1.2 sp**<sup>2</sup> **hybridization**

origin of the *π* band.

When the s orbital and two of the p orbitals for each carbon are mixed, the hybridization for each carbon is *sp*2. The resulting geometry is the trigonal (hexagonal) planar geometry, with the bond angle between the hybrid orbitals equal to 120*o*, the additional p electron is at the

SiC Cage Like Based Materials 25

Fig. 2. how to build up graphite, nanotube or fullerene from a graphene sheet (after the

Graphene is of importance both for its unusual transport properties and as the mother for fullerene and nanotube families (figure 2). Graphene can be defined as an infinite periodic arrangement of (only six-member carbon ring) polycyclic aromatic carbon. It can be looked at as a fullerene with an infinite number of atoms. Owing the theoretical unstability of 2D networks, graphene sheets are stable over several microns enough for applications. Graphene has a two atom basis (A and B) per primitive cell arranged in a perfect hexagonal honeycomb. Except the center of the Brillouin zone Γ, the structure can be entirely described by symmetry with the particular setpoints **M**, **K** and **K'** related by the relationship **K**=-**K'**. For each atom, three electrons form tight bonds with neighbor atoms in the plane, the fourth electron in the *pz* orbital does not interact with them leading to zero *pz* orbital energy *Ez* = 0. It can be easily seen that the electron energy is zero at **K** and **K'**, graphene being a semiconductor with a zero bandgap. The most striking result is the linear relationship for the dispersion curve near **K** and **K'** . Since the effective mass is related to the second derivation of the energy, this implies a zero mass for the two electrons (one by site A and B). As a consequence, the classical picture of the Schrödinger equation must be replaced by the Dirac equation where Dirac spinors (two component wave function) are required in the mathematical description of the quantum state of the relativistic electron. This linear dispersion involving a multi degenerated states at the intersecting cones is broken by several ways: impurities, defects, interaction with two or

original figure from Geim *et al* ( Geim and Novoselov, 2007))

#### **1.1 Carbon**

Carbon has six electrons. Two of them will be found in the *1s* orbital close to the nucleus forming a compact core, the next two going into the 2s orbital. The remaining ones will be in two separate *2p* orbitals. The electronic structure of carbon is normally written 1*s*22*s*22*p*2. Contrary to silicon, germanium and tin, the unlikely promotion of an outer shell electron in a d state avoids the formation of compact structures. This clearly indicates that most of the chemical bonding involves valence electrons with *sp* character. In order to form two, three or four hybrid orbitals, the corresponding number of atomic orbitals has to be mixed within the framework of "hybridization concept". When the *s* orbital and all three *p* orbitals are mixed, the hybridization is *sp*3. The geometry that achieves this is the tetrahedral geometry *Td*, where any bond angle is 109.47*<sup>o</sup>* (see fig. 1).

Fig. 1. elementary molecules corresponding to the three possible types of bonding. Acetylene *C*2*H*<sup>2</sup> (sp bonding), ethylene *C*2*H*<sup>4</sup> (*sp*<sup>2</sup> bonding) and ethane *C*2*H*<sup>6</sup> (*sp*<sup>3</sup> bonding).

#### **1.1.1 sp hybridization**

When the s orbital and one p orbital are mixed, the hybridization is *sp*. The geometry is now linear, with the bond angle between the hybrid orbitals equal to 180*o*. The additional p electrons which do not participate to the *σ* bonding (strong bond resulting from the overlap of hybrid orbitals) form the *π* bond, each orbital being perpendicular to the basal plane containing the *σ* bond. The *sp* carbon chains can present alternating single and triple bonds (polyyne)[*α*-carbyne] or only double bonds (polycumulene)[*β*-carbyne]; polyynes being more stable owing to the Peierls distortion (Kavan et al., 1995) which lifts the symmetry: double-double bond to simple-triple bond. The existence of carbyne is a subject of controversy and strictly speaking cannot be classified as a carbon allotrope. The existence of long linear chains becomes unlikely as soon as the length grows up. Crystalline carbyne must be unstable against virulent graphitization (sp to sp2 transition) under normal conditions (Baughman, 2006). Up to date, the largest synthesized carbyne chain was *HC*16*H* (Lucotti et al., 2006) where terminated hydrogen ensures the stabilization of the carbyne. Even though, carbyne is the best prototype of the 1D network, the purity of the samples and the low chemical stability are the major hindrance for applications.

#### **1.1.2 sp**<sup>2</sup> **hybridization**

2 Will-be-set-by-IN-TECH

Carbon has six electrons. Two of them will be found in the *1s* orbital close to the nucleus forming a compact core, the next two going into the 2s orbital. The remaining ones will be in two separate *2p* orbitals. The electronic structure of carbon is normally written 1*s*22*s*22*p*2. Contrary to silicon, germanium and tin, the unlikely promotion of an outer shell electron in a d state avoids the formation of compact structures. This clearly indicates that most of the chemical bonding involves valence electrons with *sp* character. In order to form two, three or four hybrid orbitals, the corresponding number of atomic orbitals has to be mixed within the framework of "hybridization concept". When the *s* orbital and all three *p* orbitals are mixed, the hybridization is *sp*3. The geometry that achieves this is the tetrahedral geometry *Td*, where

Fig. 1. elementary molecules corresponding to the three possible types of bonding. Acetylene

When the s orbital and one p orbital are mixed, the hybridization is *sp*. The geometry is now linear, with the bond angle between the hybrid orbitals equal to 180*o*. The additional p electrons which do not participate to the *σ* bonding (strong bond resulting from the overlap of hybrid orbitals) form the *π* bond, each orbital being perpendicular to the basal plane containing the *σ* bond. The *sp* carbon chains can present alternating single and triple bonds (polyyne)[*α*-carbyne] or only double bonds (polycumulene)[*β*-carbyne]; polyynes being more stable owing to the Peierls distortion (Kavan et al., 1995) which lifts the symmetry: double-double bond to simple-triple bond. The existence of carbyne is a subject of controversy and strictly speaking cannot be classified as a carbon allotrope. The existence of long linear chains becomes unlikely as soon as the length grows up. Crystalline carbyne must be unstable against virulent graphitization (sp to sp2 transition) under normal conditions (Baughman, 2006). Up to date, the largest synthesized carbyne chain was *HC*16*H* (Lucotti et al., 2006) where terminated hydrogen ensures the stabilization of the carbyne. Even though, carbyne is the best prototype of the 1D network, the purity of the samples and the low chemical stability

*C*2*H*<sup>2</sup> (sp bonding), ethylene *C*2*H*<sup>4</sup> (*sp*<sup>2</sup> bonding) and ethane *C*2*H*<sup>6</sup> (*sp*<sup>3</sup> bonding).

**1.1 Carbon**

any bond angle is 109.47*<sup>o</sup>* (see fig. 1).

**1.1.1 sp hybridization**

are the major hindrance for applications.

When the s orbital and two of the p orbitals for each carbon are mixed, the hybridization for each carbon is *sp*2. The resulting geometry is the trigonal (hexagonal) planar geometry, with the bond angle between the hybrid orbitals equal to 120*o*, the additional p electron is at the origin of the *π* band.

Fig. 2. how to build up graphite, nanotube or fullerene from a graphene sheet (after the original figure from Geim *et al* ( Geim and Novoselov, 2007))

Graphene is of importance both for its unusual transport properties and as the mother for fullerene and nanotube families (figure 2). Graphene can be defined as an infinite periodic arrangement of (only six-member carbon ring) polycyclic aromatic carbon. It can be looked at as a fullerene with an infinite number of atoms. Owing the theoretical unstability of 2D networks, graphene sheets are stable over several microns enough for applications. Graphene has a two atom basis (A and B) per primitive cell arranged in a perfect hexagonal honeycomb. Except the center of the Brillouin zone Γ, the structure can be entirely described by symmetry with the particular setpoints **M**, **K** and **K'** related by the relationship **K**=-**K'**. For each atom, three electrons form tight bonds with neighbor atoms in the plane, the fourth electron in the *pz* orbital does not interact with them leading to zero *pz* orbital energy *Ez* = 0. It can be easily seen that the electron energy is zero at **K** and **K'**, graphene being a semiconductor with a zero bandgap. The most striking result is the linear relationship for the dispersion curve near **K** and **K'** . Since the effective mass is related to the second derivation of the energy, this implies a zero mass for the two electrons (one by site A and B). As a consequence, the classical picture of the Schrödinger equation must be replaced by the Dirac equation where Dirac spinors (two component wave function) are required in the mathematical description of the quantum state of the relativistic electron. This linear dispersion involving a multi degenerated states at the intersecting cones is broken by several ways: impurities, defects, interaction with two or

*<sup>C</sup>*<sup>2</sup> units are in the staggered mode. The space group is Fd3¯*<sup>m</sup>* <sup>−</sup> *<sup>O</sup>*<sup>7</sup>

and three p orbitals) leading to tetrahedrally coordinated phases.

Γ �

polytypism.

**1.2 Silicon**

**1.2.1 sp**<sup>3</sup>

Γ �

this structure is *<sup>P</sup>*63/*mmc* <sup>−</sup> *<sup>D</sup>*<sup>4</sup>

eight atoms in the conventional unit cell (two in the primitive cell). The two atoms are in position a (0,0,0) and (1/4,1/4,1/4) respectively with the coordinates of equivalent positions (0,0,0;0,1/2,1/2;1/2,0,1/2;1/2,1/2,0). The lattice constant is a=3.5669Å and the interatomic distance 1.5445Å (see figure 14). Contrary to graphite, the lack of the delocalized *π* band ensures an insulator character. Diamond is indeed a wide indirect band gap material with the

SiC Cage Like Based Materials 27

<sup>25</sup> − Γ<sup>15</sup> transition of 7.3 eV and the indirect band gap of 5.45 eV. A (metastable) hexagonal polymorph of diamond (lonsdaleite) is also reported. The crystallographic description of

4f ±(1/3,2/3,1/16; 2/3,1/3,9/16). The lattice parameters are a=2.522Å and c=4.119Å, respectively. The main difference between the hexagonal structure and that of diamond is that in one quarter of the *C*<sup>2</sup> units the bonds are eclipsed. Other stacking sequence allows

Silicon has 14 electrons. Ten of them will be found in the *1s*, *2s* and *2p* orbitals close to the nucleus, the next two going into the *3s* orbital. The remaining ones will be in two separate *3p* orbitals. The electronic structure of silicon is written in the form 1*s*22*s*22*p*63*s*23*p*<sup>2</sup> . Because of this configuration, Si atoms most frequently establish sp3 bonds (hybridization of a s orbital

The most stable phase in silicon is the cubic diamond. The structure is identical to the one discussed for carbon. The lattice constant is a=5.43Å. Each silicon is linked to the four neighboring atoms by 2.3515Å bond. Silicon diamond is an indirect band gap material. The

<sup>25</sup> − Γ<sup>15</sup> transition is at 3.5 eV and the indirect band gap at 1.17 eV. As in carbon polytypism in hexagonal phase is also reported (combining eclipsed and staggered modes). Recently, a new metastable form has been isolated: the clathrate II (fig. 4. In the clathrates, the tetrahedra are mainly stacked in eclipsed mode while diamond is formed by stacking them in the staggered mode. Clathrate II is built by the coalescence of two *Si*<sup>28</sup> and four *Si*<sup>20</sup> per unit cell. It belongs to the same space group than the cubic diamond structure Fd3¯*m*. Using the crystallographic notation, clathrate II is labeled Si-34 since we have 1/4(2 × 28 + 4 × 20) = 34 atoms in the primitive cell. Such a structure is obtained by template one Si atom in the *Si*<sup>5</sup> basic *sp*<sup>3</sup> tetrahedron with *Si*<sup>28</sup> cage, this latter having *Td* point group symmetry. *Si*<sup>28</sup> has four hexagons and share these hexagons with its four *Si*<sup>28</sup> neighboring cages. The space filling needs additional silicon atoms in a tetrahedral symmetry forming *Si*<sup>20</sup> cages. 85,7% of the membered rings are pentagons, implying that the electronic properties are sensitive to the frustration effect (contrary to bonding states, antibonding states contain one bonding node in odd membered rings). The difference in energy within DFT between Si-34 and Si-2 is of 0.06 eV per bond compared to 0.17 eV in the first metastable beta-tin structure .Clathrate II (Si-34) is obtained by heating the *NaSi*<sup>2</sup> silicide under vacuum or using a high pressure belt. Note that carbon clathrate is not yet synthesized as long as the precursor does not exist while the competition between clathrate and graphite (the most stable) phase operates. Several authors mentioned the Si clathrate potentiality for applications in optoelectronic devices. First of all, the wide band gap opening (around 1.9 eV) (Gryko et al., 2000; Melinon et al., 1998 ; Connetable et al., 2003; Connetable, 2003a ; Adams et al., 1994) ensures electronic transition

<sup>6</sup>*<sup>h</sup>* (number 194) with four atoms per unit cell in position

*<sup>h</sup>* (number 227) with

many graphene sheets (Partoens and Peeters, 2006)(Charlier et al., 1991), confinement effect (Nakada et al., 1996)(Son et al., 2006). After the degeneracy splitting, the dispersion tends to be parabolic with a "classical" effective mass. 3D graphite is formed by the stacking of graphene layers (Chung, 2002). The space group is *<sup>P</sup>*63*mmc* <sup>−</sup> *<sup>D</sup>*<sup>14</sup> <sup>6</sup>*<sup>h</sup>* (number 194) with four atoms in the unit cell , two in position 2b at <sup>±</sup>(<sup>00</sup> <sup>1</sup> <sup>4</sup> ), and two in position *2d* at ( <sup>2</sup> 3 1 3 1 <sup>4</sup> ). The two planes are connected by a translation **t** = (**a**<sup>1</sup> + **a**2)/3 + **a**3/2 or by a C6 rotation about the sixfold symmetry axis followed by a translation **a**3/2 (**a***<sup>i</sup>* are the graphite lattice vectors)(fig. 3). This geometry permits the overlap of the *π* electrons leading to the *π* bonding. The electrons participating in this *π*-bonding seem able to move across these *π*-bonds from one atom to the next. This feature explains graphite's ability to conduct electricity along the sheets of carbon atom parallel to the (0001) direction just as graphene does.

Fig. 3. left panel: Image of a single suspended sheet of graphene taken with a transmission electron microscope, showing individual carbon atoms (yellow) on the honeycomb lattice (after Zettl Research Group Condensed Matter Physics Department of Physics University of California at Berkeley). Right panel: ball and stick representation with unit vectors *a*<sup>1</sup> and *a*2. The first 2D Brillouin zone is shown with the irreductible points (for further details about the figure see (Melinon and Masenelli, 2011)).

#### **1.1.3 sp**<sup>3</sup> **hybridization**

The most popular form is the cubic diamond (called diamond C-2), the second allotrope of carbon where each atom joined to four other carbons in regular tetrahedrons. The crystal structure is a face- centered cubic lattice with two atoms in the primitive cell. All the 4 Will-be-set-by-IN-TECH

many graphene sheets (Partoens and Peeters, 2006)(Charlier et al., 1991), confinement effect (Nakada et al., 1996)(Son et al., 2006). After the degeneracy splitting, the dispersion tends to be parabolic with a "classical" effective mass. 3D graphite is formed by the stacking of

two planes are connected by a translation **t** = (**a**<sup>1</sup> + **a**2)/3 + **a**3/2 or by a C6 rotation about the sixfold symmetry axis followed by a translation **a**3/2 (**a***<sup>i</sup>* are the graphite lattice vectors)(fig. 3). This geometry permits the overlap of the *π* electrons leading to the *π* bonding. The electrons participating in this *π*-bonding seem able to move across these *π*-bonds from one atom to the next. This feature explains graphite's ability to conduct electricity along the sheets of carbon

Fig. 3. left panel: Image of a single suspended sheet of graphene taken with a transmission electron microscope, showing individual carbon atoms (yellow) on the honeycomb lattice (after Zettl Research Group Condensed Matter Physics Department of Physics University of California at Berkeley). Right panel: ball and stick representation with unit vectors *a*<sup>1</sup> and *a*2. The first 2D Brillouin zone is shown with the irreductible points (for further details about the

The most popular form is the cubic diamond (called diamond C-2), the second allotrope of carbon where each atom joined to four other carbons in regular tetrahedrons. The crystal structure is a face- centered cubic lattice with two atoms in the primitive cell. All the

<sup>6</sup>*<sup>h</sup>* (number 194) with four

3 1 3 1 <sup>4</sup> ). The

<sup>4</sup> ), and two in position *2d* at ( <sup>2</sup>

graphene layers (Chung, 2002). The space group is *<sup>P</sup>*63*mmc* <sup>−</sup> *<sup>D</sup>*<sup>14</sup>

atoms in the unit cell , two in position 2b at <sup>±</sup>(<sup>00</sup> <sup>1</sup>

atom parallel to the (0001) direction just as graphene does.

figure see (Melinon and Masenelli, 2011)).

**1.1.3 sp**<sup>3</sup> **hybridization**

*<sup>C</sup>*<sup>2</sup> units are in the staggered mode. The space group is Fd3¯*<sup>m</sup>* <sup>−</sup> *<sup>O</sup>*<sup>7</sup> *<sup>h</sup>* (number 227) with eight atoms in the conventional unit cell (two in the primitive cell). The two atoms are in position a (0,0,0) and (1/4,1/4,1/4) respectively with the coordinates of equivalent positions (0,0,0;0,1/2,1/2;1/2,0,1/2;1/2,1/2,0). The lattice constant is a=3.5669Å and the interatomic distance 1.5445Å (see figure 14). Contrary to graphite, the lack of the delocalized *π* band ensures an insulator character. Diamond is indeed a wide indirect band gap material with the Γ � <sup>25</sup> − Γ<sup>15</sup> transition of 7.3 eV and the indirect band gap of 5.45 eV. A (metastable) hexagonal polymorph of diamond (lonsdaleite) is also reported. The crystallographic description of this structure is *<sup>P</sup>*63/*mmc* <sup>−</sup> *<sup>D</sup>*<sup>4</sup> <sup>6</sup>*<sup>h</sup>* (number 194) with four atoms per unit cell in position 4f ±(1/3,2/3,1/16; 2/3,1/3,9/16). The lattice parameters are a=2.522Å and c=4.119Å, respectively. The main difference between the hexagonal structure and that of diamond is that in one quarter of the *C*<sup>2</sup> units the bonds are eclipsed. Other stacking sequence allows polytypism.

#### **1.2 Silicon**

Silicon has 14 electrons. Ten of them will be found in the *1s*, *2s* and *2p* orbitals close to the nucleus, the next two going into the *3s* orbital. The remaining ones will be in two separate *3p* orbitals. The electronic structure of silicon is written in the form 1*s*22*s*22*p*63*s*23*p*<sup>2</sup> . Because of this configuration, Si atoms most frequently establish sp3 bonds (hybridization of a s orbital and three p orbitals) leading to tetrahedrally coordinated phases.

#### **1.2.1 sp**<sup>3</sup>

The most stable phase in silicon is the cubic diamond. The structure is identical to the one discussed for carbon. The lattice constant is a=5.43Å. Each silicon is linked to the four neighboring atoms by 2.3515Å bond. Silicon diamond is an indirect band gap material. The Γ � <sup>25</sup> − Γ<sup>15</sup> transition is at 3.5 eV and the indirect band gap at 1.17 eV. As in carbon polytypism in hexagonal phase is also reported (combining eclipsed and staggered modes). Recently, a new metastable form has been isolated: the clathrate II (fig. 4. In the clathrates, the tetrahedra are mainly stacked in eclipsed mode while diamond is formed by stacking them in the staggered mode. Clathrate II is built by the coalescence of two *Si*<sup>28</sup> and four *Si*<sup>20</sup> per unit cell. It belongs to the same space group than the cubic diamond structure Fd3¯*m*. Using the crystallographic notation, clathrate II is labeled Si-34 since we have 1/4(2 × 28 + 4 × 20) = 34 atoms in the primitive cell. Such a structure is obtained by template one Si atom in the *Si*<sup>5</sup> basic *sp*<sup>3</sup> tetrahedron with *Si*<sup>28</sup> cage, this latter having *Td* point group symmetry. *Si*<sup>28</sup> has four hexagons and share these hexagons with its four *Si*<sup>28</sup> neighboring cages. The space filling needs additional silicon atoms in a tetrahedral symmetry forming *Si*<sup>20</sup> cages. 85,7% of the membered rings are pentagons, implying that the electronic properties are sensitive to the frustration effect (contrary to bonding states, antibonding states contain one bonding node in odd membered rings). The difference in energy within DFT between Si-34 and Si-2 is of 0.06 eV per bond compared to 0.17 eV in the first metastable beta-tin structure .Clathrate II (Si-34) is obtained by heating the *NaSi*<sup>2</sup> silicide under vacuum or using a high pressure belt. Note that carbon clathrate is not yet synthesized as long as the precursor does not exist while the competition between clathrate and graphite (the most stable) phase operates. Several authors mentioned the Si clathrate potentiality for applications in optoelectronic devices. First of all, the wide band gap opening (around 1.9 eV) (Gryko et al., 2000; Melinon et al., 1998 ; Connetable et al., 2003; Connetable, 2003a ; Adams et al., 1994) ensures electronic transition

applications are numerous (Choyke, 2004; Feng, 2004)) including the hardness (almost as hard as diamond), the extreme resistance to chemicals and radiation, a refractory compound, a tuning (wide) bandgap with high electron mobility, high breakdown electric field and good

SiC Cage Like Based Materials 29

Then, starting from a crystal with a perfect chemical order, introducing some disorder will cost two energetic contributions: a chemical enthalpy Δ*Hchem*, which is about 0.35 eV/atom in the ordered phase (Martins and Zunger, 1986) as mentioned above, and a strain enthalpy Δ*Hsize*. Indeed, the large atomic size difference introduces a microscopic strain by incorporating *C-C* or *Si-Si* bonds while an ordered crystal is intrinsically strain free (we neglect the small variations in the atomic positions in polytypes). Δ*Hsize* is of the same order of magnitude than the chemical contribution (Δ*Hsize* � 0.4 eV/atom(Tersoff, 1994)). With a simple Arrhenius' law giving the measure of disorder, we can check that the occurence of *Si-Si* and/or *C-C* bonds is negligible over a large range of temperature. This differs from other compounds, such as *SiGe* where the chemical contribution is almost zero (a few meV negative (Martins and Zunger, 1986), meaning that *Si-Ge* bonds are slightly less favorable than *Si-Si* and *Ge-Ge* bonds and since *Si* and *Ge* have a comparable atomic size (*dSi*−*Si* = 2.35 Å, *dGe*−*Ge* = 2.445 Å), the gain in strain energy is low enough to allow a significant chemical

There is a charge transfer from *Si* to *C* in relation with the electronegativity difference between *Si* and *C* atoms (Zhao and Bagayoko, 2000). This charge transfer 0.66 |*e*| (Segall et al., 1996 ) is affected by the d orbitals in silicon. The ionicity can be defined according to empirical laws stated by Pauling and Phillips or more accurate model within the calculated valence-charge asymmetry (Garcia and Cohen, 1993). Pauling made use of thermochemical arguments based from the electronegativities to determine the ionicity *fi* = 0.11. Another standard picture based from the dielectric model first introduced by Phillips gives f*<sup>i</sup>* = 0.177. However, Phillips' or Pauling's models do not take into account the crystal structure. This can be done in the simple static model where the ionicity parameter is defined in terms of the symmetric and antisymmetric parts of the atomic valence-charge density (Garcia and Cohen, 1993). According to the considered polytype, the static ionicity values *fi* are 0.4724 (*2H*), 0.4718 (*3C*), 0.4720 (*4H*), and 0.4719 (*6H*). They do not change much from one polytype to another but they strongly differ from Pauling's ionicity (Wellenhofer et al., 1996). One possible consequence of the ionicity, depending on the structure, is the appearance of a spontaneous

No information about a *SiC* clathrate is available. Moriguchi *et al* (Moriguchi et al., 2000) and Wang *et al* (Wang et al., 2008) investigated the theoretical *SixGe*1−*<sup>x</sup>* type II clathrate (see chapter 4). To minimize the homonuclear bonding *Si-Si* or *Ge-Ge* in pentagonal rings, non stoichiometric compounds (x=1/17,4/17,5/17,12/17,13/17,16/17) have been investigated. Some of these clathrate alloys with an ideal *Fd*3¯*m* symmetry are found to have direct band gap at the *π*/a(111) L point in the Brillouin zone which could be important for optoelectronic devices. However, the clathrate lattice needs a set of *Si-Si*, *Si-Ge* and *Ge-Ge* bonds which are close in distance values. This will be not the case in the *SiC* clathrate and questions the

thermal conductivity. This is also a safe bio compatible compound.

disorder.

polarization.

**1.5 Clathrate**

existence of such lattices in *SiC*.

**1.4 The bottleneck: ionicity in SiC crystal**

in the visible region and offers new potentialities in "all silicon" optoelectronic devices. Endohedrally doping is also possible. The Fermi level can be tailored by varying both the concentration and the type of atom inside the cage up to large concentration (>10%) without stress,vacancy-containing centers or misfits. For example, Fermi level easily lies at 0.5 eV above the conduction band minimum in n-doped clathrate (see fig. 13). Doped semiconducting clathrates (Tse et al., 2000) as candidates for thermoelectric power since endohedral atoms can effectively rattle around the cages.

Fig. 4. a piece of clathrate II reported in silicon with a combination of *Si*<sup>28</sup> and *Si*20.

#### **1.2.2 . . . and beyond**

Contrary to carbon, the first transition observed in the excited state allows *spd* hybridizations. This is out of scope of this paper. *spd* hybridizations are reported in very small silicon clusters or in bulk phase at high pressure/temperature.

#### **1.2.3 The case of sp**<sup>2</sup>

*The elements with a principal quantum number equal to or greater than three are not capable of forming multiple bonds because of the considerable Pauli repulsion between the electrons of the inner shells*. This golden rule summarizes the absence of *π* bonding in silicon. "Silicon graphite" is less stable than its diamond phase by 0.71 eV per atom (Yin and Cohen, 1984).

#### **1.3 Silicon carbide**

SiC is a compound of silicon and carbon with the net formula SiC. The first thing to note is that, from a bond point of view, chemical ordering is energetically favored: a *Si-C* bond (6.34 eV/atom (Kackell, 1994a;b)) is more stable by -0.35 eV/atom than the average of a *Si-Si* (4.63 eV/atom (Alfe et al., 2004)) and a *C-C* bond (7.35 eV/atom (Yin and Cohen, 1984)). The 6 Will-be-set-by-IN-TECH

in the visible region and offers new potentialities in "all silicon" optoelectronic devices. Endohedrally doping is also possible. The Fermi level can be tailored by varying both the concentration and the type of atom inside the cage up to large concentration (>10%) without stress,vacancy-containing centers or misfits. For example, Fermi level easily lies at 0.5 eV above the conduction band minimum in n-doped clathrate (see fig. 13). Doped semiconducting clathrates (Tse et al., 2000) as candidates for thermoelectric power since

Fig. 4. a piece of clathrate II reported in silicon with a combination of *Si*<sup>28</sup> and *Si*20.

Contrary to carbon, the first transition observed in the excited state allows *spd* hybridizations. This is out of scope of this paper. *spd* hybridizations are reported in very small silicon clusters

*The elements with a principal quantum number equal to or greater than three are not capable of forming multiple bonds because of the considerable Pauli repulsion between the electrons of the inner shells*. This golden rule summarizes the absence of *π* bonding in silicon. "Silicon graphite" is less stable

SiC is a compound of silicon and carbon with the net formula SiC. The first thing to note is that, from a bond point of view, chemical ordering is energetically favored: a *Si-C* bond (6.34 eV/atom (Kackell, 1994a;b)) is more stable by -0.35 eV/atom than the average of a *Si-Si* (4.63 eV/atom (Alfe et al., 2004)) and a *C-C* bond (7.35 eV/atom (Yin and Cohen, 1984)). The

endohedral atoms can effectively rattle around the cages.

**1.2.2 . . . and beyond**

**1.2.3 The case of sp**<sup>2</sup>

**1.3 Silicon carbide**

or in bulk phase at high pressure/temperature.

than its diamond phase by 0.71 eV per atom (Yin and Cohen, 1984).

applications are numerous (Choyke, 2004; Feng, 2004)) including the hardness (almost as hard as diamond), the extreme resistance to chemicals and radiation, a refractory compound, a tuning (wide) bandgap with high electron mobility, high breakdown electric field and good thermal conductivity. This is also a safe bio compatible compound.

Then, starting from a crystal with a perfect chemical order, introducing some disorder will cost two energetic contributions: a chemical enthalpy Δ*Hchem*, which is about 0.35 eV/atom in the ordered phase (Martins and Zunger, 1986) as mentioned above, and a strain enthalpy Δ*Hsize*. Indeed, the large atomic size difference introduces a microscopic strain by incorporating *C-C* or *Si-Si* bonds while an ordered crystal is intrinsically strain free (we neglect the small variations in the atomic positions in polytypes). Δ*Hsize* is of the same order of magnitude than the chemical contribution (Δ*Hsize* � 0.4 eV/atom(Tersoff, 1994)). With a simple Arrhenius' law giving the measure of disorder, we can check that the occurence of *Si-Si* and/or *C-C* bonds is negligible over a large range of temperature. This differs from other compounds, such as *SiGe* where the chemical contribution is almost zero (a few meV negative (Martins and Zunger, 1986), meaning that *Si-Ge* bonds are slightly less favorable than *Si-Si* and *Ge-Ge* bonds and since *Si* and *Ge* have a comparable atomic size (*dSi*−*Si* = 2.35 Å, *dGe*−*Ge* = 2.445 Å), the gain in strain energy is low enough to allow a significant chemical disorder.

#### **1.4 The bottleneck: ionicity in SiC crystal**

There is a charge transfer from *Si* to *C* in relation with the electronegativity difference between *Si* and *C* atoms (Zhao and Bagayoko, 2000). This charge transfer 0.66 |*e*| (Segall et al., 1996 ) is affected by the d orbitals in silicon. The ionicity can be defined according to empirical laws stated by Pauling and Phillips or more accurate model within the calculated valence-charge asymmetry (Garcia and Cohen, 1993). Pauling made use of thermochemical arguments based from the electronegativities to determine the ionicity *fi* = 0.11. Another standard picture based from the dielectric model first introduced by Phillips gives f*<sup>i</sup>* = 0.177. However, Phillips' or Pauling's models do not take into account the crystal structure. This can be done in the simple static model where the ionicity parameter is defined in terms of the symmetric and antisymmetric parts of the atomic valence-charge density (Garcia and Cohen, 1993). According to the considered polytype, the static ionicity values *fi* are 0.4724 (*2H*), 0.4718 (*3C*), 0.4720 (*4H*), and 0.4719 (*6H*). They do not change much from one polytype to another but they strongly differ from Pauling's ionicity (Wellenhofer et al., 1996). One possible consequence of the ionicity, depending on the structure, is the appearance of a spontaneous polarization.

#### **1.5 Clathrate**

No information about a *SiC* clathrate is available. Moriguchi *et al* (Moriguchi et al., 2000) and Wang *et al* (Wang et al., 2008) investigated the theoretical *SixGe*1−*<sup>x</sup>* type II clathrate (see chapter 4). To minimize the homonuclear bonding *Si-Si* or *Ge-Ge* in pentagonal rings, non stoichiometric compounds (x=1/17,4/17,5/17,12/17,13/17,16/17) have been investigated. Some of these clathrate alloys with an ideal *Fd*3¯*m* symmetry are found to have direct band gap at the *π*/a(111) L point in the Brillouin zone which could be important for optoelectronic devices. However, the clathrate lattice needs a set of *Si-Si*, *Si-Ge* and *Ge-Ge* bonds which are close in distance values. This will be not the case in the *SiC* clathrate and questions the existence of such lattices in *SiC*.



Table 1. The space group, unit cell lattice parameters (a and c), carbon and silicon fractional coordinates (x, y, z), multiplicities and Wyckoff positions of the sites for selected polytypes. A refinement of the positions is given by Bauer *et al* (Bauer et al., 1998)

Polytypism occurs when a structural change occurs within the same hybridization. In the case of SiC, we have some degrees of freedom in the way individual layers are stacked within a crystal structure, the driving force being the conservation of the chemical ordering. Silicon carbide exhibits a pronounced polytypism, the most simple polytypes are zinc-blende SiC (*3C-SiC* ) and wurtzite (*2H-SiC*), the two structures correspond to the cubic and hexagonal diamonds when all the atoms are *Si* or *C* (see figure 5). The crystallographic data for selected polytypes are displayed in table 1

A single *Si-C* bilayer can be viewed as a planar sheet of silicon atoms coupled with a planar sheet of carbon atoms. The plane formed by a *Si-C* bilayer is known as the basal plane, while the crystallographic c-axis direction, also known as the stacking direction or the [0001] direction in the hexagonal lattice, is defined normal to the *Si-C* bilayer plane. All the *SiC* polytypes are classified following the arrangements of cubic or hexagonal *SiC* bilayers, stacking along the cubic [111] or the equivalent hexagonal [0001] direction.

The differences of cohesive energy in polytypes range in a few 0.01 eV (see table 2), state of the art *ab initio* calculations are not straightforward and out of range. Simple empirical potential (Ito and Kangawa, 2002; Ito et al., 2006), which incorporates electrostatic energies due to bond charges and ionic charges or Ising's model (Heine et al., 1992a) are reliable as depicted in table 2. According to Heine et al Heine et al. (1992a) one defines

$$
\Delta E\_{\text{ANNNI},2H-\text{SiC}} = 2f\_1 + 2f\_3 \tag{1}
$$

Fig. 5. ball and stick representation in three dimensional perspective of the first polytypes *2H-SiC*, *4H-SiC* and *6H-SiC* compared to *3C-SiC*. The chains structures which defined the stacking sequence are in dark color while selected *Si-C* bonds are in red color. The *SiC* bilayer is also shown. (Kackell, 1994a) after the original figure in reference (Melinon and Masenelli,

SiC Cage Like Based Materials 31

<sup>Δ</sup>*EANNNI*,6*H*−*SiC* <sup>=</sup> <sup>2</sup>

**1.7 Application of the polytypism: quantum wells**

<sup>Δ</sup>*EANNNI*,4*H*−*SiC* = *<sup>J</sup>*<sup>1</sup> + <sup>2</sup>*J*<sup>2</sup> + *<sup>J</sup>*<sup>3</sup> (2)

<sup>3</sup> *<sup>J</sup>*<sup>2</sup> <sup>+</sup> <sup>2</sup>*J*<sup>3</sup> (3)

<sup>3</sup> *<sup>J</sup>*<sup>1</sup> <sup>+</sup>

Multi quantum wells first introduced by Esaki (Esaki and Chang, 1974) are potential wells that confines particles periodically, particles which were originally free to move in three dimensions. Esaki (Esaki and Chang, 1974) has defined a multi quantum well structure (*MQWS*) as a periodic variation of the crystal potential on a scale longer than the lattice constant, the most popular heterostructure being GaAs/AlAs superlattice (Sibille et al., 1990). *MQWS* devices are of prime importance in the development of optoelectronic devices. Unfortunately, these *MQWS* use elements which are not compatible with the basic "silicon" technology. This limits the integration of optoelectronic devices in complex chips. MQWS SiC based materials are under consideration keeping at mind that the stacking (a combination of eclipsed and staggered modes) of tetrahedra cell *CSi*<sup>4</sup> or *SiC*<sup>4</sup> strongly modify the bandgap value. This can be achieved controlling the stacking mode (polytypism assimilated to stacking

4

2011)

8 Will-be-set-by-IN-TECH

name space group a c x y z Wyckoff 3C-SiC *F*43¯ *m* 216 4.368 - (Si)0 0 0 *4a*

3C-SiC *P*63*mc* 186 3.079 7.542 (Si)0 0 0 *2a*

2H-SiC *P*63*mc* 186 3.079 5.053 (Si) 1/3 2/3 0 *2b*

4H-SiC *P*63*mc* 186 3.079 10.07 (Si) 0 0 0 *2a*

6H-SiC *P*63*mc* 186 3.079 15.12 (Si) 0 0 0 *2a*

Table 1. The space group, unit cell lattice parameters (a and c), carbon and silicon fractional coordinates (x, y, z), multiplicities and Wyckoff positions of the sites for selected polytypes.

Polytypism occurs when a structural change occurs within the same hybridization. In the case of SiC, we have some degrees of freedom in the way individual layers are stacked within a crystal structure, the driving force being the conservation of the chemical ordering. Silicon carbide exhibits a pronounced polytypism, the most simple polytypes are zinc-blende SiC (*3C-SiC* ) and wurtzite (*2H-SiC*), the two structures correspond to the cubic and hexagonal diamonds when all the atoms are *Si* or *C* (see figure 5). The crystallographic data for selected

A single *Si-C* bilayer can be viewed as a planar sheet of silicon atoms coupled with a planar sheet of carbon atoms. The plane formed by a *Si-C* bilayer is known as the basal plane, while the crystallographic c-axis direction, also known as the stacking direction or the [0001] direction in the hexagonal lattice, is defined normal to the *Si-C* bilayer plane. All the *SiC* polytypes are classified following the arrangements of cubic or hexagonal *SiC* bilayers,

The differences of cohesive energy in polytypes range in a few 0.01 eV (see table 2), state of the art *ab initio* calculations are not straightforward and out of range. Simple empirical potential (Ito and Kangawa, 2002; Ito et al., 2006), which incorporates electrostatic energies due to bond charges and ionic charges or Ising's model (Heine et al., 1992a) are reliable as depicted in table

A refinement of the positions is given by Bauer *et al* (Bauer et al., 1998)

stacking along the cubic [111] or the equivalent hexagonal [0001] direction.

2. According to Heine et al Heine et al. (1992a) one defines

polytypes are displayed in table 1

(C)3/4 3/4 3/4 *4d*

(C)0 0 1/4 *2a* (Si)1/3 2/3 1/3 *2b* (C)1/3 2/3 7/12 *2b* (Si)2/3 1/3 2/3 *2b* (C)2/3 1/3 11/12 *2b*

(C) 1/3 2/3 3/8 *2b*

(C) 0 0 3/16 *2a* (Si) 1/3 2/3 1/4 *2b* (C) 1/3 2/3 7/16 *2b*

(C) 0 0 1/8 *2a* (Si) 1/3 2/3 1/6 *2b* (C) 1/3 2/3 7/24 *2b* (Si) 2/3 1/3 1/3 *2b* (C) 2/3 1/3 11/24 *2b*

<sup>Δ</sup>*EANNNI*,2*H*−*SiC* = <sup>2</sup>*J*<sup>1</sup> + <sup>2</sup>*J*<sup>3</sup> (1)

**1.6 Polytypism**

Fig. 5. ball and stick representation in three dimensional perspective of the first polytypes *2H-SiC*, *4H-SiC* and *6H-SiC* compared to *3C-SiC*. The chains structures which defined the stacking sequence are in dark color while selected *Si-C* bonds are in red color. The *SiC* bilayer is also shown. (Kackell, 1994a) after the original figure in reference (Melinon and Masenelli, 2011)

$$
\Delta E\_{\text{ANNNI}, \text{4H}-\text{SiC}} = f\_1 + 2f\_2 + f\_3 \tag{2}
$$

$$
\Delta E\_{\rm ANNINI,6H-SiC} = \frac{2}{3}I\_1 + \frac{4}{3}I\_2 + 2I\_3 \tag{3}
$$

#### **1.7 Application of the polytypism: quantum wells**

Multi quantum wells first introduced by Esaki (Esaki and Chang, 1974) are potential wells that confines particles periodically, particles which were originally free to move in three dimensions. Esaki (Esaki and Chang, 1974) has defined a multi quantum well structure (*MQWS*) as a periodic variation of the crystal potential on a scale longer than the lattice constant, the most popular heterostructure being GaAs/AlAs superlattice (Sibille et al., 1990). *MQWS* devices are of prime importance in the development of optoelectronic devices. Unfortunately, these *MQWS* use elements which are not compatible with the basic "silicon" technology. This limits the integration of optoelectronic devices in complex chips. MQWS SiC based materials are under consideration keeping at mind that the stacking (a combination of eclipsed and staggered modes) of tetrahedra cell *CSi*<sup>4</sup> or *SiC*<sup>4</sup> strongly modify the bandgap value. This can be achieved controlling the stacking mode (polytypism assimilated to stacking

**1.7.1 Antiphase boundary**

gap ranges around 1 eV.

**1.8 Amorphous phase**

**1.8.1 Carbon**

**1.8.2 Silicon**

state and rapidly quenched.

for applications in optoelectronics devices.

**1.8.3 Silicon carbon**

**1.7.2 Cubic/hexagonal stacking**

network by the suppression of dangling bonds.

In the *APB*s (see fig. 6), the crystallographic direction remains unchanged but each side of the boundary has an opposite phase. For example, in *3C-SiC* described by *ABCABCABC* layers, one or two layer interruption in the stacking sequence gives the following sequence ABC**ABAB**CAB which is the alternance of *fcc/hcp/fcc* layers. The chemical ordering is disrupted with the appearance of *Si-Si* and *C-C* bonds. The associated bandgap modulation depends to several: the difference in valence, the difference in size of the atoms and the electrostatic repulsion in the *Si-Si* and *C-C* bond near the interface. *APB* formation is obtained when *3C-SiC* grows epitaxially on (100) silicon clean substrate (Pirouz et al., 1987). Deak *et al.* (Deak et al., 2006) reported a theoretical work where the expected tuning of the effective band

SiC Cage Like Based Materials 33

As mentioned above (fig. 6) , MQWS can be built from the stacking of different crystal structures of the same material as in wurtzite/zincblende heterostructures (Sibille et al., 1990).

The maximum disorder can be observed in carbon where a large spread in hybridization and bonds coexist. Amorphous carbon can be rich in *sp*<sup>2</sup> bonding (vitreous carbon) or rich in *sp*<sup>3</sup> bonding (tetrahedral amorphous carbon and diamond like carbon).The properties of amorphous carbon films depend on the parameters used during the deposition especially the presence of doping such as hydrogen or nitrogen. Note that hydrogen stabilizes the *sp*<sup>3</sup>

Since Si adopts a *sp*<sup>3</sup> hybridization, the amorphous state will be a piece of *sp*<sup>3</sup> network. The most popular model is the continuous random network (CRN) first introduced by Polk and Boudreaux (Polk and Boudreaux, 1973). As a consequence, five or seven-membered rings are introduced in the initial diamond lattice to avoid the occurrence of a long range order. Finally, dangling bonds are created at the surface and a spread in bond lengths and bond angles was observed (within 1% and 10%, respectively). Elemental a-Si cannot be used practically because of the dangling bonds, whose energy levels appear in the bandgap of silicon. Fortunately, this problem is solved by hydrogen incorporation which passive of the dangling bonds and participates to the relaxation of the stress in the matrix (a-Si:H). CRN models are hand-built models. A more rigorous approach is done by classical, semi empirical or *ab initio* calculations using molecular dynamics algorithms where a cluster of crystalline Si is prepared in a liquid

The major question is the extent of chemical disorder present in amorphous *SiC* network. There is not a consensus in the a-SiC network because of the huge number of parameters (chemical ordering, carbon hybridization, spread in angles and bonds, odd membered rings, dangling bonds . . . ). The control of the chemical ordering in amorphous phase is the key point


Table 2. calculated energy difference (in eV) for selected polytypes within different models. *<sup>a</sup>* from reference (Ito et al., 2006)

*<sup>b</sup>* from reference (Cheng et al., 1988)


*<sup>e</sup>* from reference (Limpijumnong and Lambrecht, 1998)

*<sup>f</sup>* from reference (Lindefelt et al., 2003)

*<sup>g</sup>* from reference (Liu and Ni, 2005)

Fig. 6. left panel: illustration of the quantum well formed by the polytypism. Right panel: illustration of the quantum well formed by antiphase boundary (after the original figures in reference (Melinon and Masenelli, 2011) and references therein)

faults) or introduced extended defects such as antiphase boundary *APB*. The maximum value modulation in the potential corresponds with the bandgap difference between 3C-SiC and 2H-SiC <sup>Δ</sup>*Emax* <sup>=</sup> *Eg*(3*C*−*SiC*) <sup>−</sup> *Eg*(2*H*−*SiC*) <sup>≈</sup> <sup>1</sup>*eV* (see fig. 6).

10 Will-be-set-by-IN-TECH

model *3C-SiC 2H-SiC 4H-SiC 6H-SiC J*<sup>1</sup> *J*<sup>2</sup> *J*<sup>3</sup> empirical*<sup>a</sup>* <sup>0</sup> 2.95×10−<sup>3</sup> 1.47 <sup>×</sup> <sup>10</sup>−<sup>3</sup> 0.92 <sup>×</sup> <sup>10</sup>−<sup>3</sup> 1.52 0.0 -0.05 DFT-GGA*<sup>a</sup>* <sup>0</sup> 2.95×10−<sup>3</sup> <sup>−</sup>0.09 <sup>×</sup> <sup>10</sup>−<sup>3</sup> <sup>−</sup>0.16 <sup>×</sup> <sup>10</sup>−<sup>3</sup> 1.55 -0.78 -0.08 DFT-LDA*<sup>b</sup>* <sup>0</sup> 4.35×10−<sup>3</sup> <sup>−</sup>0.39 <sup>×</sup> <sup>10</sup>−<sup>3</sup> <sup>−</sup>0.60 <sup>×</sup> <sup>10</sup>−<sup>3</sup> 4.85 -2.56 -0.50 DFT-LDA*<sup>c</sup>* <sup>0</sup> 1.80×10−<sup>3</sup> <sup>−</sup>2.5 <sup>×</sup> <sup>10</sup>−<sup>3</sup> <sup>−</sup>1.80 <sup>×</sup> <sup>10</sup>−<sup>3</sup> 2.00 -3.40 -0.20 DFT-LDA*<sup>d</sup>* <sup>0</sup> 0.9×10−<sup>3</sup> <sup>−</sup>2.0 <sup>×</sup> <sup>10</sup>−<sup>3</sup> <sup>−</sup>1.45 <sup>×</sup> <sup>10</sup>−<sup>3</sup> 1.08 -2.45 -0.18 FP-LMTO*<sup>e</sup>* <sup>0</sup> 2.7×10−<sup>3</sup> <sup>−</sup>1.2 <sup>×</sup> <sup>10</sup>−<sup>3</sup> <sup>−</sup>1.05 <sup>×</sup> <sup>10</sup>−<sup>3</sup> 3.06 -2.57 -0.35 DFT-LDA*<sup>f</sup>* <sup>0</sup> 2.14×10−<sup>3</sup> <sup>−</sup>1.24 <sup>×</sup> <sup>10</sup>−<sup>3</sup> <sup>−</sup>1.09 <sup>×</sup> <sup>10</sup>−<sup>3</sup> 2.53 -2.31 -0.40 DFT-LDA*<sup>g</sup>* <sup>0</sup> 2.32×10−<sup>3</sup> <sup>−</sup>1.27 <sup>×</sup> <sup>10</sup>−<sup>3</sup> <sup>−</sup>1.10 <sup>×</sup> <sup>10</sup>−<sup>3</sup> 2.71 -2.43 -0.39 DFT-GGA*<sup>g</sup>* <sup>0</sup> 3.40×10−<sup>3</sup> <sup>−</sup>0.35 <sup>×</sup> <sup>10</sup>−<sup>3</sup> <sup>−</sup>0.45 <sup>×</sup> <sup>10</sup>−<sup>3</sup> 3.72 -20.5 -0.33 Table 2. calculated energy difference (in eV) for selected polytypes within different models.

Fig. 6. left panel: illustration of the quantum well formed by the polytypism. Right panel: illustration of the quantum well formed by antiphase boundary (after the original figures in

faults) or introduced extended defects such as antiphase boundary *APB*. The maximum value modulation in the potential corresponds with the bandgap difference between 3C-SiC and

reference (Melinon and Masenelli, 2011) and references therein)

2H-SiC <sup>Δ</sup>*Emax* <sup>=</sup> *Eg*(3*C*−*SiC*) <sup>−</sup> *Eg*(2*H*−*SiC*) <sup>≈</sup> <sup>1</sup>*eV* (see fig. 6).

*<sup>a</sup>* from reference (Ito et al., 2006) *<sup>b</sup>* from reference (Cheng et al., 1988) *<sup>c</sup>* from reference (Park et al., 1994) *<sup>d</sup>* from reference (Kackell, 1994a)

*<sup>f</sup>* from reference (Lindefelt et al., 2003) *<sup>g</sup>* from reference (Liu and Ni, 2005)

*<sup>e</sup>* from reference (Limpijumnong and Lambrecht, 1998)

#### **1.7.1 Antiphase boundary**

In the *APB*s (see fig. 6), the crystallographic direction remains unchanged but each side of the boundary has an opposite phase. For example, in *3C-SiC* described by *ABCABCABC* layers, one or two layer interruption in the stacking sequence gives the following sequence ABC**ABAB**CAB which is the alternance of *fcc/hcp/fcc* layers. The chemical ordering is disrupted with the appearance of *Si-Si* and *C-C* bonds. The associated bandgap modulation depends to several: the difference in valence, the difference in size of the atoms and the electrostatic repulsion in the *Si-Si* and *C-C* bond near the interface. *APB* formation is obtained when *3C-SiC* grows epitaxially on (100) silicon clean substrate (Pirouz et al., 1987). Deak *et al.* (Deak et al., 2006) reported a theoretical work where the expected tuning of the effective band gap ranges around 1 eV.

#### **1.7.2 Cubic/hexagonal stacking**

As mentioned above (fig. 6) , MQWS can be built from the stacking of different crystal structures of the same material as in wurtzite/zincblende heterostructures (Sibille et al., 1990).

#### **1.8 Amorphous phase**

#### **1.8.1 Carbon**

The maximum disorder can be observed in carbon where a large spread in hybridization and bonds coexist. Amorphous carbon can be rich in *sp*<sup>2</sup> bonding (vitreous carbon) or rich in *sp*<sup>3</sup> bonding (tetrahedral amorphous carbon and diamond like carbon).The properties of amorphous carbon films depend on the parameters used during the deposition especially the presence of doping such as hydrogen or nitrogen. Note that hydrogen stabilizes the *sp*<sup>3</sup> network by the suppression of dangling bonds.

#### **1.8.2 Silicon**

Since Si adopts a *sp*<sup>3</sup> hybridization, the amorphous state will be a piece of *sp*<sup>3</sup> network. The most popular model is the continuous random network (CRN) first introduced by Polk and Boudreaux (Polk and Boudreaux, 1973). As a consequence, five or seven-membered rings are introduced in the initial diamond lattice to avoid the occurrence of a long range order. Finally, dangling bonds are created at the surface and a spread in bond lengths and bond angles was observed (within 1% and 10%, respectively). Elemental a-Si cannot be used practically because of the dangling bonds, whose energy levels appear in the bandgap of silicon. Fortunately, this problem is solved by hydrogen incorporation which passive of the dangling bonds and participates to the relaxation of the stress in the matrix (a-Si:H). CRN models are hand-built models. A more rigorous approach is done by classical, semi empirical or *ab initio* calculations using molecular dynamics algorithms where a cluster of crystalline Si is prepared in a liquid state and rapidly quenched.

#### **1.8.3 Silicon carbon**

The major question is the extent of chemical disorder present in amorphous *SiC* network. There is not a consensus in the a-SiC network because of the huge number of parameters (chemical ordering, carbon hybridization, spread in angles and bonds, odd membered rings, dangling bonds . . . ). The control of the chemical ordering in amorphous phase is the key point for applications in optoelectronics devices.

method geometry *Ering* -*Ebowl Ering*-*Ecage* rank *<sup>a</sup>*MP2/TZVd optimized 2.08 0.03 bowl-cage-ring *<sup>a</sup>*MP2/TZV2d optimized 2.06 -0.66 cage-bowl-ring *<sup>a</sup>*MP2/TZV2d1f optimized 2.10 -0.54 cage-bowl-ring *<sup>a</sup>*MP2/TZV2d1f HF/6-31G<sup>∗</sup> 2.61 0.69 bowl-cage-ring *<sup>a</sup>*MR-MP2/TZV2d MP2/TZV2d1f 2.42 -0.02 cage-bowl-ring *<sup>a</sup>*MR-MP2/TZV2d1f MP2/TZV2d1f 2.53 0.19 bowl-cage-ring *<sup>a</sup>*MR-MP2/TZV2d1f HF/6-31G<sup>∗</sup> 3.00 1.27 bowl-cage-ring

SiC Cage Like Based Materials 35

*<sup>b</sup>*QMC HF/6-31G<sup>∗</sup> 1.1 2.10 bowl-ring-cage

<sup>20</sup> . These high degeneracies are lifted by a Jahn Teller effect

0.4 1.9 ring-bowl-cage

*<sup>a</sup>*LDA/TZV2df//MP2/TZV2df 2.00 -1.0 cage-bowl-ring

Table 3. energy difference in eV (± 0.5 eV) between the ring (expected ground state), bowl and cage against several methods which different treatments of correlation and polarization

The *HOMO* state in *Ih C*<sup>20</sup> has a G*<sup>u</sup>* state occupied by two electrons, the closed-shell

which distorts the cage (Parasuk and Almlof, 1991). Indeed after relaxation, the degeneracies can be removed lowering the total energy (-1.33eV in *D*2*<sup>h</sup>* with respect to *Ih* (Wang et al., 2005)) and opening a *HOMO LUMO* separation (Sawtarie et al., 1994). It has been stated that dodecahedrane *C*20*H*<sup>20</sup> first synthesized by Paquette's group (Ternansky et al., 1982) is stable with a heat of formation about 18.2 kcal/mol (Disch and Schulman, 1996). The dodecahedron is characterized by a 7.3 eV *HOMO (hu) LUMO ag* separation (Zdetsis, 2007). However, the *HOMO-LUMO* separation does not increases monotonically with the hydrogen content indicating particular stable structures such as *IhC*20*H*<sup>10</sup> with the same *HOMO-LUMO* separation than the fully saturated *IhC*20*H*<sup>20</sup> (Milani et al., 1996). Coming back to the equation 4. Another solution is *N*<sup>5</sup> = 0 giving *N*<sup>4</sup> = 6 (square rings as reported in in cyclobutane where the strain is maximum). The first polyhedron (equivalent to *C*60) where isolated square rule is achieved is the hexagonal cuboctahedron with *Oh* symmetry (24 atoms) (the first Brillouin zone in fcc lattice, see fig. 15). However, the strain energy gained in squares is too large to ensure the stability as compared to *D*<sup>6</sup> *C*<sup>24</sup> fullerene with (Jensen and Toftlund, 1993). *C*<sup>24</sup> with *N*<sup>5</sup> = 12 is the first fullerene with hexagonal faces which presents in the upper symmetry a D6*<sup>d</sup>* structure compatible with the translational symmetry (D6 after relaxation). This is a piece of clathrate I described later (see fig. 13). Another fullerene *TdC*<sup>28</sup> has a ground state with *a*5*A*<sup>2</sup> high-spin open-shell electronic state, with one electron in the *a*<sup>1</sup> molecular orbital and three electrons in the *t*<sup>2</sup> orbital (Guo et al., 1992) (see fig. 7). The close shell structure needs four electrons with a particular symmetry, three of them will be distributed on the *t*<sup>2</sup> orbital (*p-like* character) the last in the *a*<sup>1</sup> orbital (*s-like* character). This is the template of the carbon atom

*<sup>c</sup>*DFT B3LYP/6-311G∗//B3LYP/6-311G\*

*<sup>b</sup>* after reference (Sokolova et al., 2000) *<sup>c</sup>* after reference (Allison and Beran, 2004)

electronic structure occurs for C2<sup>+</sup>

effects. The last column indicates the rank in stability *<sup>a</sup>* after reference (Grimme and Muck-Lichtenfeld, 2002)

#### **2. Cage-like molecules**

#### **2.1 Carbon: a rapid survey**

#### **2.1.1 Size range**

Due to the high flexibility of the carbon atom, numerous isomers can be expected exhibiting complex forms such as linear chains (*sp* hybridization), rings , fused planar cycles (sp<sup>2</sup> hybridization), compact (sp<sup>3</sup> hybridization) and fullerene structures. We focus on particular structures in relation with complex architectures (zeolites) in bulk phase. From this point of view, fullerenes play a important role (Melinon et al., 2007).

#### **2.1.2 Empty cages (fullerenes)**

Starting with a piece of graphene (fully *sp*<sup>2</sup> hybridized) , the final geometry is given by a subtle balance between two antagonistic effects. One is the minimization of the unpaired electrons at the surface of the apex, the other is the strain energy brought by the relaxation due this minimization. The suppression of unpaired electrons is given by the standard topology (Euler's theorem). it is stated that (Melinon and Masenelli, 2011; Melinon and San Miguel, 2010) (and references therein)

$$\text{2N}\_{4} + \text{N}\_{5} = 12 \tag{4}$$

where *Ni* is the number of i membered- rings. The first case is *N*<sup>4</sup> = 0. This is achieved introducing at least and no more twelve pentagons (*N*<sup>5</sup> = 12), the number of hexagons (the elemental cell of the graphene) being *N*<sup>6</sup> = 2*i* where *i* is an integer. Chemists claim that adjacent pentagons are chemically reactive and then introduce the concept of pentagonal rule (Kroto, 1987). Inspecting the Euler's relationship clearly indicates that the first fullerene with isolated pentagons is *C*<sup>60</sup> with *Ih* symmetry. The mean hybridization is given by the *π*-Orbital Axis Vector Analysis

$$n = \frac{2}{1 - \frac{4\pi}{\sqrt{3}N}}\tag{5}$$

then taking graphene as reference for energy, the difference in energy writes

$$
\Delta E = -3.1 \times 10^{-3} (\theta\_{\pi \sigma} - \frac{\pi}{2})^2 \tag{6}
$$

where

$$\sin(\theta\_{\pi\sigma} - \frac{\pi}{2}) = \frac{2\pi^{1/2}N^{-1/2}}{3^{3/4}}\tag{7}$$

*θπσ* is the angle between *π* and *σ* orbitals.

The first (n=3, *N*<sup>6</sup> = 0) is the popular dodecahedron with *Ih* symmetry. Equation 5 gives a fully *sp*<sup>3</sup> hybridization. C20 is an open shell structure with a zero *HOMO-LUMO* separation. This structure is not stable as long the pentagons are fused and the strain energy maximum. Prinzbach *et al* (Prinzbach et al., 2000) prepared the three isomers according to different routes for the synthesis. The determination of the ground state in C20 is a subject of controversy as depicted in table 3 despite state of the art calculations.

12 Will-be-set-by-IN-TECH

Due to the high flexibility of the carbon atom, numerous isomers can be expected exhibiting complex forms such as linear chains (*sp* hybridization), rings , fused planar cycles (sp<sup>2</sup> hybridization), compact (sp<sup>3</sup> hybridization) and fullerene structures. We focus on particular structures in relation with complex architectures (zeolites) in bulk phase. From this point of

Starting with a piece of graphene (fully *sp*<sup>2</sup> hybridized) , the final geometry is given by a subtle balance between two antagonistic effects. One is the minimization of the unpaired electrons at the surface of the apex, the other is the strain energy brought by the relaxation due this minimization. The suppression of unpaired electrons is given by the standard topology (Euler's theorem). it is stated that (Melinon and Masenelli, 2011; Melinon and San Miguel,

where *Ni* is the number of i membered- rings. The first case is *N*<sup>4</sup> = 0. This is achieved introducing at least and no more twelve pentagons (*N*<sup>5</sup> = 12), the number of hexagons (the elemental cell of the graphene) being *N*<sup>6</sup> = 2*i* where *i* is an integer. Chemists claim that adjacent pentagons are chemically reactive and then introduce the concept of pentagonal rule (Kroto, 1987). Inspecting the Euler's relationship clearly indicates that the first fullerene with isolated pentagons is *C*<sup>60</sup> with *Ih* symmetry. The mean hybridization is given by the *π*-Orbital

> *<sup>n</sup>* <sup>=</sup> <sup>2</sup> 1 − <sup>√</sup> 4*π* 3*N*

<sup>Δ</sup>*<sup>E</sup>* <sup>=</sup> <sup>−</sup>3.1 <sup>×</sup> <sup>10</sup>−3(*θπσ* <sup>−</sup> *<sup>π</sup>*

The first (n=3, *N*<sup>6</sup> = 0) is the popular dodecahedron with *Ih* symmetry. Equation 5 gives a fully *sp*<sup>3</sup> hybridization. C20 is an open shell structure with a zero *HOMO-LUMO* separation. This structure is not stable as long the pentagons are fused and the strain energy maximum. Prinzbach *et al* (Prinzbach et al., 2000) prepared the three isomers according to different routes for the synthesis. The determination of the ground state in C20 is a subject of controversy as

<sup>2</sup> ) = <sup>2</sup>*π*1/2*N*−1/2

then taking graphene as reference for energy, the difference in energy writes

sin(*θπσ* <sup>−</sup> *<sup>π</sup>*

2*N*<sup>4</sup> + *N*<sup>5</sup> = 12 (4)

<sup>2</sup> )<sup>2</sup> (6)

33/4 (7)

(5)

view, fullerenes play a important role (Melinon et al., 2007).

**2. Cage-like molecules**

**2.1 Carbon: a rapid survey**

**2.1.2 Empty cages (fullerenes)**

2010) (and references therein)

Axis Vector Analysis

*θπσ* is the angle between *π* and *σ* orbitals.

depicted in table 3 despite state of the art calculations.

where

**2.1.1 Size range**


Table 3. energy difference in eV (± 0.5 eV) between the ring (expected ground state), bowl and cage against several methods which different treatments of correlation and polarization effects. The last column indicates the rank in stability

*<sup>a</sup>* after reference (Grimme and Muck-Lichtenfeld, 2002)

*<sup>b</sup>* after reference (Sokolova et al., 2000)

*<sup>c</sup>* after reference (Allison and Beran, 2004)

The *HOMO* state in *Ih C*<sup>20</sup> has a G*<sup>u</sup>* state occupied by two electrons, the closed-shell electronic structure occurs for C2<sup>+</sup> <sup>20</sup> . These high degeneracies are lifted by a Jahn Teller effect which distorts the cage (Parasuk and Almlof, 1991). Indeed after relaxation, the degeneracies can be removed lowering the total energy (-1.33eV in *D*2*<sup>h</sup>* with respect to *Ih* (Wang et al., 2005)) and opening a *HOMO LUMO* separation (Sawtarie et al., 1994). It has been stated that dodecahedrane *C*20*H*<sup>20</sup> first synthesized by Paquette's group (Ternansky et al., 1982) is stable with a heat of formation about 18.2 kcal/mol (Disch and Schulman, 1996). The dodecahedron is characterized by a 7.3 eV *HOMO (hu) LUMO ag* separation (Zdetsis, 2007). However, the *HOMO-LUMO* separation does not increases monotonically with the hydrogen content indicating particular stable structures such as *IhC*20*H*<sup>10</sup> with the same *HOMO-LUMO* separation than the fully saturated *IhC*20*H*<sup>20</sup> (Milani et al., 1996). Coming back to the equation 4. Another solution is *N*<sup>5</sup> = 0 giving *N*<sup>4</sup> = 6 (square rings as reported in in cyclobutane where the strain is maximum). The first polyhedron (equivalent to *C*60) where isolated square rule is achieved is the hexagonal cuboctahedron with *Oh* symmetry (24 atoms) (the first Brillouin zone in fcc lattice, see fig. 15). However, the strain energy gained in squares is too large to ensure the stability as compared to *D*<sup>6</sup> *C*<sup>24</sup> fullerene with (Jensen and Toftlund, 1993). *C*<sup>24</sup> with *N*<sup>5</sup> = 12 is the first fullerene with hexagonal faces which presents in the upper symmetry a D6*<sup>d</sup>* structure compatible with the translational symmetry (D6 after relaxation). This is a piece of clathrate I described later (see fig. 13). Another fullerene *TdC*<sup>28</sup> has a ground state with *a*5*A*<sup>2</sup> high-spin open-shell electronic state, with one electron in the *a*<sup>1</sup> molecular orbital and three electrons in the *t*<sup>2</sup> orbital (Guo et al., 1992) (see fig. 7). The close shell structure needs four electrons with a particular symmetry, three of them will be distributed on the *t*<sup>2</sup> orbital (*p-like* character) the last in the *a*<sup>1</sup> orbital (*s-like* character). This is the template of the carbon atom

Fig. 7. scenario the an efficient doping in *C*<sup>28</sup> and *Si*<sup>28</sup> cage. Contrary to carbon , silicon needs a giant tetravalent atom. (a) endohedrally doped *C*<sup>28</sup> cage stable for a tetravalent atom (uranium for example). (b) endohedral doping in *Si*<sup>28</sup> cage by incorporation of two *Si*<sup>5</sup> clusters. The two isomers have roughly the same cohesive energy within DFT-GGA framework. (after the original figure in reference (Melinon and Masenelli, 2009)

SiC Cage Like Based Materials 37

The driving force in bulk is the chemical ordering. Inspecting equation 4 gives two possibilities: fullerene or cuboctahedron families. The first leads to non chemical ordering,

Starting from a spherically truncated bulk diamond structure, relaxation gives (Yu et al., 2009) a buckydiamond structure where the facets are reconstructed with the same manner as *Si* or *C* surfaces (figure 8). The inner shells have a diamond-like structure and the cluster surface a fullerene-like structure. Even though, the chemical ordering is not strictly achieved at the surface, the ratio of C-C and Si-Si bonds due to pentagons decreases as the cluster size increases. The reconstruction presents some striking features with the surface reconstruction

Most of the experiments done in SiC nanoclusters indicate a phase separation which does not validate a buckyball structure even though the buckyball is expected stable. The kinetic pathway plays an important role and the final state strongly depends to the synthesis: route

the second to chemical ordering with a large stress because of four fold rings.

**2.3.1 Quasi chemical ordering: buckydiamond**

**2.3.2 Non chemical ordering: core shell structure**

**2.3 Silicon carbon**

in bulk phase.

making a *sp*<sup>3</sup> network. The four unpaired electrons make *C*<sup>28</sup> behave like a sort of hollow superatom with an effective valence of 4. Introducing four hydrogen atoms outside in the *Td* symmetry induces a close shell structure with the filling of the *t*<sup>2</sup> and *a*<sup>1</sup> states is checked by a *HOMO LUMO* separation of about 2.5 eV (Pederson and Laouini, 1993). *C*28*H*<sup>4</sup> is the template of *CH*<sup>4</sup> leading to the hyperdiamond lattice. A closed shell structure is also done by the transfer of four electrons from a tetravalent embryo inside the cage. Since the size of *C*<sup>28</sup> is low, this can be realized by incorporating one "tetravalent" atom inside the cage (X=Ti, Zr, Hf, U, Sc)(Guo et al., 1992)(Pederson and Laouini, 1993)(Makurin et al., 2001) (figure 7).

#### **2.2 Silicon**

#### **2.2.1 Surface reconstruction**

Theoretical determination of the ground-state geometry of Si clusters is a difficult task. One of the key point is the massive surface reconstruction applied to a piece of diamond (Kaxiras, 1990). The surface reconstruction was first introduced by Haneman (Haneman, 1961). The presence of a lone pair (dangling bond) destabilizes the network. One of the solution is the pairing. Since the surface is flat, this limits the possibility of curvature as reported in fullerenes. However, the surface relaxation is possible introducing pentagons (see for example references ( Pandey, 1981; Himpsel et al., 1984; Lee and Kang, 1996; Xu et al., 2004; Ramstad et al., 1995)). This the key point to understand the stuffed fullerenes.

#### **2.2.2 Stuffed fullerenes**

Even though, the hybridization is fully *sp*<sup>3</sup> as in crystalline phase, *Ih Si*<sup>20</sup> is not a stable molecule, the ground state for this particular number of Si atoms corresponding to two *Si*<sup>10</sup> clusters (Sun et al., 2002; Li and Cao, 2000). *Si*<sup>20</sup> cage -like structure is a distorted icosahedron with an open-shell electronic configuration as reported in *C*<sup>20</sup> fullerene. Likewise, *TdSi*<sup>28</sup> fullerene is not a stable molecule. Starting from the *Td* symmetry, a relaxation leads to a distorted structure which is a local minimum. Contrary to *C*<sup>28</sup> (see above), the *HOMO* in *Td Si*<sup>28</sup> is formed by the *t*<sup>2</sup> symmetry level and the *a*<sup>1</sup> symmetry level for *LUMO* (Gao and Zheng, 2005). Si in *Si*<sup>28</sup> is more atomic like than C in *C*<sup>28</sup> (Gong, 1995). Except these discrepancies, *Si*<sup>28</sup> can be stabilized by four additional electrons coming from four hydrogen atoms outside or a tetravalent atom inside. However the cage diameter is too big for an efficient coupling with one tetravalent atom, even for the bigger known (uranium). Consequently, a single metal atom cannot prevent the *Th Si*<sup>28</sup> cage from puckering and distortion. This problem can be solved introduced a molecule which mimics a giant tetravalent atom, the best being *TdSi*<sup>5</sup> referred to *Si*5*H*<sup>12</sup> which has a perfect *Td* symmetry (figure 7). *TdSi*<sup>5</sup> has a completely filled twofold degenerated level at the *HOMO* state (Gao and Zheng, 2005). The final cluster *Si*5@*Si*<sup>28</sup> is noted *Si*<sup>33</sup> . *Si*<sup>33</sup> has two classes of network: one corresponding to the fullerene family which exhibits *Td* symmetry and can be deduced from a piece of clathrate, and one corresponding to the surface reconstruction of the *Si* crystal having a *Td*<sup>1</sup> space group (Kaxiras, 1990). The difference is the exact position of *Si*<sup>5</sup> inside the *Si*<sup>28</sup> cage. Since the total energy in the two isomers are very close, this emphasizes the concept of "superatom" with a large isotropy. The hybridization picture is not the good approach and a charge transfer picture seems more appropriate. Stuffed fullerene *Si*<sup>33</sup> is found to be unreactive in agreement with the *HOMO LUMO* separation.

14 Will-be-set-by-IN-TECH

making a *sp*<sup>3</sup> network. The four unpaired electrons make *C*<sup>28</sup> behave like a sort of hollow superatom with an effective valence of 4. Introducing four hydrogen atoms outside in the *Td* symmetry induces a close shell structure with the filling of the *t*<sup>2</sup> and *a*<sup>1</sup> states is checked by a *HOMO LUMO* separation of about 2.5 eV (Pederson and Laouini, 1993). *C*28*H*<sup>4</sup> is the template of *CH*<sup>4</sup> leading to the hyperdiamond lattice. A closed shell structure is also done by the transfer of four electrons from a tetravalent embryo inside the cage. Since the size of *C*<sup>28</sup> is low, this can be realized by incorporating one "tetravalent" atom inside the cage (X=Ti, Zr, Hf, U, Sc)(Guo et al., 1992)(Pederson and Laouini, 1993)(Makurin et al., 2001) (figure 7).

Theoretical determination of the ground-state geometry of Si clusters is a difficult task. One of the key point is the massive surface reconstruction applied to a piece of diamond (Kaxiras, 1990). The surface reconstruction was first introduced by Haneman (Haneman, 1961). The presence of a lone pair (dangling bond) destabilizes the network. One of the solution is the pairing. Since the surface is flat, this limits the possibility of curvature as reported in fullerenes. However, the surface relaxation is possible introducing pentagons (see for example references ( Pandey, 1981; Himpsel et al., 1984; Lee and Kang, 1996; Xu et al., 2004;

Even though, the hybridization is fully *sp*<sup>3</sup> as in crystalline phase, *Ih Si*<sup>20</sup> is not a stable molecule, the ground state for this particular number of Si atoms corresponding to two *Si*<sup>10</sup> clusters (Sun et al., 2002; Li and Cao, 2000). *Si*<sup>20</sup> cage -like structure is a distorted icosahedron with an open-shell electronic configuration as reported in *C*<sup>20</sup> fullerene. Likewise, *TdSi*<sup>28</sup> fullerene is not a stable molecule. Starting from the *Td* symmetry, a relaxation leads to a distorted structure which is a local minimum. Contrary to *C*<sup>28</sup> (see above), the *HOMO* in *Td Si*<sup>28</sup> is formed by the *t*<sup>2</sup> symmetry level and the *a*<sup>1</sup> symmetry level for *LUMO* (Gao and Zheng, 2005). Si in *Si*<sup>28</sup> is more atomic like than C in *C*<sup>28</sup> (Gong, 1995). Except these discrepancies, *Si*<sup>28</sup> can be stabilized by four additional electrons coming from four hydrogen atoms outside or a tetravalent atom inside. However the cage diameter is too big for an efficient coupling with one tetravalent atom, even for the bigger known (uranium). Consequently, a single metal atom cannot prevent the *Th Si*<sup>28</sup> cage from puckering and distortion. This problem can be solved introduced a molecule which mimics a giant tetravalent atom, the best being *TdSi*<sup>5</sup> referred to *Si*5*H*<sup>12</sup> which has a perfect *Td* symmetry (figure 7). *TdSi*<sup>5</sup> has a completely filled twofold degenerated level at the *HOMO* state (Gao and Zheng, 2005). The final cluster *Si*5@*Si*<sup>28</sup> is noted *Si*<sup>33</sup> . *Si*<sup>33</sup> has two classes of network: one corresponding to the fullerene family which exhibits *Td* symmetry and can be deduced from a piece of clathrate, and one corresponding to the surface reconstruction of the *Si* crystal having a *Td*<sup>1</sup> space group (Kaxiras, 1990). The difference is the exact position of *Si*<sup>5</sup> inside the *Si*<sup>28</sup> cage. Since the total energy in the two isomers are very close, this emphasizes the concept of "superatom" with a large isotropy. The hybridization picture is not the good approach and a charge transfer picture seems more appropriate. Stuffed fullerene *Si*<sup>33</sup> is found to be unreactive in agreement with the *HOMO*

Ramstad et al., 1995)). This the key point to understand the stuffed fullerenes.

**2.2 Silicon**

**2.2.1 Surface reconstruction**

**2.2.2 Stuffed fullerenes**

*LUMO* separation.

Fig. 7. scenario the an efficient doping in *C*<sup>28</sup> and *Si*<sup>28</sup> cage. Contrary to carbon , silicon needs a giant tetravalent atom. (a) endohedrally doped *C*<sup>28</sup> cage stable for a tetravalent atom (uranium for example). (b) endohedral doping in *Si*<sup>28</sup> cage by incorporation of two *Si*<sup>5</sup> clusters. The two isomers have roughly the same cohesive energy within DFT-GGA framework. (after the original figure in reference (Melinon and Masenelli, 2009)

#### **2.3 Silicon carbon**

The driving force in bulk is the chemical ordering. Inspecting equation 4 gives two possibilities: fullerene or cuboctahedron families. The first leads to non chemical ordering, the second to chemical ordering with a large stress because of four fold rings.

#### **2.3.1 Quasi chemical ordering: buckydiamond**

Starting from a spherically truncated bulk diamond structure, relaxation gives (Yu et al., 2009) a buckydiamond structure where the facets are reconstructed with the same manner as *Si* or *C* surfaces (figure 8). The inner shells have a diamond-like structure and the cluster surface a fullerene-like structure. Even though, the chemical ordering is not strictly achieved at the surface, the ratio of C-C and Si-Si bonds due to pentagons decreases as the cluster size increases. The reconstruction presents some striking features with the surface reconstruction in bulk phase.

#### **2.3.2 Non chemical ordering: core shell structure**

Most of the experiments done in SiC nanoclusters indicate a phase separation which does not validate a buckyball structure even though the buckyball is expected stable. The kinetic pathway plays an important role and the final state strongly depends to the synthesis: route

Fig. 9. (a) Relaxation of different hypothetic structures. from left to right: (*Sin*@*Cm*, *Sim*@*Cn*) showing the complex "amorphous structure" and the lack of the spherical shape, *Cn*@*Sim*, *Cm*@*Sin* showing the C-rich region in the core, the spherical shape being preserved, the non chemical ordering phase showing the strong relaxation and the incomplete chemical ordering due to the large barriers in the diffusion and the buckyball structure. The cohesive energy per atom is also displayed. The original figure is in reference (Yu et al., 2009). (b) size

SiC Cage Like Based Materials 39

assembled film is subsequently prepared by low energy cluster beam deposition. (c) valence band spectra deduced from XPS spectroscopy and (d) Raman band spectra showing siliconand carbon-rich local phases. To guide the eye, the Raman modes and their symmetries in the crystal are given. The Raman spectrum of a *2H-SiC* is also displayed. the spread in bond lengths and bond angles due to the multiple hybridization is well illustrated by the broad bands in Raman and XPS spectra. In a crude approximation, these bands reflect the *p-DOS* in

clusters, heterofullerenes (*C*2*<sup>N</sup>* − *nSin*) and *C*2*<sup>N</sup>* fullerenes, respectively. The figure 10 displays the landscape of the phase transition between a pure fullerene like structure up to a piece of

Figure 11 displays the symbolic ball and stick models for two heterofullerenes with one silicon atom, respectively, *C*<sup>60</sup> being the mother. Inspecting the region near the gap (HOMO-LUMO region)shows the analogy with doped semiconductors by substitution. HOMO-LUMO separation in heterofullerenes are weakly affected by Si atoms compared to pure C60 fullerenes. The Si-related orbitals (dashed lines) can be described in terms of defect levels. Because Si and C belong to the same column, Si atom plays the role of co doping with two acceptor-like and donor-like levels. For two Si atoms substituted in C60, the mechanism is the

distribution of SiC nanoparticles prepared in a laser vaporization source. A cluster

the infinite lattice. The original figure is in reference (Melinon et al., 1998a)

adamantane, the stoichiometry being the tuning parameter.

same excepted the splitting of each donor level in two levels.

Fig. 8. A piece of *β* − *SiC* (truncated octahedron with (111) facets) and the final geometry after relaxation. The more spherical shape indicates a massive reconstruction of the surface. The inner shell remains sp<sup>3</sup> hybridized with a nearly *Td* symmetry while the surface presents a set of pentagons and hexagons which is common in fullerenes. The original figure is in reference (Yu et al., 2009)

chemical or physical. The key point is the stoichiometry. When carbon and silicon are in the same ratio, one observes a complete phase separation with a core shell structure for the corresponding clusters.

#### **2.3.3 Non chemical ordering: amorphous structure**

Figure 9 displays the structure of the cluster starting with a core shell structure. It is found that for *Si* core (*Sin*@*Cm*, *Sim*@*Cn*), *Si* atoms are dragged to the exterior and the relaxation process leads to a strong distortion, with some Si and C atoms bonded. The spread in angles indicate a complexity in the hybridization close to the amorphous state. One of the key point is the phase separation in small nanoclusters as depicted on figure 9 where Si-Si, C-C bonds coexist with Si-C bonds at the interface of Si- and C-rich regions, respectively.

#### **3. SiC cage like**

For a low percentage of silicon, carbon adopts a geometry close to the fullerene where a few Si-atoms (less than twelve) are substituted to carbon atoms in the fullerene structure (Ray et al., 1998; Pellarin et al., 1999). The effect of the stoichiometry can be studied by selective laser evaporation. One takes advantage of the difference in cohesive energy (bonding) between Si-Si and C-C bonds within a a parent SiC stoichiometric cluster. As a function of time during laser irradiation, sequential evaporation of Si atoms (or molecules) yield is more efficient than carbon evaporation leading to pure carbon clusters after total evaporation of silicon atoms. Inspecting the different size distributions deduced from a time of flight mass spectrometer against time reveals sequentially different structures: stoichiometric 16 Will-be-set-by-IN-TECH

Fig. 8. A piece of *β* − *SiC* (truncated octahedron with (111) facets) and the final geometry after relaxation. The more spherical shape indicates a massive reconstruction of the surface. The inner shell remains sp<sup>3</sup> hybridized with a nearly *Td* symmetry while the surface presents a set of pentagons and hexagons which is common in fullerenes. The original figure is in

chemical or physical. The key point is the stoichiometry. When carbon and silicon are in the same ratio, one observes a complete phase separation with a core shell structure for the

Figure 9 displays the structure of the cluster starting with a core shell structure. It is found that for *Si* core (*Sin*@*Cm*, *Sim*@*Cn*), *Si* atoms are dragged to the exterior and the relaxation process leads to a strong distortion, with some Si and C atoms bonded. The spread in angles indicate a complexity in the hybridization close to the amorphous state. One of the key point is the phase separation in small nanoclusters as depicted on figure 9 where Si-Si, C-C bonds coexist

For a low percentage of silicon, carbon adopts a geometry close to the fullerene where a few Si-atoms (less than twelve) are substituted to carbon atoms in the fullerene structure (Ray et al., 1998; Pellarin et al., 1999). The effect of the stoichiometry can be studied by selective laser evaporation. One takes advantage of the difference in cohesive energy (bonding) between Si-Si and C-C bonds within a a parent SiC stoichiometric cluster. As a function of time during laser irradiation, sequential evaporation of Si atoms (or molecules) yield is more efficient than carbon evaporation leading to pure carbon clusters after total evaporation of silicon atoms. Inspecting the different size distributions deduced from a time of flight mass spectrometer against time reveals sequentially different structures: stoichiometric

reference (Yu et al., 2009)

corresponding clusters.

**3. SiC cage like**

**2.3.3 Non chemical ordering: amorphous structure**

with Si-C bonds at the interface of Si- and C-rich regions, respectively.

Fig. 9. (a) Relaxation of different hypothetic structures. from left to right: (*Sin*@*Cm*, *Sim*@*Cn*) showing the complex "amorphous structure" and the lack of the spherical shape, *Cn*@*Sim*, *Cm*@*Sin* showing the C-rich region in the core, the spherical shape being preserved, the non chemical ordering phase showing the strong relaxation and the incomplete chemical ordering due to the large barriers in the diffusion and the buckyball structure. The cohesive energy per atom is also displayed. The original figure is in reference (Yu et al., 2009). (b) size distribution of SiC nanoparticles prepared in a laser vaporization source. A cluster assembled film is subsequently prepared by low energy cluster beam deposition. (c) valence band spectra deduced from XPS spectroscopy and (d) Raman band spectra showing siliconand carbon-rich local phases. To guide the eye, the Raman modes and their symmetries in the crystal are given. The Raman spectrum of a *2H-SiC* is also displayed. the spread in bond lengths and bond angles due to the multiple hybridization is well illustrated by the broad bands in Raman and XPS spectra. In a crude approximation, these bands reflect the *p-DOS* in the infinite lattice. The original figure is in reference (Melinon et al., 1998a)

clusters, heterofullerenes (*C*2*<sup>N</sup>* − *nSin*) and *C*2*<sup>N</sup>* fullerenes, respectively. The figure 10 displays the landscape of the phase transition between a pure fullerene like structure up to a piece of adamantane, the stoichiometry being the tuning parameter.

Figure 11 displays the symbolic ball and stick models for two heterofullerenes with one silicon atom, respectively, *C*<sup>60</sup> being the mother. Inspecting the region near the gap (HOMO-LUMO region)shows the analogy with doped semiconductors by substitution. HOMO-LUMO separation in heterofullerenes are weakly affected by Si atoms compared to pure C60 fullerenes. The Si-related orbitals (dashed lines) can be described in terms of defect levels. Because Si and C belong to the same column, Si atom plays the role of co doping with two acceptor-like and donor-like levels. For two Si atoms substituted in C60, the mechanism is the same excepted the splitting of each donor level in two levels.

Fig. 11. a:symbolic ball and stick representation of *C*60.b1,2: selected energy levels near the HOMO-LUMO *C*<sup>60</sup> region. c: symbolic ball and stick representation of *SiC*<sup>59</sup> , the geometries are deduced from DFT-LDA calculations and relaxed following the standard conjugate gradient scheme (see reference (Ray et al., 1998)). The red sphere is the silicon atom. d: selected energy levels near the *SiC*<sup>59</sup> HOMO-LUMO region. Full lines and dotted lines indicate the carbon- and silicon-related orbitals, respectively. Taking only carbon-related orbitals, the HOMO-LUMO separation is respectively 1.68 eV,1.60 eV for *C*60, *C*59*Si* and respectively. The arrow gives the HOMO LUMO separation. In this way, the HOMO-LUMO separation is 1.2 eV in *C*59*Si* . e: ball and stick representation of C60-Si-C60 (after reference (Tournus et al., 2002)).f: selected energy levels near the HOMO-LUMO C60-Si-C60 region

SiC Cage Like Based Materials 41

There is a entanglement between empty or stuffed fullerenes and zeolite lattices. The interest on these nanocage based materials has been impelled by their potentialities in different domains from which we mention the optoelectronic engineering, integrated batteries, thermoelectric power, hard materials or superconductivity. These expanded-volume phases 12 are formed by triplicate arrangement of a combination of these elemental cages (fullerenes

*i)* A large flexibility in the nature and the strength of the coupling between the guest atom and

*ii)* a large flexibility in doping (n or p) as long no significant stress is observed for a very large concentration (up to 10%). Two kinds of open structures are under consideration. The first is the Kelvin's lattice (named bitruncated cubic honeycomb or "sodalite" in zeolite language formed by a regular stacking of truncated octahedra which are Archimedean solids with 14

for example). The doped expanded-volume phases offer new advantages

the host cage following the valence and the size of the guest atom.

**4. Zeolites: expanded-volume phases of SiC**

Fig. 10. Photoionization mass spectra of initial stoichiometric SiC clusters for increasing laser fluences. The time of flight mass spectrometer can be equipped with a reflectron device. Experimental details are given in the reference (Pellarin et al., 1999). The horizontal scale is given in equivalent number of carbon atoms. (a) High resolution one-photon ionization mass spectrum obtained in the reflectron configuration. (b) to (e) Multiphoton ionization mass spectra obtained at lower resolution without the reflectron configuration to avoid blurring from possible unimolecular evaporation in the time of flight mass spectrometer. The right part of the spectra (b) to (e) have been magnified for a better display. In (b) the heterofullerene series with one and two silicon atoms are indicated. Insets (1) and (2) give a zoomed portion of spectra 3(a) and 3(b). The 4 a.m.u. separation between *SinCm* mass clumps is shown in (1) and the composition of heterofullerenes (8 a.m.u. apart) is indicated in (2). The mass resolution in (2) is too low to resolve individual mass peaks as in (1) (after the original figure (Pellarin et al., 1999)).

#### **3.1 C**<sup>60</sup> **functionnalized by Si**

Because of the closed shell structure, *C*<sup>60</sup> packing forms a Van der Waals solid. Many research have been done to functionalize the *C*<sup>60</sup> molecules without disrupt the *π*-*π* conjugation (Martin et al., 2009). Most of the methods are derived from chemical routes. Silicon atom can be also incorporated between two *C*<sup>60</sup> molecules (Pellarin et al., 2002) by physical route. Bridging *C*<sup>60</sup> is evidenced in free phase by photofragmentation experiments (Pellarin et al., 2002) and in cluster assembled films by EXAFS spectroscopy performed at the Si K edge (Tournus et al., 2002). Such experiments are compatible with a silicon atom bridging two *C*<sup>60</sup> molecules. Different geometries are tested and the best configuration for the fit corresponds to a silicon atom bridging two *C*60. Figure 11 displays the configuration where two nearest *C*<sup>60</sup> face the silicon atom with a pentagonal face. In this case, we have ten neighbors located at 2.52Å as compared to four neighbors located at 1.88Å in SiC carbide. The geometry around silicon suggests an unusual bonding close to intercalated graphite rather than a *sp*<sup>3</sup> basic set.

18 Will-be-set-by-IN-TECH

Fig. 10. Photoionization mass spectra of initial stoichiometric SiC clusters for increasing laser fluences. The time of flight mass spectrometer can be equipped with a reflectron device. Experimental details are given in the reference (Pellarin et al., 1999). The horizontal scale is given in equivalent number of carbon atoms. (a) High resolution one-photon ionization mass spectrum obtained in the reflectron configuration. (b) to (e) Multiphoton ionization mass spectra obtained at lower resolution without the reflectron configuration to avoid blurring from possible unimolecular evaporation in the time of flight mass spectrometer. The right

heterofullerene series with one and two silicon atoms are indicated. Insets (1) and (2) give a zoomed portion of spectra 3(a) and 3(b). The 4 a.m.u. separation between *SinCm* mass clumps is shown in (1) and the composition of heterofullerenes (8 a.m.u. apart) is indicated in (2). The mass resolution in (2) is too low to resolve individual mass peaks as in (1) (after

Because of the closed shell structure, *C*<sup>60</sup> packing forms a Van der Waals solid. Many research have been done to functionalize the *C*<sup>60</sup> molecules without disrupt the *π*-*π* conjugation (Martin et al., 2009). Most of the methods are derived from chemical routes. Silicon atom can be also incorporated between two *C*<sup>60</sup> molecules (Pellarin et al., 2002) by physical route. Bridging *C*<sup>60</sup> is evidenced in free phase by photofragmentation experiments (Pellarin et al., 2002) and in cluster assembled films by EXAFS spectroscopy performed at the Si K edge (Tournus et al., 2002). Such experiments are compatible with a silicon atom bridging two *C*<sup>60</sup> molecules. Different geometries are tested and the best configuration for the fit corresponds to a silicon atom bridging two *C*60. Figure 11 displays the configuration where two nearest *C*<sup>60</sup> face the silicon atom with a pentagonal face. In this case, we have ten neighbors located at 2.52Å as compared to four neighbors located at 1.88Å in SiC carbide. The geometry around silicon suggests an unusual bonding close to intercalated graphite rather than a *sp*<sup>3</sup> basic set.

part of the spectra (b) to (e) have been magnified for a better display. In (b) the

the original figure (Pellarin et al., 1999)).

**3.1 C**<sup>60</sup> **functionnalized by Si**

Fig. 11. a:symbolic ball and stick representation of *C*60.b1,2: selected energy levels near the HOMO-LUMO *C*<sup>60</sup> region. c: symbolic ball and stick representation of *SiC*<sup>59</sup> , the geometries are deduced from DFT-LDA calculations and relaxed following the standard conjugate gradient scheme (see reference (Ray et al., 1998)). The red sphere is the silicon atom. d: selected energy levels near the *SiC*<sup>59</sup> HOMO-LUMO region. Full lines and dotted lines indicate the carbon- and silicon-related orbitals, respectively. Taking only carbon-related orbitals, the HOMO-LUMO separation is respectively 1.68 eV,1.60 eV for *C*60, *C*59*Si* and respectively. The arrow gives the HOMO LUMO separation. In this way, the HOMO-LUMO separation is 1.2 eV in *C*59*Si* . e: ball and stick representation of C60-Si-C60 (after reference (Tournus et al., 2002)).f: selected energy levels near the HOMO-LUMO C60-Si-C60 region

#### **4. Zeolites: expanded-volume phases of SiC**

There is a entanglement between empty or stuffed fullerenes and zeolite lattices. The interest on these nanocage based materials has been impelled by their potentialities in different domains from which we mention the optoelectronic engineering, integrated batteries, thermoelectric power, hard materials or superconductivity. These expanded-volume phases 12 are formed by triplicate arrangement of a combination of these elemental cages (fullerenes for example). The doped expanded-volume phases offer new advantages

*i)* A large flexibility in the nature and the strength of the coupling between the guest atom and the host cage following the valence and the size of the guest atom.

*ii)* a large flexibility in doping (n or p) as long no significant stress is observed for a very large concentration (up to 10%). Two kinds of open structures are under consideration. The first is the Kelvin's lattice (named bitruncated cubic honeycomb or "sodalite" in zeolite language formed by a regular stacking of truncated octahedra which are Archimedean solids with 14

and the type of atom inside the cage. This is well illustrated in clathrate Si-46, *Na*8@*Si* − 46 and *Ba*8@*Si* − 46 (see figure 13) (the notation *Ba*8@*Si* − 46 indicates eight barium atoms for name space group a x y z Wyckoff X-34 *Fd*3¯*m* origin at center 3¯*m* a 1/8 1/8 1/8 *8a*

SiC Cage Like Based Materials 43

X-46 *Pm*3¯*m* origin at 43¯*m* a 1/4 0 1/2 *6c*

sodalite *Pm*3*n* b 1/4 0 1/2 *6c*

Table 4. The space group, unit cell lattice parameters (a and c) in Å, carbon and silicon fractional coordinates (x, y, z), multiplicities and Wyckoff positions of the sites for selected

Fig. 13. Band structures and density of states for (a) *Si-46* , (b) *Na*8@*Si* − 46 , and (c) *Ba*8@*Si* − 46. The ball and stick representation displays the *X*8@*Si* − 46 lattice (X=Na,Ba). Density of states are calculated using 0.1 eV Gaussian broadening of the band structure. Energy is measured from the top of the valence band or the Fermi level, which is denoted by horizontal broken lines. The blue filled region displays the occupied states in the conduction band. Note the strong hybridization of the Barium states responsible of the high density of states at *EF* in *Ba*8@*Si* − 46. This sample is superconductor with a *Tc* = 8*K*. (after the original

clathrates I and II and sodalite.

figure from (Moriguchi et al., 2000a)).

0.782 0.782 0.782 *32e* 0.817 0.817 0.629 *96g*

0.1847 0.1847 0.1847 *16i* 0 0.3088 0.1173 *24k*

1/4 1/2 0 *6d*

faces (8 regular hexagons and 6 squares), 36 edges, and 24 vertices leading to the net formula (*AB*)<sup>12</sup> (A=C,Si, B=C,Si) the second the clathrate formed by a stacking of fullerenes.

From a topological point of view, the clathrate is the best candidate to the complex mathematical problem of minimal partitioning of space into equal volumes is given by the Weare-Phelan conjecture. However, SiC is not stable in clathrate structure because of the odd parity in five fold rings.

Fig. 12. sodalite structure compared to clathrate II. Both lattices are expanded volume phases but sodalite presents even membered rings allowing a chemical ordering. The "disclination lines" (for the definition see (Melinon and San Miguel, 2010)) display the lattice formed by endohedral atoms in the case of doped structures.

#### **4.1 Clathrates: a survey**

Clathrates are 3D periodic networks of dodecahedral fullerenes with either X24 or X28 polyhedral cage-like nanoclusters respectively. In type-I clusters, only X20 and X24 can be found, while the so-called type-II phases contain X20 and X28. The silicon clusters are sharing faces, giving rise to full *sp*<sup>3</sup> -based networks of slightly distorted tetrahedra.

#### **4.2 Endohedral doping**

Elemental electronic devices need n and p doping. n-type doping of diamond is one of the most important issues for electronic application of diamond and remains a great challenge. This is due to the fact that the solubility of donor impurities in the diamond lattice is predicted to be low. Highly conductive silicon obtained by heavy doping is limited by the maximum solubility of the dopants provided it can be kept in solid solution. Beyond this limit precipitates or vacancy-containing centers are reported. Endohedral doping is one of the solution as long as the Fermi level can be tailored by varying both the concentration

20 Will-be-set-by-IN-TECH

faces (8 regular hexagons and 6 squares), 36 edges, and 24 vertices leading to the net formula

From a topological point of view, the clathrate is the best candidate to the complex mathematical problem of minimal partitioning of space into equal volumes is given by the Weare-Phelan conjecture. However, SiC is not stable in clathrate structure because of the odd

(*AB*)<sup>12</sup> (A=C,Si, B=C,Si) the second the clathrate formed by a stacking of fullerenes.

Fig. 12. sodalite structure compared to clathrate II. Both lattices are expanded volume phases but sodalite presents even membered rings allowing a chemical ordering. The "disclination lines" (for the definition see (Melinon and San Miguel, 2010)) display the lattice

Clathrates are 3D periodic networks of dodecahedral fullerenes with either X24 or X28 polyhedral cage-like nanoclusters respectively. In type-I clusters, only X20 and X24 can be found, while the so-called type-II phases contain X20 and X28. The silicon clusters are sharing

Elemental electronic devices need n and p doping. n-type doping of diamond is one of the most important issues for electronic application of diamond and remains a great challenge. This is due to the fact that the solubility of donor impurities in the diamond lattice is predicted to be low. Highly conductive silicon obtained by heavy doping is limited by the maximum solubility of the dopants provided it can be kept in solid solution. Beyond this limit precipitates or vacancy-containing centers are reported. Endohedral doping is one of the solution as long as the Fermi level can be tailored by varying both the concentration

faces, giving rise to full *sp*<sup>3</sup> -based networks of slightly distorted tetrahedra.

formed by endohedral atoms in the case of doped structures.

parity in five fold rings.

**4.1 Clathrates: a survey**

**4.2 Endohedral doping**

and the type of atom inside the cage. This is well illustrated in clathrate Si-46, *Na*8@*Si* − 46 and *Ba*8@*Si* − 46 (see figure 13) (the notation *Ba*8@*Si* − 46 indicates eight barium atoms for


Table 4. The space group, unit cell lattice parameters (a and c) in Å, carbon and silicon fractional coordinates (x, y, z), multiplicities and Wyckoff positions of the sites for selected clathrates I and II and sodalite.

Fig. 13. Band structures and density of states for (a) *Si-46* , (b) *Na*8@*Si* − 46 , and (c) *Ba*8@*Si* − 46. The ball and stick representation displays the *X*8@*Si* − 46 lattice (X=Na,Ba). Density of states are calculated using 0.1 eV Gaussian broadening of the band structure. Energy is measured from the top of the valence band or the Fermi level, which is denoted by horizontal broken lines. The blue filled region displays the occupied states in the conduction band. Note the strong hybridization of the Barium states responsible of the high density of states at *EF* in *Ba*8@*Si* − 46. This sample is superconductor with a *Tc* = 8*K*. (after the original figure from (Moriguchi et al., 2000a)).

**4.3 Carbon clathrate**

**4.4 Silicon clathrate**

**4.5 Silicon carbon: topology**

compounds are expected.

**4.6 Sodalite and other simple phases**

structures could be synthesized by chemists.

width.

The carbon clathrate synthesis is a major challenge since no precursor exists except intercalated graphite and doped fullerites. The competition between *sp* <sup>−</sup> *sp*<sup>2</sup> and *sp*<sup>3</sup> phases avoids the natural formation of carbon clathrate at high pressure and/or temperature.

SiC Cage Like Based Materials 45

In the absence of angle-resolved photoemission data, the band structure of clathrates has been discussed on the basis of tight-binding (Adams et al., 1994) and *ab-initio* density functional (Hohenberg and Kohn, 1964; Kohn, 1999) (DFT) calculations (Melinon et al., 1998 ; Moriguchi et al., 2000; Saito and Oshiyama, 1995; Adams et al., 1994). In particular, DFT studies within the local density approximation (Kohn and Sham, 1965) (LDA) predict (Moriguchi et al., 2000a; Adams et al., 1994) that the Si-34 phase displays a "nearly-direct" band gap which is ∼ 0.7 eV larger than the one of bulk Si-2 diamond. Such a large band gap has been attributed to the presence of pentagons which frustrates the formation of completely bonding states between Si-*3p* orbitals at the top of the valence bands, thus reducing the *p*-band

As mentioned above, chemical ordering is the driving force and expanded volume phases as candidates need odd parity in rings. No clathrate lattice excepted may be non stoichiometric

The Atlas of Zeolite Framework Types (Ch. Baerlocher, L.B. McCusker and D.H. Olson, Elsevier, Amsterdam, 2007) contains 176 topological distinct tetrahedral *TO*<sup>4</sup> frameworks, where T may be Si. Some examples are illustrated in figure 15. The crystallographic data are given in table 5. From a theoretical point of view, the *SiO*<sup>4</sup> unit cell can be replaced by *SiC*<sup>4</sup> or *CSi*4. The most compact is the sodalite mentioned above. Within DFT-LDA calculations, the difference in energy between the sodalite and the cubic 3C-SiC is 0.6 eV per SiC units (16.59 eV per SiC in 3C-SiC within the DFT-LDA framework (Hapiuk et al., 2011)). Among the huge family of structures, ATV is more stable with a net difference of 0.52 eV per SiC units (see table 6). This energy is small enough to take in consideration cage-like SiC based materials and the potentiality for its synthesis. This opens a new field in doping as long the elements located at the right side in the periodic table induce a p-like doping while elements at the left side induce a n-like doping. Moreover, one can takes advantage to the wide band opening in expanded-volume phases. Inspecting the table reveals a direct gap in ATV structure within DFT-LDA level. This structure is the most stable and presents interesting features for optical devices in near UV region. Even though DFT/LDA has the well-known problem of band-gap underestimation, it is still capable of capturing qualitatively important aspects by comparison between 3C- and other structures. Open structures have a promising way as long as the

Numerous authors have attempted the synthesis without success.

46 silicon atoms corresponding to the number of Si atoms in the primitive cell, in this case all the cages *Si*<sup>20</sup> and *Si*<sup>24</sup> are occupied . Note that the decoupling between the host lattice (the clathrate) and the guest lattice (doping atoms) is the key point for thermoelectric power generation and superconductivity applications in cage-like based materials. Moreover, the cage-like based materials present an interesting feature due to the great number of the atoms inside the elemental cell. This is well illustrated in the figure showing two {111} cleavage planes in a diamond lattice. The first (labeled "diamond") displays the well known honeycomb lattice with a nice "open" structure. The second corresponds to the clathrate with a more complex structure. This partially explained why the cage-like structures contrary to diamond ( unlike hardness, which only denotes absolute resistance to scratching) the toughness is high and no vulnerable to breakage (Blase et al., 2004)(fig. 14).

Fig. 14. cleavage plane along 111 projection in diamond and clathrate structures showing the large difference in atomic density. The toughness is high and no vulnerable to breakage in clathrate despite a weaker bonding (10% lower than in diamond phase). Fore more details see reference (Blase et al., 2004).

#### **4.3 Carbon clathrate**

22 Will-be-set-by-IN-TECH

46 silicon atoms corresponding to the number of Si atoms in the primitive cell, in this case all the cages *Si*<sup>20</sup> and *Si*<sup>24</sup> are occupied . Note that the decoupling between the host lattice (the clathrate) and the guest lattice (doping atoms) is the key point for thermoelectric power generation and superconductivity applications in cage-like based materials. Moreover, the cage-like based materials present an interesting feature due to the great number of the atoms inside the elemental cell. This is well illustrated in the figure showing two {111} cleavage planes in a diamond lattice. The first (labeled "diamond") displays the well known honeycomb lattice with a nice "open" structure. The second corresponds to the clathrate with a more complex structure. This partially explained why the cage-like structures contrary to diamond ( unlike hardness, which only denotes absolute resistance to scratching) the toughness is high

Fig. 14. cleavage plane along 111 projection in diamond and clathrate structures showing the large difference in atomic density. The toughness is high and no vulnerable to breakage in clathrate despite a weaker bonding (10% lower than in diamond phase). Fore more details

and no vulnerable to breakage (Blase et al., 2004)(fig. 14).

see reference (Blase et al., 2004).

The carbon clathrate synthesis is a major challenge since no precursor exists except intercalated graphite and doped fullerites. The competition between *sp* <sup>−</sup> *sp*<sup>2</sup> and *sp*<sup>3</sup> phases avoids the natural formation of carbon clathrate at high pressure and/or temperature. Numerous authors have attempted the synthesis without success.

#### **4.4 Silicon clathrate**

In the absence of angle-resolved photoemission data, the band structure of clathrates has been discussed on the basis of tight-binding (Adams et al., 1994) and *ab-initio* density functional (Hohenberg and Kohn, 1964; Kohn, 1999) (DFT) calculations (Melinon et al., 1998 ; Moriguchi et al., 2000; Saito and Oshiyama, 1995; Adams et al., 1994). In particular, DFT studies within the local density approximation (Kohn and Sham, 1965) (LDA) predict (Moriguchi et al., 2000a; Adams et al., 1994) that the Si-34 phase displays a "nearly-direct" band gap which is ∼ 0.7 eV larger than the one of bulk Si-2 diamond. Such a large band gap has been attributed to the presence of pentagons which frustrates the formation of completely bonding states between Si-*3p* orbitals at the top of the valence bands, thus reducing the *p*-band width.

#### **4.5 Silicon carbon: topology**

As mentioned above, chemical ordering is the driving force and expanded volume phases as candidates need odd parity in rings. No clathrate lattice excepted may be non stoichiometric compounds are expected.

#### **4.6 Sodalite and other simple phases**

The Atlas of Zeolite Framework Types (Ch. Baerlocher, L.B. McCusker and D.H. Olson, Elsevier, Amsterdam, 2007) contains 176 topological distinct tetrahedral *TO*<sup>4</sup> frameworks, where T may be Si. Some examples are illustrated in figure 15. The crystallographic data are given in table 5. From a theoretical point of view, the *SiO*<sup>4</sup> unit cell can be replaced by *SiC*<sup>4</sup> or *CSi*4. The most compact is the sodalite mentioned above. Within DFT-LDA calculations, the difference in energy between the sodalite and the cubic 3C-SiC is 0.6 eV per SiC units (16.59 eV per SiC in 3C-SiC within the DFT-LDA framework (Hapiuk et al., 2011)). Among the huge family of structures, ATV is more stable with a net difference of 0.52 eV per SiC units (see table 6). This energy is small enough to take in consideration cage-like SiC based materials and the potentiality for its synthesis. This opens a new field in doping as long the elements located at the right side in the periodic table induce a p-like doping while elements at the left side induce a n-like doping. Moreover, one can takes advantage to the wide band opening in expanded-volume phases. Inspecting the table reveals a direct gap in ATV structure within DFT-LDA level. This structure is the most stable and presents interesting features for optical devices in near UV region. Even though DFT/LDA has the well-known problem of band-gap underestimation, it is still capable of capturing qualitatively important aspects by comparison between 3C- and other structures. Open structures have a promising way as long as the structures could be synthesized by chemists.

name energy difference per SiC units bandgap type d*SiC* 3C-SiC 0 1.376 indirect 1.88 ATV 0.524 1.949 direct Γ − Γ (1.842-1.923) sodalite 0.598 1.718 indirect 1.881 VFI 1.065 1.063 indirect (1.889-1.904) LTA 1.126 1.586 indirect (1.883-1.887) ATO 1.210 1.035 indirect (1.908-2.104)

SiC Cage Like Based Materials 47

Table 6. energy difference to the ground state per SiC in eV, LDA bandgap, transition and neighboring distance at the DFT-LDA level. Calculations were done within the density functional theory DFT in the local density approximation . The Perdew-Zunger

parametrization of the Ceperley-Alder homogeneous electron gas exchange-correlation potential was used. The valence electrons were treated explicitly while the influence of the core electrons and atomic nuclei was replaced by norm-conserving Trouiller-Martins pseudo

potentials were generated including scalar relativistic effects and a nonlinear core correction was used to mimic some of the effects of the d shell on the valence electrons. We employed the SIESTA program package which is a self-consistent pseudo potential code based on numerical pseudo atomic orbitals as the basis set for decomposition of the one-electron wave

Fig. 15. selected zeolites forms. (a) sodalite with single 6-rings in ABC sequence with single 4-rings or 6-2 rings. (b) ATO with single 4- or 6-rings. (c) AFI with single 4- or 6-rings. (d) VFI with single 6-rings. (e) ATV with single 4-rings. (f) LTA with double 4-rings, (single 4-rings), 8-rings or 6-2 rings. (g) melanophlogite with 5-rings (clathrate I see above). (h) MTN with 5-rings (clathrate II see text). The two clathrate forms are unlikely because the breakdown of the chemical ordering. Fore more details see the "Commission of the International Zeolite

Association (IZA-SC)" http://izasc-mirror.la.asu.edu/fmi/xsl/IZA-SC/ft.xsl

potentials factorized in Kleinman-Bylander form. For the doping elements, pseudo

functions (Hapiuk et al., 2011).


Table 5. The space group, unit cell lattice parameters (a and c) in Å, carbon and silicon fractional coordinates (x, y, z), multiplicities and Wyckoff positions of the sites for selected zeolites. 3C-SiC and sodalite are displayed in tables 1 and 4 respectively. The lattice parameters are deduced from DFT-LDA calculations within SIESTA code and standard procedure (Hapiuk et al., 2011). The coordinates are in reference (Demkov et al., 1997).

24 Will-be-set-by-IN-TECH

name space group a x y z Wyckoff

Si 0.849 .25 0.692 *4c* Si 0.651 0.099 0.192 *8d* C 0.849 0.25 0.308 *4c* C 0.651 0.0.099 0.808 *8d*

Si 0.455 0.122 0.192 *12d* C 0.545 0.878 0.808 *12d*

Si 0 0.0924 0.1848 *96i* C 0 0.1848 0.0924 *96i*

Si 0.1786 0.512 0.563 *12d* C 0.5773 0 0.937 *6c* C 0.8214 0.488 0.437 *12d*

Si 0.1992 0.251 0.250 *18f* C 0.0518 0.251 0.250 *18f*

b=9.236 c=5.007

b=a c=5.003

c=5.0307

c=3.0284

Table 5. The space group, unit cell lattice parameters (a and c) in Å, carbon and silicon fractional coordinates (x, y, z), multiplicities and Wyckoff positions of the sites for selected zeolites. 3C-SiC and sodalite are displayed in tables 1 and 4 respectively. The lattice parameters are deduced from DFT-LDA calculations within SIESTA code and standard procedure (Hapiuk et al., 2011). The coordinates are in reference (Demkov et al., 1997).

Si 0.4227 0 0.063 *6c*

ATV *ABm2*[number 39] a=5.788

AFI *P6cc* [number 184] a=8.4669

LTA *Fm*3¯*c* [number 226] a=b=c=10.2129

VFI *P*63*cm* [number 185] a=b=11.6075

ATO *R*3 [number 148] a=b=12.942


Table 6. energy difference to the ground state per SiC in eV, LDA bandgap, transition and neighboring distance at the DFT-LDA level. Calculations were done within the density functional theory DFT in the local density approximation . The Perdew-Zunger parametrization of the Ceperley-Alder homogeneous electron gas exchange-correlation potential was used. The valence electrons were treated explicitly while the influence of the core electrons and atomic nuclei was replaced by norm-conserving Trouiller-Martins pseudo potentials factorized in Kleinman-Bylander form. For the doping elements, pseudo potentials were generated including scalar relativistic effects and a nonlinear core correction was used to mimic some of the effects of the d shell on the valence electrons. We employed the SIESTA program package which is a self-consistent pseudo potential code based on numerical pseudo atomic orbitals as the basis set for decomposition of the one-electron wave functions (Hapiuk et al., 2011).

Fig. 15. selected zeolites forms. (a) sodalite with single 6-rings in ABC sequence with single 4-rings or 6-2 rings. (b) ATO with single 4- or 6-rings. (c) AFI with single 4- or 6-rings. (d) VFI with single 6-rings. (e) ATV with single 4-rings. (f) LTA with double 4-rings, (single 4-rings), 8-rings or 6-2 rings. (g) melanophlogite with 5-rings (clathrate I see above). (h) MTN with 5-rings (clathrate II see text). The two clathrate forms are unlikely because the breakdown of the chemical ordering. Fore more details see the "Commission of the International Zeolite Association (IZA-SC)" http://izasc-mirror.la.asu.edu/fmi/xsl/IZA-SC/ft.xsl

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#### **5. Conclusion: future research**

Most of the SiC forms are nearly *sp*<sup>3</sup> hybridized. Inspecting the new architectures based from cage-like cells do not reveal anyway another hybridization. The silicon make one's mark, other hybridizations are definitively discarded. However, the topology of the open-structures like zeolites is still interesting since its offer a set of unique features: low density, tunable bandgap (direct or indirect), endohedral doping hydrogen storage . . . This is enough to promote a renewable interest and some efforts for their synthesis. In addition, all the properties attributed to the open structures in cage-like based materials are universal since the driving force is the topology, namely the symmetry of the cage and the symmetry of the whole lattice. Same features are observed in other binary compounds such as GaAs or ZnO. In addition, the inspection of the bulk and molecular phases underlines the prominent role of the pentagons where the chemical ordering is broken. This is the striking difference between C,Si and SiC.

#### **6. References**


26 Will-be-set-by-IN-TECH

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Adams,G.B. O'Keeffe,M. Demkov,A.A. Sankey,O.F. and Huang,Y. (1994) *Wide-band-gap Si in open fourfold-coordinated clathrate structures*,*Phys. Rev. B* 49,8048–8053. Melinon, P., Keghelian, P., Blase, X., Le Brusc, J., and Perez, A. (1998). *Electronic sig- nature of*

Connetable, D., Timoshevskii, V., Masenelli, B., Beille, J., Marcus, J., Barbara, B., Saitta, A.,

(2000) *Low-density framework form of crystalline silicon with a wide optical band gap Phys.*

*the pentagonal rings in silicon clathrate phases: Comparison with cluster- assembled films*

Rignanese, G., Melinon, P., Yamanaka, S. and Blase, X. (2003) *Superconduc- tivity in Doped sp3 Semiconductors: The Case of the Clathrates Phys. Rev. Lett.* 91,247001 1–4.

Baugham,R.H. (2006) *Dangerously Seeking Linear Carbon Science* 312,1009 –1110.

*isolated sp carbon chains* , *Chemical Physics Letters*417, p78–82. Geim,AK. and Novoselov,K.S. (2007) *The rise of graphene*,*Nature Materials* 6,183–191.

*point*,*Phys. Rev. B* 74,075404 1–11.

Stanford Publishing Pte Ltd (2011)

Chung,D.D.L. (2002) *Review Graphite*,*J. of Mat. Sci.* 37,1475 –1489.

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A. Li Russo, V. Bogana, M. and Bottani, C.E. (2006). *Raman and SERS investigation of*

**5. Conclusion: future research**

C,Si and SiC.

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**0**

**3**

*Japan*

**Metastable Solvent Epitaxy of SiC,**

Shigeto R. Nishitani1, Kensuke Togase1, Yosuke Yamamoto1,

Professor W. Shockley, a Nobel prize winner and the 'father' of the transistor, predicted in the 1950s that SiC would soon replace Si in devices because of its superior material properties(Cited from Choyke, 1960). His prediction, however, has not yet come true because of the high cost of manufacturing SiC wafers. The current price of 2-inch SiC wafers is close to that of diamond jewellery rather than to that of Si wafers. Nevertheless, owing to its promising physical properties for high-power devices and for achieving significant reductions in CO2 emission, many researchers and companies are purchasing many SiC wafers(Madar, 2004; Nakamura et al., 2004). Very recently, the present authors reported a novel process for fabricating epitaxial SiC(Nishitani & Kaneko, 2008). This process has the potential to cost less and to provide SiC wafers with high crystalline quality. Here we present a new synthesis process for manufacturing SiC. In this process, the driving force for crystal growth is elucidated by considering a similarity—the coexistence of the stable and metastable phases—with the diamond synthesis process reported by Bonenkirk et al. (1959) of General

In this review, the authors introduce the experimental procedures and the results of this novel process of making stable phase of SiC at first. Then they will show the speculated mechanism from the thermodynamical point of view, especially the concept of the double phase diagram and the concentration profile. In the end, understanding the phase stability of many polytypes of SiC, the reported phase diagrams, the difficulty of the equilibrium state achievement, and

While SiC was first synthesized by Acheson at the end of the 19th century(Acheson, 1896), single-crystal wafers of SiC became commercially available only in the early 1990s. Boules of other important semiconductors such as Si, GaAs and InP are manufactured through a liquid process, while those of SiC are produced through a vapor process. Owing to the

the results of the first principles calculations will be discussed.

**1. Introduction**

Electric.

**2. Experimental results 2.1 Conventional methods** **the Other Diamond Synthetics**

<sup>1</sup>*Kwansei Gakuin University, Department of Informatics,* <sup>2</sup>*(Late) Kyoto University, Department of Energy Science,* <sup>3</sup>*Kwansei Gakuin University, Department of Physics,*

Hiroyasu Fujiwara2, and Tadaaki Kaneko3


### **Metastable Solvent Epitaxy of SiC, the Other Diamond Synthetics**

Shigeto R. Nishitani1, Kensuke Togase1, Yosuke Yamamoto1, Hiroyasu Fujiwara2, and Tadaaki Kaneko3

> *Kwansei Gakuin University, Department of Informatics, (Late) Kyoto University, Department of Energy Science, Kwansei Gakuin University, Department of Physics, Japan*

#### **1. Introduction**

30 Will-be-set-by-IN-TECH

52 Silicon Carbide – Materials, Processing and Applications in Electronic Devices

M. Pellarin, E. Cottancin, J. Lerme, J.L. Vialle, M. Broyer, F. Tournus, B. Masenelli, P. Melinon

Melinon, P., Keghelian, P., Perez, A., Ray, C., Lerme, J., Pellarin, M., Broyer, M., Boudeulle, M.,

F. Tournus, B. Masenelli, P. Melinon, X. Blase, A. Perez, M. Pellarin, M. Broyer, A.M. Flanck, P.

Blase,X. Gillet,P. San Miguel,A. and Melinon,P. (2004). *Exceptional Ideal Strength of Carbon*

Hohenberg,P. and Kohn,W. (1999). *Electronic structure of matter Rev. Mod. Phys.* 71,1253–1266. Saito,S. and Oshiyama,A. (1995). *Electronic structure of Si46 and Na2Ba6Si46 Phys. Rev. B*

Moriguchi, K., Yonemura, M., Shintani, A. and Yamanaka, S. (2000a). *Electronic structures of*

Kohn, W. and Sham, L. (1965). *Self-Consistent Equations Including Exchange and Correlation*

Demkov,A.A. Sankey,O.F. Gryko,J. and McMillan,P.F. (1997) *Theoretical predictions of*

P.Melinon and A. San Miguel (2010). *From silicon to carbon clathrates : nanocage materials Chapter*

Adams, G., O'Keekke, M., Demkov, A., Sankey, O. and Huang, Y. (1994). *Wide-band gap Si in open fourfold-coordinated clatrate structures Phys. Rev. B* 49,8048–8053. Melinon, P. and Masenelli,B. (2009) . *Cage-like based materials with carbon and silicon ECS*

*in the vol. "Clusters and Fullerenes" The HANDBOOK OF NANOPHYSICS* Taylor &

Hohenberg,P. and Kohn,W. *Inhomogeneous Electron Gas Phys. Rev. B* 136,864–871.

*study J. Chem. Phys.* 117,3088–3097.

*Phys. Rev. B* 65,165417 1–6.

51,2628–2631.

*transaction* 13.

to be published

*depositions Phys. Rev. B* 58,16481–16490.

*Clathrates Phys. Rev. Lett.* 65,215505 1–4.

*Na8Si46 and Ba8Si46 Phys. Rev. B* 61,9859–9862.

*expanded-volume phases of GaAs Phys. Rev. B* 55,6904–6913.

Francis. (K.Sattler guest editor). ISBN: 9781420075540.

*Effects Phys. Rev.* 140,A1133–A1138.

(2002). *Coating and polymerization of C60 with carbon : A gas phase photodissociation*

Champagnon, B. and Rousset, J. *Nanostructured SiC films obtained by neutral-cluster*

Lagarde (2002). *Bridging C60 by silicon : towards non-van der Waals C60-based materials*

Professor W. Shockley, a Nobel prize winner and the 'father' of the transistor, predicted in the 1950s that SiC would soon replace Si in devices because of its superior material properties(Cited from Choyke, 1960). His prediction, however, has not yet come true because of the high cost of manufacturing SiC wafers. The current price of 2-inch SiC wafers is close to that of diamond jewellery rather than to that of Si wafers. Nevertheless, owing to its promising physical properties for high-power devices and for achieving significant reductions in CO2 emission, many researchers and companies are purchasing many SiC wafers(Madar, 2004; Nakamura et al., 2004). Very recently, the present authors reported a novel process for fabricating epitaxial SiC(Nishitani & Kaneko, 2008). This process has the potential to cost less and to provide SiC wafers with high crystalline quality. Here we present a new synthesis process for manufacturing SiC. In this process, the driving force for crystal growth is elucidated by considering a similarity—the coexistence of the stable and metastable phases—with the diamond synthesis process reported by Bonenkirk et al. (1959) of General Electric.

In this review, the authors introduce the experimental procedures and the results of this novel process of making stable phase of SiC at first. Then they will show the speculated mechanism from the thermodynamical point of view, especially the concept of the double phase diagram and the concentration profile. In the end, understanding the phase stability of many polytypes of SiC, the reported phase diagrams, the difficulty of the equilibrium state achievement, and the results of the first principles calculations will be discussed.

#### **2. Experimental results**

#### **2.1 Conventional methods**

While SiC was first synthesized by Acheson at the end of the 19th century(Acheson, 1896), single-crystal wafers of SiC became commercially available only in the early 1990s. Boules of other important semiconductors such as Si, GaAs and InP are manufactured through a liquid process, while those of SiC are produced through a vapor process. Owing to the

the Other Diamond Synthetics 3

Metastable Solvent Epitaxy of SiC, the Other Diamond Synthetics 55

~2100

~1800

temperature [˚C]

distance

10~20 mm

distance

30~100 μm

~2400 temperature [˚C]

TaC crucible

graphite crucible

seed

Ar

epitaxially grown 4H-SiC

single-crystalline 4H-SiC

media, as illustrated in the panels on the right-hand side.

temperature inside the crucible is held constant.

of the solvent movement.

poly-crystalline 3C-SiC

**a**

**b**

SiC powder

liquid Si

Fig. 2. Schematic illustrations of **a** the conventional sublimation method and **b** the new solvent method for the preparation of SiC. Their setups are similar and comprise the sources (SiC powder and polycrystalline 3C-SiC), transfer media (Ar and liquid Si), produced crystals (the seed and 4H-SiC fine particles) and crucibles (graphite and TaC). The

characteristic differences are in the thicknesses and the temperature profiles of the transfer

between them. The solvent is a very thin layer with a thickness of 30∼100 *μ*m. The

After holding at the growth temperature of 1800◦C for 10 min, the newly grown 4H-SiC layer is observed on the original 4H-SiC single-crystalline plate as shown in Fig. 3(Nishitani & Kaneko, 2008). The scanning electron microscopy image shows the transverse section of a sample with the sandwiched structure of SiC and Si layers. Because the substrate of 4H-SiC is n-doped, the newly grown 4H-SiC layer is easily distinguished from the original substrate. The feed of polycrystalline 3C-SiC was dense before the operation. Its boundaries dissolve preferentially, and it becomes porous during the operation. The wave dispersion X-ray (WDX) profile of carbon in Fig. 3 shows a concentration of 50% in the SiC layers and almost zero in the Si solvent. Upon reversing the configuration of 3C- and 4H-SiC plates, 4H-SiC grew epitaxially again, which indicates that no unintentional temperature gradient occurs in the crucible; thus, the temperature gradient cannot be the driving force

In the case of replacing the single-crystalline 4H-SiC to poly-crystalline 3C-SiC in the configuration of Fig. 2b, many fine particles with diameters of 30∼300 *μ*m are observed to be produced on the both sides of polycrystalline 3C-SiC source plates, as shown in Fig. 4a. Multifaceted crystals grow like mushrooms and no grain boundaries are observed in them.

peritectic reaction of SiC at above 2500 ◦C as shown in the phase diagram of Fig. 1, growth from a stoichiometric melt is not possible at normal pressure. The incongruent compounds are usually produced by the solution method. The low carbon solubility in liquid Si leads to insufficient mass transport of C, and this in turn results in the crystal growth in the Si-C solution method being quite slow(Hofmann & Müller, 1999). The solution method provides crystals with better crystallinity and a smaller defect density as compared to vapor methods. Thus, the solution method is preferred for preparing SiC(Hofmann & Müller, 1999). Many attempts have been made to increase the carbon solubility in liquid Si, especially by the addition of metallic elements or the application of high pressures. Nevertheless, the productivity of such methods does not exceed that of the vapor methods(Casady & Johnson, 1996; Chaussende et al., 2007; Hofmann & Müller, 1999; Wesch, 1996).

Fig. 1. Phase diagram of Si-C binary system(Olesinski & Abbaschian, 1996).

Among the vapor processes, the sublimation process, which is schematically illustrated in Fig. 2a and which was first proposed Tairov & Tsvetkov (1978), is the standard process used for the commercial manufacture of SiC. In this process, the source powder and a seed crystal are placed in a graphite crucible. SiC powder is then heated to typically 2400 ◦C and allowed to sublimate. Si and C vapors are transferred in an inert gas, and they recrystallize on a slightly cooler single-crystal seed. The temperature dependency of the crucible is schematically shown in the left-hand panel of Fig. 2a. The main drawback of this method is that the obtained boules contain many types of grown-in defects, such as micropipes, step bunching, dislocations and stacking faults. For the reduction of these defects, the operation parameters such as the growth temperature, gas flow rate and total pressure should be controlled quite steadily for a long operation time. This long and sensitive operation performed at a high temperature and involving a temperature gradient makes SiC wafers expensive. Researches on alternative processes such as chemical vapor deposition and the vapor-liquid-solid process are continuing with the objective of improving the growth rate and crystal quality(Chaussende et al., 2007).

#### **2.2 Metastable solvent epitaxial method**

Our proposed method employs the solution growth technique. A schematic drawing of the apparatus is presented in Fig. 2b. In this method, C is transferred through liquid Si instead of Ar gas, which is used in the conventional method. Poly-crystalline 3C-SiC source and sigle-crystalline 4H-SiC plate are placed in a TaC crucible and liquid Si solvent is sandwiched 2 Will-be-set-by-IN-TECH

peritectic reaction of SiC at above 2500 ◦C as shown in the phase diagram of Fig. 1, growth from a stoichiometric melt is not possible at normal pressure. The incongruent compounds are usually produced by the solution method. The low carbon solubility in liquid Si leads to insufficient mass transport of C, and this in turn results in the crystal growth in the Si-C solution method being quite slow(Hofmann & Müller, 1999). The solution method provides crystals with better crystallinity and a smaller defect density as compared to vapor methods. Thus, the solution method is preferred for preparing SiC(Hofmann & Müller, 1999). Many attempts have been made to increase the carbon solubility in liquid Si, especially by the addition of metallic elements or the application of high pressures. Nevertheless, the productivity of such methods does not exceed that of the vapor methods(Casady & Johnson,

C [at%]

Among the vapor processes, the sublimation process, which is schematically illustrated in Fig. 2a and which was first proposed Tairov & Tsvetkov (1978), is the standard process used for the commercial manufacture of SiC. In this process, the source powder and a seed crystal are placed in a graphite crucible. SiC powder is then heated to typically 2400 ◦C and allowed to sublimate. Si and C vapors are transferred in an inert gas, and they recrystallize on a slightly cooler single-crystal seed. The temperature dependency of the crucible is schematically shown in the left-hand panel of Fig. 2a. The main drawback of this method is that the obtained boules contain many types of grown-in defects, such as micropipes, step bunching, dislocations and stacking faults. For the reduction of these defects, the operation parameters such as the growth temperature, gas flow rate and total pressure should be controlled quite steadily for a long operation time. This long and sensitive operation performed at a high temperature and involving a temperature gradient makes SiC wafers expensive. Researches on alternative processes such as chemical vapor deposition and the vapor-liquid-solid process are continuing with the objective of improving the growth rate and crystal quality(Chaussende et al., 2007).

Our proposed method employs the solution growth technique. A schematic drawing of the apparatus is presented in Fig. 2b. In this method, C is transferred through liquid Si instead of Ar gas, which is used in the conventional method. Poly-crystalline 3C-SiC source and sigle-crystalline 4H-SiC plate are placed in a TaC crucible and liquid Si solvent is sandwiched

0 10 20 30 40 50 60 70 80 90 100

2545±40°C

L+C

SiC+C

(C)

SiC

1996; Chaussende et al., 2007; Hofmann & Müller, 1999; Wesch, 1996).

G

1404±5°C

Fig. 1. Phase diagram of Si-C binary system(Olesinski & Abbaschian, 1996).

L+SiC

L

~3200°C B.P.

1414°C M.P.

(Si)

3500

4000 4500

Temperature [°C]

**2.2 Metastable solvent epitaxial method**

Fig. 2. Schematic illustrations of **a** the conventional sublimation method and **b** the new solvent method for the preparation of SiC. Their setups are similar and comprise the sources (SiC powder and polycrystalline 3C-SiC), transfer media (Ar and liquid Si), produced crystals (the seed and 4H-SiC fine particles) and crucibles (graphite and TaC). The characteristic differences are in the thicknesses and the temperature profiles of the transfer media, as illustrated in the panels on the right-hand side.

between them. The solvent is a very thin layer with a thickness of 30∼100 *μ*m. The temperature inside the crucible is held constant.

After holding at the growth temperature of 1800◦C for 10 min, the newly grown 4H-SiC layer is observed on the original 4H-SiC single-crystalline plate as shown in Fig. 3(Nishitani & Kaneko, 2008). The scanning electron microscopy image shows the transverse section of a sample with the sandwiched structure of SiC and Si layers. Because the substrate of 4H-SiC is n-doped, the newly grown 4H-SiC layer is easily distinguished from the original substrate. The feed of polycrystalline 3C-SiC was dense before the operation. Its boundaries dissolve preferentially, and it becomes porous during the operation. The wave dispersion X-ray (WDX) profile of carbon in Fig. 3 shows a concentration of 50% in the SiC layers and almost zero in the Si solvent. Upon reversing the configuration of 3C- and 4H-SiC plates, 4H-SiC grew epitaxially again, which indicates that no unintentional temperature gradient occurs in the crucible; thus, the temperature gradient cannot be the driving force of the solvent movement.

In the case of replacing the single-crystalline 4H-SiC to poly-crystalline 3C-SiC in the configuration of Fig. 2b, many fine particles with diameters of 30∼300 *μ*m are observed to be produced on the both sides of polycrystalline 3C-SiC source plates, as shown in Fig. 4a. Multifaceted crystals grow like mushrooms and no grain boundaries are observed in them.

the Other Diamond Synthetics 5

Metastable Solvent Epitaxy of SiC, the Other Diamond Synthetics 57

**c**

intensity (arbitrary unit)

Fig. 4. **a** Side view and **b** top view of fine particles on the polycrystalline 3C-SiC source plate and **c** Raman spectra of the regions in **b** indicated by the circles. **a** is a scanning electron microscopy image and **b** is an optical microscopy image. The spectrum of the single-crystal

where dissolution and deposition occur simultaneously. The driving force for crystal growth is supersaturation, which can be schematically explained by considering the solubility limit

> alum powder

> > single crystal

Fig. 5. Schematic drawings of **a** alum deposition and **b** the solvent zone technique in which a temperature gradient is present; **c** the phase diagram of the potassium alum-water system. In **a** and **b**, the vertical positions of the alum powder (source), water (solvent) and single crystal

The solubility of potassium alum in water is measured as shown in Fig. 5c. The solubility limit, or liquidus of alum, separates the water solution region from the region where water and alum

water

fine particle polycrystals

Raman shift (cm-1)

760 780 800 820

water solution

temperature [˚C]

80

60

40

20

0

water + alum coexisting region

alum [g]/water [100 g]

400 80 120 160

4H-SiC wafer

**b**

4H-SiC wafer is also shown in **c** as a standard.

alum powder

> single crystal

water

high temp.

low temp.

water

of alum or the so-called phase diagram of an alum-water system.

**a b c**

high temp.

low temp.

(seed) represent their relative energies or chemical potentials.

**a**

Fig. 3. Scanning electron microscopy image and wave dispersion X-ray (WDX) profile of carbon of epitaxially grown 4H-SiC in the transverse section of a sample with the sandwiched structure of SiC and Si layers(Nishitani & Kaneko, 2008).

Figure 4c shows the Raman spectra of the fine crystalline particles and the polycrystalline 3C-SiC substrate obtained using a 488-nm excitation laser at room temperature. The spectra of the substrate show broad peaks at around 768 cm−<sup>1</sup> and 797 cm−1, which are typical of 3C-SiC with randomly distributed stacking faults(Rohmfeld et al., 1998-I). On the other hand, the fine particles show a sharp peak at 776 cm−1, which is typical of 4H-SiC. Thus, we conclude that fine single-crystal 4H-SiC particles are crystallized from polycrystalline 3C-SiC in the absence of a temperature gradient. 4H-SiC crystals grow without a temperature gradient nor a concentration difference between sources and products of SiC.

#### **3. Speculated mechanism**

#### **3.1 Solution method**

The origin of the driving force for crystal growth is the same as that in the case of diamond synthesis from a solvent of a metal-carbon binary system. Both the diamond synthesis method and the proposed method for SiC synthesis are solution growth methods; a typical example of a solution growth method is the method used for the growth of alum crystals, which is very familiar as a topic frequently dealt with in science classes, even in primary schools. Thus, a review of the growth process of alum crystals would be a good starting point for explaining as well as understanding the growth of diamond and SiC crystals. Large alum single crystals can be obtained as follows. First, alum powder is dissolved in hot water. Next, a seed tied to a long thread is inserted into the solution, and the solution is cooled and left to stand. A crystal starts growing from the seed and develops into a large single crystal.

Figure 5a shows schematic representations of the alum deposition process. The upper panel represents the dissolution of alum in water at a high temperature and the lower panel represents the deposition of alum on the seed at a low temperature. In the system shown in Fig. 5b, the source and seed are sandwiching the water solution; a temperature gradient is applied in the water solution. This is the setup in the so-called solvent zone technique,

4 Will-be-set-by-IN-TECH

Fig. 3. Scanning electron microscopy image and wave dispersion X-ray (WDX) profile of carbon of epitaxially grown 4H-SiC in the transverse section of a sample with the

Figure 4c shows the Raman spectra of the fine crystalline particles and the polycrystalline 3C-SiC substrate obtained using a 488-nm excitation laser at room temperature. The spectra of the substrate show broad peaks at around 768 cm−<sup>1</sup> and 797 cm−1, which are typical of 3C-SiC with randomly distributed stacking faults(Rohmfeld et al., 1998-I). On the other hand, the fine particles show a sharp peak at 776 cm−1, which is typical of 4H-SiC. Thus, we conclude that fine single-crystal 4H-SiC particles are crystallized from polycrystalline 3C-SiC in the absence of a temperature gradient. 4H-SiC crystals grow without a temperature gradient nor

The origin of the driving force for crystal growth is the same as that in the case of diamond synthesis from a solvent of a metal-carbon binary system. Both the diamond synthesis method and the proposed method for SiC synthesis are solution growth methods; a typical example of a solution growth method is the method used for the growth of alum crystals, which is very familiar as a topic frequently dealt with in science classes, even in primary schools. Thus, a review of the growth process of alum crystals would be a good starting point for explaining as well as understanding the growth of diamond and SiC crystals. Large alum single crystals can be obtained as follows. First, alum powder is dissolved in hot water. Next, a seed tied to a long thread is inserted into the solution, and the solution is cooled and left to stand. A crystal

Figure 5a shows schematic representations of the alum deposition process. The upper panel represents the dissolution of alum in water at a high temperature and the lower panel represents the deposition of alum on the seed at a low temperature. In the system shown in Fig. 5b, the source and seed are sandwiching the water solution; a temperature gradient is applied in the water solution. This is the setup in the so-called solvent zone technique,

sandwiched structure of SiC and Si layers(Nishitani & Kaneko, 2008).

a concentration difference between sources and products of SiC.

starts growing from the seed and develops into a large single crystal.

**3. Speculated mechanism**

**3.1 Solution method**

Fig. 4. **a** Side view and **b** top view of fine particles on the polycrystalline 3C-SiC source plate and **c** Raman spectra of the regions in **b** indicated by the circles. **a** is a scanning electron microscopy image and **b** is an optical microscopy image. The spectrum of the single-crystal 4H-SiC wafer is also shown in **c** as a standard.

where dissolution and deposition occur simultaneously. The driving force for crystal growth is supersaturation, which can be schematically explained by considering the solubility limit of alum or the so-called phase diagram of an alum-water system.

Fig. 5. Schematic drawings of **a** alum deposition and **b** the solvent zone technique in which a temperature gradient is present; **c** the phase diagram of the potassium alum-water system. In **a** and **b**, the vertical positions of the alum powder (source), water (solvent) and single crystal (seed) represent their relative energies or chemical potentials.

The solubility of potassium alum in water is measured as shown in Fig. 5c. The solubility limit, or liquidus of alum, separates the water solution region from the region where water and alum

the Other Diamond Synthetics 7

Metastable Solvent Epitaxy of SiC, the Other Diamond Synthetics 59

liquid Ni(C)

atomic fraction of carbon

0 0.1 0.2 0.996 0.998 1.0

1661 K (Ni + graphite)

Fig. 6. Schematic drawings of **a** diamond synthesis and **b** enlarged sections of the Ni-C phase diagram at 54 Kbar. In **a**, graphite, liquid Ni and diamond are the source, solvent and seed,

is driven spontaneously by the diffusion between small (S) and large (L) precipitates due to Gibbs-Thomson effect. In this section, the matrix and precipitate phases are represented as *α* and *β*, respectively. The precipitates show the same composition of *x<sup>β</sup>* but different pressures

free-energy vs. concentration diagram of Fig. 7a. The common tangents of free-energy curves between matrix solution and precipitates show different angles and touch at the different

difference of matrix appears at the interfaces of the precipitates. Fig. 7b shows the schematic diagram of the solute concentration profile of the system of *α* matrix and small(S) and large(L) *β* precipitates. The matrix concentration equilibrating with the small precipitates should be higher than that with the large precipitates. This difference drives the solute diffusion and

Ostwald ripening is the reaction in a solid solutions, which means the life time of metastable phase may be longer at lower temperatures and lower diffusivity. Does such a metastable

The typical example of the behavior of the coexistence of stable and metastable phases is observed in the Fe-C system. As mentioned before, the double phase diagram of Fe-C and Fe-Fe3C systems is well studied and established. The melting behavior of metastable Fe3C phase has investigated in detail by Okada et al. (1981). They measured the differential thermal analysis (DTA) curves for the white, gray and mixture cast irons at the eutectic temperature and composition region. Fig. 8 shows the summarized results of DTA curves as well as the schematic double phase diagram. The endothermic temperatures shift due to the kinetic reason of the measuring apparatus, but the corrected temperatures show the stable and metastable eutectic temperatures of 1426K and 1416K, respectively. The specimens of gray cast iron contains stable phases of graphite and fcc-Fe(autenite), where they all melt only

respectively. In **b**, the stable Ni-diamond and metastable Ni-graphite reactions are represented by solid and dashed lines, respectively(Strong & Hanneman, 1967).

1728 K

liquid + graphite

liquid + diamond

1667 K (Ni + diamond)

*<sup>α</sup>* of the free energy curve of the matrix solution. This concentration

graphite graphite + diamond

1740 K

*<sup>β</sup>* and *<sup>G</sup><sup>L</sup>*

*<sup>β</sup>* , as shown in

diamond

liquid Ni

concentrations *x<sup>L</sup>*

*<sup>α</sup>* and *<sup>x</sup><sup>S</sup>*

**3.4 Direct melting of metastable phases**

phase directly melt in liquid?

diamond

graphite

**a b**

temperature [K]

1800

1750

1700

1650

Ni

of small and large radii, which makes the different free energies, *G<sup>s</sup>*

thus the simultaneous growth and dissolution of precipitates.

α

α + liquid

coexist. As the temperature increases, the solubility limit shifts to higher alum contents. At 80 ◦C, 321 g of potassium alum dissolves in 100 g of water. Such a solution can be cooled to a temperature where the solubility limit is considerably low, and it is called a supersaturated solution. At lower temperatures around the seed crystal, the small solubility limit facilitates the deposition of alum on the seed crystal. As marked in Fig. 5c, the temperature gradient between the source and the seed alum results in different solubility limits around them; this difference is the driving force for the dissolution and deposition of alum.

#### **3.2 Double phase diagram**

Although diamond synthesis in a metal-carbon system at high pressures is slightly complex, it is based on the same mechanism as that of alum deposition. The initial materials used for diamond synthesis in the original General Electric process were graphite and group VIII transition metals(Bonenkirk et al., 1959). At a high pressure and a high temperature, metal melts and comes into contact with graphite. The liquid metal was initially thought to function as a catalyst by the workers at General Electric, but was later clarified to act as a transport medium by Giardini and Tydings(Giardini & Tydings, 1962). Similar to Fig. 5b, a schematic drawing of a diamond synthesis system is shown in Fig. 6a. The liquid metal that is commonly used in diamond synthesis is Ni; the Ni-C phase diagram at 54 Kbar is shown in Fig. 6b(Strong & Hanneman, 1967). Although the graphite phase is the only stable phase at normal pressure, at 54 Kbar, the diamond phase is stable below 1740 K. Liquid Ni coexists with the diamond phase between 1667 K and 1728 K. Thus, the solution growth of diamond from liquid Ni is possible in this temperature range. The true trick in diamond synthesis is not the 'stability' of the diamond phase, but the 'metastability' of the graphite phase, as indicated by the dashed lines in Fig. 6b. The synthetic capsule in high-pressure anvils is small and it is very difficult to manage sensitive temperature gradients. Thus, each process of crystal growth, i.e. the melting of metastable graphite in liquid Ni, carbon transfer within the solvent and crystallization of stable diamond on the seed, occurs in a very small temperature range. The driving forces for these reactions cannot be obtained from the temperature gradient, but can be obtained from the difference in the stability between graphite and diamond. For example in Fig. 6b, at 1700 K, the solubility of metastable graphite in liquid Ni represented by the dashed line is higher than that of stable diamond denoted by the solid line. The driving force for the crystal growth of the alum shown in Fig. 5 is generated when there is a spatial or temporal temperature difference, but that in diamond synthesis can be produced even at a constant temperature.

Figure 6b shows the so-called double phase diagram that is well known in metallurgy, e.g. the Fe-C system(Hansen & Anderko, 1958), and that is commonly observed for the systems containing metastable phases(Ishihara et al., 1984-5). The mechanism of crystal growth in the presence of a solubility difference between the stable and metastable phases, which is discussed in the present study, can be observed in the work of Van Lent (1961) on the transformation of mercury/white tin amalgams to gray tin, and it was first elucidated by Hurle et al. (1967) using the so-called thin alloy zone (TAZ) crystallization.

#### **3.3 Ostwald ripening and concentration profile**

The solution growth is easily understood by the phase diagrams, but the simultaneous growth and dissolution processes of polytypes are hardly recognized. Such a puzzling process can be observed in the Ostwald ripening, which is shown schematically in Figs. 7. Ostwald ripening, also called coarsening, which occurs at the late stage of the precipitation,

6 Will-be-set-by-IN-TECH

coexist. As the temperature increases, the solubility limit shifts to higher alum contents. At 80 ◦C, 321 g of potassium alum dissolves in 100 g of water. Such a solution can be cooled to a temperature where the solubility limit is considerably low, and it is called a supersaturated solution. At lower temperatures around the seed crystal, the small solubility limit facilitates the deposition of alum on the seed crystal. As marked in Fig. 5c, the temperature gradient between the source and the seed alum results in different solubility limits around them; this

Although diamond synthesis in a metal-carbon system at high pressures is slightly complex, it is based on the same mechanism as that of alum deposition. The initial materials used for diamond synthesis in the original General Electric process were graphite and group VIII transition metals(Bonenkirk et al., 1959). At a high pressure and a high temperature, metal melts and comes into contact with graphite. The liquid metal was initially thought to function as a catalyst by the workers at General Electric, but was later clarified to act as a transport medium by Giardini and Tydings(Giardini & Tydings, 1962). Similar to Fig. 5b, a schematic drawing of a diamond synthesis system is shown in Fig. 6a. The liquid metal that is commonly used in diamond synthesis is Ni; the Ni-C phase diagram at 54 Kbar is shown in Fig. 6b(Strong & Hanneman, 1967). Although the graphite phase is the only stable phase at normal pressure, at 54 Kbar, the diamond phase is stable below 1740 K. Liquid Ni coexists with the diamond phase between 1667 K and 1728 K. Thus, the solution growth of diamond from liquid Ni is possible in this temperature range. The true trick in diamond synthesis is not the 'stability' of the diamond phase, but the 'metastability' of the graphite phase, as indicated by the dashed lines in Fig. 6b. The synthetic capsule in high-pressure anvils is small and it is very difficult to manage sensitive temperature gradients. Thus, each process of crystal growth, i.e. the melting of metastable graphite in liquid Ni, carbon transfer within the solvent and crystallization of stable diamond on the seed, occurs in a very small temperature range. The driving forces for these reactions cannot be obtained from the temperature gradient, but can be obtained from the difference in the stability between graphite and diamond. For example in Fig. 6b, at 1700 K, the solubility of metastable graphite in liquid Ni represented by the dashed line is higher than that of stable diamond denoted by the solid line. The driving force for the crystal growth of the alum shown in Fig. 5 is generated when there is a spatial or temporal temperature difference, but that in diamond synthesis can be produced even at a constant

Figure 6b shows the so-called double phase diagram that is well known in metallurgy, e.g. the Fe-C system(Hansen & Anderko, 1958), and that is commonly observed for the systems containing metastable phases(Ishihara et al., 1984-5). The mechanism of crystal growth in the presence of a solubility difference between the stable and metastable phases, which is discussed in the present study, can be observed in the work of Van Lent (1961) on the transformation of mercury/white tin amalgams to gray tin, and it was first elucidated by

The solution growth is easily understood by the phase diagrams, but the simultaneous growth and dissolution processes of polytypes are hardly recognized. Such a puzzling process can be observed in the Ostwald ripening, which is shown schematically in Figs. 7. Ostwald ripening, also called coarsening, which occurs at the late stage of the precipitation,

Hurle et al. (1967) using the so-called thin alloy zone (TAZ) crystallization.

**3.3 Ostwald ripening and concentration profile**

difference is the driving force for the dissolution and deposition of alum.

**3.2 Double phase diagram**

temperature.

Fig. 6. Schematic drawings of **a** diamond synthesis and **b** enlarged sections of the Ni-C phase diagram at 54 Kbar. In **a**, graphite, liquid Ni and diamond are the source, solvent and seed, respectively. In **b**, the stable Ni-diamond and metastable Ni-graphite reactions are represented by solid and dashed lines, respectively(Strong & Hanneman, 1967).

is driven spontaneously by the diffusion between small (S) and large (L) precipitates due to Gibbs-Thomson effect. In this section, the matrix and precipitate phases are represented as *α* and *β*, respectively. The precipitates show the same composition of *x<sup>β</sup>* but different pressures of small and large radii, which makes the different free energies, *G<sup>s</sup> <sup>β</sup>* and *<sup>G</sup><sup>L</sup> <sup>β</sup>* , as shown in free-energy vs. concentration diagram of Fig. 7a. The common tangents of free-energy curves between matrix solution and precipitates show different angles and touch at the different concentrations *x<sup>L</sup> <sup>α</sup>* and *<sup>x</sup><sup>S</sup> <sup>α</sup>* of the free energy curve of the matrix solution. This concentration difference of matrix appears at the interfaces of the precipitates. Fig. 7b shows the schematic diagram of the solute concentration profile of the system of *α* matrix and small(S) and large(L) *β* precipitates. The matrix concentration equilibrating with the small precipitates should be higher than that with the large precipitates. This difference drives the solute diffusion and thus the simultaneous growth and dissolution of precipitates.

#### **3.4 Direct melting of metastable phases**

Ostwald ripening is the reaction in a solid solutions, which means the life time of metastable phase may be longer at lower temperatures and lower diffusivity. Does such a metastable phase directly melt in liquid?

The typical example of the behavior of the coexistence of stable and metastable phases is observed in the Fe-C system. As mentioned before, the double phase diagram of Fe-C and Fe-Fe3C systems is well studied and established. The melting behavior of metastable Fe3C phase has investigated in detail by Okada et al. (1981). They measured the differential thermal analysis (DTA) curves for the white, gray and mixture cast irons at the eutectic temperature and composition region. Fig. 8 shows the summarized results of DTA curves as well as the schematic double phase diagram. The endothermic temperatures shift due to the kinetic reason of the measuring apparatus, but the corrected temperatures show the stable and metastable eutectic temperatures of 1426K and 1416K, respectively. The specimens of gray cast iron contains stable phases of graphite and fcc-Fe(autenite), where they all melt only

the Other Diamond Synthetics 9

Metastable Solvent Epitaxy of SiC, the Other Diamond Synthetics 61

The solubility limit of each phase is determined by the tangent common to the free-energy curves of the coexisting phases. At the temperature indicated by the dotted line, the solubility

liquidus. The concentration gradient in the layers consisting of 3C-SiC and 4H-SiC and a very thin layer of liquid Si in between is obtained. The schematic carbon concentration profile in the liquid Si layer is shown in Fig. 9c. The concentration gradient at the metastable solubility limit of 3C-SiC leads to the extraction of C from the source plates. This concentration gradient also causes carbon diffusion across the liquid Si solvent and to the interface of the seed, where C is deposited due to the supersaturation of 4H-SiC. Although the small solubility limit of C in liquid Si, which is the cause of the slow growth of SiC in the conventional liquid method, still remains, the small thickness of the Si solvent in the new method leads to a sufficient

The key data in order to rationalize this novel process is the phase stability or the hierarchy of

The standard data book Chase (1998) shows the standard formation enthalpies for *α* and *β*

Δ*<sup>f</sup> H*(*α* − SiC, 298.15*K*) = −71.546 ± 6.3kJ/mol Δ*<sup>f</sup> H*(*β* − SiC, 298.15*K*) = −73.220 ± 6.3kJ/mol. Although the data shows that the *β*(cubic) phase is more stable than the *α*(hexagonal) phase at 298.15K, the difference of the measured values are within the measurement errors. The *α*(hexagonal) phase indicated in Chase (1998) is 6H, but also mentioned that the many polytypes have not been adequately differentiated thermodynamically. The heat capacity and Gibbs free energy are also reported as shown in Fig. 10. The measured values and the adapted functions in Chase (1998) suggest that *α*(hexagonal) phase is less stable up to 2000K, and they

The most widely adapted phase diagram should be that by Olesinski & Abbaschian (1996) as shown in Fig. 1, where the *β*(cubic) phase is more stable than the *α*(hexagonal) phase at any temperatures below the periodic temperature of the decomposition of SiC, 2545◦C. Although the evaluators of Olesinski & Abbaschian (1996) mentioned nothing on the types of *α*(hexagonal) phase, the same authors reported the co-existence of polytypes of *α* phases, 6H, 15R, and 4H(Olesinski & Abbaschian, 1984). Furthermore, it also mentioned on the report of Verma & Krishna (1966), the existence of *α* stability above 2000◦C. On the other hand, Fromm & Gebhardt (1976) reported the different type of phase diagram as shown in Fig. 11,

Solubilities of carbon in liquid silicon measured by Hall (1958), Scace & Slack (1959), Dash (1958), Dolloff (1960), Nozaki et al. (1970), Oden & McCune (1987), Suhara et al. (1989), Kleykamp & Schumacher (1993), Iguchi & Narushima (1993), Ottem (1993), and Yanabe et al. (1997) are summarized as in Figs. 12. Two reported phase diagrams as shown in Fig. 1 and Fig. 11 are based on the data given by Dolloff (1960). Dolloff (1960)'s data, however, are distinctively different from the others, where the solubility limits are larger than the others.

SiC polytypes. The reported phase diagrams, however, are somewhat conflicting.

concluded unlikely the transformation to *β*(cubic) phase at about 2300K.

where the phase transition from *β* to *α* phases occurs at around 2000◦C.

<sup>l</sup> , which corresponds to the dashed line of the liquidus in

<sup>l</sup> , which corresponds to the solid line of the

limit of metastable 3C-SiC is *x*3C

**4. Phase stability of SiC polytypes**

phases, as follows:

**4.1 Phase diagram assessment of Si-C system**

Fig. 9a. The solubility limit of stable 4H-SiC is *x*4H

concentration gradient for the growth of 4H-SiC crystals.

at the stable eutectic temperature of 1426K. On the other hand, the specimens of white cast iron shows the double peaks of endothermic reactions at the slow heating rates. Okada et al. (1981) found that at the first peak the metastable Fe3C melts but soon graphite solidifies and then remelt at the second peak. At the faster heating rates, only the melting of the metastable Fe3C phase occurs. For the specimens of mixture cast iron, the reactions are complicated but the melting and solidifying occur simultaneously. These experimental results indicate that the metastable phase is so stable that can melt directly.

Fig. 8. **a** DTA curves of cast irons(Okada et al., 1981) and **b** the double phase diagram of equiblibrium Fe-Graphite and metastable Fe-Fe3C systems.

#### **3.5 Speculated mechanism**

From the experimental result shown in Fig. 4, 4H-SiC is expected to be more stable than 3C-SiC. The Si-C system should show a double phase diagram, as schematically shown in Fig. 9a. The corresponding free-energy vs. concentration diagram is also illustrated in Fig. 9b. The solubility limit of each phase is determined by the tangent common to the free-energy curves of the coexisting phases. At the temperature indicated by the dotted line, the solubility limit of metastable 3C-SiC is *x*3C <sup>l</sup> , which corresponds to the dashed line of the liquidus in Fig. 9a. The solubility limit of stable 4H-SiC is *x*4H <sup>l</sup> , which corresponds to the solid line of the liquidus. The concentration gradient in the layers consisting of 3C-SiC and 4H-SiC and a very thin layer of liquid Si in between is obtained. The schematic carbon concentration profile in the liquid Si layer is shown in Fig. 9c. The concentration gradient at the metastable solubility limit of 3C-SiC leads to the extraction of C from the source plates. This concentration gradient also causes carbon diffusion across the liquid Si solvent and to the interface of the seed, where C is deposited due to the supersaturation of 4H-SiC. Although the small solubility limit of C in liquid Si, which is the cause of the slow growth of SiC in the conventional liquid method, still remains, the small thickness of the Si solvent in the new method leads to a sufficient concentration gradient for the growth of 4H-SiC crystals.

#### **4. Phase stability of SiC polytypes**

8 Will-be-set-by-IN-TECH

Concentration

*G*β *L*

*G*β *S*

**a b**

*x*α *L x*α *S*

Concentration Distance

Fig. 7. Schematic drawings of **a** free energy vs. concentration diagram and **b**concentration

at the stable eutectic temperature of 1426K. On the other hand, the specimens of white cast iron shows the double peaks of endothermic reactions at the slow heating rates. Okada et al. (1981) found that at the first peak the metastable Fe3C melts but soon graphite solidifies and then remelt at the second peak. At the faster heating rates, only the melting of the metastable Fe3C phase occurs. For the specimens of mixture cast iron, the reactions are complicated but the melting and solidifying occur simultaneously. These experimental results indicate that the

gray cast iron

Fig. 8. **a** DTA curves of cast irons(Okada et al., 1981) and **b** the double phase diagram of

From the experimental result shown in Fig. 4, 4H-SiC is expected to be more stable than 3C-SiC. The Si-C system should show a double phase diagram, as schematically shown in Fig. 9a. The corresponding free-energy vs. concentration diagram is also illustrated in Fig. 9b.

mixture iron

white cast iron

Free energy G

profile of the Ostwald ripening.

Temperature

**3.5 Speculated mechanism**

*x*<sup>β</sup> *x*<sup>α</sup> *L x*α *S*

metastable phase is so stable that can melt directly.

**a b**

Exothermic Endothermic

equiblibrium Fe-Graphite and metastable Fe-Fe3C systems.

Δ*T*

*G*α

*x*β

*l*

#### **4.1 Phase diagram assessment of Si-C system**

The key data in order to rationalize this novel process is the phase stability or the hierarchy of SiC polytypes. The reported phase diagrams, however, are somewhat conflicting. The standard data book Chase (1998) shows the standard formation enthalpies for *α* and *β* phases, as follows:

$$
\Delta\_f H(\alpha - \text{SiC}, 298.15K) = -71.546 \pm 6.3 \text{kJ/mol}
$$

$$
\Delta\_f H(\beta - \text{SiC}, 298.15K) = -73.220 \pm 6.3 \text{kJ/mol.}
$$

Although the data shows that the *β*(cubic) phase is more stable than the *α*(hexagonal) phase at 298.15K, the difference of the measured values are within the measurement errors. The *α*(hexagonal) phase indicated in Chase (1998) is 6H, but also mentioned that the many polytypes have not been adequately differentiated thermodynamically. The heat capacity and Gibbs free energy are also reported as shown in Fig. 10. The measured values and the adapted functions in Chase (1998) suggest that *α*(hexagonal) phase is less stable up to 2000K, and they concluded unlikely the transformation to *β*(cubic) phase at about 2300K.

The most widely adapted phase diagram should be that by Olesinski & Abbaschian (1996) as shown in Fig. 1, where the *β*(cubic) phase is more stable than the *α*(hexagonal) phase at any temperatures below the periodic temperature of the decomposition of SiC, 2545◦C. Although the evaluators of Olesinski & Abbaschian (1996) mentioned nothing on the types of *α*(hexagonal) phase, the same authors reported the co-existence of polytypes of *α* phases, 6H, 15R, and 4H(Olesinski & Abbaschian, 1984). Furthermore, it also mentioned on the report of Verma & Krishna (1966), the existence of *α* stability above 2000◦C. On the other hand, Fromm & Gebhardt (1976) reported the different type of phase diagram as shown in Fig. 11, where the phase transition from *β* to *α* phases occurs at around 2000◦C.

Solubilities of carbon in liquid silicon measured by Hall (1958), Scace & Slack (1959), Dash (1958), Dolloff (1960), Nozaki et al. (1970), Oden & McCune (1987), Suhara et al. (1989), Kleykamp & Schumacher (1993), Iguchi & Narushima (1993), Ottem (1993), and Yanabe et al. (1997) are summarized as in Figs. 12. Two reported phase diagrams as shown in Fig. 1 and Fig. 11 are based on the data given by Dolloff (1960). Dolloff (1960)'s data, however, are distinctively different from the others, where the solubility limits are larger than the others.

the Other Diamond Synthetics 11

Metastable Solvent Epitaxy of SiC, the Other Diamond Synthetics 63

C [at%]

0 20 40 60 80 100

2830°C

L+C

α-SiC+C

β-SiC+C

Fig. 10. Heat capacity and Gibbs energy of SiC(Chase, 1998).

Temperature [°C]

around 2000◦C(Fromm & Gebhardt, 1976).

Fig. 12. Solubility of carbon in liquid silicon.

3600

3200

2800

2400

2000

1600 1200 L

1414°C

Si(s)+β-SiC

Fig. 11. Phase diagram of Si-C binary system including the phase transition from *β* to *α* phase

L+β-SiC

L+α-SiC

Fig. 9. Schematic drawings of **a** the predicted Si-C double phase diagram, **b** related free-energy vs. concentration diagram and **c** carbon concentration profile in the liquid Si solvent between the 3C-SiC source and the 4H-SiC fine particles. The metastable eutectic temperature of the reaction liquid Si <sup>→</sup> Si<sup>S</sup> <sup>+</sup> SiC3C is lower than the stable eutectic temperature of the reaction liquid Si <sup>→</sup> Si<sup>S</sup> <sup>+</sup> SiC4H, where SiS denotes solid Si. The chemical potentials of C, *μ*c, are given by the intersections of the common tangents with the pure-carbon line in **b**, and are spatially different in the liquid Si solvent contacting with 3C-SiC and 4H-SiC in **c**. The configuration of **c** is related to that of the panel on the left-hand side in Fig. 2b.

10 Will-be-set-by-IN-TECH

liquid Si

Fig. 9. Schematic drawings of **a** the predicted Si-C double phase diagram, **b** related free-energy vs. concentration diagram and **c** carbon concentration profile in the liquid Si solvent between the 3C-SiC source and the 4H-SiC fine particles. The metastable eutectic temperature of the reaction liquid Si <sup>→</sup> Si<sup>S</sup> <sup>+</sup> SiC3C is lower than the stable eutectic

potentials of C, *μ*c, are given by the intersections of the common tangents with the pure-carbon line in **b**, and are spatially different in the liquid Si solvent contacting with 3C-SiC and 4H-SiC in **c**. The configuration of **c** is related to that of the panel on the left-hand

temperature of the reaction liquid Si <sup>→</sup> Si<sup>S</sup> <sup>+</sup> SiC4H, where SiS denotes solid Si. The chemical

SiS + SiC4H

SiS + SiC3C

*x*l 3C *x*<sup>l</sup> 4H

SiC

3C-SiC

carbon concentration

4H-SiC

carbon concentration

carbon concentration

3C-SiC source polycrystals

liquid Si solvent

4H-SiC fine particle μC 4H

μC 3C

temperature

free energy

distance

**a**

**b**

**c**

side in Fig. 2b.

liquid Si

Fig. 10. Heat capacity and Gibbs energy of SiC(Chase, 1998).

Fig. 11. Phase diagram of Si-C binary system including the phase transition from *β* to *α* phase around 2000◦C(Fromm & Gebhardt, 1976).

Fig. 12. Solubility of carbon in liquid silicon.

the Other Diamond Synthetics 13

Metastable Solvent Epitaxy of SiC, the Other Diamond Synthetics 65

only reliable at low temperatures. For including the finite temperature effect, the vibrational entropy effect is crucial, because the configurational entropies should be similar among these SiC polytypes due to the similar local configurations of tetrahedrons. One calculating result

6H

0 1,000 2,000 3,000 Temperature [K]

Fig. 13. First principles calculations of temperature dependency of free energy difference of 6H, 3C, and 2H against 4H SiC(Nishitani et al., 2009). Finite temperature effects are included through the vibrational free energy calculated by Phonon codes(Medea-phonon, n.d.;

These first principles calculations were carried out using the Vienna Ab initio Simulation Package (VASP) code(Kresse & Furthmüller, 1996a;b; Kresse & Hafner, 1993; 1994). The interaction between the ions and valence electrons was described by a projector augmented-wave (PAW) method(Kresse & Joubert, 1999). A plane-wave basis set with a cutoff of 400 eV was used. The exchange-correlation functional was described by the generalized gradient approximation (GGA) of the Perdew-Wang91 form(Perdew & Wang, 1992). Phonon calculation was performed by a commercial pre-processor of Medea-phonon(Medea-phonon, n.d.) with the direct method developed by Parlinski et al. (1997). The volumes and/or c/a

Fig. 13 shows the temperature dependencies of free energy of 6H, 3C, and 2H SiC polytypes measured from 4H SiC. 4H SiC is most stable at low temperatures, but 6H SiC is most stable at higher temperatures. 3C SiC is less stable against 4H or 6H SiC except at very high temperature region. Those results are consistent with the other speculations but the precisions of the calculations are not enough. Although the more precise calculations will alter the results of hierarchy of polytypes, their result pointed out the possibility of the phase transition in the

We have utilized a new method for manufacturing SiC from liquid Si; in this method, single crystals of 4H-SiC are obtained from polycrystalline 3C-SiC source in the absence of a temperature gradient. The origin of the driving force for crystal growth is the same as that in the case of diamond synthesis from a metal-carbon solvent, and it is elucidated by considering the stable-metastable double phase diagrams. This similarity in the growth mechanism indicates that the methods developed for diamond synthesis can be directly used

3C

Temperature [K]

2H

including the vibrational effect is shown by Nishitani et al. (2009) as in Fig. 13.


ratios were fitted to the most stable point at each temperature.

for growing large-size SiC crystals from a metastable solvent of Si.

Si-C system from the first principles calculations.

0

4H

0.002

Free energy difference [eV/SiC-pair]

Parlinski et al., 1997).

**5. Conclusions**

0.004

0.006

The reported phase stability between *α*(hexagonal) and *β*(cubic) might be 6H and 3C. If this assumption is true, 4H stability has not been shown experimentally. Furthermore, the distinct difference of solubility limits indicates that the coexistence of stable and metastable phases.

#### **4.2 Difficulty of the equilibrium state**

Although the conflicts of phase diagrams shown above remain, there have been many attempts of experimental and theoretical researches on the kinetic process of crystal growth of SiC polytypes. Famous stability diagrams of SiC polytypes proposed by Knippenberg (1963) and Inomata et al. (1968) show that the crystalized phases are controlled both by the temperature and growth rate of the operations.

The limit to slow growth rate of kinetic processes or results of long period holding should be equal to static results. But it is very difficult to dissolve whole amount of SiC crystals due to small solubility limit of SiC in liquid Si. If there remain seeds of metastable phases during the previous processes, it is difficult to remove all of them. The metastable phase also grows due to the co-exsitence of less stable phases as shown in Ostwald ripening, or from super-saturated liquid Si. Furthermore, the required high temperature and inert environment make the static conditions very difficult.

Inomata et al. (1969) performed careful experimental observations on the relationship between the polytypes of SiC and the supersaturation of the solution at 1800◦C with the solution method, and have shown the following results;


Those results indicate that the difference between 4H and 6H is crucial for determining the hierarchy of SiC polytypes.

Izhevskyi et al. (2000) summarized not only the kinetic observations, but also pointed out the impurity effects, especially nitrogen affects the transformations among 6H, 3C and 4H SiCs. Not only through the contamination of the higher temperature operations, but also from the starting materials made by Acheson method, specimens contain non-negligible nitrogen. Very recent improvements on materials and apparatuses make it possible to avoid nitrogen inclusions and get the hierarchy of pure SiC polytypes experimentally soon.

#### **4.3 First principles calculations**

For some cases of hardly measuring experimental value, the first principles calculations give some hints of the puzzles, and have been applied on the topic of the hierarchy of SiC polytypes. Liu & Ni (2005) have summarized the results of the first principles calculations of SiC. All calculations show that *β*-SiC is less stable than *α*-SiCs of 2H, 4H and 6H. The hierarchy between 4H and 6H is subtle; two of nine calculations shows that 6H SiC is most stable, but the majority of the results indicates that 4H SiC is most stable. Of course the calculating results should be judged by the precisions, the energy differences, however, are too small from 0.2 to 2 meV/Si-C pair to identify. Although the reliability of the first principles calculations of the hierarchy of SiC polytypes are insufficient, it is important that the calculating results show against the experimental results. Those are ground state results, which means that is

12 Will-be-set-by-IN-TECH

The reported phase stability between *α*(hexagonal) and *β*(cubic) might be 6H and 3C. If this assumption is true, 4H stability has not been shown experimentally. Furthermore, the distinct difference of solubility limits indicates that the coexistence of stable and metastable phases.

Although the conflicts of phase diagrams shown above remain, there have been many attempts of experimental and theoretical researches on the kinetic process of crystal growth of SiC polytypes. Famous stability diagrams of SiC polytypes proposed by Knippenberg (1963) and Inomata et al. (1968) show that the crystalized phases are controlled both by the

The limit to slow growth rate of kinetic processes or results of long period holding should be equal to static results. But it is very difficult to dissolve whole amount of SiC crystals due to small solubility limit of SiC in liquid Si. If there remain seeds of metastable phases during the previous processes, it is difficult to remove all of them. The metastable phase also grows due to the co-exsitence of less stable phases as shown in Ostwald ripening, or from super-saturated liquid Si. Furthermore, the required high temperature and inert environment make the static

Inomata et al. (1969) performed careful experimental observations on the relationship between the polytypes of SiC and the supersaturation of the solution at 1800◦C with the

1. *β*-SiC crystallizes from highly supersaturated solution. The crystals obtained at the condition of low supersaturation, however, consist of mainly *α*-SiC such as 4H, 15R and

3. From the results stated above, it is concluded that 4H is the most stable structure at 1800◦C

Those results indicate that the difference between 4H and 6H is crucial for determining the

Izhevskyi et al. (2000) summarized not only the kinetic observations, but also pointed out the impurity effects, especially nitrogen affects the transformations among 6H, 3C and 4H SiCs. Not only through the contamination of the higher temperature operations, but also from the starting materials made by Acheson method, specimens contain non-negligible nitrogen. Very recent improvements on materials and apparatuses make it possible to avoid nitrogen

For some cases of hardly measuring experimental value, the first principles calculations give some hints of the puzzles, and have been applied on the topic of the hierarchy of SiC polytypes. Liu & Ni (2005) have summarized the results of the first principles calculations of SiC. All calculations show that *β*-SiC is less stable than *α*-SiCs of 2H, 4H and 6H. The hierarchy between 4H and 6H is subtle; two of nine calculations shows that 6H SiC is most stable, but the majority of the results indicates that 4H SiC is most stable. Of course the calculating results should be judged by the precisions, the energy differences, however, are too small from 0.2 to 2 meV/Si-C pair to identify. Although the reliability of the first principles calculations of the hierarchy of SiC polytypes are insufficient, it is important that the calculating results show against the experimental results. Those are ground state results, which means that is

2. Relative amount of 4H increased markedly with decreasing the supersaturation.

inclusions and get the hierarchy of pure SiC polytypes experimentally soon.

**4.2 Difficulty of the equilibrium state**

conditions very difficult.

hierarchy of SiC polytypes.

**4.3 First principles calculations**

6H.

temperature and growth rate of the operations.

solution method, and have shown the following results;

among the basic polytypes of SiC, 3C, 4H, 15R and 6H.

only reliable at low temperatures. For including the finite temperature effect, the vibrational entropy effect is crucial, because the configurational entropies should be similar among these SiC polytypes due to the similar local configurations of tetrahedrons. One calculating result including the vibrational effect is shown by Nishitani et al. (2009) as in Fig. 13.

Fig. 13. First principles calculations of temperature dependency of free energy difference of 6H, 3C, and 2H against 4H SiC(Nishitani et al., 2009). Finite temperature effects are included through the vibrational free energy calculated by Phonon codes(Medea-phonon, n.d.; Parlinski et al., 1997).

These first principles calculations were carried out using the Vienna Ab initio Simulation Package (VASP) code(Kresse & Furthmüller, 1996a;b; Kresse & Hafner, 1993; 1994). The interaction between the ions and valence electrons was described by a projector augmented-wave (PAW) method(Kresse & Joubert, 1999). A plane-wave basis set with a cutoff of 400 eV was used. The exchange-correlation functional was described by the generalized gradient approximation (GGA) of the Perdew-Wang91 form(Perdew & Wang, 1992). Phonon calculation was performed by a commercial pre-processor of Medea-phonon(Medea-phonon, n.d.) with the direct method developed by Parlinski et al. (1997). The volumes and/or c/a ratios were fitted to the most stable point at each temperature.

Fig. 13 shows the temperature dependencies of free energy of 6H, 3C, and 2H SiC polytypes measured from 4H SiC. 4H SiC is most stable at low temperatures, but 6H SiC is most stable at higher temperatures. 3C SiC is less stable against 4H or 6H SiC except at very high temperature region. Those results are consistent with the other speculations but the precisions of the calculations are not enough. Although the more precise calculations will alter the results of hierarchy of polytypes, their result pointed out the possibility of the phase transition in the Si-C system from the first principles calculations.

#### **5. Conclusions**

We have utilized a new method for manufacturing SiC from liquid Si; in this method, single crystals of 4H-SiC are obtained from polycrystalline 3C-SiC source in the absence of a temperature gradient. The origin of the driving force for crystal growth is the same as that in the case of diamond synthesis from a metal-carbon solvent, and it is elucidated by considering the stable-metastable double phase diagrams. This similarity in the growth mechanism indicates that the methods developed for diamond synthesis can be directly used for growing large-size SiC crystals from a metastable solvent of Si.

the Other Diamond Synthetics 15

Metastable Solvent Epitaxy of SiC, the Other Diamond Synthetics 67

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**4** 

*Kazakhstan* 

**The Formation of Silicon Carbide in the SiCx**

Promising application of thin-film technology is the synthesis of SiC, possessing such valuable properties as high hardness (33400 Mn/m2), chemical resistance, high melting point (2830°C), wide bandgap (2.3–3.3 eV), etc (Lindner , 2003). Unfortunately, since it is still difficult to grow SiC material of crystalline quality to meet requirements for a large scale industrial application, small-size and high-cost SiC wafers severely limit their applications at present (Liangdeng et al., 2008). Doped with different impurities, silicon carbide is used in semiconductor technology (Yаn et al., 2000; Chen et al., 2003). Field-effect transistors, diodes and other electronic devices based on SiC have several advantages compared to similar silicon devices. Among them, the opportunity to work at temperatures up to 600°C, high speed and high radiation resistance. A large number of polytypes of SiC makes it possible to create heteropolytype structures (Lebedev et al., 2001, 2002a, 2005) to form a defect-free, near-perfect contacts with unusual electronic properties (Fissel et al., 2001; Lebedev et al., 2002b; Semenov et al., 2010). Diode structures have been established (Lebedev et al., 2002b), in which the value of uncompensated donors Nd−Na was (1.7−2)×1017 см-3 in the layer (n) 6H-SiC and acceptors Na−Nd ~ 3×1018 см-3 in the layer (p) 3C-SiC. In the spectrum of the electroluminescence of diodes revealed two bands with maxima hνmax ≈ 2.9 eV (430 nm) and 2.3 eV (540 nm), close the band gaps of 6H-and 3C-SiC. Currently, using the methods of vacuum sublimation (Savkina et al., 2000), molecular beam epitaxy (Fissel et al., 1996), the epitaxial and heteropolytype layers based on the cubic 3C-SiC and two hexagonal 6H-SiC, 4H-SiC on substrates of SiC, are grown. By chemical vapor deposition (CVD) (Nishino et al., 2002) are grown heteroepitaxial layers of 3C-SiC on substrates of Si. At the temperatures below 1200°C there are conditions for the growth of both poly- and nanocrystalline SiC with different degrees of crystallinity and structure of the cubic polytype 3C-SiC. Such conditions were realized in the magnetron sputtering (Kerdiles et al., 2000; Sun et al., 1998), laser ablation (Spillman et al., 2000) and plasma deposition (Liao et al., 2005), plasma-enhanced chemical vapor deposition (George et al., 2002; Pajagopalan et al., 2005), molecular beam epitaxy (Fissel et al., 2000). At temperatures below 1500°C in the direct deposition of carbon and silicon ions with an energy of ~100 eV, the growth of nanocrystalline films with a consistent set of the polytypes 3C, 21R, 27R, 51R, 6H is possible (Semenov et al., 2008, 2009, 2010). Photoluminescence spectrum from the front surface of the nanocrystalline film

**1. Introduction** 

**Layers (x = 0.03–1.4) Formed by Multiple** 

**Implantation of C Ions in Si** 

*Kazakh-British Technical University* 

Kair Kh. Nussupov and Nurzhan B. Beisenkhanov


### **The Formation of Silicon Carbide in the SiCx Layers (x = 0.03–1.4) Formed by Multiple Implantation of C Ions in Si**

Kair Kh. Nussupov and Nurzhan B. Beisenkhanov *Kazakh-British Technical University Kazakhstan* 

#### **1. Introduction**

16 Will-be-set-by-IN-TECH

68 Silicon Carbide – Materials, Processing and Applications in Electronic Devices

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Wesch, W. (1996). Silicon carbide: Synthesis and processing, *Nuclear Inst. Methods Phys. Res. B*

Yanabe, K., Akasaka, M., Takeuchi, M., Watanabe, M., Narushima, T. & Iguchi, Y. (1997).

New York.

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*Materials Trans. JIM* 38(11): 990–994.

Promising application of thin-film technology is the synthesis of SiC, possessing such valuable properties as high hardness (33400 Mn/m2), chemical resistance, high melting point (2830°C), wide bandgap (2.3–3.3 eV), etc (Lindner , 2003). Unfortunately, since it is still difficult to grow SiC material of crystalline quality to meet requirements for a large scale industrial application, small-size and high-cost SiC wafers severely limit their applications at present (Liangdeng et al., 2008). Doped with different impurities, silicon carbide is used in semiconductor technology (Yаn et al., 2000; Chen et al., 2003). Field-effect transistors, diodes and other electronic devices based on SiC have several advantages compared to similar silicon devices. Among them, the opportunity to work at temperatures up to 600°C, high speed and high radiation resistance. A large number of polytypes of SiC makes it possible to create heteropolytype structures (Lebedev et al., 2001, 2002a, 2005) to form a defect-free, near-perfect contacts with unusual electronic properties (Fissel et al., 2001; Lebedev et al., 2002b; Semenov et al., 2010). Diode structures have been established (Lebedev et al., 2002b), in which the value of uncompensated donors Nd−Na was (1.7−2)×1017 см-3 in the layer (n) 6H-SiC and acceptors Na−Nd ~ 3×1018 см-3 in the layer (p) 3C-SiC. In the spectrum of the electroluminescence of diodes revealed two bands with maxima hνmax ≈ 2.9 eV (430 nm) and 2.3 eV (540 nm), close the band gaps of 6H-and 3C-SiC. Currently, using the methods of vacuum sublimation (Savkina et al., 2000), molecular beam epitaxy (Fissel et al., 1996), the epitaxial and heteropolytype layers based on the cubic 3C-SiC and two hexagonal 6H-SiC, 4H-SiC on substrates of SiC, are grown. By chemical vapor deposition (CVD) (Nishino et al., 2002) are grown heteroepitaxial layers of 3C-SiC on substrates of Si. At the temperatures below 1200°C there are conditions for the growth of both poly- and nanocrystalline SiC with different degrees of crystallinity and structure of the cubic polytype 3C-SiC. Such conditions were realized in the magnetron sputtering (Kerdiles et al., 2000; Sun et al., 1998), laser ablation (Spillman et al., 2000) and plasma deposition (Liao et al., 2005), plasma-enhanced chemical vapor deposition (George et al., 2002; Pajagopalan et al., 2005), molecular beam epitaxy (Fissel et al., 2000). At temperatures below 1500°C in the direct deposition of carbon and silicon ions with an energy of ~100 eV, the growth of nanocrystalline films with a consistent set of the polytypes 3C, 21R, 27R, 51R, 6H is possible (Semenov et al., 2008, 2009, 2010). Photoluminescence spectrum from the front surface of the nanocrystalline film

The Formation of Silicon Carbide in the SiCx Layers

the physical properties of the films.

SiC layer using this approach.

**2. Experimental** 

formation of a polycrystalline β-SiC layer.

ion current density was kept below 4 μA/cm2.

×10-8 Pa, angle of Ar+ beam incidence 45°.

(x = 0.03–1.4) Formed by Multiple Implantation of C Ions in Si 71

annealing. It is of considerable interest to study the effect of the concentration component, nanoclusters, the phase composition of SiC films and their heat or plasma treatment on the crystallization processes and clustering, the size of nanocrystals and, consequently,

A number of studies have shown that the implantation of ions with multiple different energies is the most suitable for obtaining a uniform layer of carbon and silicon atoms to form SiC (Liangdeng et al., 2008, Calcagno et al ., 1996, Srikanth et al., 1988, Rothemund&Fritzsche, 1974, Reeson et al., 1990, Lindner et al., 1996; Martin et al., 1990). By carefully selecting the values of implantation energy and corresponding doses of carbon ions, a rectangular carbon concentration profile can be achieved for the buried β-

Implantation of carbon ions at temperatures of silicon substrate well above room temperature by in-situ annealing helps to form SiC crystalline layers immediately during implantation or after annealing at lower temperatures (Durupt et al., 1980; Frangis et al., 1997; Edelman et al., 1976; Simon et al., 1996; Preckwinkel et al., 1996). High temperature of the substrate can be achieved also by using beams with high current density of carbon ions (Reeson et al., 1990; Alexandrov et al., 1986). Treatment of carbon implanted silicon layers by power ion (Liangdeng et al., 2008; Bayazitov et al., 2003), electron (Theodossiu et al., 1999) or laser (Bayazitov et al., 2003a, 2003b) beams like thermal annealing also leads to the

In this paper, the composition and structure of homogeneous SiC1.4, SiC0.95, SiC0.7, SiC0.4, SiC0.12 and SiC0.03 layers, received by multiple high-dose implantation of carbon ions with energies of 40, 20, 10, 5 and 3 keV are investigated. The influence of decay of carbon- and carbon-silicon clusters during thermal annealing or hydrogen glow discharge plasma processing on the formation of tetrahedral Si–C-bonds and crystallization processes in

Single-crystal (100) silicon wafers of sizes 7×12×0.4 mm3 with an electrical resistivity 4–5 Ω⋅сm were implanted by 12C+ ions with energies of 40, 20, 10, 5, and 3 keV at room temperature in vacuum reached by fully oil-free pumping. To prevent sample heating, the

The SiCx films structure was investigated by X-ray diffraction using a narrow collimated (0.05×1.5 mm2) monochromatic (CuKα) X-ray beam directed at an angle of 5º to the sample surface. The average crystallite size was estimated from the width of X-rays lines by Jones method. The surface of the layers was analyzed by Atomic force microscopy (JSPM 5200, Jeol, Japan) using AFM AC technique. The investigation of morphology and structure of the SiCx layers was carried out by transmission electron microscopy (JEM-100CX, JEOL, Japan). The IR transmission spectra were recorded in differential regime on double-beam infrared spectrometer UR-20 (400−5000 cm-1). The spectra both at perpendicular incidence of infrared rays on the sample surface and at an angle of 73o with respect to the normal to the sample surface were measured. The composition of the layers was examined by Auger electron spectroscopy. The parameters were as follows: incident electron beam of diameter 1 μm, energy 10 keV, angle of incidence 45°, diameter of scanning region 300 μm, vacuum 1.33

silicon layers with high and low concentrations of carbon, is studied.

containing cubic 3C and rhombohedral 21R, has a band emission with three peaks at 2.65, 2.83, 2.997 eV (469, 439, 415 nm), the shoulder of 2.43 eV (511 nm) and a weak peak at 3.366 eV (369 nm) (Semenov et al., 2010).

Of particular interest is the synthesis of SiC layers in silicon by ion implantation (Lindner, 2003; Liangdeng et al., 2008; Kimura et al., 1982, 1984) due to the possibilities to obtain the films of a given thickness and composition, nanolayers of chemical compounds and multilayer structures, as well as the insulating layers in the manufacture of integrated circuits. Silicon structures with a hidden layer of silicon carbide can be used as a SOIstructure (silicon-on-insulator), which have advantages over structures with a hidden layer of SiO2, obtained by the SIMOX (Separation by IMplantation of OXygen). Crystalline films of high-quality β-SiC on SiO2 can be obtained by multiple ion implantation of C in Si and selective oxidation of the top layer of Si (Serre et al., 1999).

High-dose carbon implantation into silicon in combination with subsequent or in situ thermal annealing has been shown to be able to form polycrystalline or epitaxial cubic SiC (β-SiC) layers in silicon (Liangdeng et al., 2008; Kantor et al., 1997; Durupt et al., 1980; Calcagno et al., 1996). To create a SiC**−**Si heterojunctions were among the first used the method of ion implantation the authors of (Borders et al., 1971; Baranova et al., 1971), in which the synthesis of silicon carbide was carried out by implantation of 12C+ ions (Е = 200 кэВ, D = ~1017 см-2 (Borders et al., 1971) or Е = 40 кэВ, D > 1017 ион/см2 (Baranova et al., 1971)) into a silicon substrate. From the position of the IR absorption band (700–725 cm-1), reducing its half-width after annealing and displacement in the region at 800 cm-1, corresponding to transverse optical phonons of SiC, it was found that the formation of crystalline SiC phase occurs in the temperature range near 850ºC (Borders et al., 1971) and 900°C (Baranova et al., 1971). Silicon carbide was identified using transverse optical phonon spectra in most of the above work on ion implantation, as well as in (Gerasimenko et al., 1974, Wong et al., 1998, Akimchenko et al., 1977a, 1980; Chen et al., 1999, Kimura et al., 1981). The detection of longitudinal optical vibrations of lattice atoms (LO phonons) and their changes during film annealing give additional information on the crystallization processes (Akimchenko et al., 1977b, 1979).

Difficulties associated with the problem of synthesis of a crystalline silicon carbide prevent the wide use of SiC in microelectronics. The Si-C mixture, after implantation of large doses of carbon, is assumed to be amorphous (Lindner , 2003; Liangdeng et al., 2008; Kimura et al., 1981). Carbon atom diffusion in the implanted layer is restricted by the strong Si-C bonds (Liangdeng et al., 2008). A negative influence of stable C- and C**−**Siclusters (Yan et al., 2000, Chen et al., 2003; Kimura et al., 1982, 1984; Durupt et al., 1980, Calcagno et al., 1996; Borders et al., 1971) on the crystallization of SiC in the implanted silicon layers with different concentration of the implanted carbon, was found. Heat treatment up to 1200°C does not lead to complete disintegration of the clusters and the release of C and Si atoms to form the Si–C-bonds with tetrahedral orientation which is characteristic of the crystalline SiC phase (Khokhlov et al., 1987). However intensively developing area is the formation in SiO2 by ion implantation of nanostructured systems with inclusions of nanocrystals and clusters of Si, SiC and C, providing the expense of size effects luminescence virtually the entire visible spectrum (Zhao et al., 1998; Tetelbaum et al., 2009; Perez-Rodrguez et al., 2003; Gonzalez-Varona et al., 2000; Belov et al., 2010). This makes it necessary to study the mechanisms of formation of nanocrystals Si, SiC, carbon nanoclusters and amorphous SiC precipitates during the implantation and annealing. It is of considerable interest to study the effect of the concentration component, nanoclusters, the phase composition of SiC films and their heat or plasma treatment on the crystallization processes and clustering, the size of nanocrystals and, consequently, the physical properties of the films.

A number of studies have shown that the implantation of ions with multiple different energies is the most suitable for obtaining a uniform layer of carbon and silicon atoms to form SiC (Liangdeng et al., 2008, Calcagno et al ., 1996, Srikanth et al., 1988, Rothemund&Fritzsche, 1974, Reeson et al., 1990, Lindner et al., 1996; Martin et al., 1990). By carefully selecting the values of implantation energy and corresponding doses of carbon ions, a rectangular carbon concentration profile can be achieved for the buried β-SiC layer using this approach.

Implantation of carbon ions at temperatures of silicon substrate well above room temperature by in-situ annealing helps to form SiC crystalline layers immediately during implantation or after annealing at lower temperatures (Durupt et al., 1980; Frangis et al., 1997; Edelman et al., 1976; Simon et al., 1996; Preckwinkel et al., 1996). High temperature of the substrate can be achieved also by using beams with high current density of carbon ions (Reeson et al., 1990; Alexandrov et al., 1986). Treatment of carbon implanted silicon layers by power ion (Liangdeng et al., 2008; Bayazitov et al., 2003), electron (Theodossiu et al., 1999) or laser (Bayazitov et al., 2003a, 2003b) beams like thermal annealing also leads to the formation of a polycrystalline β-SiC layer.

In this paper, the composition and structure of homogeneous SiC1.4, SiC0.95, SiC0.7, SiC0.4, SiC0.12 and SiC0.03 layers, received by multiple high-dose implantation of carbon ions with energies of 40, 20, 10, 5 and 3 keV are investigated. The influence of decay of carbon- and carbon-silicon clusters during thermal annealing or hydrogen glow discharge plasma processing on the formation of tetrahedral Si–C-bonds and crystallization processes in silicon layers with high and low concentrations of carbon, is studied.

#### **2. Experimental**

70 Silicon Carbide – Materials, Processing and Applications in Electronic Devices

containing cubic 3C and rhombohedral 21R, has a band emission with three peaks at 2.65, 2.83, 2.997 eV (469, 439, 415 nm), the shoulder of 2.43 eV (511 nm) and a weak peak at 3.366

Of particular interest is the synthesis of SiC layers in silicon by ion implantation (Lindner, 2003; Liangdeng et al., 2008; Kimura et al., 1982, 1984) due to the possibilities to obtain the films of a given thickness and composition, nanolayers of chemical compounds and multilayer structures, as well as the insulating layers in the manufacture of integrated circuits. Silicon structures with a hidden layer of silicon carbide can be used as a SOIstructure (silicon-on-insulator), which have advantages over structures with a hidden layer of SiO2, obtained by the SIMOX (Separation by IMplantation of OXygen). Crystalline films of high-quality β-SiC on SiO2 can be obtained by multiple ion implantation of C in Si and

High-dose carbon implantation into silicon in combination with subsequent or in situ thermal annealing has been shown to be able to form polycrystalline or epitaxial cubic SiC (β-SiC) layers in silicon (Liangdeng et al., 2008; Kantor et al., 1997; Durupt et al., 1980; Calcagno et al., 1996). To create a SiC**−**Si heterojunctions were among the first used the method of ion implantation the authors of (Borders et al., 1971; Baranova et al., 1971), in which the synthesis of silicon carbide was carried out by implantation of 12C+ ions (Е = 200 кэВ, D = ~1017 см-2 (Borders et al., 1971) or Е = 40 кэВ, D > 1017 ион/см2 (Baranova et al., 1971)) into a silicon substrate. From the position of the IR absorption band (700–725 cm-1), reducing its half-width after annealing and displacement in the region at 800 cm-1, corresponding to transverse optical phonons of SiC, it was found that the formation of crystalline SiC phase occurs in the temperature range near 850ºC (Borders et al., 1971) and 900°C (Baranova et al., 1971). Silicon carbide was identified using transverse optical phonon spectra in most of the above work on ion implantation, as well as in (Gerasimenko et al., 1974, Wong et al., 1998, Akimchenko et al., 1977a, 1980; Chen et al., 1999, Kimura et al., 1981). The detection of longitudinal optical vibrations of lattice atoms (LO phonons) and their changes during film annealing give additional information on the crystallization

Difficulties associated with the problem of synthesis of a crystalline silicon carbide prevent the wide use of SiC in microelectronics. The Si-C mixture, after implantation of large doses of carbon, is assumed to be amorphous (Lindner , 2003; Liangdeng et al., 2008; Kimura et al., 1981). Carbon atom diffusion in the implanted layer is restricted by the strong Si-C bonds (Liangdeng et al., 2008). A negative influence of stable C- and C**−**Siclusters (Yan et al., 2000, Chen et al., 2003; Kimura et al., 1982, 1984; Durupt et al., 1980, Calcagno et al., 1996; Borders et al., 1971) on the crystallization of SiC in the implanted silicon layers with different concentration of the implanted carbon, was found. Heat treatment up to 1200°C does not lead to complete disintegration of the clusters and the release of C and Si atoms to form the Si–C-bonds with tetrahedral orientation which is characteristic of the crystalline SiC phase (Khokhlov et al., 1987). However intensively developing area is the formation in SiO2 by ion implantation of nanostructured systems with inclusions of nanocrystals and clusters of Si, SiC and C, providing the expense of size effects luminescence virtually the entire visible spectrum (Zhao et al., 1998; Tetelbaum et al., 2009; Perez-Rodrguez et al., 2003; Gonzalez-Varona et al., 2000; Belov et al., 2010). This makes it necessary to study the mechanisms of formation of nanocrystals Si, SiC, carbon nanoclusters and amorphous SiC precipitates during the implantation and

eV (369 nm) (Semenov et al., 2010).

selective oxidation of the top layer of Si (Serre et al., 1999).

processes (Akimchenko et al., 1977b, 1979).

Single-crystal (100) silicon wafers of sizes 7×12×0.4 mm3 with an electrical resistivity 4–5 Ω⋅сm were implanted by 12C+ ions with energies of 40, 20, 10, 5, and 3 keV at room temperature in vacuum reached by fully oil-free pumping. To prevent sample heating, the ion current density was kept below 4 μA/cm2.

The SiCx films structure was investigated by X-ray diffraction using a narrow collimated (0.05×1.5 mm2) monochromatic (CuKα) X-ray beam directed at an angle of 5º to the sample surface. The average crystallite size was estimated from the width of X-rays lines by Jones method. The surface of the layers was analyzed by Atomic force microscopy (JSPM 5200, Jeol, Japan) using AFM AC technique. The investigation of morphology and structure of the SiCx layers was carried out by transmission electron microscopy (JEM-100CX, JEOL, Japan). The IR transmission spectra were recorded in differential regime on double-beam infrared spectrometer UR-20 (400−5000 cm-1). The spectra both at perpendicular incidence of infrared rays on the sample surface and at an angle of 73o with respect to the normal to the sample surface were measured. The composition of the layers was examined by Auger electron spectroscopy. The parameters were as follows: incident electron beam of diameter 1 μm, energy 10 keV, angle of incidence 45°, diameter of scanning region 300 μm, vacuum 1.33 ×10-8 Pa, angle of Ar+ beam incidence 45°.

The Formation of Silicon Carbide in the SiCx Layers

 N <sup>C</sup> (3 keV)

0.0 0.5 1.0 1.5 2.0 2.5 3.0

N C / N S i ( N O / N S i )

c)

0.0

0.5

1.0 1.5

(3 keV)

N C / N S i ( N O / N S i )

**b)**

N C / N S i ( N O / N S i )

2.0

2.5

0.0

0.5

1.0

1.5

2.0

2.5

**a )**

(x = 0.03–1.4) Formed by Multiple Implantation of C Ions in Si 73

C )

0 40 80 120 160 200 х, nm

Fig. 1. 12С distribution profiles in Si produced by ion implantation (see table 1). (a) SiC1.4; (b) SiC0.95; (c) SiC0.7. NC(Burenkov) and NC(Gibbons) are the profiles calculated according to Burenkov et al. (1985) and Gibbons et al. (1975), respectively, where NC(Gibbons) = NC(40 keV) + NC(20 keV) + NC(10 keV) + NC(5 keV) + NC(3 keV). NС(200С), NС(12500С) and NО(12500С) are the Auger profiles of carbon and oxygen, respectively, in a layer after high-

NC(40 keV) NC(20 keV)

<sup>0</sup> 40 80 120 160 200 <sup>х</sup>, nm

NC(40 keV)

0 40 80 120 160 200 х, nm

N <sup>C</sup> (20 keV)

NC(1250°C)

N <sup>C</sup> (40 keV)

NC(20°C)

NC NC(10 keV) (3 keV)

NC(20°C)

NС(5 keV)

dose implantation and annealing at T = 1250°C for 30 min.

NC(1250°C) NO(1250°C)

NC(20 keV)

N <sup>C</sup> (10 keV)

N <sup>C</sup> (5 keV)

N <sup>O</sup> (1250 <sup>o</sup>

NC(10 keV) NC

NC(5 keV)

NO(1250°C)

NС(Gibbons)

NC(Gibbons)

N <sup>C</sup> (G ib b o ns)

N <sup>C</sup> (1250 <sup>o</sup>

N <sup>C</sup> (Burenkov)

C )

NC(Burenkov)

NC(Burenkov)

The glow discharge hydrogen plasma was generated at a pressure of 6.5 Pa with a capacitive coupled radio frequency (r.f.) power (27.12 MHz) of about 12.5 W. The temperature of processing did not exceed 100°С and it was measured by thermocouple. The processing time was 5 min.

#### **3. Results and discussion**

#### **3.1 Depth profiles of multiple-energy implanted carbon in Si**

To produce a rectangular profile of the distribution of carbon atoms in silicon five energies and doses have been chosen in such a way **(**Table 1) that the concentration ratio of C and Si atoms to a depth **(**up to ~120 nm) was equal to the values of NC/NSi = 1.0 , 0.8, 0.5, 0.3, 0.1 and 0.03. The calculated profiles NC**(**Burenkov) are the sums of the distributions **(**Figs. 1 and 2), constructed for the chosen values of energies (E) and doses (D) of carbon ions using the values of the ion mean projective range, Rp(E), and the rootmean-square deviation, ΔRp(Е), **(**Table 1) and moment Sk(Eo)**,** according to Burenkov et al. (1985). On these figures are presented the calculated profiles NC(Gibbons), which are the sums of Gaussian distributions constructed by using values of Rp(Е) and ΔRp(Е) according to Gibbons et al. (1975) (LSS):

$$N(\mathbf{x}) = \frac{D}{\Delta R\_p \left(2\pi\right)^{1/2}} \exp[-\frac{\left(\mathbf{x} - R\_p\right)^2}{2\Delta R\_p}\mathbf{I}\_\prime \tag{1}$$

where х is the distance from the surface**.** 

Figs. 1 and 2 also show the experimental profiles NC(20°С), NC(1250°С) and NО(1250°С), obtained by Auger electron spectroscopy, which show the concentration ratio of carbon and oxygen atoms (NC/NSi and NО/NSi) over the sample depth after implantation and annealing at 1250°C for 30 min in an argon atmosphere with low oxygen content. Fig. 1 shows that the average concentrations of carbon and oxygen were: a)NC/NSi = 1.4 and NО/NSi ≈ 2.6; b) NC/NSi = 0.95 and NО/NSi ≈ 2.33; c) NC/NSi = 0.7 and NО/NSi ≈ 3.0; and as follows from Fig. 2: a)NC/NSi = 0.4; b)NC/NSi = 0.12.

Thus, the average carbon concentration over the depth exceeded the corresponding calculated values (NC/NSi = 0.1; 0.3; 0.5; 0.8 and 1.0) and led to the formation of layers SiC0.12, SiC0.4 , SiC0.7, SiC0.95 and SiC1.4 (Table 2). The average value of the ratio of NО/NSi exceeded the stoichiometric value for SiO2 (NО/NSi = 2), indicating on the saturation of the surface layer by oxygen. In high-temperature annealing a desorption of carbon atoms from the surface and an adsorption of oxygen atoms are occurred. There are clear interfaces SiO3.0:SiC0.7, SiO2.33:SiC0.95 and SiO2.6:SiC1.4 suggesting the interconnectedness of these processes. The mechanism of desorption of carbon may be associated with a diffusion process along the grain boundaries of counter flow of oxygen molecules O2 into deep layer and molecules of CO and CO2 from the layer toward the surface.

Penetration of oxygen deep into the implanted layer until the substrate was also shown in (Chen et al., 2003). The mechanism of instability of silicon carbide films during hightemperature annealing in the presence of oxygen is of special interest (Singh et al., 2002).

Process can occur in accordance with the expression 950 1700 2 2 23 2 2 *<sup>C</sup> SiC O SiO CO* − ° + ⎯⎯⎯⎯⎯→ + .

The glow discharge hydrogen plasma was generated at a pressure of 6.5 Pa with a capacitive coupled radio frequency (r.f.) power (27.12 MHz) of about 12.5 W. The temperature of processing did not exceed 100°С and it was measured by thermocouple. The processing time

To produce a rectangular profile of the distribution of carbon atoms in silicon five energies and doses have been chosen in such a way **(**Table 1) that the concentration ratio of C and Si atoms to a depth **(**up to ~120 nm) was equal to the values of NC/NSi = 1.0 , 0.8, 0.5, 0.3, 0.1 and 0.03. The calculated profiles NC**(**Burenkov) are the sums of the distributions **(**Figs. 1 and 2), constructed for the chosen values of energies (E) and doses (D) of carbon ions using the values of the ion mean projective range, Rp(E), and the rootmean-square deviation, ΔRp(Е), **(**Table 1) and moment Sk(Eo)**,** according to Burenkov et al. (1985). On these figures are presented the calculated profiles NC(Gibbons), which are the sums of Gaussian distributions constructed by using values of Rp(Е) and ΔRp(Е) according

2

<sup>−</sup> = − Δ Δ , (1)

2 2 23 2 2 *<sup>C</sup> SiC O SiO CO* − ° + ⎯⎯⎯⎯⎯→ + .

*p*

1 2 <sup>2</sup> 2 2 / ( ) ( ) exp[ ] ( )

*p p D x R*

*R R*

Figs. 1 and 2 also show the experimental profiles NC(20°С), NC(1250°С) and NО(1250°С), obtained by Auger electron spectroscopy, which show the concentration ratio of carbon and oxygen atoms (NC/NSi and NО/NSi) over the sample depth after implantation and annealing at 1250°C for 30 min in an argon atmosphere with low oxygen content. Fig. 1 shows that the average concentrations of carbon and oxygen were: a)NC/NSi = 1.4 and NО/NSi ≈ 2.6; b) NC/NSi = 0.95 and NО/NSi ≈ 2.33; c) NC/NSi = 0.7 and NО/NSi ≈ 3.0; and as follows from Fig.

Thus, the average carbon concentration over the depth exceeded the corresponding calculated values (NC/NSi = 0.1; 0.3; 0.5; 0.8 and 1.0) and led to the formation of layers SiC0.12, SiC0.4 , SiC0.7, SiC0.95 and SiC1.4 (Table 2). The average value of the ratio of NО/NSi exceeded the stoichiometric value for SiO2 (NО/NSi = 2), indicating on the saturation of the surface layer by oxygen. In high-temperature annealing a desorption of carbon atoms from the surface and an adsorption of oxygen atoms are occurred. There are clear interfaces SiO3.0:SiC0.7, SiO2.33:SiC0.95 and SiO2.6:SiC1.4 suggesting the interconnectedness of these processes. The mechanism of desorption of carbon may be associated with a diffusion process along the grain boundaries of counter flow of oxygen molecules O2 into

Penetration of oxygen deep into the implanted layer until the substrate was also shown in (Chen et al., 2003). The mechanism of instability of silicon carbide films during hightemperature annealing in the presence of oxygen is of special interest (Singh et al., 2002).

deep layer and molecules of CO and CO2 from the layer toward the surface.

Process can occur in accordance with the expression 950 1700

π

was 5 min.

**3. Results and discussion** 

to Gibbons et al. (1975) (LSS):

where х is the distance from the surface**.** 

2: a)NC/NSi = 0.4; b)NC/NSi = 0.12.

**3.1 Depth profiles of multiple-energy implanted carbon in Si** 

*N x*

Fig. 1. 12С distribution profiles in Si produced by ion implantation (see table 1). (a) SiC1.4; (b) SiC0.95; (c) SiC0.7. NC(Burenkov) and NC(Gibbons) are the profiles calculated according to Burenkov et al. (1985) and Gibbons et al. (1975), respectively, where NC(Gibbons) = NC(40 keV) + NC(20 keV) + NC(10 keV) + NC(5 keV) + NC(3 keV). NС(200С), NС(12500С) and NО(12500С) are the Auger profiles of carbon and oxygen, respectively, in a layer after highdose implantation and annealing at T = 1250°C for 30 min.

The Formation of Silicon Carbide in the SiCx Layers

and C-clusters, double and triple Si–C- and C–C-bonds.

**3.2 Investigation of the structure by electron microscopy** 

is a three-layer structure [layer-Si + transition layer "Si-SiCx "+ layer SiCx].

*1*

to be analyzed by transmission electron microscopy.

expression of SiC + O2 = SiO2 + CO/CO2.

Auger electron spectroscopy

(x = 0.03–1.4) Formed by Multiple Implantation of C Ions in Si 75

In (Mandal et al., 2001) reported 100% conversion of SiC into SiO2 in accordance with the

In the case of high concentrations of carbon (SiC1.4, SiC0.95, SiC0.7 and SiC0.4) the experimentally obtained profiles of the carbon atoms were almost rectangular (Figs. 1 and 2) and close in concentration value to the calculated concentration profile according Gibbons et al. (1975), while for layers with low carbon concentration SiC0.12 is closer to the calculated profile according Burenkov et al. (1985) (Fig. 2). Factors contributing to the excess concentration of carbon in the surface silicon layer in comparison with the calculated values by (Burenkov et al., 1985) at high-dose 12С ion implantation can be considered sputtering the surface in conjunction with a decrease in the values of Rp due to the presence of strong Si-C-

Depth range, nm 40–110 20–120 25–120 10–120 20–120 SiCх (Burenkov) SiC1.0 SiC0.8 SiC0.5 SiC0.3 SiC0.1 SiCх (Gibbons) SiC1.38 SiC1.06 SiC0.67 SiC0.40 SiC0.13 SiCх (AES) SiC1.4 SiC0.95 SiC0.7 SiC0.4 SiC0.12 Тable 2. Average values of carbon concentration x = NC/NSi in the SiCх layers calculated according Burenkov et al. (1985) and Gibbons et al. (1975) and experimentally obtained by

By transmission electron microscopy structural features of the SiC1.4, SiC0.95 and SiC0.7 films, formed in the surface layer of single crystal Si wafers using multiple ion implantation, after annealing at 1200°C for 30 minutes were investigated. Figure 3 schematically shows a section of the objects. The investigated area can be divided into three sections: section 1 consists of a layer SiCx; section 2 includes a [transition layer "Si-SiCx" + layer SiCx]; section 3

*5*

Fig. 3. Schematic cross section of the sample under study: (*1*) SiCx regions, (*2*) regions of an intermediate Si-SiCx layer, (*3*) double-diffraction regions, (*4*) a through hole, and (*5*) the area

The layers SiC1.4, SiC0.95 and SiC0.7 are solid, homogeneous, fine polycrystalline films (Figs. 4a-c, 5a, b and 6a, b, light areas, respectively). Some electron diffraction patterns contain superimposed point (*c*-Si) and ring (SiC) electron diffraction patterns (Fig.4b, c, 5b and 6b).

**SiCx SiCx Si** *1* **Si**

*4*

*2 2*

*3 3*

Fig. 2. 12С distribution profiles in Si produced by ion implantation (see table 1). (a) SiC0.4; (b) SiC0.12. NC(Burenkov) and NC(Gibbons) are the profiles calculated according to Burenkov et al. (1985) and Gibbons et al. (1975), respectively, where NC(Gibbons) = NC(40 keV) + NC(20 keV) + NC(10 keV) + NC(5 keV) + NC(3 keV). NС(200С) and NО(200С) are the Auger profiles of carbon and oxygen, respectively, in a layer after high-dose implantation.


Table 1. Values of energy, *E*, dose, *D*, projected range, *Rp*(*E*), and straggling, Δ*Rp*(*E*), for 12C+ ions in Si, used for constructing a rectangular distribution profile

NC(10 keV)

0 40 80 120 160 200 х, nm

Fig. 2. 12С distribution profiles in Si produced by ion implantation (see table 1). (a) SiC0.4; (b) SiC0.12. NC(Burenkov) and NC(Gibbons) are the profiles calculated according to Burenkov et al. (1985) and Gibbons et al. (1975), respectively, where NC(Gibbons) = NC(40 keV) + NC(20 keV) + NC(10 keV) + NC(5 keV) + NC(3 keV). NС(200С) and NО(200С) are the Auger profiles

Е, keV 40 20 10 5 3 D(SiC1.0), 1017 cm-2 5.60 1.92 0.990 0.330 0.230 D(SiC0.8), 1017 cm-2 4.48 1.54 0.792 0.264 0.184 D(SiC0.5), 1017 cm-2 2.80 0.96 0.495 0.165 0.115 D(SiC0.3), 1017 cm-2 1.68 0.576 0.297 0.099 0.069 D(SiC0.1), 1017 cm-2 0.56 0.192 0.099 0.033 0.023 D(SiC0.03), 1017 cm-2 0.168 0.058 0.030 0.010 0.007

Table 1. Values of energy, *E*, dose, *D*, projected range, *Rp*(*E*), and straggling, Δ*Rp*(*E*), for 12C+

0 40 80 120 160 200 х, nm

NC(40 keV) NC(20 keV)

NC(20 keV)

NC(20°C) NC(40 keV)

of carbon and oxygen, respectively, in a layer after high-dose implantation.

NC(10 keV)

Rp(Е). nm

ΔRp(Е). nm

Rp(Е). nm

ΔRp(Е). nm

ions in Si, used for constructing a rectangular distribution profile

NС(5 кэВ)

NС(5 keV)

NO(20°C)

NC(3 keV)

NC(Burenkov) .

NC(Burenkov)

NС(Gibbons)

NC(20°C)

NС(Gibbons)

120.4 60.0 30.3 16.1 10.5

46.0 28.3 16.9 10.2 7.2

93.0 47.0 24.0 12.3 7.5

34.0 21.0 13.0 7.00 4.3

0.0

NC(Burenkov) profile (Burenkov et al., 1985)

NC(Gibbons) profile (Gibbons et al., 1975)

0.1

N

C/NSi

**b)**

N

C/NSi (N

O/NSi)

**а)**

0.2

NC(3 keV)

0.3

0.0 0.1 0.2 0.3 0.4 0.5 0.6 In (Mandal et al., 2001) reported 100% conversion of SiC into SiO2 in accordance with the expression of SiC + O2 = SiO2 + CO/CO2.

In the case of high concentrations of carbon (SiC1.4, SiC0.95, SiC0.7 and SiC0.4) the experimentally obtained profiles of the carbon atoms were almost rectangular (Figs. 1 and 2) and close in concentration value to the calculated concentration profile according Gibbons et al. (1975), while for layers with low carbon concentration SiC0.12 is closer to the calculated profile according Burenkov et al. (1985) (Fig. 2). Factors contributing to the excess concentration of carbon in the surface silicon layer in comparison with the calculated values by (Burenkov et al., 1985) at high-dose 12С ion implantation can be considered sputtering the surface in conjunction with a decrease in the values of Rp due to the presence of strong Si-Cand C-clusters, double and triple Si–C- and C–C-bonds.


Тable 2. Average values of carbon concentration x = NC/NSi in the SiCх layers calculated according Burenkov et al. (1985) and Gibbons et al. (1975) and experimentally obtained by Auger electron spectroscopy

#### **3.2 Investigation of the structure by electron microscopy**

By transmission electron microscopy structural features of the SiC1.4, SiC0.95 and SiC0.7 films, formed in the surface layer of single crystal Si wafers using multiple ion implantation, after annealing at 1200°C for 30 minutes were investigated. Figure 3 schematically shows a section of the objects. The investigated area can be divided into three sections: section 1 consists of a layer SiCx; section 2 includes a [transition layer "Si-SiCx" + layer SiCx]; section 3 is a three-layer structure [layer-Si + transition layer "Si-SiCx "+ layer SiCx].

Fig. 3. Schematic cross section of the sample under study: (*1*) SiCx regions, (*2*) regions of an intermediate Si-SiCx layer, (*3*) double-diffraction regions, (*4*) a through hole, and (*5*) the area to be analyzed by transmission electron microscopy.

The layers SiC1.4, SiC0.95 and SiC0.7 are solid, homogeneous, fine polycrystalline films (Figs. 4a-c, 5a, b and 6a, b, light areas, respectively). Some electron diffraction patterns contain superimposed point (*c*-Si) and ring (SiC) electron diffraction patterns (Fig.4b, c, 5b and 6b).

The Formation of Silicon Carbide in the SiCx Layers

**200 nm**

**a)** 

(x = 0.03–1.4) Formed by Multiple Implantation of C Ions in Si 77

Fig. 6. Electron diffraction patterns and microstructure (×50000) of the SiC0.7 layer after annealing at temperature 12000С for 30 min: rings – SiC, point reflections – Si, bright regions – SiC0.7 layer, dark regions – c-Si. a) SiC0.7 region; b) SiC0.7 regions + intermediate Si–SiC0.7 layer + с-Si, c) SiC crystallites in dark-field image regime: (*1*) SiC0.7 regions, (*2*) regions of an

The value of D⋅d of device, calculated from the point patterns of the silicon lattice, was equal D⋅d = (3.53±0.01) nm⋅mm. The diameters D of the most intensive rings of SiC1.4 pattern were 10.4, 14.0, 22.9 and 26.9 mm, corresponding to the (002) plane of graphite (d = 0.338 nm) and silicon carbide β-SiC(111), β-SiC(220), β-SiC(311) (Fig. 4), respectively. The absence of some rings on the patterns is caused by their weak intensity. The diameters of the most intensive rings of SiC0.95 were also 14.0, 22.9 and 26.9 mm and correspond to β-SiC(111), β-SiC(220), β-SiC(311) (Fig. 5). The diameters of rings of SiC0.7 diffraction pattern were 14.0, 22.9, 26.9, 28.0, 35.3, 39.7 mm (Fig. 6) and agree well with the calculated values of the diameters of 1, 3, 4, 5, 7 and 9 of the silicon carbide rings, corresponding to a system of planes β-SiC(111), β-SiC(220), β-SiC(311), β-SiC(222), β-SiC(331), β-SiC(422), (d = 0.2518 nm, 0.1542 nm, 0.1311 nm, 0.1259 nm, 0.1000 nm, 0.0890 nm, respectively). Graphite rings in the electron diffraction patterns of SiC0.7 and SiC0.95 are not explicitly observed, which may be due to the absence of excess carbon. In dark-field image regime the individual grains are visible as bright light spots. For a layer SiC0.95 (Fig. 5c), as well as for the layer SiC1.4, the presence of small and large grains of size from 10 to 80 nm was observed. The crystallites have various shapes - globular or plate-like. For a layer SiC0.7 (Fig. 6c) crystallites were globular, needle or plate-like and had sizes from 10 to 400 nm after annealing at 1200ºC. Small crystallites have a globular shape. These data differ from the X-ray diffraction data which was 5**−**10 nm (Akimchenko et al., 1977, 1980, Calcagno et al., 1996). It should be noted that by X-ray diffraction the average crystallite size was determined. In the layer SiC0.7 due to the high concentration of carbon atoms one can expect a large number of stable clusters that hinder the crystallization process. In this case a significant prevalence of nanocrystals of a few nanometers sizes can be expected that are making a major contribution to the value of the average grain size. Small nanocrystals should give a reflection of the size in hundredths and tenths of a millimeter on the pattern, it is difficult to distinguish them and they are observed as a bright diffuse background

**200 nm**

**c)** 

**b)** 

**1** 

**2** 

**3** 

intermediate Si–SiC0.7 layer, (*3*) double-diffraction regions

between the larger crystallites (Fig. 6c).

These patterns were recorded from areas 3 where the objects were presented together with single- and polycrystalline structures (for example Si + SiC1.4). In Figs. 4b, 5b and 6b the microstructure of sections 1 (light area), 2 (intermediate region) and 3 (dark area) are shown.

Fig. 4. Electron diffraction patterns and microstructure (×50000) of the SiC1.4 layer after annealing at temperature 12000С for 30 min: rings – SiC, point reflections – Si, bright regions – SiC1.4 layer, dark regions – c-Si. a) SiC1.4 region; b) SiC1.4 regions + intermediate Si– SiC1.4 layer + с-Si: (*1*) SiC1.4 regions, (*2*) regions of an intermediate Si– SiC1.4 layer, (*3*) doublediffraction regions.

Fig. 5. Electron diffraction patterns and microstructure (×50000) of the SiC0.95 layer after annealing at temperature 12000С for 30 min: rings – SiC, point reflections – Si, bright regions – SiC0.95 layer, dark regions – c-Si. a) SiC0.95 region; b) SiC0.95 regions + intermediate Si– SiC0.95 layer + с-Si, c) SiC crystallites in dark-field image regime: (*1*) SiC0.95 regions, (*2*) regions of an intermediate Si–SiC0.95 layer, (*3*) double-diffraction regions, (4) SiC crystallites.

These patterns were recorded from areas 3 where the objects were presented together with single- and polycrystalline structures (for example Si + SiC1.4). In Figs. 4b, 5b and 6b the microstructure of sections 1 (light area), 2 (intermediate region) and 3 (dark area) are shown.

**a) b)** 

**1 1 2 3** 

Fig. 4. Electron diffraction patterns and microstructure (×50000) of the SiC1.4 layer after annealing at temperature 12000С for 30 min: rings – SiC, point reflections – Si, bright regions – SiC1.4 layer, dark regions – c-Si. a) SiC1.4 region; b) SiC1.4 regions + intermediate Si– SiC1.4 layer + с-Si: (*1*) SiC1.4 regions, (*2*) regions of an intermediate Si– SiC1.4 layer, (*3*) double-

**1** 

Fig. 5. Electron diffraction patterns and microstructure (×50000) of the SiC0.95 layer after annealing at temperature 12000С for 30 min: rings – SiC, point reflections – Si, bright regions – SiC0.95 layer, dark regions – c-Si. a) SiC0.95 region; b) SiC0.95 regions + intermediate Si– SiC0.95 layer + с-Si, c) SiC crystallites in dark-field image regime: (*1*) SiC0.95 regions, (*2*) regions of an intermediate Si–SiC0.95 layer, (*3*) double-diffraction regions, (4) SiC crystallites.

**1 2 3** 

**4** 

**a) b) c)** 

diffraction regions.

Fig. 6. Electron diffraction patterns and microstructure (×50000) of the SiC0.7 layer after annealing at temperature 12000С for 30 min: rings – SiC, point reflections – Si, bright regions – SiC0.7 layer, dark regions – c-Si. a) SiC0.7 region; b) SiC0.7 regions + intermediate Si–SiC0.7 layer + с-Si, c) SiC crystallites in dark-field image regime: (*1*) SiC0.7 regions, (*2*) regions of an intermediate Si–SiC0.7 layer, (*3*) double-diffraction regions

The value of D⋅d of device, calculated from the point patterns of the silicon lattice, was equal D⋅d = (3.53±0.01) nm⋅mm. The diameters D of the most intensive rings of SiC1.4 pattern were 10.4, 14.0, 22.9 and 26.9 mm, corresponding to the (002) plane of graphite (d = 0.338 nm) and silicon carbide β-SiC(111), β-SiC(220), β-SiC(311) (Fig. 4), respectively. The absence of some rings on the patterns is caused by their weak intensity. The diameters of the most intensive rings of SiC0.95 were also 14.0, 22.9 and 26.9 mm and correspond to β-SiC(111), β-SiC(220), β-SiC(311) (Fig. 5). The diameters of rings of SiC0.7 diffraction pattern were 14.0, 22.9, 26.9, 28.0, 35.3, 39.7 mm (Fig. 6) and agree well with the calculated values of the diameters of 1, 3, 4, 5, 7 and 9 of the silicon carbide rings, corresponding to a system of planes β-SiC(111), β-SiC(220), β-SiC(311), β-SiC(222), β-SiC(331), β-SiC(422), (d = 0.2518 nm, 0.1542 nm, 0.1311 nm, 0.1259 nm, 0.1000 nm, 0.0890 nm, respectively). Graphite rings in the electron diffraction patterns of SiC0.7 and SiC0.95 are not explicitly observed, which may be due to the absence of excess carbon. In dark-field image regime the individual grains are visible as bright light spots. For a layer SiC0.95 (Fig. 5c), as well as for the layer SiC1.4, the presence of small and large grains of size from 10 to 80 nm was observed. The crystallites have various shapes - globular or plate-like. For a layer SiC0.7 (Fig. 6c) crystallites were globular, needle or plate-like and had sizes from 10 to 400 nm after annealing at 1200ºC. Small crystallites have a globular shape. These data differ from the X-ray diffraction data which was 5**−**10 nm (Akimchenko et al., 1977, 1980, Calcagno et al., 1996). It should be noted that by X-ray diffraction the average crystallite size was determined. In the layer SiC0.7 due to the high concentration of carbon atoms one can expect a large number of stable clusters that hinder the crystallization process. In this case a significant prevalence of nanocrystals of a few nanometers sizes can be expected that are making a major contribution to the value of the average grain size. Small nanocrystals should give a reflection of the size in hundredths and tenths of a millimeter on the pattern, it is difficult to distinguish them and they are observed as a bright diffuse background between the larger crystallites (Fig. 6c).

The Formation of Silicon Carbide in the SiCx Layers

β-SiC(111) ~ 3 nm, β-SiC(220) ~ 6.5 nm, Si(111) ~ 4.5 nm.

**0,6**

**0,7**

**0,8**

**I, arb.un.**

**0,9**

**1,0**

**b)** 

**а)** 

(x = 0.03–1.4) Formed by Multiple Implantation of C Ions in Si 79

destructive effect of plasma on the structure of the β-SiC crystallites, although the capacity of plasma was only 12,5 W, and SiC on the hardness scale, according to Knoop holds a high place (SiC, 2480) after diamond (C, 7000), boron carbide (B4C , 2750), and aluminum boride (AlB, 2500). In addition, the processing by H-plasma for 5 minutes led to complete disappearance of the lines Si(111) and Si(220), reflected by the crystallites of silicon in the transition layer "filmsubstrate" ("SiC-Si"). It follows that the effect of hydrogen plasma propagates on the entire depth of the implanted layer (200 nm) and involves a intensive penetration of hydrogen ions through the solid film. Thus, the characteristics of the hydrogen glow discharge plasma and treatment (27.12 MHz, 12.5 W, 6.5 Pa, 100°С, 5 min) were sufficient to break the Si-Si and Si-C tetrahedral bonds and can be used to decay the stable carbon and carbon-silicon clusters. Immediately after implantation and annealing of the SiC0.95 layer at 1100ºC and below (Fig. 8a) on the diffraction patterns not seen any lines of polycrystalline phases. A weak line of β-SiC(111) after annealing at 1150ºC is observed, which becomes more pronounced after annealing at 12500С (Fig. 8b). In contrast to the layers SiC1.4 and SiC0.95, the diffraction pattern of the SiC0.7 layer (Fig. 8c) demonstrates the presence of β-SiC(111) line and weak Si (111) line after annealing at relatively low temperature of 1000ºC for 30 minutes, due to the decrease of carbon concentration and, consequently, the concentration of stable carbon clusters. Annealing at 1100ºC led to an increase in the intensity of the β-SiC(111) and Si(111) lines (Fig. 8d) and to an appearance of β-SiC(200), β-SiC(220), β-SiC(311) и Si(220) lines, which indicates an improvement in the crystallite structure. Line intensity from the SiC0.7 layer shows a preferred content of polycrystalline β-SiC phase after annealing in comparison with the phase content of poly-Si, which is caused by a relatively high concentration of carbon. The average crystallite size of β-SiC and Si was about 3–7 nm in the planes:

**d)** 

**0**

θ**, degree 2**θ**, degree**  Fig. 8. X-ray diffraction patterns of the SiC0.95 layer annealed at (a) 1100ºС, (b) 1250°C and of the SiC0.7 layer annealed at (c) 1000ºС, (d) 1100°C , for 30 min obtained using X-ray chambers RKD (a, b) and RKU-114M1 (c, d). Intensity curves correspond to X-ray patterns (b, d).

**10 30 50 70 2**Η**, degree**

**Si (111)**

**Si**

**Si**

**С (200)**

**С (111)**

**Si (220)**

**Si**

**Si**

**С (311)**

**С (220)**

**0,1**

**0,2**

**0,3**

**I, ar**

**10 20 30 2, degree**

**b.un.**

**Si (substrate)**

**Si**

**С (111)**

**0,4**

**0,5**

**0,6**

**c)** 

Transition layer with a lower concentration of carbon between the Si substrate and SiC0.7 is not uniform. It can be assumed that excess silicon atoms that are between the large SiC grains, in the process of recrystallization are combined with the substrate, forming a sawtooth SiC–Si structure (Fig. 6b).

#### **3.3 Investigation of the structure by X-ray diffraction**

After annealing of the SiC1.4 layer in vacuum 10-4 Pa at temperatures 1200 and 1400°С in the Xray diffraction patterns the intensive lines of polycrystalline silicon carbide are observed (Fig. 7a, b). There are also weak lines of polycrystalline silicon, apparently, from the transition layer "Si–SiC1.4", where presents excess silicon, forming in the annealing process the Si crystallites. The integrated intensity of SiC lines after annealing at 1400°C was significantly lower than after annealing at 1200°C. This may occur because of the disintegration of silicon carbide and desorption of carbon from the layer at temperatures above 950°С (see section 3.1). The decrease in phase volume of nanocrystalline SiC at temperatures above 1200ºC can also occur due to evaporation of silicon in a vacuum, the melting point (1423ºC) of which is less than the sublimation temperature of carbon (Semenov et al., 2009).

Fig. 7. X-ray diffraction patterns of the SiC1.4 layer annealed for 30 min at (a) 1200 ºС, (b) 1400°C, (c) after annealing at 1400°C and processing by glow discharge hydrogen plasma for 5 min.

An absence of SiC crystallites and the corresponding X-ray lines at high annealing temperatures 900–1100°C indicates a low ability of atoms to diffusion in the layer SiC1.4. This may be caused by high concentrations of stable double and triple bonds like Si=C, Si≡C, C=C, C≡С, Si=Si, Si≡Si and strong clusters that prevent the diffusion of atoms in the layer and are decomposed at temperatures of 1200°C and above. An attempt was made to use processing by the hydrogen glow discharge plasma for the modification of the structural properties of the SiCх films. For this purpose, the SiC1.4 layer annealed at 1400ºC was treated by the hydrogen glow discharge plasma (27.12 MHz, 12.5 W, 6.5 Pa, 100°С, 5 min).

After treatment by H-plasma is not taken place the complete destruction of the SiC crystallites (Fig. 7c). However, the intensity of X-ray lines of SiC decreased in comparison with the corresponding lines on the diffraction pattern before treatment (Fig. 7b). This demonstrates the

Transition layer with a lower concentration of carbon between the Si substrate and SiC0.7 is not uniform. It can be assumed that excess silicon atoms that are between the large SiC grains, in the process of recrystallization are combined with the substrate, forming a

After annealing of the SiC1.4 layer in vacuum 10-4 Pa at temperatures 1200 and 1400°С in the Xray diffraction patterns the intensive lines of polycrystalline silicon carbide are observed (Fig. 7a, b). There are also weak lines of polycrystalline silicon, apparently, from the transition layer "Si–SiC1.4", where presents excess silicon, forming in the annealing process the Si crystallites. The integrated intensity of SiC lines after annealing at 1400°C was significantly lower than after annealing at 1200°C. This may occur because of the disintegration of silicon carbide and desorption of carbon from the layer at temperatures above 950°С (see section 3.1). The decrease in phase volume of nanocrystalline SiC at temperatures above 1200ºC can also occur due to evaporation of silicon in a vacuum, the melting point (1423ºC) of which is less than the

**0,4**

10 30 50 70 90 110 **2**θ**, degree** 

Fig. 7. X-ray diffraction patterns of the SiC1.4 layer annealed for 30 min at (a) 1200 ºС, (b) 1400°C, (c) after annealing at 1400°C and processing by glow discharge hydrogen plasma for 5 min.

An absence of SiC crystallites and the corresponding X-ray lines at high annealing temperatures 900–1100°C indicates a low ability of atoms to diffusion in the layer SiC1.4. This may be caused by high concentrations of stable double and triple bonds like Si=C, Si≡C, C=C, C≡С, Si=Si, Si≡Si and strong clusters that prevent the diffusion of atoms in the layer and are decomposed at temperatures of 1200°C and above. An attempt was made to use processing by the hydrogen glow discharge plasma for the modification of the structural properties of the SiCх films. For this purpose, the SiC1.4 layer annealed at 1400ºC was treated

After treatment by H-plasma is not taken place the complete destruction of the SiC crystallites (Fig. 7c). However, the intensity of X-ray lines of SiC decreased in comparison with the corresponding lines on the diffraction pattern before treatment (Fig. 7b). This demonstrates the

by the hydrogen glow discharge plasma (27.12 MHz, 12.5 W, 6.5 Pa, 100°С, 5 min).

**10 30 50 70 90 110 2**θ**, degree**

**2**θ**, degree** 

**2**θ**2**θ**, degree , degree**

**Si**

**С (220)**

**0,6**

**0,8**

**1,0**

**Si (111)**

**Si**

**С (111)**

**1,2**

**1,4**

**c)** 

sawtooth SiC–Si structure (Fig. 6b).

**3.3 Investigation of the structure by X-ray diffraction** 

sublimation temperature of carbon (Semenov et al., 2009).

Si

Si

С (422)

С (331)

0,2

0,4

0,6

0,8

Si (111)

Si

Si

С (200)

С (111)

Si (220)

Si

Si

С (311)

С (220)

1,0

1,2

**a) b)**

10 30 50 70 90 110 **2**θ**, degree**

0,6

0,8

1,0

1,2

Si (111)

Si

С (111)

Si (220)

Si

Si

Si

С (311)

С (220)

С (200)

**I, arb. units**

1,4

1,6

destructive effect of plasma on the structure of the β-SiC crystallites, although the capacity of plasma was only 12,5 W, and SiC on the hardness scale, according to Knoop holds a high place (SiC, 2480) after diamond (C, 7000), boron carbide (B4C , 2750), and aluminum boride (AlB, 2500). In addition, the processing by H-plasma for 5 minutes led to complete disappearance of the lines Si(111) and Si(220), reflected by the crystallites of silicon in the transition layer "filmsubstrate" ("SiC-Si"). It follows that the effect of hydrogen plasma propagates on the entire depth of the implanted layer (200 nm) and involves a intensive penetration of hydrogen ions through the solid film. Thus, the characteristics of the hydrogen glow discharge plasma and treatment (27.12 MHz, 12.5 W, 6.5 Pa, 100°С, 5 min) were sufficient to break the Si-Si and Si-C tetrahedral bonds and can be used to decay the stable carbon and carbon-silicon clusters.

Immediately after implantation and annealing of the SiC0.95 layer at 1100ºC and below (Fig. 8a) on the diffraction patterns not seen any lines of polycrystalline phases. A weak line of β-SiC(111) after annealing at 1150ºC is observed, which becomes more pronounced after annealing at 12500С (Fig. 8b). In contrast to the layers SiC1.4 and SiC0.95, the diffraction pattern of the SiC0.7 layer (Fig. 8c) demonstrates the presence of β-SiC(111) line and weak Si (111) line after annealing at relatively low temperature of 1000ºC for 30 minutes, due to the decrease of carbon concentration and, consequently, the concentration of stable carbon clusters. Annealing at 1100ºC led to an increase in the intensity of the β-SiC(111) and Si(111) lines (Fig. 8d) and to an appearance of β-SiC(200), β-SiC(220), β-SiC(311) и Si(220) lines, which indicates an improvement in the crystallite structure. Line intensity from the SiC0.7 layer shows a preferred content of polycrystalline β-SiC phase after annealing in comparison with the phase content of poly-Si, which is caused by a relatively high concentration of carbon. The average crystallite size of β-SiC and Si was about 3–7 nm in the planes: β-SiC(111) ~ 3 nm, β-SiC(220) ~ 6.5 nm, Si(111) ~ 4.5 nm.

Fig. 8. X-ray diffraction patterns of the SiC0.95 layer annealed at (a) 1100ºС, (b) 1250°C and of the SiC0.7 layer annealed at (c) 1000ºС, (d) 1100°C , for 30 min obtained using X-ray chambers RKD (a, b) and RKU-114M1 (c, d). Intensity curves correspond to X-ray patterns (b, d).

The Formation of Silicon Carbide in the SiCx Layers

**0,0**

20 300 600 900 1200

**1**

С

**3**

Fig. 11. Average sizes (a) of Si and SiC crystallites in the (111) plane and (b) the integrated intensities of the Si(111) and SiC(111) lines after implantation of carbon ions in silicon and annealing. 1 − Si (for layer SiC**0.03**), 2 − Si (for layer SiC**0.12**), 3 − SiС (for layer SiC**0.12**).

**2**

Temperature, <sup>o</sup>

**10 20 30 40 50 60** θ**, degree**

at (b) 1100ºС and (c) 1250°C.

**a)**

0

10

20

30

Crystallite sizes, nm .

40

50

**Si (matrix)**

**1,1**

**1,6**

**2,1**

**2,6**

**I, arb. units**

**3,1**

**Si (111)**

**3,6**

**0,5**

**1,0**

**1,5**

**2,0**

**Si (111)**

**a) b) c)**

**Si (220)**

**SiC (111)**

**Si (311)**

**Si (matrix)**

**SiC (311)**

**Si (422)**

**Si (511)**

**2,5**

(x = 0.03–1.4) Formed by Multiple Implantation of C Ions in Si 81

**0,2**

**10 20 30 40 50 60** θ**, degree**

Fig. 10. X-ray diffraction patterns of the SiC0.12 layer (a) before and after annealing for 30 min

θ**, degree** θ**, degree** θ**, degree** 

0,00

0,04

0,08

Iint, arb.un.

0,12

0,16

**10 20 30 40 50 60** θ**, degree**

2

20 300 600 900 1200 Temperature, <sup>o</sup>

3

1

**b)**

С

**0,7**

**1,2**

**1,7**

**2,2**

**Si (531)** 

**2,7**

**Si (111)**

**SiC (111)**

**Si (220)**

**Si (311)**

**SiC (220)**

**SiC (311)**

**Si (422)**

**SiC (400)**

**SiC (331)**

**SiC (422)**

**Si (331)**

**Si (511)**

**Si (531) Si (matrix)**

In the layer SiC0.4 the presence of polycrystalline phases of SiC and Si after implantation and annealing at 1000, 1100 and 1250°C are revealed. High intensity peaks of SiC after annealing at 1100ºC (Fig. 9a) indicates on intensive process of crystallization of β-SiC due to lower content of stable clusters in comparison with the layers SiC1.4, SiC0.95 and SiC0.7. High amplitude of β-SiC peaks after annealing at 1250оС confirms this assertion. In diffraction pattern of SiC0.12 layer after implantation a broad diffuse line of amorphous silicon Si(111) (θ = 14.3º) is observed (Fig.10a). After annealing at 800ºC a narrowing of this line, at 900ºC a sharp narrowing of the line Si(111) and the appearance of Si(220) and Si(311) lines of polycrystalline Si phase, as well as two weak lines of β-SiC, at 1250ºC - a decrease of the integrated intensity of Si lines, are observed.

Fig. 9. X-ray diffraction patterns of the SiC0.4 layer annealed for 30 min at (a) 1100ºС and (b) 1250°C.

The implantation of carbon causes the formation of weakly ordered set of randomly oriented Si regions of size ~1.5 nm. Temperature dependence of the average crystallite size Si (Fig. 11a, curve 1) and SiC (curve 2) in plane (111) shows that at low temperatures the curve 1 is characterized by slow growth in the size of weakly ordered Si nanocrystals. Their transformation into well ordered Si crystallites at 800ºC is taken place. Average size of Si crystallites is 47 nm after annealing at 1250ºC. The formation of β-SiC crystallites prevent a complete recrystallization of layer at this temperature.

The integrated intensity curve of Si(111) line, which is proportional to the phase volume, has three sections in the temperature ranges of 20– 800ºC, 800−900ºC and 900−1250ºC (Fig. 11b). In the range of 20-800ºC Iint decreases, indicating a decrease in the total volume of nanocrystals Si, although their sizes increase up to 2.2 nm. The growth of weak ordered Si crystallites is accompanied by the displacement of carbon atoms in the surrounding space, which no longer contribute to the intensity of the Si (111) line due to increased concentration of carbon. In addition, there is recrystallization of silicon near the substrate. It is assumed that, after annealing at 800ºC (Figs. 11b and 12) approximately k800 ≈ [Iint(800ºС)/Iint(20ºС)]×100% = 72% of silicon atoms in the layer is incorporated into crystallites of Si. The remaining atoms of Si (28%) are in an amorphous mixture of Si and C atoms, or reunited with the substrate.

In the layer SiC0.4 the presence of polycrystalline phases of SiC and Si after implantation and annealing at 1000, 1100 and 1250°C are revealed. High intensity peaks of SiC after annealing at 1100ºC (Fig. 9a) indicates on intensive process of crystallization of β-SiC due to lower content of stable clusters in comparison with the layers SiC1.4, SiC0.95 and SiC0.7. High amplitude of β-SiC peaks after annealing at 1250оС confirms this assertion. In diffraction pattern of SiC0.12 layer after implantation a broad diffuse line of amorphous silicon Si(111) (θ = 14.3º) is observed (Fig.10a). After annealing at 800ºC a narrowing of this line, at 900ºC a sharp narrowing of the line Si(111) and the appearance of Si(220) and Si(311) lines of polycrystalline Si phase, as well as two weak lines of β-SiC, at 1250ºC - a decrease of the

**0,4**

**10 20 30 40** θ**, degree**

**Si**

**С (111)**

Si (substrate)

**Si (311)**

**Si**

**Si**

**С (311)**

**С (220)**

**Si (220)**

**0,6**

**0,8**

**1,0**

**I, arb.un.**

Fig. 9. X-ray diffraction patterns of the SiC0.4 layer annealed for 30 min at (a) 1100ºС and (b)

The implantation of carbon causes the formation of weakly ordered set of randomly oriented Si regions of size ~1.5 nm. Temperature dependence of the average crystallite size Si (Fig. 11a, curve 1) and SiC (curve 2) in plane (111) shows that at low temperatures the curve 1 is characterized by slow growth in the size of weakly ordered Si nanocrystals. Their transformation into well ordered Si crystallites at 800ºC is taken place. Average size of Si crystallites is 47 nm after annealing at 1250ºC. The formation of β-SiC crystallites prevent a

The integrated intensity curve of Si(111) line, which is proportional to the phase volume, has three sections in the temperature ranges of 20– 800ºC, 800−900ºC and 900−1250ºC (Fig. 11b). In the range of 20-800ºC Iint decreases, indicating a decrease in the total volume of nanocrystals Si, although their sizes increase up to 2.2 nm. The growth of weak ordered Si crystallites is accompanied by the displacement of carbon atoms in the surrounding space, which no longer contribute to the intensity of the Si (111) line due to increased concentration of carbon. In addition, there is recrystallization of silicon near the substrate. It is assumed that, after annealing at 800ºC (Figs. 11b and 12) approximately k800 ≈ [Iint(800ºС)/Iint(20ºС)]×100% = 72% of silicon atoms in the layer is incorporated into crystallites of Si. The remaining atoms of Si (28%) are in an amorphous mixture of Si and

**Si**

**С (220)**

**5 15 25 35 45** θ**, degree**

**SiC (111)**

**Si (220)**

**Si (311)**

**1,2**

**Si (111)**

**b)**

**1,4**

**1,6**

integrated intensity of Si lines, are observed.

**Si (111)**

complete recrystallization of layer at this temperature.

C atoms, or reunited with the substrate.

**а)**

**0,1**

**0,3**

**0,5**

**0,7**

**I, arb.un.**

1250°C.

**0,9**

**1,1**

**1,3**

Fig. 10. X-ray diffraction patterns of the SiC0.12 layer (a) before and after annealing for 30 min at (b) 1100ºС and (c) 1250°C.

Fig. 11. Average sizes (a) of Si and SiC crystallites in the (111) plane and (b) the integrated intensities of the Si(111) and SiC(111) lines after implantation of carbon ions in silicon and annealing. 1 − Si (for layer SiC**0.03**), 2 − Si (for layer SiC**0.12**), 3 − SiС (for layer SiC**0.12**).

The Formation of Silicon Carbide in the SiCx Layers

characteristic of crystalline phases of Si and SiC.

**Si (111) .**

**Si**

**Si**

**С (200)** 

**.** 

**С (111) .**

**0,25**

recrystallization near the substrate.

**0,35**

**0,45**

**0,55**

**I, arb.units**

**0,65**

**0,75**

(x = 0.03–1.4) Formed by Multiple Implantation of C Ions in Si 83

two grains is taken place, if it is accompanied by a gain in energy which is greater than its costs for the destruction of the crystallites. In this case, the redistribution of atoms with a change in chemical bond lengths and angles between them is taken place, in order to select a more favorable energy state, which is the states with tetrahedral oriented bonds,

**10 30 50 70 90**

The X-ray diffraction results are in accordance with the data of Auger electron spectroscopy, whereby the concentration of carbon atoms in a layer is NC/NSi = 0.12/1 (Fig. 2). Then the maximum possible ratio of atoms, forming part of SiC and Si, will be: NSiC/NSi = 0.24/0.88 = 0.27. As seen in Figure 11b, the maximum quantity of poly-SiC, obtained at 1250ºC, was Iint(SiC) = 0.040, and poly-Si was Iint(Si) = 0.131 at 900ºС, i.e., Iint(SiC)/Iint(Si) = 0.040/0.131 =

Similar features are observed for a layer with a lower carbon concentration SiC0.03. Immediately after the implantation the same broad diffuse line of amorphous silicon Si(111) at θ = 14.3º is observed (Fig. 14). Increase of annealing temperature above 800ºC causes narrowing of this line, increasing the number and amplitude of the line intensity which reaches its maximum at 1100ºC. However, in the X-ray diffraction patterns of SiC0.03 layer no lines of polycrystalline silicon carbide in the whole temperature range are observed due to insufficient concentration of the carbon atoms to form a large number of SiC crystallites. Annealing at temperatures above 1100º C reduces the intensity of Si lines and results their

For comparison, in Table 3 the grain sizes of silicon and silicon carbide in plane (111) in layers Si(111) and β-SiС(111) are given. Dimensions of weakly ordered regions in SiC0.03 layer, contributing to the intensity of the Si(111) line, exceed the same values for SiC0.12. This is associated with a lower concentration of carbon and larger volume of Si regions with extremely low concentrations of carbon. At temperatures of 1200 and 1250ºC a decrease in the average crystallite size up to 10 nm is observed, which is associated with the process of

Fig. 13. X-ray diffraction pattern of the SiC0.12 layer after annealing at 1400°C for 30 min.

0.30, which is comparable with the data of Auger electron spectroscopy.

disappearance after annealing at 1250ºC due to recrystallization of the layer.

**Si (220) .**

**Si**

**Si**

**С (311) .**

**С (220) .**

**2**θ**, degree**

Fig. 12 schematically shows the variation of the structure of the layer, its phase composition and phase volume, as well as the average grain size as a function of annealing temperature (a) and scheme of Si and SiC crystallite formation in this layer (b). The diagram is based on the curves in Fig. 11a, b for SiC0.12. Regions "amorphous Si-C mixture" and "c-Si" are formed adhering to the relation: "amorphous Si-C mixture" + "c-Si" = 100% − ("poly-SiC" + "poly-Si"+"amorphous -Si").

Fig. 12. Crystallization of the SiC0.12 layer: (a) the phase volumes at various annealing temperatures and (b) the formation of crystalline Si and SiC crystallites in the temperature range 900−1000°C.

In the range of 800−900°C the increase in both size crystallites Si (from 2.2 to 4.7 nm) and the volume of polycrystalline phase of Si (Fig. 11a and 12) is observed. This is due to the formation of SiC crystallites at 900°C in the regions of carbon accumulation and the joining of excess silicon atoms to Si crystallites. So, k is increased: k900 ≈ 82%. This leads to a decrease in Si−C-mixture volume (Fig. 12). After annealing at 1000ºC and 1250ºC, an increase in the phase volume and crystallite sizes of β-SiC as well as a decrease in k due to recrystallization of regions near the Si substrate, are taken place: k1000 ≈ 73% and k1250 ≈ 46%. Si crystallite sizes increased almost 10 times (up to 47 nm). Probably, there is destruction of defective silicon crystallites and the uniting of their atoms into crystallites with a perfect structure or with the substrate. As can be seen from the diagram, after annealing at 1200°C in the layer SiC0.12 ~50% of silicon atoms are incorporated into Si crystallites with an average size of 25 nm, 25% of Si atoms are included into β-SiC crystallite with size of 5 nm and 25% are joined with Si substrate. Since the unit cell volume for Si is twice more than the cell volume for SiC, the volume of the surface layer of Si after implantation and annealing of carbon should not change appreciably, and the above relations can be regarded as a volume ratio of phases.

During annealing at 1400ºC there is the destruction of most of the silicon crystallites and connection of their atoms to the substrate. The intensity of the lines Si was significantly lower than the intensities of β-SiC lines (Fig. 13). It is assumed that recrystallized Si layer with ingrained in him crystallites of β-SiC and Si on a silicon substrate was obtained.

During a growth of the crystallite size is manifested basic thermodynamic law: in an isolated system, the processes occurring with increasing free energy, is prohibited. Combining the

Fig. 12 schematically shows the variation of the structure of the layer, its phase composition and phase volume, as well as the average grain size as a function of annealing temperature (a) and scheme of Si and SiC crystallite formation in this layer (b). The diagram is based on the curves in Fig. 11a, b for SiC0.12. Regions "amorphous Si-C mixture" and "c-Si" are formed adhering to the relation: "amorphous Si-C mixture" + "c-Si" = 100% − ("poly-SiC" + "poly-

Fig. 12. Crystallization of the SiC0.12 layer: (a) the phase volumes at various annealing temperatures and (b) the formation of crystalline Si and SiC crystallites in the temperature

with ingrained in him crystallites of β-SiC and Si on a silicon substrate was obtained.

During a growth of the crystallite size is manifested basic thermodynamic law: in an isolated system, the processes occurring with increasing free energy, is prohibited. Combining the

In the range of 800−900°C the increase in both size crystallites Si (from 2.2 to 4.7 nm) and the volume of polycrystalline phase of Si (Fig. 11a and 12) is observed. This is due to the formation of SiC crystallites at 900°C in the regions of carbon accumulation and the joining of excess silicon atoms to Si crystallites. So, k is increased: k900 ≈ 82%. This leads to a decrease in Si−C-mixture volume (Fig. 12). After annealing at 1000ºC and 1250ºC, an increase in the phase volume and crystallite sizes of β-SiC as well as a decrease in k due to recrystallization of regions near the Si substrate, are taken place: k1000 ≈ 73% and k1250 ≈ 46%. Si crystallite sizes increased almost 10 times (up to 47 nm). Probably, there is destruction of defective silicon crystallites and the uniting of their atoms into crystallites with a perfect structure or with the substrate. As can be seen from the diagram, after annealing at 1200°C in the layer SiC0.12 ~50% of silicon atoms are incorporated into Si crystallites with an average size of 25 nm, 25% of Si atoms are included into β-SiC crystallite with size of 5 nm and 25% are joined with Si substrate. Since the unit cell volume for Si is twice more than the cell volume for SiC, the volume of the surface layer of Si after implantation and annealing of carbon should not change appreciably, and the above relations can be regarded as a volume ratio of phases. During annealing at 1400ºC there is the destruction of most of the silicon crystallites and connection of their atoms to the substrate. The intensity of the lines Si was significantly lower than the intensities of β-SiC lines (Fig. 13). It is assumed that recrystallized Si layer

Si"+"amorphous -Si").

range 900−1000°C.

two grains is taken place, if it is accompanied by a gain in energy which is greater than its costs for the destruction of the crystallites. In this case, the redistribution of atoms with a change in chemical bond lengths and angles between them is taken place, in order to select a more favorable energy state, which is the states with tetrahedral oriented bonds, characteristic of crystalline phases of Si and SiC.

Fig. 13. X-ray diffraction pattern of the SiC0.12 layer after annealing at 1400°C for 30 min.

The X-ray diffraction results are in accordance with the data of Auger electron spectroscopy, whereby the concentration of carbon atoms in a layer is NC/NSi = 0.12/1 (Fig. 2). Then the maximum possible ratio of atoms, forming part of SiC and Si, will be: NSiC/NSi = 0.24/0.88 = 0.27. As seen in Figure 11b, the maximum quantity of poly-SiC, obtained at 1250ºC, was Iint(SiC) = 0.040, and poly-Si was Iint(Si) = 0.131 at 900ºС, i.e., Iint(SiC)/Iint(Si) = 0.040/0.131 = 0.30, which is comparable with the data of Auger electron spectroscopy.

Similar features are observed for a layer with a lower carbon concentration SiC0.03. Immediately after the implantation the same broad diffuse line of amorphous silicon Si(111) at θ = 14.3º is observed (Fig. 14). Increase of annealing temperature above 800ºC causes narrowing of this line, increasing the number and amplitude of the line intensity which reaches its maximum at 1100ºC. However, in the X-ray diffraction patterns of SiC0.03 layer no lines of polycrystalline silicon carbide in the whole temperature range are observed due to insufficient concentration of the carbon atoms to form a large number of SiC crystallites. Annealing at temperatures above 1100º C reduces the intensity of Si lines and results their disappearance after annealing at 1250ºC due to recrystallization of the layer.

For comparison, in Table 3 the grain sizes of silicon and silicon carbide in plane (111) in layers Si(111) and β-SiС(111) are given. Dimensions of weakly ordered regions in SiC0.03 layer, contributing to the intensity of the Si(111) line, exceed the same values for SiC0.12. This is associated with a lower concentration of carbon and larger volume of Si regions with extremely low concentrations of carbon. At temperatures of 1200 and 1250ºC a decrease in the average crystallite size up to 10 nm is observed, which is associated with the process of recrystallization near the substrate.

The Formation of Silicon Carbide in the SiCx Layers

**3.4 Investigations by infrared spectroscopy** 

**IR transmittance,** 

**67**

**87**

**65**

**85**

**%**

**17**

**87**

**23**

**83**

**72**

**22**

**68**

**38**

**75**

**45**

**58 63**

**83**

**78**

**63**

**83**

**65 66**

**85**

**86**

temperature range 200−1400°C were measured (Figs. 16−21).

**a) sample**

**90<sup>o</sup>**

T1

**IR-beam**

**500 700 900 1100 Wave number, cm-1** 

(x = 0.03–1.4) Formed by Multiple Implantation of C Ions in Si 85

The influence of carbon concentration in the SiCx layers and annealing temperature on the parameters of the spectra of infrared spectroscopy was investigated. For this purpose, using two-beam infrared spectrometer UR-20 the IR transmission spectra of SiC1.4, SiC0.95, SiC0.7, SiC0.4, SiC0.12 and SiC0.03 layers before and after isochronous annealing in vacuum at

**IR-beam**

**b)**

**59**

**76 56**

**79**

**46**

**66**

**20<sup>o</sup> C**

Fig. 16. IR transmission spectra of the SiC1.4 layer recorded (a) under normal incidence of IR radiation on the sample and (b) at an angle of 73° to the normal to the sample surface.

**200<sup>o</sup> C**

**400<sup>o</sup> C**

**900<sup>o</sup> C**

**800<sup>o</sup> C**

**700<sup>o</sup> C**

**600<sup>o</sup> C**

**1200<sup>o</sup> C**

**1100<sup>o</sup> C**

**1000<sup>o</sup> C**

**1300<sup>o</sup> C**

**1400<sup>о</sup> C**

T2

**78 58**

**82 62**

**78 58**

**76**

**40**

**56**

**60**

**67 37**

**23**

**73**

**16**

**76**

**22**

**72**

**<sup>73</sup><sup>o</sup> <sup>90</sup><sup>o</sup>**

**sample**

**500 700 900 1100**

**-1**

**Wave number, cm**

Fig. 14. X-ray diffraction of SiC0.03 layer after implantation of carbon ions in Si (а) and annealing at 1100°C (b) and 1200°C (c) for 30 min.


Table 3. Average size (ε) of Si- and β-SiC crystallites in SiCx layers

Temperature dependences of the integrated intensity of Si(111) line (Fig. 15) for the SiC0.03 and SiC0.12 layers are similar in nature. A lower carbon concentration in SiC0.03 layer results more intensive decrease in the phase volume of poly-Si at temperatures above 700ºC due to more intensive recrystallization near the substrate. The value of k were: k800 ≈ 40%, k900 ≈ 27%, k1000 ≈ 44%, k1100 ≈ 41%, k1250 ≈ 6%. Growth of k up to 44% at 1000ºC for SiC0.03 layer due to accession of excess silicon atoms from the carbon-rich Si-C-mixture to the Si crystallite is taken place. For a layer SiC0.12, that is observed at a temperature of 100ºC below due to a higher concentration of carbon, therefore the carbon rich region is formed at lower temperatures and does not require significant movements of atoms. Annealing at 1250ºC results in uniting of SiC0.03 layer with single-crystal substrate (K1250×100% = [0,007/0,116]×100% = 6%) and the decrease in the average size of residual crystallites up to 10 nm.

#### **3.4 Investigations by infrared spectroscopy**

84 Silicon Carbide – Materials, Processing and Applications in Electronic Devices

Si (220)

Si (311)

Si (400)

Si (331)

Si (111)

(b)

10 20 30 40 θ, degree

20 2 – 1.1 – – – 700 3 – 1.3 – – – 800 13 – 2 – – –

1000 17 – 5 3 4 3 1100 20 – 7 3.5 4 3

1250 10 – 46 5 9 4.5

Temperature dependences of the integrated intensity of Si(111) line (Fig. 15) for the SiC0.03 and SiC0.12 layers are similar in nature. A lower carbon concentration in SiC0.03 layer results more intensive decrease in the phase volume of poly-Si at temperatures above 700ºC due to more intensive recrystallization near the substrate. The value of k were: k800 ≈ 40%, k900 ≈ 27%, k1000 ≈ 44%, k1100 ≈ 41%, k1250 ≈ 6%. Growth of k up to 44% at 1000ºC for SiC0.03 layer due to accession of excess silicon atoms from the carbon-rich Si-C-mixture to the Si crystallite is taken place. For a layer SiC0.12, that is observed at a temperature of 100ºC below due to a higher concentration of carbon, therefore the carbon rich region is formed at lower temperatures and does not require significant movements of atoms. Annealing at 1250ºC results in uniting of SiC0.03 layer with single-crystal substrate (K1250×100% = [0,007/0,116]×100% = 6%) and the decrease in the average size of residual

ε (nm) SiC0.03 SiC0.12 SiC0.4 Si β-SiC Si β-SiC Si β-SiC

Fig. 14. X-ray diffraction of SiC0.03 layer after implantation of carbon ions in Si (а) and

0.2

900 15 – 4.5 2

1150 27 – 12 4 1200 10 – 25 4.5

Table 3. Average size (ε) of Si- and β-SiC crystallites in SiCx layers

0.6

1.0

1.4

I, arb.un.

Si (matrix)

0.4

Temperature (ºС)

crystallites up to 10 nm.

10 20 30 40 θ, degree

annealing at 1100°C (b) and 1200°C (c) for 30 min.

0.8

1.2

1.6

I, arb.un.

2.0

Si (111)

(a)

2.4

1.8

2.2

0.0

10 20 30 40 θ, degree

0.4

0.8

1.2

I, arb.un.

1.6

Si (111)

(c)

Si (matrix) Si (220)

Si (311)

2.0

The influence of carbon concentration in the SiCx layers and annealing temperature on the parameters of the spectra of infrared spectroscopy was investigated. For this purpose, using two-beam infrared spectrometer UR-20 the IR transmission spectra of SiC1.4, SiC0.95, SiC0.7, SiC0.4, SiC0.12 and SiC0.03 layers before and after isochronous annealing in vacuum at temperature range 200−1400°C were measured (Figs. 16−21).

Fig. 16. IR transmission spectra of the SiC1.4 layer recorded (a) under normal incidence of IR radiation on the sample and (b) at an angle of 73° to the normal to the sample surface.

The Formation of Silicon Carbide in the SiCx Layers

**90o**

 **IR-beam**

a)

**IR transmittance (%)**

**26**

**81**

**76**

**11**

**77**

**27**

**38**

**78**

**90**

**50 59**

**79**

**62**

**82**

**63**

**83 83**

**63**

**85**

**65**

**87**

**67**

**67**

**87**

**500 700 900 1100 Wave number, cm-1** 

(x = 0.03–1.4) Formed by Multiple Implantation of C Ions in Si 87

**sample**

 **IR-beam**

б)

**70 40**

**75 55**

**77 57**

**20o C**

Fig. 17. IR transmission spectra of the SiC0.95 layer recorded (a) under normal incidence of IR radiation on the sample and (b) at an angle of 73° to the normal to the sample surface.

**200o C**

**900o C**

**1000o C**

**800o C**

**700o C**

**600o C**

**400o C**

**1200o C**

**1100o C**

**1300o C**

**1400<sup>о</sup> C**

> **75 55**

> **77 57**

> **77 57**

> **78 58**

> **77 57**

> **80 50**

> **29**

**69**

**14**

**74**

**30**

**70**

**73o 90o**

**sample**

**500 700 900 1100 Wave number, cm-1**

At respecting certain condition, one can observe not only the transverse optical oscillations of atoms (TO-phonons), as well as longitudinal optical lattice oscillations (LO-phonons). For this purpose, we measured IR transmittance spectra of the implanted layers both at normal incidence of radiation on the sample, and at 73° to the normal to the surface (Figs. 16−21a, b). For a visual comparison of spectra from the SiCх layers in Fig. 22 series of spectra of these layers before and after annealing at 600, 1000 and 1300°C measured at normal incidence of radiation on the sample, are presented. It is seen that among these layers a SiC-peak of the IR transmittance for the SiC0.7 layer has maximum value of amplitude and minimum half-width after annealing at 1300°C. This implies a maximum number of tetrahedral oriented Si–C-bonds and high crystallinity of this layer, although the carbon concentration below the stoichiometric SiC. This phenomenon requires an explanation. For this purpose, an analysis of dependence of SiC-peak parameters on both annealing temperature and concentration of carbon for SiCх layers was carried out.

It is well known that the spectral range 500−1100 cm-1 considered here includes the absorption bands corresponding to valence oscillations (in which the lengths of bonds vary predominantly) of the Si−C, C−C, and C−O-bonds, as well as deformation vibrations (in which the angles between the bonds are changed). As a result of interactions of these oscillations, it is impossible in principle to attribute the absorption band to individual bonds. If we assume that in the ideal case each type of Si−C-bonds corresponds to absorption at a certain frequency or in a narrow frequency interval, it can be concluded from the spectra in Figs. 16−22 that after implantation of carbon into silicon, the contour curve of the IR spectrum covers a large frequency (or wavenumber) range; i.e., the ion implanted layer contains a large number of different types of Si−C-bonds absorbing at different frequencies. Tetrahedral oriented Si−C-bonds with a length of 0.194 nm in crystalline silicon carbide absorb at the frequency corresponding to a wavenumber of 800 cm–1, while the silicon layer amorphized by implantation of carbon ions contains Si−Cbonds with a length larger and smaller than this value and absorb at the frequencies slightly different from 800 cm–1. This may be due to the fact that the stopping particles form a new Si−C-bonds which are not covalent because of variations in their length and in the angles between them. In the implanted amorphous Si−C-layer, one can also expect the presence of shorter double Si=C and triple Si≡C bonds, whose length is much smaller. Among the bonds can be present also the bonds, distances and angles between them (between atoms) are exactly the same as in the crystallite of SiC. For example, Kimura et al. (1981) by electron diffraction observed the crystallites of SiC immediately after implantation. In this case, one can observe non-zero absorption at a frequency of 800 cm-1 after implantation.

In addition, in the implanted layer can be expected the presence of long single bonds, free (dangling) bonds and hybridized Si−C-bonds, resonance and other higher order interactions. If the absorption of double C=C-bonds (1620-1680 cm-1) and the triple C≡Cbonds (2100−2200 cm-1) is beyond the study of the contour curve of the IR spectrum 500−1100 cm-1, but the vibrations of C−C are in the region 900−1100 cm-1. Nevertheless, the contribution to change the contour of the curve in this range and, in particular, to change the peak area will have a decay of single C−C, double C=C, Si=C or Si=Si, and triple C≡C, Si≡C or Si≡Si bonds, because of the formation after their decay of Si−C-bonds absorbing in this range (Silverstein et al., 1977].

At respecting certain condition, one can observe not only the transverse optical oscillations of atoms (TO-phonons), as well as longitudinal optical lattice oscillations (LO-phonons). For this purpose, we measured IR transmittance spectra of the implanted layers both at normal incidence of radiation on the sample, and at 73° to the normal to the surface (Figs. 16−21a, b). For a visual comparison of spectra from the SiCх layers in Fig. 22 series of spectra of these layers before and after annealing at 600, 1000 and 1300°C measured at normal incidence of radiation on the sample, are presented. It is seen that among these layers a SiC-peak of the IR transmittance for the SiC0.7 layer has maximum value of amplitude and minimum half-width after annealing at 1300°C. This implies a maximum number of tetrahedral oriented Si–C-bonds and high crystallinity of this layer, although the carbon concentration below the stoichiometric SiC. This phenomenon requires an explanation. For this purpose, an analysis of dependence of SiC-peak parameters on both annealing temperature and concentration of carbon for

It is well known that the spectral range 500−1100 cm-1 considered here includes the absorption bands corresponding to valence oscillations (in which the lengths of bonds vary predominantly) of the Si−C, C−C, and C−O-bonds, as well as deformation vibrations (in which the angles between the bonds are changed). As a result of interactions of these oscillations, it is impossible in principle to attribute the absorption band to individual bonds. If we assume that in the ideal case each type of Si−C-bonds corresponds to absorption at a certain frequency or in a narrow frequency interval, it can be concluded from the spectra in Figs. 16−22 that after implantation of carbon into silicon, the contour curve of the IR spectrum covers a large frequency (or wavenumber) range; i.e., the ion implanted layer contains a large number of different types of Si−C-bonds absorbing at different frequencies. Tetrahedral oriented Si−C-bonds with a length of 0.194 nm in crystalline silicon carbide absorb at the frequency corresponding to a wavenumber of 800 cm–1, while the silicon layer amorphized by implantation of carbon ions contains Si−Cbonds with a length larger and smaller than this value and absorb at the frequencies slightly different from 800 cm–1. This may be due to the fact that the stopping particles form a new Si−C-bonds which are not covalent because of variations in their length and in the angles between them. In the implanted amorphous Si−C-layer, one can also expect the presence of shorter double Si=C and triple Si≡C bonds, whose length is much smaller. Among the bonds can be present also the bonds, distances and angles between them (between atoms) are exactly the same as in the crystallite of SiC. For example, Kimura et al. (1981) by electron diffraction observed the crystallites of SiC immediately after implantation. In this case, one can observe non-zero absorption at a frequency of 800 cm-1

In addition, in the implanted layer can be expected the presence of long single bonds, free (dangling) bonds and hybridized Si−C-bonds, resonance and other higher order interactions. If the absorption of double C=C-bonds (1620-1680 cm-1) and the triple C≡Cbonds (2100−2200 cm-1) is beyond the study of the contour curve of the IR spectrum 500−1100 cm-1, but the vibrations of C−C are in the region 900−1100 cm-1. Nevertheless, the contribution to change the contour of the curve in this range and, in particular, to change the peak area will have a decay of single C−C, double C=C, Si=C or Si=Si, and triple C≡C, Si≡C or Si≡Si bonds, because of the formation after their decay of Si−C-bonds absorbing in this

SiCх layers was carried out.

after implantation.

range (Silverstein et al., 1977].

Fig. 17. IR transmission spectra of the SiC0.95 layer recorded (a) under normal incidence of IR radiation on the sample and (b) at an angle of 73° to the normal to the sample surface.

The Formation of Silicon Carbide in the SiCx Layers

**<sup>o</sup>**

**sample**

**IR-be am**

**500 700 900 1100 Wave number, cm-1** 

**IR transmittance, %.**

 

 

 

(x = 0.03–1.4) Formed by Multiple Implantation of C Ions in Si 89

**IR-beam**

**<sup>o</sup> <sup>90</sup><sup>o</sup>**

**sample**

 

**<sup>o</sup> C**

**<sup>o</sup> C**

Fig. 19. IR transmission spectra of the SiC0.4 layer recorded (a) under normal incidence of IR radiation on the sample and (b) at an angle of 73° to the normal to the sample surface.

**<sup>o</sup> C**

**<sup>o</sup> C**

**<sup>o</sup> C**

**<sup>o</sup> C**

**<sup>o</sup> C**

**<sup>o</sup> C**

**<sup>o</sup> C**

**<sup>o</sup> C**

**<sup>o</sup> C**

**<sup>o</sup> C**

**500 700 900 1100 Wave number, cm-1** 

Fig. 18. IR transmission spectra of the SiC0.7 layer recorded (a) under normal incidence of IR radiation on the sample and (b) at an angle of 73° to the normal to the sample surface.

б)

 

  **IR-beam**

<sup>β</sup>**=73o 90o**

**sample**

**500 700 900 1100 Wave number, cm-1** 

**500 700 900 1100 Wave number, cm-1** 

**IR transmittance, % .**

α**=90<sup>o</sup>**

a) **sample**

**IR-beam**

 

 

**20o C**

Fig. 18. IR transmission spectra of the SiC0.7 layer recorded (a) under normal incidence of IR radiation on the sample and (b) at an angle of 73° to the normal to the sample surface.

**200o C**

**400o C**

**900o C**

**1000o C**

**800o C**

**700o C**

**600o C**

**1200o C**

**1100o C**

**1300o C**

**<sup>о</sup> C**

Fig. 19. IR transmission spectra of the SiC0.4 layer recorded (a) under normal incidence of IR radiation on the sample and (b) at an angle of 73° to the normal to the sample surface.

The Formation of Silicon Carbide in the SiCx Layers

**<sup>o</sup>**

**sample**

**IR-be am**

**a)**

**IR transmittance, %.**

 

> **500 700 900 1100 Wave number, см**

**-1** 

(x = 0.03–1.4) Formed by Multiple Implantation of C Ions in Si 91

**б)**

**IR-beam**

**<sup>o</sup> <sup>90</sup><sup>o</sup>**

**sample**

**500 700 900 1100**

**-1**

**Wave number, см**

 

**<sup>o</sup> C**

Fig. 21. IR transmission spectra of the SiC0.03 layer recorded (a) under normal incidence of IR radiation on the sample and (b) at an angle of 73° to the normal to the sample surface.

The position of the minimum of the IR transmission peak determines a certain type of bonds, which corresponds to the maximum of absorption at a given temperature. All layers considered here, exhibit after implantation, a transmission peak with the minimum at a frequency of 720−750 cm–1, which is usually typical of amorphous silicon

**<sup>o</sup> C**

**<sup>o</sup> C**

**<sup>o</sup> C**

**<sup>o</sup> C**

**<sup>o</sup> C**

**<sup>o</sup> C**

**<sup>o</sup> C**

**<sup>o</sup> C**

**<sup>o</sup> C**

Fig. 20. IR transmission spectra of the SiC0.12 layer recorded (a) under normal incidence of IR radiation on the sample and (b) at an angle of 73° to the normal to the sample surface.

**IR-beam**

б)

**<sup>o</sup> <sup>90</sup><sup>o</sup>**

**sample**

 

 

 

> **500 700 900 1100 Wave numbe r, cm-1**

**500 700 900 1100 Wave numbe r, cm-1** 

**IR transmittance, %.**

**<sup>o</sup>**

a) **sample**

**IR -beam**

 

 

**<sup>o</sup> C**

**T<sup>к</sup>**

Fig. 20. IR transmission spectra of the SiC0.12 layer recorded (a) under normal incidence of IR radiation on the sample and (b) at an angle of 73° to the normal to the sample surface.

**<sup>o</sup> C**

**<sup>o</sup> C**

**<sup>o</sup> C**

**<sup>o</sup> C**

**<sup>o</sup> C**

**<sup>o</sup> C**

**<sup>o</sup> C**

**<sup>o</sup> C**

**<sup>o</sup> C**

**<sup>o</sup> C**

Fig. 21. IR transmission spectra of the SiC0.03 layer recorded (a) under normal incidence of IR radiation on the sample and (b) at an angle of 73° to the normal to the sample surface.

The position of the minimum of the IR transmission peak determines a certain type of bonds, which corresponds to the maximum of absorption at a given temperature. All layers considered here, exhibit after implantation, a transmission peak with the minimum at a frequency of 720−750 cm–1, which is usually typical of amorphous silicon

The Formation of Silicon Carbide in the SiCx Layers

(Fig. 23, curve 1).

**950**

**710**

SiC0.03.

**730**

**750**

**770**

**3**

**2 4**

**1**

**790**

IR peak wave number, см-1 .

**810**

**830**

**970**

**990**

(x = 0.03–1.4) Formed by Multiple Implantation of C Ions in Si 93

As a result of subsequent annealing, the peak is displaced to the right up to 800 cm-1 (Fig. 23), indicating the formation of tetrahedral bonds typical of SiC, increases in amplitude and narrows. In the case of incidence of infrared radiation on the sample surface at the Brewster angle (73° from the normal), after annealing at 1000°C the appearance of the LO-phonon peak of SiC at frequency 955−965 cm-1 is observed for the layers with a high concentration of carbon SiC1.4, SiC0.95 and SiC0.7. With increasing of annealing temperature, this peak increases in amplitude synchronously with the peak of TO-phonons of silicon carbide (Figs. 16−18, 23). For layers with low carbon concentration SiC0.4, SiC0.12 and SiC0.03 the LO-phonon peak of SiC was not observed (Fig. 19−21), which may be associated with small crystallite sizes of silicon carbide. At normal incidence of infrared radiation LO-phonon peak was not observed at both high and low concentrations of carbon (Figs. 16−21). Increase of the annealing temperature in the range 1000−1300°C results in some increase in the wavelength of the amplitude maximum of LO-phonon peak in the case of an excess of carbon for SiC1.4

**0 200 400 600 800 1000 1200 1400**

 **TO**

**6**

**0 200 400 600 800 1000 1200 1400** Annealing temperature, <sup>о</sup>

Fig. 23. Wavenumber of the IR transmittance peak for TO- and LO-phonons SiC as a function of the annealing temperature: 1 - SiC1.4, 2 - SiC0.95, 3 - SiC0.7, 4 - SiC0.4, 5 - SiC0.12, 6 -

**5**

С

**LO**

**1**

**3**

**2**

carbide (Figs. 16-22). For the layers with low carbon concentration SiC0.4, SiC0.12 and SiC0.03, the minimum of IR transmission is shifted in the region 720−725 cm-1 to the left relative position of the minimum peak for the layers with a high concentration of carbon SiC1.4, SiC0.95 and SiC0.7, located in the region 735−750 cm-1 (Fig. 23). This may be due to the prevalence of long weak Si−C-bonds in the layers with low carbon concentration.

Fig. 22. IR transmission spectra of the SiC1.4, SiC0.95, SiC0.7, SiC0.4, SiC0.12 and SiC0.03 layers recorded after implantation of C12 ions (E = 40, 20, 10, 5 and 3 kev) into Si (a) and annealing for 30 min at temperatures 600°С (b), 1000°С (c) and 1300°С (d).

carbide (Figs. 16-22). For the layers with low carbon concentration SiC0.4, SiC0.12 and SiC0.03, the minimum of IR transmission is shifted in the region 720−725 cm-1 to the left relative position of the minimum peak for the layers with a high concentration of carbon SiC1.4, SiC0.95 and SiC0.7, located in the region 735−750 cm-1 (Fig. 23). This may be due to the prevalence of long weak Si−C-bonds in the layers with low carbon

**C c)1000o**

**500 700 900 1100**

**500 700 900 1100**

**500 700 900 1100 Wave number, cm-1** 

for 30 min at temperatures 600°С (b), 1000°С (c) and 1300°С (d).

**500 700 900 1100 Wave number, cm-1** 

SiC1.

SiC0.95

SiC0.7

SiC0.4

SiC0.12

SiC0.03

**C b)600**

**а)20o**

SiC1.4

Fig. 22. IR transmission spectra of the SiC1.4, SiC0.95, SiC0.7, SiC0.4, SiC0.12 and SiC0.03 layers recorded after implantation of C12 ions (E = 40, 20, 10, 5 and 3 kev) into Si (a) and annealing

SiC0.95

SiC0.7

SiC0.4

SiC0.12

SiC0.03

**o**

SiC1.4

SiC0.95

SiC0.7

Т<sup>1</sup> Т<sup>2</sup>

SiC0.4

SiC0.12

SiC0.03

**C d)1300o**

**Wave number, cm-1**  SiC1.4

SiC0.95

SiC0.7

SiC0.4

SiC0.12

**C**

**Wave number, cm-1** 

concentration.

**80**

**40**

**80**

**40**

**80**

**40**

**IR transmittance, %.**

**80**

**40**

**80**

**40**

**40**

**80**

As a result of subsequent annealing, the peak is displaced to the right up to 800 cm-1 (Fig. 23), indicating the formation of tetrahedral bonds typical of SiC, increases in amplitude and narrows. In the case of incidence of infrared radiation on the sample surface at the Brewster angle (73° from the normal), after annealing at 1000°C the appearance of the LO-phonon peak of SiC at frequency 955−965 cm-1 is observed for the layers with a high concentration of carbon SiC1.4, SiC0.95 and SiC0.7. With increasing of annealing temperature, this peak increases in amplitude synchronously with the peak of TO-phonons of silicon carbide (Figs. 16−18, 23). For layers with low carbon concentration SiC0.4, SiC0.12 and SiC0.03 the LO-phonon peak of SiC was not observed (Fig. 19−21), which may be associated with small crystallite sizes of silicon carbide. At normal incidence of infrared radiation LO-phonon peak was not observed at both high and low concentrations of carbon (Figs. 16−21). Increase of the annealing temperature in the range 1000−1300°C results in some increase in the wavelength of the amplitude maximum of LO-phonon peak in the case of an excess of carbon for SiC1.4 (Fig. 23, curve 1).

Fig. 23. Wavenumber of the IR transmittance peak for TO- and LO-phonons SiC as a function of the annealing temperature: 1 - SiC1.4, 2 - SiC0.95, 3 - SiC0.7, 4 - SiC0.4, 5 - SiC0.12, 6 - SiC0.03.

The Formation of Silicon Carbide in the SiCx Layers

**g**

**h C C**

**Si**

**f C C C**

**C**

133 173

213

234

**C**

**Si**

**Si**

**Si**

**C**

**Si**

**C C**

**Si**

**Si**

200

194

120

154

160

Fig. 24. Possible variants of both the infrared inactive clusters (a-h), chains of them (b) and a flat net of clusters (a) with various types of bonds between the atoms of Si (great circles) and

It was found that for the layers SiCx with low carbon concentrations (Fig. 23), the minimum of IR transmission peak for the TO-phonons is shifted to above 800 cm-1 as the annealing temperature is increased. In the case of SiC0,4 the position of the peak minimum shifts from 725 to 810 cm-1 in the temperature range 20−1100°C and returns to the 800 cm-1 at 1300°C. In the case of SiC0.12 − from 720 to 820 cm-1 in the range 20−1000°C and returns to 800 cm-1 at 1200°C. In the case of SiC0.03 – from 720 to 830 cm-1 in the range 20−1000°C and does not change its position during 1100−1200°C. Displacement of the peak minimum into the region above 800 cm-1 may be due to the presence of SiC nanocrystals of small size (≤ 3 nm), and an increase in the contribution to the IR absorption amplitude of their surfaces and surfaces of the crystallites Si, containing strong shortened Si−C-bonds. For a layer SiC0.12 and SiC0.4, return of the minimum to 800 cm-1 at temperatures of 1100−1400°C may be caused by incorporation of carbon atoms into the nanocrystals of SiC and the growth of their size up to

The observed shift of the peak minimum indicates the following fact: the absorbing at low frequencies energetically unfavorable long single Si−C-bonds decay during annealing at 600−1000°C, and the stronger short or tetrahedral Si−C-bonds absorbing at higher frequencies, are formed. Since the amplitude of IR transmission at 800 cm–1 is proportional to the concentration of tetrahedral oriented Si−C-bonds, and the amplitude at a certain frequency is assumed to be proportional to the absorption of Si−C-bonds at this frequency, we measured the IR transmittance amplitude for transverse optical (TO) phonons at wavenumbers of 700, 750, 800, 850 and 900 cm–1 after implantation and annealing at 200–

It can be seen from Figs. 25a–c that in the temperature range 20−1300°C, the amplitude of the peak at 800 cm–1 increases from 15 to 62% for the SiC1.4 layer, from 14 to 68% for the SiC0.95 layer, and from 18 to 87% for the SiC0.7 layer. In the interval 20−900°C, the amplitude varies insignificantly. The maximal number of tetrahedral Si−C-bonds at 1300°C is observed in the SiC0.7 layer. For these layers with high carbon concentration, the amplitudes of almost all frequencies (except 900 cm–1) increase at 400°C, which can be due to ordering of the layer

**C**

**e**

3.5-5 nm and higher.

1400°C (Fig. 25).

**Si Si**

**d**

**C Si Si**

**c Si Si**

**Si**

**Si**

**C**

**Si**

**C**

**C**

C (small circles). Bond lengths are presented in pm.

(x = 0.03–1.4) Formed by Multiple Implantation of C Ions in Si 95

**b a**

**15**

**1**

**2**

**19**

**18 29**

**<sup>17</sup> <sup>28</sup>**

**27 16**

**<sup>3</sup> <sup>4</sup> <sup>5</sup>**

**<sup>30</sup> <sup>23</sup> <sup>8</sup>**

**<sup>20</sup> <sup>21</sup> <sup>22</sup>**

**<sup>24</sup> <sup>32</sup> 31**

**14 13**

**26**

**25**

**6**

**7**

**9**

**10**

**12 11**

In the case of layers with high concentrations of carbon, position of the minimum of IR transmission peak for TO-phonons is smoothly shifted from 750 to 805 cm-1 for SiC1.4 with the increase of the annealing temperature in the range of 20−1000°C, from 735 to 807 cm-1 for SiC0.95, from 750 to 800 cm-1 for SiC0.7, indicating the formation of tetrahedral oriented Si−Cbonds characteristic of SiC (Fig. 23). The minimum of peak most intensively shifts after annealing in the range 800−900°C, which indicates on intensive processes of the layer ordering. Further annealing up to 1400°C does not lead to a noticeable shift of the minimum peak.

In several studies any changes in the IR transmission spectra have also not revealed after annealing at 1000°C (Borders et al., 1971) and 1100°C (Akimchenko et al., 1977b). This was attributed to the completion of the formation of β-SiC. However, as shown in Fig. 23 for SiC1.4, SiC0.95 and SiC0.7 layers, if the curves of the peak position for TO phonons saturates and does not provide additional information in the temperature range 900−1400°C, then the curves for LO-phonon peak position undergo changes at these temperatures, indicating a structural change in ion-implanted layer. It can be assumed that the formation of tetrahedral Si−C-bonds of required length and angle between them is not completed up to 1300°C.

Although the shift of the minimum of the peak to 800 cm–1 indicating that tetrahedral Si−C-bonds prevail is observed at 1000°C, X-ray diffraction data show that the formation of SiC crystallites begins at 1000°C for SiC0.7, 1150°C for SiC0.95 and 1200°C for SiC1.4 (Figs. 7 and 8), which means that Si−C-bonds are transformed into tetrahedral oriented bonds in the bulk of crystallites only at these temperatures. The increase in the intensity and number of X-ray lines of SiC upon an increase in the annealing temperature (Fig. 8) indicates an increase in the amount of SiC at the expense of the amorphous phase and perfection of its structure due to annealing of structural defects, respectively. It follows that the location of the minimum of transmission peak at ~800 cm-1 and the predominance of the tetrahedral oriented Si-C-bonds among the optically active bonds at temperatures 900−1000°C is not a sufficient condition for the formation of crystallites of silicon carbide in layers with high carbon content SiC0.7 − SiC1.4. At this temperature, a significant part of C and Si atoms can be incorporated in composition of an optically inactive stable clusters, which does not contribute to the amplitude of the IR transmission peak and are decompose at higher temperatures (>1150°C). This results an increase in the amplitude of the infrared transmission at a frequency of 800 cm-1 (Figs. 16, 18 and 22) at these temperatures.

Fig. 24 schematically shows the optically inactive Si−C-clusters, the atoms of which are connected by single, double and triple bonds, lie in one plane. In a flat optically inactive net the free (dangling) bonds to the silicon atoms (atoms №30 and 24) and carbon atoms (№21 and 27) are shown. Free bonds of these and other atoms (№ 4, 11, 12, 15, 17) can connected them with groups of atoms which do not lie on one plane and can form the association of optically active clusters. Since the distance between atoms № 22−4 and №5−22 are equal, the bond can oscillate forming 22−4 and 22−5. One double bond connected three atoms № 5, 6 and 7, i.e. there is the presence of resonance. The presence of two free bonds of the atom № 26 might lead to hybridization, i.e., association. Long single bonds between atoms № 2−3 and 1−18, which decay during low temperature annealing, are shown. Long optically inactive chains, and closed stable clusters of several atoms, connected to each other by double bonds, are also shown in Fig. 24.

In the case of layers with high concentrations of carbon, position of the minimum of IR transmission peak for TO-phonons is smoothly shifted from 750 to 805 cm-1 for SiC1.4 with the increase of the annealing temperature in the range of 20−1000°C, from 735 to 807 cm-1 for SiC0.95, from 750 to 800 cm-1 for SiC0.7, indicating the formation of tetrahedral oriented Si−Cbonds characteristic of SiC (Fig. 23). The minimum of peak most intensively shifts after annealing in the range 800−900°C, which indicates on intensive processes of the layer ordering. Further annealing up to 1400°C does not lead to a noticeable shift of the minimum

In several studies any changes in the IR transmission spectra have also not revealed after annealing at 1000°C (Borders et al., 1971) and 1100°C (Akimchenko et al., 1977b). This was attributed to the completion of the formation of β-SiC. However, as shown in Fig. 23 for SiC1.4, SiC0.95 and SiC0.7 layers, if the curves of the peak position for TO phonons saturates and does not provide additional information in the temperature range 900−1400°C, then the curves for LO-phonon peak position undergo changes at these temperatures, indicating a structural change in ion-implanted layer. It can be assumed that the formation of tetrahedral Si−C-bonds of required length and angle between them is not completed up to 1300°C. Although the shift of the minimum of the peak to 800 cm–1 indicating that tetrahedral Si−C-bonds prevail is observed at 1000°C, X-ray diffraction data show that the formation of SiC crystallites begins at 1000°C for SiC0.7, 1150°C for SiC0.95 and 1200°C for SiC1.4 (Figs. 7 and 8), which means that Si−C-bonds are transformed into tetrahedral oriented bonds in the bulk of crystallites only at these temperatures. The increase in the intensity and number of X-ray lines of SiC upon an increase in the annealing temperature (Fig. 8) indicates an increase in the amount of SiC at the expense of the amorphous phase and perfection of its structure due to annealing of structural defects, respectively. It follows that the location of the minimum of transmission peak at ~800 cm-1 and the predominance of the tetrahedral oriented Si-C-bonds among the optically active bonds at temperatures 900−1000°C is not a sufficient condition for the formation of crystallites of silicon carbide in layers with high carbon content SiC0.7 − SiC1.4. At this temperature, a significant part of C and Si atoms can be incorporated in composition of an optically inactive stable clusters, which does not contribute to the amplitude of the IR transmission peak and are decompose at higher temperatures (>1150°C). This results an increase in the amplitude of the infrared transmission at a frequency of 800 cm-1 (Figs. 16, 18 and 22) at these

Fig. 24 schematically shows the optically inactive Si−C-clusters, the atoms of which are connected by single, double and triple bonds, lie in one plane. In a flat optically inactive net the free (dangling) bonds to the silicon atoms (atoms №30 and 24) and carbon atoms (№21 and 27) are shown. Free bonds of these and other atoms (№ 4, 11, 12, 15, 17) can connected them with groups of atoms which do not lie on one plane and can form the association of optically active clusters. Since the distance between atoms № 22−4 and №5−22 are equal, the bond can oscillate forming 22−4 and 22−5. One double bond connected three atoms № 5, 6 and 7, i.e. there is the presence of resonance. The presence of two free bonds of the atom № 26 might lead to hybridization, i.e., association. Long single bonds between atoms № 2−3 and 1−18, which decay during low temperature annealing, are shown. Long optically inactive chains, and closed stable clusters of several atoms, connected to each other by

peak.

temperatures.

double bonds, are also shown in Fig. 24.

Fig. 24. Possible variants of both the infrared inactive clusters (a-h), chains of them (b) and a flat net of clusters (a) with various types of bonds between the atoms of Si (great circles) and C (small circles). Bond lengths are presented in pm.

It was found that for the layers SiCx with low carbon concentrations (Fig. 23), the minimum of IR transmission peak for the TO-phonons is shifted to above 800 cm-1 as the annealing temperature is increased. In the case of SiC0,4 the position of the peak minimum shifts from 725 to 810 cm-1 in the temperature range 20−1100°C and returns to the 800 cm-1 at 1300°C. In the case of SiC0.12 − from 720 to 820 cm-1 in the range 20−1000°C and returns to 800 cm-1 at 1200°C. In the case of SiC0.03 – from 720 to 830 cm-1 in the range 20−1000°C and does not change its position during 1100−1200°C. Displacement of the peak minimum into the region above 800 cm-1 may be due to the presence of SiC nanocrystals of small size (≤ 3 nm), and an increase in the contribution to the IR absorption amplitude of their surfaces and surfaces of the crystallites Si, containing strong shortened Si−C-bonds. For a layer SiC0.12 and SiC0.4, return of the minimum to 800 cm-1 at temperatures of 1100−1400°C may be caused by incorporation of carbon atoms into the nanocrystals of SiC and the growth of their size up to 3.5-5 nm and higher.

The observed shift of the peak minimum indicates the following fact: the absorbing at low frequencies energetically unfavorable long single Si−C-bonds decay during annealing at 600−1000°C, and the stronger short or tetrahedral Si−C-bonds absorbing at higher frequencies, are formed. Since the amplitude of IR transmission at 800 cm–1 is proportional to the concentration of tetrahedral oriented Si−C-bonds, and the amplitude at a certain frequency is assumed to be proportional to the absorption of Si−C-bonds at this frequency, we measured the IR transmittance amplitude for transverse optical (TO) phonons at wavenumbers of 700, 750, 800, 850 and 900 cm–1 after implantation and annealing at 200– 1400°C (Fig. 25).

It can be seen from Figs. 25a–c that in the temperature range 20−1300°C, the amplitude of the peak at 800 cm–1 increases from 15 to 62% for the SiC1.4 layer, from 14 to 68% for the SiC0.95 layer, and from 18 to 87% for the SiC0.7 layer. In the interval 20−900°C, the amplitude varies insignificantly. The maximal number of tetrahedral Si−C-bonds at 1300°C is observed in the SiC0.7 layer. For these layers with high carbon concentration, the amplitudes of almost all frequencies (except 900 cm–1) increase at 400°C, which can be due to ordering of the layer

The Formation of Silicon Carbide in the SiCx Layers

SiC1.4, SiC0.95, SiC0.7. SiC0.12 and SiC0.03.

approximation:

layers.

(x = 0.03–1.4) Formed by Multiple Implantation of C Ions in Si 97

high carbon concentration are almost analogous, but differ considerably from the dependences for SiC0.4, SiC0.12 and SiC0.03 layers with a low carbon concentration. This indicates the same nature of carbon and carbon–silicon clusters in SiC1.4, SiC0.95 and SiC0.7

For SiC0.4, SiC0.12 and SiC0.03 layers with a low carbon concentration, measurements of the IR transmission amplitude show **(**Figure 25, d-f) that in the temperature range 20–1300°C, the amplitude at 800 cm–1 increases from 13 to 52% for the SiC0.4 layer, from 11 to 37% for the SiC0.12 layer, and from 2.8 to 8% for the SiC0.03 layer. At temperatures 20–600°C, in these layers dominate the long and weak Si−C-bonds, which absorb at frequencies of 700 and 750 cm–1 (Fig. 25d-f, curves 1 and 2) and decay at low temperatures. A noticeable increase in the amplitudes is observed at frequencies of 800 and 850 cm–1 in the temperature range 700−1000°C, which indicates an increase in the number of tetrahedral and nearly to tetrahedral short Si−C-bonds. A distinguishing feature for SiC0.4, SiC0.12 and SiC0.03 layers with a low carbon concentration is an intense increase in the number of tetrahedral bonds at low temperatures (700°C), which is due to a low concentration of stable carbon clusters (chains, flat nets, etc.) disintegrating at higher temperatures, because low content of carbon atoms. Consequently, in the range of 800−900ºC by the number of tetrahedral Si−C-bonds and the amplitude at 800 cm-1 (35%) the SiC0.4 layers exceed all the above considered layers

For SiC0.4 and SiC0.12 layers in the temperature range 700−1100°C, the increase in the amplitudes at frequencies of 800, 850, and 900 cm–1 is accompanied by a decrease in the amplitudes at 700 and 750 cm–1, indicating an increase in the number of tetrahedral and strong short Si−C-bonds due to disintegration of long weak bonds that prevailed after implantation. Intensive formation of Si−C-bonds with the tetrahedral orientation, which absorb at a frequency of 800 cm–1 (Fig 25d and e, curves 3) at 1200°C is due to disintegration of strong optically inactive clusters of C and Si atoms. The SiC0.4 layer with a higher carbon concentration differs from the SiC0.12 layer because it contains stronger clusters disintegrating at 1300°C, which is manifested in a sharp increase in the amplitude at this temperature. As in the case of SiC1.4, SiC0.95 and SiC0.7 layers with a high carbon concentration, the decrease in the amplitudes for SiC0.4 at 1400°C is due to disintegration of

Increase in the number of tetrahedral bonds in the layer SiC0.03 in the temperature range 800−900°C occurs simultaneously with some increase in amplitude for all frequencies, i.e. not due to the decay of optically active bonds. For this layer with very low carbon concentration is difficult to assume the presence of a noticeable amount of stable carbon and carbon-silicon clusters. We can assume that a significant increase of tetrahedral bonds can

We assume that the total area of the SiC-peak of IR transmission is the area of region between the curve of the IR spectrum and the baseline |Т1Т2| (Fig. 16a), and it is equal to the total absorption of infrared radiation at all frequencies and is roughly proportional to the number of all types of absorbing Si−C-bonds (Wong et al., 1998; Chen et al., 1999). Peak area was determined from the spectra of IR transmission (Figs. 16−21), based on the

1 22 1 1 22 1

 τν ν

*A TT* = + −− ( )( ) ( ) ( )( ) ( )

*d TT* ≈ + −−

ν ν  τ ν δν

, (2)

SiC crystallites and desorption of carbon from the layer (Fig. 25d, curves 2–5).

occur by reducing the number of dangling bonds of carbon atoms.

1 1 2 2

ν ν

and the formation of optically active Si−C-bonds. A certain increase in the amplitude at 800 cm–1 indicates the formation of tetrahedral Si−C-bonds at low temperatures.

Fig. 25. Effect of the annealing temperature on the IR transmittance amplitude at wavenumbers of (1-□) 700 cm-1, (2-∆) 750 cm-1, (3-○) 800 cm-1, (4-▲) 850 cm-1, and (5-■) 900 cm-1 under normal incidence of IR radiation on the sample surface: a) SiC1.4; b) SiC0.95; c) SiC0.7, d) SiC0.4, e) SiC0.12; f) SiC0.03.

The amplitudes at 800 cm–1 and close frequencies of 750 and 850 cm–1 considerably increase after annealing at temperatures in the interval 900−1300°C. This means that in SiC1.4, SiC0.95 and SiC0.7 layers with a high carbon concentration, intense formation of tetrahedral Si–C bonds begins at 900−1000°C and continues up to 1300°C. This can be due to breakdown of carbon and silicon clusters (chains and flat nets) as well as single Si−C-bonds during annealing. The most pronounced decay of long single Si−C-bonds absorbing at a frequency of 700 cm–1 **(**Fig. 25a**-c**, curve 1) occurs during annealing at 800−1200°C. Annealing of SiC1.4, SiC0.95 and SiC0.7 layers at 1400°C resulted in a decrease in the amplitudes in the entire frequency range 700−900 cm–1, which is apparently due to decomposition of SiC as a result of carbon desorption from the layer. It can be seen from Fig. 25 that the dependences of IR transmission amplitudes on the annealing temperature for different wavenumbers for SiC1.4, SiC0.95 and SiC0.7 layers with a

and the formation of optically active Si−C-bonds. A certain increase in the amplitude at 800

**b)SiC0.95**

**3**

**0 400 800 1200 Температура,** 

**e)SiC0.12**

**0 400 800 1200 Тemperature, <sup>о</sup>**

**1**

**5 1**

**о С**

**3 4**

**5**

**2**

**С**

**4**

**2**

**0 400 800 1200 Температура,** 

**f)SiC0.03**

**3**

**1**

**0 400 800 1200 Тemperature, <sup>о</sup>**

**c)SiC0.7**

**о С**

**4**

**С**

**2**

**5**

**2**

**1 5**

**<sup>3</sup> <sup>4</sup>**

cm–1 indicates the formation of tetrahedral Si−C-bonds at low temperatures.

**Amplitude,** 

**%**

**5**

**Amplitude, %.**

**0 400 800 1200 Температура,** 

**d)SiC0.4**

**0 400 800 1200 Тemperature, <sup>о</sup>**

c) SiC0.7, d) SiC0.4, e) SiC0.12; f) SiC0.03.

**5 1**

**а)SiC1.4**

**3**

**1**

**о С**

**3 4**

**2**

**С**

Fig. 25. Effect of the annealing temperature on the IR transmittance amplitude at

wavenumbers of (1-□) 700 cm-1, (2-∆) 750 cm-1, (3-○) 800 cm-1, (4-▲) 850 cm-1, and (5-■) 900 cm-1 under normal incidence of IR radiation on the sample surface: a) SiC1.4; b) SiC0.95;

The amplitudes at 800 cm–1 and close frequencies of 750 and 850 cm–1 considerably increase after annealing at temperatures in the interval 900−1300°C. This means that in SiC1.4, SiC0.95 and SiC0.7 layers with a high carbon concentration, intense formation of tetrahedral Si–C bonds begins at 900−1000°C and continues up to 1300°C. This can be due to breakdown of carbon and silicon clusters (chains and flat nets) as well as single Si−C-bonds during annealing. The most pronounced decay of long single Si−C-bonds absorbing at a frequency of 700 cm–1 **(**Fig. 25a**-c**, curve 1) occurs during annealing at 800−1200°C. Annealing of SiC1.4, SiC0.95 and SiC0.7 layers at 1400°C resulted in a decrease in the amplitudes in the entire frequency range 700−900 cm–1, which is apparently due to decomposition of SiC as a result of carbon desorption from the layer. It can be seen from Fig. 25 that the dependences of IR transmission amplitudes on the annealing temperature for different wavenumbers for SiC1.4, SiC0.95 and SiC0.7 layers with a

**4**

**2**

high carbon concentration are almost analogous, but differ considerably from the dependences for SiC0.4, SiC0.12 and SiC0.03 layers with a low carbon concentration. This indicates the same nature of carbon and carbon–silicon clusters in SiC1.4, SiC0.95 and SiC0.7 layers.

For SiC0.4, SiC0.12 and SiC0.03 layers with a low carbon concentration, measurements of the IR transmission amplitude show **(**Figure 25, d-f) that in the temperature range 20–1300°C, the amplitude at 800 cm–1 increases from 13 to 52% for the SiC0.4 layer, from 11 to 37% for the SiC0.12 layer, and from 2.8 to 8% for the SiC0.03 layer. At temperatures 20–600°C, in these layers dominate the long and weak Si−C-bonds, which absorb at frequencies of 700 and 750 cm–1 (Fig. 25d-f, curves 1 and 2) and decay at low temperatures. A noticeable increase in the amplitudes is observed at frequencies of 800 and 850 cm–1 in the temperature range 700−1000°C, which indicates an increase in the number of tetrahedral and nearly to tetrahedral short Si−C-bonds. A distinguishing feature for SiC0.4, SiC0.12 and SiC0.03 layers with a low carbon concentration is an intense increase in the number of tetrahedral bonds at low temperatures (700°C), which is due to a low concentration of stable carbon clusters (chains, flat nets, etc.) disintegrating at higher temperatures, because low content of carbon atoms. Consequently, in the range of 800−900ºC by the number of tetrahedral Si−C-bonds and the amplitude at 800 cm-1 (35%) the SiC0.4 layers exceed all the above considered layers SiC1.4, SiC0.95, SiC0.7. SiC0.12 and SiC0.03.

For SiC0.4 and SiC0.12 layers in the temperature range 700−1100°C, the increase in the amplitudes at frequencies of 800, 850, and 900 cm–1 is accompanied by a decrease in the amplitudes at 700 and 750 cm–1, indicating an increase in the number of tetrahedral and strong short Si−C-bonds due to disintegration of long weak bonds that prevailed after implantation. Intensive formation of Si−C-bonds with the tetrahedral orientation, which absorb at a frequency of 800 cm–1 (Fig 25d and e, curves 3) at 1200°C is due to disintegration of strong optically inactive clusters of C and Si atoms. The SiC0.4 layer with a higher carbon concentration differs from the SiC0.12 layer because it contains stronger clusters disintegrating at 1300°C, which is manifested in a sharp increase in the amplitude at this temperature. As in the case of SiC1.4, SiC0.95 and SiC0.7 layers with a high carbon concentration, the decrease in the amplitudes for SiC0.4 at 1400°C is due to disintegration of SiC crystallites and desorption of carbon from the layer (Fig. 25d, curves 2–5).

Increase in the number of tetrahedral bonds in the layer SiC0.03 in the temperature range 800−900°C occurs simultaneously with some increase in amplitude for all frequencies, i.e. not due to the decay of optically active bonds. For this layer with very low carbon concentration is difficult to assume the presence of a noticeable amount of stable carbon and carbon-silicon clusters. We can assume that a significant increase of tetrahedral bonds can occur by reducing the number of dangling bonds of carbon atoms.

We assume that the total area of the SiC-peak of IR transmission is the area of region between the curve of the IR spectrum and the baseline |Т1Т2| (Fig. 16a), and it is equal to the total absorption of infrared radiation at all frequencies and is roughly proportional to the number of all types of absorbing Si−C-bonds (Wong et al., 1998; Chen et al., 1999). Peak area was determined from the spectra of IR transmission (Figs. 16−21), based on the approximation:

$$A = \frac{1}{2}(T\_1 + T\_2)(\nu\_2 - \nu\_1) - \frac{1}{2}\pi(\nu)d\nu = \frac{1}{2}(T\_1 + T\_2)(\nu\_2 - \nu\_1) - \Sigma\,\pi(\nu)\delta\nu\,\,\tag{2}$$

The Formation of Silicon Carbide in the SiCx Layers

carbon concentration, basing on data of the peak area (Table 4).

spectra for SiCх layers after implantation and annealing

T, ºС A, arb. un.

(x = 0.03–1.4) Formed by Multiple Implantation of C Ions in Si 99

partial decay of the clusters at 1300°C, the estimations of the proportion of carbon atoms included in the optically inactive clusters suggest even higher values. In general, the assertions do not contradict the data (Chen et al., 2003; Wong et al., 1998; Chen et al., 1999), where the growths of area of Si−C-peak after annealing, were shown. We evaluated the linearity of the dependence of the area and number of optically active Si−C-bonds on the

SiC0.03 SiC0.12 SiC0.4 SiC0.7 SiC0.95 SiC1.4

20ºС 1709 3588 4719 6622 3848 4384 200ºС 1840 3990 4929 6966 4198 5347 400ºС 1464 3921 4638 7647 4571 5757 600ºС 1672 3979 4595 8296 5152 5442 700ºС 1963 4248 5035 8227 5394 5665 800ºС 1127 3795 6061 7428 5458 5864 900ºС 1924 4004 5150 7772 5571 6619 1000ºС 2708 3958 4499 7674 5386 7664 1100ºС 2069 3910 4437 8158 6296 7190 1200ºС 2428 5181 5428 7980 7570 8011 1300ºС 0 4886 5805 10169 10221 10953 1400ºС 5473 4749 5510 7741 8670 Table 4. Area, A, under the IR transmittance SiC-peak for TO phonons obtained from the IR

In the layer SiC0.03 the number of optically active Si−C-bonds after annealing should be roughly proportional to the quantity of carbon atoms due to the low concentration of carbon and stable carbon or carbon-silicon clusters as well. We take the maximum value of the area of Si−C-peak for the SiC0.03 layer at 1000ºC as equal to 1. If the proportionality is linear, an increase in the concentration of carbon in SiCх layer on n1 times (n1= (NC/NSi)/0.03 = х/0.03) should increase the peak area on n2 times (n2 = Aх(T)/A0.03(1000ºС)), and n1 = n2, if not come saturation in the amplitude of the transmission, and the carbon atoms are not included in the optically inactive clusters. Since the saturation amplitude of the IR transmission is not reached (Fig. 25) and n2 < n1, so a values 100%×n2/n1 show the portion of carbon atoms forming optically active Si−Cbonds in the SiCx layer. As it turned out, at 1300ºC in the layer SiC1.4 only 9% of the C atoms form the optically active Si−C-bonds, in SiC0.95 − 12%, in SiC0.7 and SiC0.4 − 16%, in SiC0.12 − 45%, while the other carbon atoms remain in the composition of strong clusters. The total number of SiC (optically active Si−C-bonds) in the SiCх layers after annealing at 1300ºC increases with the

fractional degree of carbon concentration (х/0.03)y, where *y* ~ 0.37±0.09 (Table 5).

one of which belonged to the amorphous SiC, while the other two to β-SiC.

In (Wong et al., 1998) at a fixed energy the total number of formed SiC increases with the fractional degree of doses, namely, Dy witg «y» defined as 0.41. In this paper, SiC layers were synthesized using the ion source MEVVA implantation in p-Si of carbon ions with energies in the range 30−60 keV and doses ranged within (0.3–1.6)×1018 см-2. In this case, the infrared absorption spectra of SiC layers were decomposed into two or three components,

where A − total absorption (or transmission) in relative units in the frequency range ν1<ν<ν2, τ(ν) − transmission at frequency ν, Т1 and Т<sup>2</sup> − the values of IR transmission at frequencies ν1 and ν2, respectively, δν − step of measurements, equal to 2.5 or 5 cm-1. Fig. 26 shows the peak area of IR transmission for TO phonons as a function of the annealing temperature and the concentration of carbon for layers SiC1.4, SiC0.95, SiC0.7, SiC0.4, SiC0.12 and SiC0.03. It is seen that in the range of 27−1200°C the number of optically active Si−C-bonds is highest in the layer SiC0.7. A smaller number of Si−C-bonds in the SiCх layers if x<0.7 is caused by lower carbon content, and if x>0.7 − due to the high concentration of stable clusters, decomposing at higher temperatures. Therefore, at 1300°C number of optical active Si−C-bonds is the highest in layer SiC1.4.

Fig. 26. Effect of the annealing temperature and concentration of carbon on the area under the IR transmittance SiC-peak for TO phonons under normal incidence of IR radiation on the sample surface: a) SiC1.4 (1), SiC0.95 (2), SiC0.7 (3), SiC0.4 (4), SiC0.12 (5) и SiC0.03 (6); b) 27 ºC (1), 400°C (2), 800°C (3), 1000°C (4), 1200°C (5), 1300°C (6), 1400°C (7).

For layers SiC1.4, SiC0.95 and SiC0.7 with high carbon concentration, the peak area of IR transmission immediately after implantation has the lowest value (Fig. 26a). In the temperature range 20−1400°C, the value of the peak area for SiC1.4 is changed in the range of values within 4380−10950 arb. units, for SiC0.95 − within 3850−10220 units, for SiC0.7 − within 6620−10170 units, and tends to increase with annealing temperature, indicating a significant amount of carbon atoms do not bound with silicon in the layers immediately after implantation: ∼[1−(4380/10950)×100/1.4] ≈ 70% for SiC1.4, ∼[1− (3850/10220)]×100% ≈ 62% for SiC0.95, ∼[1–(6620/10170)]×100% ≈ 35% for SiC0.7. These estimates can be valid if we assuming that after annealing at 1300°C all clusters broke up and all carbon atoms formed optically active Si−C-bonds in the layer (except the excess atoms in SiC1.4). In the case of a

where A − total absorption (or transmission) in relative units in the frequency range ν1<ν<ν2, τ(ν) − transmission at frequency ν, Т1 and Т<sup>2</sup> − the values of IR transmission at

Fig. 26 shows the peak area of IR transmission for TO phonons as a function of the annealing temperature and the concentration of carbon for layers SiC1.4, SiC0.95, SiC0.7, SiC0.4, SiC0.12 and SiC0.03. It is seen that in the range of 27−1200°C the number of optically active Si−C-bonds is highest in the layer SiC0.7. A smaller number of Si−C-bonds in the SiCх layers if x<0.7 is caused by lower carbon content, and if x>0.7 − due to the high concentration of stable clusters, decomposing at higher temperatures. Therefore, at 1300°C number of optical

**4**

**0**

**0 0,3 0,6 0,9 1,2 Nc/Nsi**

**1**

**4**

**5**

**2**

**3**

**7**

**2000**

**4000**

**6000**

**8000**

**10000**

**6**

**b)** 

**12000**

**2**

**1 а) b)**

frequencies ν1 and ν2, respectively, δν − step of measurements, equal to 2.5 or 5 cm-1.

active Si−C-bonds is the highest in layer SiC1.4.

**3**

**0**

**0 300 600 900 1200 Temperature, <sup>о</sup>**

(1), 400°C (2), 800°C (3), 1000°C (4), 1200°C (5), 1300°C (6), 1400°C (7).

**5**

**С**

Fig. 26. Effect of the annealing temperature and concentration of carbon on the area under the IR transmittance SiC-peak for TO phonons under normal incidence of IR radiation on the sample surface: a) SiC1.4 (1), SiC0.95 (2), SiC0.7 (3), SiC0.4 (4), SiC0.12 (5) и SiC0.03 (6); b) 27 ºC

For layers SiC1.4, SiC0.95 and SiC0.7 with high carbon concentration, the peak area of IR transmission immediately after implantation has the lowest value (Fig. 26a). In the temperature range 20−1400°C, the value of the peak area for SiC1.4 is changed in the range of values within 4380−10950 arb. units, for SiC0.95 − within 3850−10220 units, for SiC0.7 − within 6620−10170 units, and tends to increase with annealing temperature, indicating a significant amount of carbon atoms do not bound with silicon in the layers immediately after implantation: ∼[1−(4380/10950)×100/1.4] ≈ 70% for SiC1.4, ∼[1− (3850/10220)]×100% ≈ 62% for SiC0.95, ∼[1–(6620/10170)]×100% ≈ 35% for SiC0.7. These estimates can be valid if we assuming that after annealing at 1300°C all clusters broke up and all carbon atoms formed optically active Si−C-bonds in the layer (except the excess atoms in SiC1.4). In the case of a

**2000**

**4000**

**6**

**6000**

**Area under the SiC-peak, arb.un.**

**8000**

**10000**

**12000**

partial decay of the clusters at 1300°C, the estimations of the proportion of carbon atoms included in the optically inactive clusters suggest even higher values. In general, the assertions do not contradict the data (Chen et al., 2003; Wong et al., 1998; Chen et al., 1999), where the growths of area of Si−C-peak after annealing, were shown. We evaluated the linearity of the dependence of the area and number of optically active Si−C-bonds on the carbon concentration, basing on data of the peak area (Table 4).


Table 4. Area, A, under the IR transmittance SiC-peak for TO phonons obtained from the IR spectra for SiCх layers after implantation and annealing

In the layer SiC0.03 the number of optically active Si−C-bonds after annealing should be roughly proportional to the quantity of carbon atoms due to the low concentration of carbon and stable carbon or carbon-silicon clusters as well. We take the maximum value of the area of Si−C-peak for the SiC0.03 layer at 1000ºC as equal to 1. If the proportionality is linear, an increase in the concentration of carbon in SiCх layer on n1 times (n1= (NC/NSi)/0.03 = х/0.03) should increase the peak area on n2 times (n2 = Aх(T)/A0.03(1000ºС)), and n1 = n2, if not come saturation in the amplitude of the transmission, and the carbon atoms are not included in the optically inactive clusters. Since the saturation amplitude of the IR transmission is not reached (Fig. 25) and n2 < n1, so a values 100%×n2/n1 show the portion of carbon atoms forming optically active Si−Cbonds in the SiCx layer. As it turned out, at 1300ºC in the layer SiC1.4 only 9% of the C atoms form the optically active Si−C-bonds, in SiC0.95 − 12%, in SiC0.7 and SiC0.4 − 16%, in SiC0.12 − 45%, while the other carbon atoms remain in the composition of strong clusters. The total number of SiC (optically active Si−C-bonds) in the SiCх layers after annealing at 1300ºC increases with the fractional degree of carbon concentration (х/0.03)y, where *y* ~ 0.37±0.09 (Table 5).

In (Wong et al., 1998) at a fixed energy the total number of formed SiC increases with the fractional degree of doses, namely, Dy witg «y» defined as 0.41. In this paper, SiC layers were synthesized using the ion source MEVVA implantation in p-Si of carbon ions with energies in the range 30−60 keV and doses ranged within (0.3–1.6)×1018 см-2. In this case, the infrared absorption spectra of SiC layers were decomposed into two or three components, one of which belonged to the amorphous SiC, while the other two to β-SiC.

The Formation of Silicon Carbide in the SiCx Layers

and annealing at higher temperature removes the differences.

graphite grains, beginning from W = 0.5 J/cm2.

(x = 0.03–1.4) Formed by Multiple Implantation of C Ions in Si 101

Evaluation results may be debatable, since the literature contains different points of view concerning inclusion of carbon into SiC. Akimchenko et al. (1977a) after implantation of Si (Е = 40 кэВ, D = 3.7×1017 см-2) in diamond and annealing at temperatures of 500-1200ºC assumed that almost 100% of implanted carbon atoms included in the SiC. This conclusion was made from accordance of calculated layer thickness (80 nm) with ones found from the absorption near 810 cm-1 (70 nm). A comparison with the magnitude of the SiC thickness (8−10 nm) obtained by X-ray diffraction, allowed to conclude that 10−15% of atoms of the disordered SiC united into β-SiC crystallites, which contribute to the X-ray reflection, and the rest remains in the amorphous state. Kimura et al. (1982) basing on data from the optical density of the infrared transmission spectra have established that all implanted carbon are included in β-SiC after annealing at 900−1200ºC, if the concentration of implanted carbon is less or equal to the stoichiometric composition of SiC at the peak of the distribution. In the case of higher doses, the excess carbon atoms form clusters and are not included into β-SiC, even after annealing at 1200°C. The activation energy required for inclusion of carbon atoms in the β-SiC, increases with increasing of implantation doses, since more energy is required for the decomposition of carbon clusters. Durupt et al. (1980) showed that if the annealing temperature below 900ºC, the formation of SiC is less pronounced in the case of high dose,

On the other hand, Borders et al. (1971) from the infrared absorption and Rutherford backscattering data found that about half of carbon atoms implanted into the silicon (Е = 200 кэВ, D = ~1017 см-2) included in micro-SiC. According to our estimates, the concentration of carbon atoms in the layer was lower than 10% (x <0.1). Kimura et al. (1981) from the analysis of infrared spectra revealed that after implantation (E = 100 keV) and annealing at 900ºC about 40-50% of carbon atoms united with Si atoms to form β-SiC, and this value monotonically increased to 70-80% with increasing of annealing temperature up to 1200ºC. The number of carbon atoms included in the β-SiC was affected by dose of carbon ions. Calcagno et al. (1996) showed that the optical band gap and the intensity of the infrared signal after annealing at 1000ºC increased linearly with carbon concentration, reaching a maximum at the stoichiometric composition of SiC. At higher carbon concentrations intensity of the infrared signal undergoes saturation, and the band gap decreases from 2.2 to 1.8 eV. By Raman spectroscopy is shown that this is due to the formation of clusters of graphite. Simon et al. (1996) after the high-temperature (700ºC) implantation of carbon ions into Si (E = 50 keV, D = 1018 and 2×1018 см-2) show that the carbon excess precipitates out, forming carbon clusters. It is assumed that the stresses and defects, formed after the first stage of implantation, form traps, which attract the following carbon atoms. Liangdeng et al. (2008) after implantation of C ions (E = 80 keV, D = 2.7×1017 ион/cм2) in the Raman spectra observed double band with center in 1380 and 1590 cm-1 corresponding to the range of graphitized amorphous carbon. The authors suggest that since solid solubility of carbon in a-Si at a temperature close to the melting point of Si, is about 1017/cm3, and almost disappears at room temperature, the carbon has a tendency to form precipitates. Bayazitov et al. (2003) after implantation of carbon ions (E = 40 keV, D = 5*×*1017 см*−*2) in silicon and pulsed ion beam annealing (*W* = 1.0 J/cm2, C+(~80%) and H+(~20%)) have formed a β-SiC layer with an average size of grain about 100 nm. Increasing the energy density per pulse up to 1.5 J/cm2 leads also to appearance of graphite grains of sizes about 100 nm, as well as visually observed darkening of the sample. When exposed by radiation of ruby laser (λ = 0.69 μm, τ = 50 nsec, W = 0.5-2 J/cm2) also formed the

Really, as seen in Table 5, the increase of carbon concentration x in the layer SiC0,12 in 4 times in comparison with SiC0.03 results to a smaller increase in the area of SiC-peak, pointing to the disproportionate increase in the number of optically active Si−C-bonds . At least, the maximum area at 1200ºC for a SiC0.12 layer exceeds the maximum area for SiC0,03 layer only in 1.91 times. Further increase in the concentration of carbon x in the SiCх layers in 13, 23, 32, 47 times leads to an increase in the number of optically active Si−C-bonds in several times less than expected − no more than 4.04 times even for high temperature annealing.

Both the peak areas and the number of bonds do not increase linearly with the increase of concentration and it is not caused by saturation of amplitude values. As in the case of NC/NSi = 0.12, the increase of concentration in 13.3 times at NC/NSi = 0.4, has led to an increase in the amplitude of only 9 times, and an area of 2.1 times (5805 un.) at 1300ºC (Tables 4 and 5), although the amplitude of the IR transmittance at the minimum of the peak is far from saturation (52%). This confirms that the determining factor is the presence of strong clusters, in the structure of which is included the majority of the carbon atoms. That is at 1300ºC in the SiC0.4 layer only n1/n2 = 2.1/13.33 = 16% of the carbon atoms form an optically active Si−C-bonds, and in the SiC0.12 layer − 45%. Then, in the optically inactive stable clusters are included the rest 84% and 55% of carbon atoms (Table 5), respectively, resulting in no increase in peak area proportionally to the concentration of carbon. Since there is a predominance of the tetrahedral oriented bonds among the optically active Si-Cbonds, the amount of tetrahedral Si−C-bonds is sufficient for the appearance of SiC crystallites in the layers, which is observed on the X-ray diffraction pattern.


Table 5. Relative values of area (n2 = Ax(T)/A0.03(1000°C)) of IR transmission SiC-peak and the proportion of carbon atoms (100% × n2/n1) which forms an optically active Si-C-bonds in the SiCx layers.

Really, as seen in Table 5, the increase of carbon concentration x in the layer SiC0,12 in 4 times in comparison with SiC0.03 results to a smaller increase in the area of SiC-peak, pointing to the disproportionate increase in the number of optically active Si−C-bonds . At least, the maximum area at 1200ºC for a SiC0.12 layer exceeds the maximum area for SiC0,03 layer only in 1.91 times. Further increase in the concentration of carbon x in the SiCх layers in 13, 23, 32, 47 times leads to an increase in the number of optically active Si−C-bonds in several times

Both the peak areas and the number of bonds do not increase linearly with the increase of concentration and it is not caused by saturation of amplitude values. As in the case of NC/NSi = 0.12, the increase of concentration in 13.3 times at NC/NSi = 0.4, has led to an increase in the amplitude of only 9 times, and an area of 2.1 times (5805 un.) at 1300ºC (Tables 4 and 5), although the amplitude of the IR transmittance at the minimum of the peak is far from saturation (52%). This confirms that the determining factor is the presence of strong clusters, in the structure of which is included the majority of the carbon atoms. That is at 1300ºC in the SiC0.4 layer only n1/n2 = 2.1/13.33 = 16% of the carbon atoms form an optically active Si−C-bonds, and in the SiC0.12 layer − 45%. Then, in the optically inactive stable clusters are included the rest 84% and 55% of carbon atoms (Table 5), respectively, resulting in no increase in peak area proportionally to the concentration of carbon. Since there is a predominance of the tetrahedral oriented bonds among the optically active Si-Cbonds, the amount of tetrahedral Si−C-bonds is sufficient for the appearance of SiC

SiCx SiC 0.03 SiC 0.12 SiC 0.4 SiC 0.7 SiC 0.95 SiC 1.4.

T, ºС A0.03 % A0.03 % A0.03 % A0.03 % A0.03 % A0.03 % 20 0.63 63 1.3. 33 1.7. 13 2.4. 10 1.4. 4 1.6. 3 200 0.68. 68 1.5. 37 1.8 14 2.6 11 1.6 5 2.0 4 400 0.54 54 1,4 36 1.7 13 2.8 12 1.7 5 2.1 5 600 0.62 62 1.5 37 1.7 13 3.1 13 1.9 6 2.0 4 700 0.72 72 1.6 39 1.9 14 3.0 13 2.0 6 2.1 4 800 0.42 42 1.4 35 2.2 17 2.7 12 2.0 6 2.2 5 900 0.71 71 1.5 37 1.9 14 2.9 12 2.1 6 2.4 5 1000 1.00 100 1.5 37 1.7 12 2.8 12 2.0 6 2.8 6 1100 0.76 76 1.4 36 1.6 12 3.0 13 2.3 7 2.7 6 1200 0.90 90 1.9 48 2.0 15 2.9 13 2.8 9 3.0 6 1300 90 1.8 45 2.1 16 3.8 16 3.8 12 4.0 9

Ax Si-C Ax Si-C Ax Si-C Ax Si-C Ax Si-C Ax Si-C

n1=х/0.03 1.0 4.0 13.3. 23.3. 31.7. 46.7.

y(1300ºС) 0.40 0.28 0.42 0.38 0.36

the SiCx layers.

Table 5. Relative values of area (n2 = Ax(T)/A0.03(1000°C)) of IR transmission SiC-peak and the proportion of carbon atoms (100% × n2/n1) which forms an optically active Si-C-bonds in

less than expected − no more than 4.04 times even for high temperature annealing.

crystallites in the layers, which is observed on the X-ray diffraction pattern.

Evaluation results may be debatable, since the literature contains different points of view concerning inclusion of carbon into SiC. Akimchenko et al. (1977a) after implantation of Si (Е = 40 кэВ, D = 3.7×1017 см-2) in diamond and annealing at temperatures of 500-1200ºC assumed that almost 100% of implanted carbon atoms included in the SiC. This conclusion was made from accordance of calculated layer thickness (80 nm) with ones found from the absorption near 810 cm-1 (70 nm). A comparison with the magnitude of the SiC thickness (8−10 nm) obtained by X-ray diffraction, allowed to conclude that 10−15% of atoms of the disordered SiC united into β-SiC crystallites, which contribute to the X-ray reflection, and the rest remains in the amorphous state. Kimura et al. (1982) basing on data from the optical density of the infrared transmission spectra have established that all implanted carbon are included in β-SiC after annealing at 900−1200ºC, if the concentration of implanted carbon is less or equal to the stoichiometric composition of SiC at the peak of the distribution. In the case of higher doses, the excess carbon atoms form clusters and are not included into β-SiC, even after annealing at 1200°C. The activation energy required for inclusion of carbon atoms

in the β-SiC, increases with increasing of implantation doses, since more energy is required for the decomposition of carbon clusters. Durupt et al. (1980) showed that if the annealing temperature below 900ºC, the formation of SiC is less pronounced in the case of high dose, and annealing at higher temperature removes the differences.

On the other hand, Borders et al. (1971) from the infrared absorption and Rutherford backscattering data found that about half of carbon atoms implanted into the silicon (Е = 200 кэВ, D = ~1017 см-2) included in micro-SiC. According to our estimates, the concentration of carbon atoms in the layer was lower than 10% (x <0.1). Kimura et al. (1981) from the analysis of infrared spectra revealed that after implantation (E = 100 keV) and annealing at 900ºC about 40-50% of carbon atoms united with Si atoms to form β-SiC, and this value monotonically increased to 70-80% with increasing of annealing temperature up to 1200ºC. The number of carbon atoms included in the β-SiC was affected by dose of carbon ions. Calcagno et al. (1996) showed that the optical band gap and the intensity of the infrared signal after annealing at 1000ºC increased linearly with carbon concentration, reaching a maximum at the stoichiometric composition of SiC. At higher carbon concentrations intensity of the infrared signal undergoes saturation, and the band gap decreases from 2.2 to 1.8 eV. By Raman spectroscopy is shown that this is due to the formation of clusters of graphite. Simon et al. (1996) after the high-temperature (700ºC) implantation of carbon ions into Si (E = 50 keV, D = 1018 and 2×1018 см-2) show that the carbon excess precipitates out, forming carbon clusters. It is assumed that the stresses and defects, formed after the first stage of implantation, form traps, which attract the following carbon atoms. Liangdeng et al. (2008) after implantation of C ions (E = 80 keV, D = 2.7×1017 ион/cм2) in the Raman spectra observed double band with center in 1380 and 1590 cm-1 corresponding to the range of graphitized amorphous carbon. The authors suggest that since solid solubility of carbon in a-Si at a temperature close to the melting point of Si, is about 1017/cm3, and almost disappears at room temperature, the carbon has a tendency to form precipitates. Bayazitov et al. (2003) after implantation of carbon ions (E = 40 keV, D = 5*×*1017 см*−*2) in silicon and pulsed ion beam annealing (*W* = 1.0 J/cm2, C+(~80%) and H+(~20%)) have formed a β-SiC layer with an average size of grain about 100 nm. Increasing the energy density per pulse up to 1.5 J/cm2 leads also to appearance of graphite grains of sizes about 100 nm, as well as visually observed darkening of the sample. When exposed by radiation of ruby laser (λ = 0.69 μm, τ = 50 nsec, W = 0.5-2 J/cm2) also formed the graphite grains, beginning from W = 0.5 J/cm2.

The Formation of Silicon Carbide in the SiCx Layers

mechanism of the formation of SiC crystallites.

place.

(x = 0.03–1.4) Formed by Multiple Implantation of C Ions in Si 103

1 (Fig. 25a, curves 1 and 2). Decrease in area at 1400°C is associated with a decrease in amplitude at all considered frequencies, especially at 800 cm-1, indicating that the decay of a large number of tetrahedral Si-C-bonds and desorption of ~ 15% of carbon atoms are taken

As shown in Fig. 26 **(**curve 3), the number of optically active **Si**−**C-**bonds in the temperature range 20−1200°C is the highest for the layer SiC0. 7. In the temperature range 20−1300°C, the amplitude at 800 cm-1 increases in 4.4 times from 20 to 87%, while the area of **SiC-**peak grow only in 3.76/2.45 = 1.54 times.. It follows that growth in the number of tetrahedral bonds is taken place not only due to the decay of optically inactive **Si**−**C-**clusters, but as a result of decay of long single **Si**−**C-**bonds as well, which absorb at a frequency of 700 cm-1 **(**Fig. 25c, curve 1 ), with their transformation into a tetrahedral (curve 3) and close to tetrahedral (curve 4) bonds, which absorb near 800 and 850 cm-1. Most intensively this process occurs near the surface of SiC crystallites (Fig.12b) in the range 900−1300°C showing the

The temperature dependence of both the amplitude of the IR transmission at different wave numbers and the area of SiC-peak for the SiC1.4, SiC0.95 and SiC0.7 layers has a similar character, which, as it was mentioned above, indicates the common nature of carbon and carbon-silicon clusters in these layers with a high concentration of carbon. Analysis of the behavior of the curves in Fig. 26 (curves 4, 5 and 6) shows that the curves of the area changes of the peak for the SiC-layers with low carbon concentration SiC0.4, SiC0.12 and SiC0.03 also have the maxima and minima of magnitude, which can be associated with the formation and breaking of bonds and clusters. These layers are characterized by an higher proportion (%) of carbon atoms forming an optically active Si−C-bonds (Table 5), although the total

The value of the area for the SiC0.4 layer in the temperature range 20−1400°C has not a continuous upward trend. Maximum of area at 800°C is due to the formation of tetrahedral and close to tetrahedral bonds, absorbing near 800 and 850 cm**-1 (**Fig. 25d, curves 3 and 4), respectively. The formation of tetrahedral bonds **(**800 cm-1) at temperatures of 900−1100°C **(**Fig. 25d, curve 3) is accompanied by decreasing of peak area due to its narrowing resulting from the decay of long single **Si**−**C-**bonds, which absorbed near 700 and 750 cm-1 and prevailed at temperatures below 800°C. The formation of Si and SiC crystallites in the layer is taken place almost simultaneously, which suggests intense movement of C and Si atoms and the increase in the number of dangling bonds. The increase in area in the range 1200−1300°C **(**Fig. 26) is caused by growth of tetrahedral (Fig. 25, curve 3) and close to tetrahedral **(**Fig. 25, curves 2 and 4) **Si**−**C-**bonds due to decay of optically inactive clusters. For layers SiC0.12 and SiC0.03 with carbon concentration much lower than stoichiometric for SiC, the absence of significant growth of area in the temperature range 200−1100°C is revealed due to the small amount of optically inactive unstable carbon flat nets and chains, the decay of which could cause an intensive formation of absorbing bonds. Nevertheless, a significant increase in amplitude at 800 cm**-**1 is observed due to the formation of tetrahedral bonds. Increase in the area after annealing at 900−1000°C for the SiC0.03 layer together with growth of the amplitudes of all types of optically active **Si**−**C-**bonds may be caused by the formation of silicon crystallites, which accompanied by the displacement of carbon atoms and a reduction in the number of dangling bonds of carbon atoms. For layers SiC0.12 and SiC0.4 the significant growth of area at temperatures 1200−1300°C caused by an increase in the number of all types of optically active bonds due to decay of stable carbon clusters.

number is low in comparison with SiC1.4, SiC0.95 and SiC0.7 layers (Fig. 26).

Tetelbaum et al. (2009) by implantation in SiO2 film of Si ions (E = 100 keV, D = 7×1016 cm-2) provided the concentration of excess silicon at the peak of the ion distribution about 10 at.%. Then the same number of carbon atoms was implanted. The obtained data of the white photoluminescence with bands at ~400, ~500 and ~625 nm, attributed to nanoinclusion of phases of SiC, C, nanoclusters and small nanocrystals Si, respectively (the arguments supported by references to the results of Perez-Rodrguez et al. (2003) and Fan et al. (2006)). Similarly, Zhao et al. (1998) received a peak at 350 nm, and a shifting by the annealing the blue peak at 410−440, 470, 490 nm. The existence of inclusions phases of carbon and silicon carbide in the films of SiO2 in (Tetelbaum et al., 2009) was confirmed by X-ray photoelectron spectroscopy by the presence of the C−C (with energy ~285 eV) and Si−C (with energy ~283 eV). Comparing the amplitudes IRFS one can conclude that a number of C−C is comparable to the number of Si−C-bonds, and a luminescence at 500 nm (carbon clusters) is considerably greater than the luminescence at 400 nm (silicon carbide). Belov et al. (2010) used higher doses of carbon ions (E = 40 keV): 6×1016 см-2, 9×1016 см-2 and 1.2×1017 см-2, in which the concentration of carbon (by our estimation) do not exceed 25% at the maximum of the carbon distribution. The authors believe that the luminescent centers, illuminated at wavelengths below 700 nm, represent the nanoclusters and nanocrystals of (Si:C), and amorphous clusters of diamond-like and graphitized carbon. In this case, with increasing of carbon doses the intensity of photoluminescence from Si nanocrystals (>700 nm) varies little, and concluded that a significant portion of the implanting carbon is included into the carbon clusters. The high content of graphitized clusters in the films also discussed in (Shimizu-Iwayama et al., 1994). All these data suggest that a significant or most of the carbon atoms are composed of carbon clusters, although the concentration of carbon atoms in a layer of "SiO2 + Si + C" was around 9 at.%. In our opinion, this confirms our high estimates of carbon content in the optically inactive C- and C−Si-clusters, made basing the analysis of IR spectra. Analysis of the behavior of the curves in Fig. 26 may be interesting from the point of studying the influence of decay of clusters and Si−C-bonds on the formation of tetrahedral oriented Si-C-bonds. Basing on the analysis one can suggest possible mechanisms of formation of silicon carbide grains in the layer and put forward a number of hypotheses. For example, the growth curves of SiC-peak area for the SiC1.4, SiC0.95 and SiC0.7 layers with a high carbon concentration have the maxima of values, which may be related with the formation and breaking of bonds and clusters in the implanted layer. Intensive growth of area in the range 1100−1300°C caused by the decay of stable optically inactive clusters (Table 5) and an increase in the number of all types of Si−C-bonds absorbing at all frequencies of considered range, in particular, the tetrahedral oriented bonds (800 cm-1). However, the growth of these bonds (curves 3 in Figure 25) is not always accompanied by an increase in area under the IR transmittance peak.

Variation of the peak area for the SiC1,4 layer (Fig. 26) has peaks at 400, 1000 and 1300°C. The growth of the peak area in the range of 20−800°C for SiC1.4, SiC0.95 and SiC0.7 layers with high carbon concentrations is caused by a weak ordering of the amorphous layer and the formation of optically active Si−C-bonds, including the tetrahedral oriented bonds (Fig. 25a). Significant growth of area in the range 800−1000°C is resulted by an increase of the absorption in the range 800±50 cm-1, i.e. by an intensive formation of the tetrahedral and near tetrahedral Si−C-bonds due to the decay of such optically inactive clusters as flat nets and chains (Fig. 24). Decrease of Si−C-peak area (Fig. 26, curves 1 and 3) in ranges of 400−600°C or 600−800°C caused by decay of long single bonds absorbing near 700 or 750 cm-

Tetelbaum et al. (2009) by implantation in SiO2 film of Si ions (E = 100 keV, D = 7×1016 cm-2) provided the concentration of excess silicon at the peak of the ion distribution about 10 at.%. Then the same number of carbon atoms was implanted. The obtained data of the white photoluminescence with bands at ~400, ~500 and ~625 nm, attributed to nanoinclusion of phases of SiC, C, nanoclusters and small nanocrystals Si, respectively (the arguments supported by references to the results of Perez-Rodrguez et al. (2003) and Fan et al. (2006)). Similarly, Zhao et al. (1998) received a peak at 350 nm, and a shifting by the annealing the blue peak at 410−440, 470, 490 nm. The existence of inclusions phases of carbon and silicon carbide in the films of SiO2 in (Tetelbaum et al., 2009) was confirmed by X-ray photoelectron spectroscopy by the presence of the C−C (with energy ~285 eV) and Si−C (with energy ~283 eV). Comparing the amplitudes IRFS one can conclude that a number of C−C is comparable to the number of Si−C-bonds, and a luminescence at 500 nm (carbon clusters) is considerably greater than the luminescence at 400 nm (silicon carbide). Belov et al. (2010) used higher doses of carbon ions (E = 40 keV): 6×1016 см-2, 9×1016 см-2 and 1.2×1017 см-2, in which the concentration of carbon (by our estimation) do not exceed 25% at the maximum of the carbon distribution. The authors believe that the luminescent centers, illuminated at wavelengths below 700 nm, represent the nanoclusters and nanocrystals of (Si:C), and amorphous clusters of diamond-like and graphitized carbon. In this case, with increasing of carbon doses the intensity of photoluminescence from Si nanocrystals (>700 nm) varies little, and concluded that a significant portion of the implanting carbon is included into the carbon clusters. The high content of graphitized clusters in the films also discussed in (Shimizu-Iwayama et al., 1994). All these data suggest that a significant or most of the carbon atoms are composed of carbon clusters, although the concentration of carbon atoms in a layer of "SiO2 + Si + C" was around 9 at.%. In our opinion, this confirms our high estimates of carbon content in the optically inactive C- and C−Si-clusters, made basing the analysis of IR spectra. Analysis of the behavior of the curves in Fig. 26 may be interesting from the point of studying the influence of decay of clusters and Si−C-bonds on the formation of tetrahedral oriented Si-C-bonds. Basing on the analysis one can suggest possible mechanisms of formation of silicon carbide grains in the layer and put forward a number of hypotheses. For example, the growth curves of SiC-peak area for the SiC1.4, SiC0.95 and SiC0.7 layers with a high carbon concentration have the maxima of values, which may be related with the formation and breaking of bonds and clusters in the implanted layer. Intensive growth of area in the range 1100−1300°C caused by the decay of stable optically inactive clusters (Table 5) and an increase in the number of all types of Si−C-bonds absorbing at all frequencies of considered range, in particular, the tetrahedral oriented bonds (800 cm-1). However, the growth of these bonds (curves 3 in Figure 25) is not always accompanied by an increase in

Variation of the peak area for the SiC1,4 layer (Fig. 26) has peaks at 400, 1000 and 1300°C. The growth of the peak area in the range of 20−800°C for SiC1.4, SiC0.95 and SiC0.7 layers with high carbon concentrations is caused by a weak ordering of the amorphous layer and the formation of optically active Si−C-bonds, including the tetrahedral oriented bonds (Fig. 25a). Significant growth of area in the range 800−1000°C is resulted by an increase of the absorption in the range 800±50 cm-1, i.e. by an intensive formation of the tetrahedral and near tetrahedral Si−C-bonds due to the decay of such optically inactive clusters as flat nets and chains (Fig. 24). Decrease of Si−C-peak area (Fig. 26, curves 1 and 3) in ranges of 400−600°C or 600−800°C caused by decay of long single bonds absorbing near 700 or 750 cm-

area under the IR transmittance peak.

1 (Fig. 25a, curves 1 and 2). Decrease in area at 1400°C is associated with a decrease in amplitude at all considered frequencies, especially at 800 cm-1, indicating that the decay of a large number of tetrahedral Si-C-bonds and desorption of ~ 15% of carbon atoms are taken place.

As shown in Fig. 26 **(**curve 3), the number of optically active **Si**−**C-**bonds in the temperature range 20−1200°C is the highest for the layer SiC0. 7. In the temperature range 20−1300°C, the amplitude at 800 cm-1 increases in 4.4 times from 20 to 87%, while the area of **SiC-**peak grow only in 3.76/2.45 = 1.54 times.. It follows that growth in the number of tetrahedral bonds is taken place not only due to the decay of optically inactive **Si**−**C-**clusters, but as a result of decay of long single **Si**−**C-**bonds as well, which absorb at a frequency of 700 cm-1 **(**Fig. 25c, curve 1 ), with their transformation into a tetrahedral (curve 3) and close to tetrahedral (curve 4) bonds, which absorb near 800 and 850 cm-1. Most intensively this process occurs near the surface of SiC crystallites (Fig.12b) in the range 900−1300°C showing the mechanism of the formation of SiC crystallites.

The temperature dependence of both the amplitude of the IR transmission at different wave numbers and the area of SiC-peak for the SiC1.4, SiC0.95 and SiC0.7 layers has a similar character, which, as it was mentioned above, indicates the common nature of carbon and carbon-silicon clusters in these layers with a high concentration of carbon. Analysis of the behavior of the curves in Fig. 26 (curves 4, 5 and 6) shows that the curves of the area changes of the peak for the SiC-layers with low carbon concentration SiC0.4, SiC0.12 and SiC0.03 also have the maxima and minima of magnitude, which can be associated with the formation and breaking of bonds and clusters. These layers are characterized by an higher proportion (%) of carbon atoms forming an optically active Si−C-bonds (Table 5), although the total number is low in comparison with SiC1.4, SiC0.95 and SiC0.7 layers (Fig. 26).

The value of the area for the SiC0.4 layer in the temperature range 20−1400°C has not a continuous upward trend. Maximum of area at 800°C is due to the formation of tetrahedral and close to tetrahedral bonds, absorbing near 800 and 850 cm**-1 (**Fig. 25d, curves 3 and 4), respectively. The formation of tetrahedral bonds **(**800 cm-1) at temperatures of 900−1100°C **(**Fig. 25d, curve 3) is accompanied by decreasing of peak area due to its narrowing resulting from the decay of long single **Si**−**C-**bonds, which absorbed near 700 and 750 cm-1 and prevailed at temperatures below 800°C. The formation of Si and SiC crystallites in the layer is taken place almost simultaneously, which suggests intense movement of C and Si atoms and the increase in the number of dangling bonds. The increase in area in the range 1200−1300°C **(**Fig. 26) is caused by growth of tetrahedral (Fig. 25, curve 3) and close to tetrahedral **(**Fig. 25, curves 2 and 4) **Si**−**C-**bonds due to decay of optically inactive clusters.

For layers SiC0.12 and SiC0.03 with carbon concentration much lower than stoichiometric for SiC, the absence of significant growth of area in the temperature range 200−1100°C is revealed due to the small amount of optically inactive unstable carbon flat nets and chains, the decay of which could cause an intensive formation of absorbing bonds. Nevertheless, a significant increase in amplitude at 800 cm**-**1 is observed due to the formation of tetrahedral bonds. Increase in the area after annealing at 900−1000°C for the SiC0.03 layer together with growth of the amplitudes of all types of optically active **Si**−**C-**bonds may be caused by the formation of silicon crystallites, which accompanied by the displacement of carbon atoms and a reduction in the number of dangling bonds of carbon atoms. For layers SiC0.12 and SiC0.4 the significant growth of area at temperatures 1200−1300°C caused by an increase in the number of all types of optically active bonds due to decay of stable carbon clusters.

The Formation of Silicon Carbide in the SiCx Layers

concentration of strong clusters.

glow discharge hydrogen plasma.

а)

at the temperature 900°С for 30 min (b).

0,20

0,30

0,40

0,50

**Transmittance**

0,60

0,70

minutes.

(x = 0.03–1.4) Formed by Multiple Implantation of C Ions in Si 105

temperatures of about 100°C lower than for the layers SiC1.4, SiC0.95 and SiC0.7 due to a lower

Thus, we have shown a negative effect of stable carbon and carbon-silicon clusters on the crystallization of SiC in the layers. Heat treatment up to 1200ºC does not lead to complete disintegration of the clusters and the release of C and Si atoms to form SiC. In this regard, identification of alternative ways of processing the films to break down clusters and form a more qualitative structure of the SiC films is important. As shown in section 3.3, the characteristics of glow discharge hydrogen plasma and treatment (27.12 MHz, 12.5 W, 6.5 Pa, 100°C, 5 min) were sufficient to decay the tetrahedral Si−Si and Si−C-bonds and can be used for the destruction of stable carbon and carbon−silicon clusters. For IR analysis, the sample with the SiC0.95 film was cut into two parts and one of these samples was treated by hydrogen plasma. Fig. 28 shows the IR transmittance spectra of these SiC0.95 layers, untreated by plasma (a) and treated by hydrogen plasma (b) after annealing at 900ºC for 30

Peak maxima occur at 790 cm-1, indicating the prevalence of tetrahedral oriented Si−C-bonds characteristic of crystalline SiC. Measurements of the half-widths of the spectra in Fig. 28a, b give the magnitudes 148 and 78 cm-1 for pre-untreated and treated by hydrogen plasma SiC0.95 layer, respectively. If the value of 148 cm-1 is characteristic for the temperature range 900−1000°C (Fig. 27, curve 2), but the value of 78 cm-1, in principle, was unattainable for the SiC0.95 layer without pre-treatment by plasma throughout the temperature range 200−1400°C. Thus, we can conclude that annealing at 900°C of SiC0.95 layers, treated by hydrogen plasma with power of 12.5 watts only, has led to the formation of β-SiC crystalline layer, which superior in structure quality the untreated by plasma layer subjected to isochronous annealing in the range 200−1400°C. Obviously, the observed effects of plasmainduced crystallization is a consequence of the decay of clusters in the pre-treatment by

0,05

Fig. 28. IR transmission spectra for SiC0.95 layer after annealing at the temperature 900°С for 30 min (a) and after processing by glow discharge hydrogen plasma for 5 min and annealing

400 700 1000 1300 **Wave number, cm-1**

0,15

0,25

0,35

**Transmittance**

400 700 1000 1300 **Wave number, cm-1**

0,45

0,55

b)

The half-width of the Si−C-peak of IR transmission were measured (Fig. 27). Narrowing of the peak occurs due to intensive formation of tetrahedral oriented Si−C-bonds, absorbing at 800 cm-1, and decay of bonds, which absorb at frequencies far from the value of 800 cm-1. Since the tetrahedral bonds correspond to the crystalline phase of silicon carbide, so the narrowing of the SiC-peak of the IR spectrum is related with the processes of the implanted layer ordering. For a layer SiC1.4 a sharp narrowing of the peak from 300 to 110 cm-1 is taken place in the range 800−1200°C, and then the half-width does not change significantly. The most intensively this process occurs in the range 900−1000°C. On X-ray diffraction patterns (Fig. 7), the appearance of lines of polycrystalline β-SiC was observed after annealing at 1200°C and above. This implies that the appearance of SiC crystallites in the layer is recorded when the formation of tetrahedral bonds (peak narrowing) is substantially complete (110 cm-1). Assumptions about the relationship between the size of SiC crystallites and half-width of the peak were also expressed in (Wong et al., 1998; Chen et al., 1999). For the SiC0. 7 layer in range 900−1000°C, a sharp narrowing of the peak from 280 to 85 cm-1 is taken place and occurred more intensive up to 67 cm-1 at 1200°C than for layers with a higher carbon concentration SiC0.95 (115 cm-1, 1200°C) and SiC1.4 (108 cm-1, 1300°C), indicating a much lower concentration of strong clusters in the layer SiC0.7.

Fig. 27. Effect of the annealing temperature on the FWHM of the IR transmittance SiC-peak for TO phonons under normal incidence of IR radiation on the sample surface: 1 − SiC1.4, 2 − SiC0.95, 3 − SiC0.7, 4 − SiC0.4, 5 − SiC0.12, 6 − SiC0.03.

For a layer SiC0.12, a sharp narrowing of the peak from 240 to 100 cm-1 (Fig. 27, curve 5) in the range 800−1100°C is shown, and then is not substantially reduced, demonstrating the formation of polycrystalline SiC phase at this temperature. In general, for the SiC0.4, SiC0.12 and SiC0.03 layers with low carbon concentration a sharp narrowing of the peak occurs at

The half-width of the Si−C-peak of IR transmission were measured (Fig. 27). Narrowing of the peak occurs due to intensive formation of tetrahedral oriented Si−C-bonds, absorbing at 800 cm-1, and decay of bonds, which absorb at frequencies far from the value of 800 cm-1. Since the tetrahedral bonds correspond to the crystalline phase of silicon carbide, so the narrowing of the SiC-peak of the IR spectrum is related with the processes of the implanted layer ordering. For a layer SiC1.4 a sharp narrowing of the peak from 300 to 110 cm-1 is taken place in the range 800−1200°C, and then the half-width does not change significantly. The most intensively this process occurs in the range 900−1000°C. On X-ray diffraction patterns (Fig. 7), the appearance of lines of polycrystalline β-SiC was observed after annealing at 1200°C and above. This implies that the appearance of SiC crystallites in the layer is recorded when the formation of tetrahedral bonds (peak narrowing) is substantially complete (110 cm-1). Assumptions about the relationship between the size of SiC crystallites and half-width of the peak were also expressed in (Wong et al., 1998; Chen et al., 1999). For the SiC0. 7 layer in range 900−1000°C, a sharp narrowing of the peak from 280 to 85 cm-1 is taken place and occurred more intensive up to 67 cm-1 at 1200°C than for layers with a higher carbon concentration SiC0.95 (115 cm-1, 1200°C) and SiC1.4 (108 cm-1, 1300°C),

indicating a much lower concentration of strong clusters in the layer SiC0.7.

**1**

 **6**

 **5**

**4**

**0 200 400 600 800 1000 1200 1400 Temperature, <sup>о</sup>**

Fig. 27. Effect of the annealing temperature on the FWHM of the IR transmittance SiC-peak for TO phonons under normal incidence of IR radiation on the sample surface: 1 − SiC1.4, 2 −

For a layer SiC0.12, a sharp narrowing of the peak from 240 to 100 cm-1 (Fig. 27, curve 5) in the range 800−1100°C is shown, and then is not substantially reduced, demonstrating the formation of polycrystalline SiC phase at this temperature. In general, for the SiC0.4, SiC0.12 and SiC0.03 layers with low carbon concentration a sharp narrowing of the peak occurs at

**2**

**С**

**3**

**50**

SiC0.95, 3 − SiC0.7, 4 − SiC0.4, 5 − SiC0.12, 6 − SiC0.03.

**100**

**150**

**200**

**FWHM of the IR transmittance SiC-peak, cm -1**

**250**

**300**

**350**

**400**

temperatures of about 100°C lower than for the layers SiC1.4, SiC0.95 and SiC0.7 due to a lower concentration of strong clusters.

Thus, we have shown a negative effect of stable carbon and carbon-silicon clusters on the crystallization of SiC in the layers. Heat treatment up to 1200ºC does not lead to complete disintegration of the clusters and the release of C and Si atoms to form SiC. In this regard, identification of alternative ways of processing the films to break down clusters and form a more qualitative structure of the SiC films is important. As shown in section 3.3, the characteristics of glow discharge hydrogen plasma and treatment (27.12 MHz, 12.5 W, 6.5 Pa, 100°C, 5 min) were sufficient to decay the tetrahedral Si−Si and Si−C-bonds and can be used for the destruction of stable carbon and carbon−silicon clusters. For IR analysis, the sample with the SiC0.95 film was cut into two parts and one of these samples was treated by hydrogen plasma. Fig. 28 shows the IR transmittance spectra of these SiC0.95 layers, untreated by plasma (a) and treated by hydrogen plasma (b) after annealing at 900ºC for 30 minutes.

Peak maxima occur at 790 cm-1, indicating the prevalence of tetrahedral oriented Si−C-bonds characteristic of crystalline SiC. Measurements of the half-widths of the spectra in Fig. 28a, b give the magnitudes 148 and 78 cm-1 for pre-untreated and treated by hydrogen plasma SiC0.95 layer, respectively. If the value of 148 cm-1 is characteristic for the temperature range 900−1000°C (Fig. 27, curve 2), but the value of 78 cm-1, in principle, was unattainable for the SiC0.95 layer without pre-treatment by plasma throughout the temperature range 200−1400°C. Thus, we can conclude that annealing at 900°C of SiC0.95 layers, treated by hydrogen plasma with power of 12.5 watts only, has led to the formation of β-SiC crystalline layer, which superior in structure quality the untreated by plasma layer subjected to isochronous annealing in the range 200−1400°C. Obviously, the observed effects of plasmainduced crystallization is a consequence of the decay of clusters in the pre-treatment by glow discharge hydrogen plasma.

Fig. 28. IR transmission spectra for SiC0.95 layer after annealing at the temperature 900°С for 30 min (a) and after processing by glow discharge hydrogen plasma for 5 min and annealing at the temperature 900°С for 30 min (b).

The Formation of Silicon Carbide in the SiCx Layers

(x = 0.03–1.4) Formed by Multiple Implantation of C Ions in Si 107

Fig. 30. Atomic force microscopy of the surface of SiCx layers with various carbon

In Fig. 31 the AFM data on changes in surface topography of the annealed at 1400°C SiC1.4 layer before (Fig. 31a) and after (Fig. 31b and c) processing by glow discharge hydrogen plasma (27.12 MHz, 12.5 W, 6.5 Pa, 100°C, 5 min) in two various areas with sizes of 1 × 1 um2, are presented. The more increased fragments are also shown. Processing by hydrogen plasma does not lead to complete destruction of the granular structure (Fig. 31b), although in some areas granular structure significantly damaged (Fig. 31c), which correlates with the

Fig. 31. Atomic force microscopy of SiC1.4 layers after annealing at the temperature of 1400°С

(a) and subsequent processing by glow discharge hydrogen plasma for 5 min (b, c).

concentration before and after high temperature annealing

X-ray data (Fig. 7).

#### **3.5 Investigations by atomic force microscopy**

AFM studies of the surface microstructure of the surface of the SiC0.95 layer of area 500 × 500 nm2, and 1 × 1 um2 show (Fig. 29a), that after implantation, the surface of the layer looks flat with fluctuations in the height ranged within 6 nm. The areas above the average line of the surface have bright light colors and the areas below the same have dark colors, from which begins the account of height. Annealing at 800°C (Fig. 29b) leads to the deformation of the surface and to an appearance of furrows indicating an intensive translations of atoms. After annealing at 1400°C the surface consists of grains with sizes of 30−50 nm. The variations in height ranged within 66 nm. Comparison of grain sizes with X-ray data on the average crystallite sizes of SiC (3−10 nm) shows that the grains are composed of crystallites of SiC.

Fig. 29. AFM images from the surface of thin (~130 nm) SiC0.95 film (a) after multiple implantation and annealing at (b) 800°C and (c) 1400°C.

In general, we can see that after implantation the surfaces of SiC1.4, SiC0.95, SiC0.7, SiC0.4 and SiC0.12 layers looks smooth with the fluctuations of the height in range of 2−6 nm (Fig. 30). At temperatures of 800−1400°C the surface of these layers are deformed with the formation of grains with sizes of ~30−100 nm. For example, after implantation the smooth surface of SiC1.4 layer looks broken with fluctuations of the height in range of 2 nm. Annealing at 1400°C leads to a clear fragmentation of grains on the surface. It is seen that the grains with sizes of ~100 nm are composed of subgrains, which probably represent the SiC crystallites with an average size of 10 nm. The surface of SiC0.7 layer, after annealing at 1250ºC for 30 minutes, consists of granules of a size of 50−100 nm and flat areas.

Amorphous after implantation, the surface structure of the SiC0.4 layer is also transformed after annealing at 1200ºC for 30 minutes and forms a granular structure consisting of spherical grains of Si and SiC with sizes of ~ 50−100 nm, which suggests an intensive movements of atoms in this layer at high temperature due to the lower content of stable clusters in the film. The surface of the SiC0.12 layer after annealing at 1400°C consists of grains with sizes of 50 nm. The smooth surface of SiC0.03 layer is recrystallized at 1250°C and contains evenly distributed inclusions of SiC in the form of point protrusions with a diameter of 20 nm (Fig. 30).

AFM studies of the surface microstructure of the surface of the SiC0.95 layer of area 500 × 500 nm2, and 1 × 1 um2 show (Fig. 29a), that after implantation, the surface of the layer looks flat with fluctuations in the height ranged within 6 nm. The areas above the average line of the surface have bright light colors and the areas below the same have dark colors, from which begins the account of height. Annealing at 800°C (Fig. 29b) leads to the deformation of the surface and to an appearance of furrows indicating an intensive translations of atoms. After annealing at 1400°C the surface consists of grains with sizes of 30−50 nm. The variations in height ranged within 66 nm. Comparison of grain sizes with X-ray data on the average crystallite sizes of SiC (3−10 nm) shows that the grains are

> **250 [nm]**

implantation and annealing at (b) 800°C and (c) 1400°C.

minutes, consists of granules of a size of 50−100 nm and flat areas.

Fig. 29. AFM images from the surface of thin (~130 nm) SiC0.95 film (a) after multiple

In general, we can see that after implantation the surfaces of SiC1.4, SiC0.95, SiC0.7, SiC0.4 and SiC0.12 layers looks smooth with the fluctuations of the height in range of 2−6 nm (Fig. 30). At temperatures of 800−1400°C the surface of these layers are deformed with the formation of grains with sizes of ~30−100 nm. For example, after implantation the smooth surface of SiC1.4 layer looks broken with fluctuations of the height in range of 2 nm. Annealing at 1400°C leads to a clear fragmentation of grains on the surface. It is seen that the grains with sizes of ~100 nm are composed of subgrains, which probably represent the SiC crystallites with an average size of 10 nm. The surface of SiC0.7 layer, after annealing at 1250ºC for 30

Amorphous after implantation, the surface structure of the SiC0.4 layer is also transformed after annealing at 1200ºC for 30 minutes and forms a granular structure consisting of spherical grains of Si and SiC with sizes of ~ 50−100 nm, which suggests an intensive movements of atoms in this layer at high temperature due to the lower content of stable clusters in the film. The surface of the SiC0.12 layer after annealing at 1400°C consists of grains with sizes of 50 nm. The smooth surface of SiC0.03 layer is recrystallized at 1250°C and contains evenly distributed inclusions of SiC in the form of point protrusions with a

**(a) (b) (c)** 

**250 [nm]** 

**3.5 Investigations by atomic force microscopy** 

composed of crystallites of SiC.

**250 [nm]** 

diameter of 20 nm (Fig. 30).

Fig. 30. Atomic force microscopy of the surface of SiCx layers with various carbon concentration before and after high temperature annealing

In Fig. 31 the AFM data on changes in surface topography of the annealed at 1400°C SiC1.4 layer before (Fig. 31a) and after (Fig. 31b and c) processing by glow discharge hydrogen plasma (27.12 MHz, 12.5 W, 6.5 Pa, 100°C, 5 min) in two various areas with sizes of 1 × 1 um2, are presented. The more increased fragments are also shown. Processing by hydrogen plasma does not lead to complete destruction of the granular structure (Fig. 31b), although in some areas granular structure significantly damaged (Fig. 31c), which correlates with the X-ray data (Fig. 7).

Fig. 31. Atomic force microscopy of SiC1.4 layers after annealing at the temperature of 1400°С (a) and subsequent processing by glow discharge hydrogen plasma for 5 min (b, c).

The Formation of Silicon Carbide in the SiCx Layers

transition "film − substrate".

~20 nm.

**5. Acknowledgement** 

**6. References** 

(x = 0.03–1.4) Formed by Multiple Implantation of C Ions in Si 109

4. The regularities of changes in the surface structure of the SiCx layers (x = 0.03−1.4) with the increase of temperature are revealed. At temperatures of 800−1400°C the surface layers are deformed with the formation of grains with sizes of ~30−100 nm, consisting of crystallites, and the recrystallized at 1250°C smooth surface of SiC0.03 layer contains evenly distributed Si:C inclusions in the form of point protrusions with a diameter of

5. Size effects were revealed, which manifested in the influence of the crystallite sizes of silicon carbide on its optical properties. The differences of the SiC0.03, SiC0.12 and SiC0.4 layers with low carbon concentration from the SiC1.4, SiC0.95 and SiC0.7 layers with high carbon concentration are manifested in the absence of LO-phonon peak of SiC in the IR transmission spectra and in a shift at 1000°C of minimum SiC-peak for TO phonons in the region of wave numbers higher than 800 cm-1 characteristic for the tetrahedral bonds of crystalline SiC, which is caused by small sizes of SiC crystallites (≤ 3 nm) and by an increase of contribution in the IR absorption of their surfaces, and the surfaces of

6. The estimations of the proportion of carbon atoms that form clusters in the SiCх layers are evaluated. At 1300°C in the SiC1.4 layer only ~9% of C atoms form the optically active Si−C-bonds, in SiC0.95 − 12%, in SiC0.7 and SiC0.4 − 16%, in SiC0.12 − 45%, while the remaining carbon atoms are included in composition of stable clusters. The total number N of formed Si−C-bonds in SiCx layers was growing with a fractional power of carbon concentration x: N = а·(n1)y, where y ≈ 0.37±0.09, n1= х/0.03, а = const. 7. It was shown that processing by hydrogen glow discharge plasma (27.12 MHz, 12.5 W, 6.5 Pa, 100°C, 5 min) of polycrystalline SiC1.4 layer leads to partial disintegration of β-SiC crystallites in layer and complete decay of Si crystallites in the transition layer "film−substrate" ("SiC−Si"). Processing by plasma and annealing at 900°C of SiC0.95 layer has led to the formation of β-SiC crystalline layer, which superior in structure quality the untreated by plasma layer subjected to isochronous annealing in the range 200−1400°C. Phenomenon of plasma-induced crystallization is a consequence of the

decay of clusters during pre-treatment by glow discharge hydrogen plasma.

The authors are very grateful to Mukhamedshina D.M. for processing the samples by glow

Akimchenko, I.P., Kisseleva, K.V., Krasnopevtsev, V.V., Milyutin, Yu.V., Touryanski, A.G.,

Akimchenko, I.P., Kazdaev, H.P., Krasopevtsev, V.V. (1977). IK-pogloshenie β-SiC,

silicon by ion implantation. Radiation Effects, Vol. 33., pp.75–80.

Vavilov, V.S. (1977). The structure of silicon carbide synthesized in diamond and

sintezirovannogo pri ionnoi implantacii C v Si. Fizika i Tekhnika Poluprovodnikov,

Si crystallites containing strong short Si−C-bonds as well.

discharge hydrogen plasma and Mit' K.A. for AFM measurements.

T.11, vyp. 10., pp.1964-1966 (in Rusiian).

Si−C-clusters, is consisted of Si crystallites with average size ~25 nm, 25% of the volume − β-SiC crystallite with size of ~5 nm and 25% − the c-Si recrystallized near the

Fig. 32a, b shows the surface areas of the untreated by hydrogen plasma SiC0.95 film after annealing at 900°C, which have a granular structure and consist of grains with sizes within ~50−250 nm. On the enlarged fragments one can also see the flat areas which can be associated with the amorphous component. Surface after treatment by glow discharge hydrogen plasma for 5 min and annealing at 900°C has a more developed granular structure (Fig. 32c, d) and consist of grains with sizes within ~150−400 nm. These results correlate with the IR spectroscopy data (Fig. 28).

Fig. 32. Atomic force microscopy of SiC0.95 layer: (a, b) after synthesis and annealing at the temperature of 900°С for 30 min; (c, d) after synthesis, processing by glow discharge hydrogen plasma for 5 min and annealing at 900°С for 30 min.

#### **4. Conclusion**


Fig. 32a, b shows the surface areas of the untreated by hydrogen plasma SiC0.95 film after annealing at 900°C, which have a granular structure and consist of grains with sizes within ~50−250 nm. On the enlarged fragments one can also see the flat areas which can be associated with the amorphous component. Surface after treatment by glow discharge hydrogen plasma for 5 min and annealing at 900°C has a more developed granular structure (Fig. 32c, d) and consist of grains with sizes within ~150−400 nm. These results correlate

Fig. 32. Atomic force microscopy of SiC0.95 layer: (a, b) after synthesis and annealing at the temperature of 900°С for 30 min; (c, d) after synthesis, processing by glow discharge

1. For SiCx layers, formed by multiple ion implantation in Si of +C12 ions with energies 40, 20, 10, 5 and 3 keV, the regularities of influence of the decay of clusters and optically active bonds on the formation of tetrahedral oriented Si−C-bonds, characteristic of crystalline silicon carbide, were revealed. Formation of these bonds in the SiC1.4, SiC0.95 and SiC0.7 layers with a high carbon concentration occurs mainly as a result of the decay of optically inactive Si−C-clusters in the temperature range 900−1300°C; in SiC0.12 and SiC0.4 layers − as a result of the decay of clusters in the range of 1200−1300°C and of optically active long single Si−C-bonds in the range of 700−1200°C; in SiC0.03 layers − by reducing the number of dangling bonds of carbon atoms in the range 900−1000°C. 2. The values of carbon concentration in silicon and the temperature ranges which are optimal for the formation of SiC, are revealed. After annealing at 1200°C of homogeneous SiCx layers, largest sizes of spherical, needle- and plate-type SiC grains up to 400 nm and the largest number of tetrahedral oriented Si−C-bonds are observed for the SiC0.7 layer, which is due to a low carbon content in the SiC0.03, SiC0.12 and SiC0.4 layers, and a high concentration of strong clusters in the SiC0.95 and SiC1.4 layers. In the range of 800−900ºC the most number of tetrahedral Si−C-bonds is characteristic for

3. A structural model of SiC0.12 layer, which shows the changes in phase composition, phase volume and average crystallite size of SiC and Si in the temperature range 20−1250°C, is proposed. After annealing at 1200°C, about 50% of its volume, free from

hydrogen plasma for 5 min and annealing at 900°С for 30 min.

with the IR spectroscopy data (Fig. 28).

**4. Conclusion** 

SiC0.4 layers.

Si−C-clusters, is consisted of Si crystallites with average size ~25 nm, 25% of the volume − β-SiC crystallite with size of ~5 nm and 25% − the c-Si recrystallized near the transition "film − substrate".


#### **5. Acknowledgement**

The authors are very grateful to Mukhamedshina D.M. for processing the samples by glow discharge hydrogen plasma and Mit' K.A. for AFM measurements.

#### **6. References**


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**5** 

J.M. Molina

*Spain* 

**SiC as Base of Composite Materials** 

*Departamento de Química Inorgánica, Universidad de Alicante* 

*Instituto Universitario de Materiales de Alicante, Universidad de Alicante* 

Some of the high-end applications in energy-related topics such as electronics, aeronautics and research in elementary particles have reached their technological limits because of the impossibility of finding materials capable of removing the excessive heat generated in running their equipments and, at the same time, maintaining their dimensional stability in environments often extremely aggressive, namely, wide temperature range of use (218- 423K), corrosive environments (>98% humidity), fast heating-cooling cycles or interaction with accelerated particles. The growing needs for thermal control are a consequence of the unlimited increasing power consumption in the operation of their equipments. These applications, that exclude the use of monolithic materials given their required unique combination of properties, force the use of composite materials that exhibit high heat transport and, at the same time, do maintain their dimensional stability under operational conditions. Despite the significant progress in the development of composite materials for these applications in recent years, nowadays there is a need to find new materials capable of withstanding the extreme conditions that are impingingly demanded for the new heat sinks. Power electronics and optoelectronics demand thermal conductivities (TC) above 350 W/mK and 450 W/mK respectively; aeronautics is less demanding (>250 W/mK). The coefficients of thermal expansion (CTE) should be matched to those of the architectures on which they are mounted to prevent failures by thermo-mechanical fatigue (it is required 3-6 ppm/K for optoelectronics and less than 12 ppm/K for power electronics, both in the 293- 500K range, and 10-14 ppm/K in the range 233-344 K for aeronautics). In applications such as collimators in particle accelerators, apart from a great resistance to radiation damage, materials with more than 300 W/mK of CT and approximately 10-12 ppm/K of CTE are needed. All applications require isotropic materials with a flexural strength of >120 MPa

SiC-based metal matrix composite materials have shown, up to now, a perfect combination of properties such that to cover the increasing demanding of the energy-related industries. Among them, Al/SiC has become a leader material and nowadays is considered the state-ofthe-art in thermal management. This material, in which SiC is present as particulate, cannot meet the future requirements for heat dissipation and dimensional control given its limited thermal conductivity (about 180 W/mK) and relatively high coefficient of thermal

and the lowest possible density, especially those for aeronautics.

**1. Introduction** 

**for Thermal Management** 


### **SiC as Base of Composite Materials for Thermal Management**

J.M. Molina

*Instituto Universitario de Materiales de Alicante, Universidad de Alicante Departamento de Química Inorgánica, Universidad de Alicante Spain* 

#### **1. Introduction**

114 Silicon Carbide – Materials, Processing and Applications in Electronic Devices

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R.W.M., Lео, W.M.L. (2000). Study on SiC layers synthesized with carbon ion beam at low substrate temperature. Diamond and related materials, Vol. 9, pp. 1795–

(1998). Intense short wavelength photoluminescence from thermal SiO2 films co-

Some of the high-end applications in energy-related topics such as electronics, aeronautics and research in elementary particles have reached their technological limits because of the impossibility of finding materials capable of removing the excessive heat generated in running their equipments and, at the same time, maintaining their dimensional stability in environments often extremely aggressive, namely, wide temperature range of use (218- 423K), corrosive environments (>98% humidity), fast heating-cooling cycles or interaction with accelerated particles. The growing needs for thermal control are a consequence of the unlimited increasing power consumption in the operation of their equipments. These applications, that exclude the use of monolithic materials given their required unique combination of properties, force the use of composite materials that exhibit high heat transport and, at the same time, do maintain their dimensional stability under operational conditions. Despite the significant progress in the development of composite materials for these applications in recent years, nowadays there is a need to find new materials capable of withstanding the extreme conditions that are impingingly demanded for the new heat sinks. Power electronics and optoelectronics demand thermal conductivities (TC) above 350 W/mK and 450 W/mK respectively; aeronautics is less demanding (>250 W/mK). The coefficients of thermal expansion (CTE) should be matched to those of the architectures on which they are mounted to prevent failures by thermo-mechanical fatigue (it is required 3-6 ppm/K for optoelectronics and less than 12 ppm/K for power electronics, both in the 293- 500K range, and 10-14 ppm/K in the range 233-344 K for aeronautics). In applications such as collimators in particle accelerators, apart from a great resistance to radiation damage, materials with more than 300 W/mK of CT and approximately 10-12 ppm/K of CTE are needed. All applications require isotropic materials with a flexural strength of >120 MPa and the lowest possible density, especially those for aeronautics.

SiC-based metal matrix composite materials have shown, up to now, a perfect combination of properties such that to cover the increasing demanding of the energy-related industries. Among them, Al/SiC has become a leader material and nowadays is considered the state-ofthe-art in thermal management. This material, in which SiC is present as particulate, cannot meet the future requirements for heat dissipation and dimensional control given its limited thermal conductivity (about 180 W/mK) and relatively high coefficient of thermal

SiC as Base of Composite Materials for Thermal Management 117

the sake of comparison we shall mention that very pure SiC particles can be as costly as three times the price of those of normal grades (less than 99.8% purity). Their thermal conductivity is somehow higher but nevertheless not sufficient to justify their use in comparison to other less expensive ceramics (like diamond). Diamond, in its turn, has a very high thermal conductivity but the performance/price ratio is still its limiting factor. However, seemingly this ceramic represents a good choice for the coming future in the electronics industry given that their price has followed a continuously decreasing tendency

> 0 10 20 30 40 coefficient of thermal expansion (ppm/K)

Al

Cu Ag

Fig. 1. Ashby's map of thermal conductivity and coefficient of thermal expansion for

On the side of metals, aluminium turns out to be one of the most attractive. Although its thermal properties are not excellent, is a light metal and has a low melting point. Its combination with SiC in proper amounts may generate composite materials with the desired properties for thermal management. Given that the thermal conductivities of both SiC and Al are very similar, the expected value of this property for their composites is rather in the same range. The most accounting effect on composites is the thermal expansion coefficient, which can be varied over a wide range by playing with the volume fraction of Al and SiC phases. In fact, in view of the Ashby's map, it becomes apparent that high volume fractions of SiC are necessary if the coefficient of thermal expansion needs to be considerably reduced. It is this last condition what limits in practice the number of fabrication procedures

As a general rule, only those processing techniques that allow obtain a high volume fraction of reinforcement are useful. In this sense, infiltration of the molten metal into packed preforms has been recognized as the most appropriate procedure. Since most ceramics are not wetted by molten metals, infiltration typically requires be pressure-assisted. The way in which the molten metal is forced into the open space of the ceramic preform determines the two main infiltration techniques, namely gas-pressure infiltration and squeeze casting (or mechanically-assisted infiltration). Alternatively, the powder-metallurgy technique has also been used for those systems where the configuration of the preform is such that intrusion techniques become difficult or where the preform might suffer of dimensional damage

metals ceramics

during the last ten years.

0

200

SiC

that can be chosen in order to manufacture composites for heat sinking.

400

600

thermal conductivity (W/mK)

different metallic and ceramic materials

when high pressures are required.

800

1000

diamond

1200

expansion (around 10 ppm/K). For this reason, during the last years research has been directed to develop new and alternative materials that can replace the traditional Al/SiC and allow the emergence and growth of new and more efficient equipments. Several solutions have been proposed, most of them based on the use of different finely divided reinforcement materials embedded in a metallic matrix. The use of metals as matrix seems to be a question with no discussion, since metal consolidates the preform, is thermally stable (something important for some applications), is lighter than many ceramics and at the same time allows in most cases an easier machining process. Moreover, the global properties of the material can be widely varied by playing with the metallurgical state of the metallic matrix. Al, Ag and Cu and their corresponding alloys with interfacial active elements have proven to be appropriate matrices for composites conceived and designed for the above mentioned applications. Nowadays, among the different options considered as reinforcements in composites for electronics we find that SiC is still leadering the choice. Different combinations of SiC with other reinforcements (such as alumina or diamond) or the use of mixtures of SiC particles of different sizes (bimodal or multimodal distributions of particles) have proven to be essential to match the extreme requirements of electronics. A very recent composite material, developed and patented at the University of Alicante, is based on the use of mixtures of graphite flakes and SiC particles (or alternatively other reinforcements) in order to make a preform in which flakes tend to form layered structures. The SiC particles act as a separator between layers of flakes and on the other hand allow reduce the thermal expansion coefficient in the transversal direction which otherwise would be inadmissibly high. One clear competitor for the SiC-based composites is the family of those fabricated with diamond particles. Even though their thermal properties are very attractive they pose important problems related to obtain pieces with complicated geometries, as diamond is very difficult or even impossible to be machined. Within this scenario the new research on composites based on machinable reinforcements seems to be the only industrially attractive option for many applications.

Most of these composites are fabricated by pressure infiltration of the metal into the preform, assisted either by gas or by mechanical means (squeeze casting). The selection of proper materials quality as well as of optimal fabrication conditions is completely essential to meet the target properties.

The present chapter presents different SiC-based composite materials which have been evolving over time aiming to be useful for thermal management. It also analyzes the different aspects of the fabrication that affect the thermal properties of these composites.

#### **2. Fabrication procedures of composites for thermal management**

The limitations of metallic materials that had traditionally been used as heat sinks in the electronic industry very soon attracted the attention of other alternative systems. The composite materials made out of metals as matrix and ceramics as reinforcement became immediately potential candidates for a wide variety of applications in electronic packaging (Clyne, 2000a). The following Ashby's map allow us to think about the different possibilities of metal-ceramic combinations for the aforementioned applications.

Among ceramics, SiC is one with relatively high thermal conductivity (500 W/mK for monocristalls, 250-350 for polycristals) and a coefficient of thermal expansion (around 4.7 ppm/K) very close to that of silicon (2.5-3.6 ppm/K). Its low price, especially for the nonmost pure forms of SiC, makes this ceramic to have a very high performance/price ratio. For

expansion (around 10 ppm/K). For this reason, during the last years research has been directed to develop new and alternative materials that can replace the traditional Al/SiC and allow the emergence and growth of new and more efficient equipments. Several solutions have been proposed, most of them based on the use of different finely divided reinforcement materials embedded in a metallic matrix. The use of metals as matrix seems to be a question with no discussion, since metal consolidates the preform, is thermally stable (something important for some applications), is lighter than many ceramics and at the same time allows in most cases an easier machining process. Moreover, the global properties of the material can be widely varied by playing with the metallurgical state of the metallic matrix. Al, Ag and Cu and their corresponding alloys with interfacial active elements have proven to be appropriate matrices for composites conceived and designed for the above mentioned applications. Nowadays, among the different options considered as reinforcements in composites for electronics we find that SiC is still leadering the choice. Different combinations of SiC with other reinforcements (such as alumina or diamond) or the use of mixtures of SiC particles of different sizes (bimodal or multimodal distributions of particles) have proven to be essential to match the extreme requirements of electronics. A very recent composite material, developed and patented at the University of Alicante, is based on the use of mixtures of graphite flakes and SiC particles (or alternatively other reinforcements) in order to make a preform in which flakes tend to form layered structures. The SiC particles act as a separator between layers of flakes and on the other hand allow reduce the thermal expansion coefficient in the transversal direction which otherwise would be inadmissibly high. One clear competitor for the SiC-based composites is the family of those fabricated with diamond particles. Even though their thermal properties are very attractive they pose important problems related to obtain pieces with complicated geometries, as diamond is very difficult or even impossible to be machined. Within this scenario the new research on composites based on machinable reinforcements seems to be

Most of these composites are fabricated by pressure infiltration of the metal into the preform, assisted either by gas or by mechanical means (squeeze casting). The selection of proper materials quality as well as of optimal fabrication conditions is completely essential

The present chapter presents different SiC-based composite materials which have been evolving over time aiming to be useful for thermal management. It also analyzes the different aspects of the fabrication that affect the thermal properties of these composites.

The limitations of metallic materials that had traditionally been used as heat sinks in the electronic industry very soon attracted the attention of other alternative systems. The composite materials made out of metals as matrix and ceramics as reinforcement became immediately potential candidates for a wide variety of applications in electronic packaging (Clyne, 2000a). The following Ashby's map allow us to think about the different possibilities

Among ceramics, SiC is one with relatively high thermal conductivity (500 W/mK for monocristalls, 250-350 for polycristals) and a coefficient of thermal expansion (around 4.7 ppm/K) very close to that of silicon (2.5-3.6 ppm/K). Its low price, especially for the nonmost pure forms of SiC, makes this ceramic to have a very high performance/price ratio. For

**2. Fabrication procedures of composites for thermal management** 

of metal-ceramic combinations for the aforementioned applications.

the only industrially attractive option for many applications.

to meet the target properties.

the sake of comparison we shall mention that very pure SiC particles can be as costly as three times the price of those of normal grades (less than 99.8% purity). Their thermal conductivity is somehow higher but nevertheless not sufficient to justify their use in comparison to other less expensive ceramics (like diamond). Diamond, in its turn, has a very high thermal conductivity but the performance/price ratio is still its limiting factor. However, seemingly this ceramic represents a good choice for the coming future in the electronics industry given that their price has followed a continuously decreasing tendency during the last ten years.

Fig. 1. Ashby's map of thermal conductivity and coefficient of thermal expansion for different metallic and ceramic materials

On the side of metals, aluminium turns out to be one of the most attractive. Although its thermal properties are not excellent, is a light metal and has a low melting point. Its combination with SiC in proper amounts may generate composite materials with the desired properties for thermal management. Given that the thermal conductivities of both SiC and Al are very similar, the expected value of this property for their composites is rather in the same range. The most accounting effect on composites is the thermal expansion coefficient, which can be varied over a wide range by playing with the volume fraction of Al and SiC phases. In fact, in view of the Ashby's map, it becomes apparent that high volume fractions of SiC are necessary if the coefficient of thermal expansion needs to be considerably reduced. It is this last condition what limits in practice the number of fabrication procedures that can be chosen in order to manufacture composites for heat sinking.

As a general rule, only those processing techniques that allow obtain a high volume fraction of reinforcement are useful. In this sense, infiltration of the molten metal into packed preforms has been recognized as the most appropriate procedure. Since most ceramics are not wetted by molten metals, infiltration typically requires be pressure-assisted. The way in which the molten metal is forced into the open space of the ceramic preform determines the two main infiltration techniques, namely gas-pressure infiltration and squeeze casting (or mechanically-assisted infiltration). Alternatively, the powder-metallurgy technique has also been used for those systems where the configuration of the preform is such that intrusion techniques become difficult or where the preform might suffer of dimensional damage when high pressures are required.

SiC as Base of Composite Materials for Thermal Management 119

equipment but at the same time has to be thermally stable in order to maintain the dimensionality of the architecture on which they are mounted. This already points out that the main properties that are essential for those materials are two: thermal conductivity and thermal expansion coefficient. While the former needs to be as high as possible the later is restricted to a certain range, typically between the limits of 3 and 14 ppm/K. Although these two properties are limiting, other characteristics of the materials (i.e. density, cost) may also take a significant importance for certain applications. In the present context only the two

Thermal conductivity is measured by mainly two means. The simplest one consists of comparing the thermal conduction of the sample with a reference material by connecting the sections of both and establishing a thermal gradient. It is called the comparative stationary method and provides accurate and relatively fast measurements. Another more sophisticated method is based on the use of a laser flash, which measures the heat propagation in nonstationary conditions caused by the flash of a laser impacting the surface of the material. The coefficient of thermal expansion is typically accessed through the use of a thermomechanical analyser, which subjects the sample to a thermal cycling over a certain range of temperature. The dimensions of the sample are followed in one, two or alternatively three axis. In fact, what is measured is the dimension change with the increase in temperature

A very simple and tentative model for the estimation of this property in composite materials

 α

where the subscripts *m* and *r* denote matrix and reinforcement, respectively. This simple approach is called the linear rule of mixtures and offers a back-of-the-envelope calculation

More sophisticated treatments are all based on thermoelasticity theory (Clyne, 2000b). Schapery's model gives upper (+) and lower (-) bounds on the CTE. The specific expression

1

*<sup>r</sup> c m <sup>m</sup>*

*<sup>V</sup> K K <sup>V</sup>*

' ' '

<sup>+</sup> <sup>−</sup> <sup>+</sup>

*K K <sup>K</sup>*

*r m m m*

( ) 1

( ) ( ) ( ) ( )

−

4 3

μ

−

−

<sup>−</sup> is Hashin and Shtrickman's lower bound to the bulk

(2)

(3)

'''

*KKK*

' '' *mr c*

*K KK*

−

*c rm*

=+− *rr m r V V* (1)

consists of averaging over the volume fraction of the corresponding phases:

αα

( ) ( )

=+ −

*r mr*

of what the coefficient of thermal expansion must approximately be.

 α αα

α

+

( )

' '

<sup>−</sup> = +

main properties are reviewed.

(units of ppm/K).

for the former is:

**3.2 Measurement of thermal properties** 

**3.3 Estimation (modelling) of thermal properties** 

**3.3.1 Coefficient of thermal expansion** 

where *K'* refers to bulk modulus; ( ) ' *<sup>K</sup> <sup>c</sup>*

modulus of the composite, namely,

#### **2.1 Gas-pressure assisted infiltration**

In general, pressure does not exceed 15MPa and this allows fabricate pieces with complex shapes without taking the risk of a considerable deformation of the preform. The method is highly versatile because, with a simple modification of the main mould, pieces of different geometries can be fabricated. Final machining is sometimes needed although, if moulds are properly designed in such a way that the demoulding process turns out not to be difficult, neat-shape fabrication is feasible. The main drawback of this technique stems from the limited rate of metal penetration into the preforms, resulting difficult the manufacture of large pieces. This restriction is a consequence of the technology characteristics; in particular of the low pressures applied and the wettability-reactivity characteristics of the system at hand.

#### **2.2 Mechanically-assisted infiltration**

The metal is forced to penetrate into the ceramic preform at very high pressures (in the range 50-100 MPa) by means of a piston mechanically driven. This method is called "squeeze casting" and its application into the fabrication of MMC's is very extended, although it is not free of drawbacks related with the high pressures used. This may cause deformations in the preforms that alter the global shape and the relative presence of metal and ceramic phases. The solution to this problem not always seems to be found by diminishing the working pressure because infiltration rate or metal-ceramic reaction are for some systems important issues to be considered. The necessity of huge installations, occasionally very expensive, is another drawback of squeeze casting. Its main advantage is that the high working pressures effectively ensure infiltration and the final composite materials can be free of remaining porosity.

#### **2.3 Powder-metallurgy**

Although powder metallurgy has become an excellent technique for the manufacturing of relatively complicate shaped metallic pieces, in the field of composite materials is not an extensively used fabrication method. This technique allows obtaining high volume fractions of reinforcement (75%) and moreover offers a perfect control of reactivity between metal and ceramic phases. However, a clear drawback is the difficulty encountered for the control of porosity in the material, which seems a phase that inherently appears when using this technique. The control of the oxygen content (as metallic oxides existing concomitantly in the metallic powder) seems also to limit the possible massive use of this technique in the industrial fabrication of composite materials.

Recently, another technique derived from the already mentioned powder-metallurgy has become a matter of interest. This technique is called "spark-plasma" and it consists of heating the metallic or graphitic mould, as well as the powder compact in case of conductive samples, by means of an electrical current that flows through it. This technique allows a fast processing of the materials but, nevertheless, it suffers from the same disadvantages of the classical powder-metallurgy route.

#### **3. Measurement and estimation of thermal properties in composites for thermal management**

#### **3.1 Property needs in materials for electronics**

As already explained, there are several requirements for those materials considered for electronics. An ideal heat sink must extract the heat generated in excess in a given running equipment but at the same time has to be thermally stable in order to maintain the dimensionality of the architecture on which they are mounted. This already points out that the main properties that are essential for those materials are two: thermal conductivity and thermal expansion coefficient. While the former needs to be as high as possible the later is restricted to a certain range, typically between the limits of 3 and 14 ppm/K. Although these two properties are limiting, other characteristics of the materials (i.e. density, cost) may also take a significant importance for certain applications. In the present context only the two main properties are reviewed.

#### **3.2 Measurement of thermal properties**

118 Silicon Carbide – Materials, Processing and Applications in Electronic Devices

In general, pressure does not exceed 15MPa and this allows fabricate pieces with complex shapes without taking the risk of a considerable deformation of the preform. The method is highly versatile because, with a simple modification of the main mould, pieces of different geometries can be fabricated. Final machining is sometimes needed although, if moulds are properly designed in such a way that the demoulding process turns out not to be difficult, neat-shape fabrication is feasible. The main drawback of this technique stems from the limited rate of metal penetration into the preforms, resulting difficult the manufacture of large pieces. This restriction is a consequence of the technology characteristics; in particular of the low

The metal is forced to penetrate into the ceramic preform at very high pressures (in the range 50-100 MPa) by means of a piston mechanically driven. This method is called "squeeze casting" and its application into the fabrication of MMC's is very extended, although it is not free of drawbacks related with the high pressures used. This may cause deformations in the preforms that alter the global shape and the relative presence of metal and ceramic phases. The solution to this problem not always seems to be found by diminishing the working pressure because infiltration rate or metal-ceramic reaction are for some systems important issues to be considered. The necessity of huge installations, occasionally very expensive, is another drawback of squeeze casting. Its main advantage is that the high working pressures effectively

pressures applied and the wettability-reactivity characteristics of the system at hand.

ensure infiltration and the final composite materials can be free of remaining porosity.

Although powder metallurgy has become an excellent technique for the manufacturing of relatively complicate shaped metallic pieces, in the field of composite materials is not an extensively used fabrication method. This technique allows obtaining high volume fractions of reinforcement (75%) and moreover offers a perfect control of reactivity between metal and ceramic phases. However, a clear drawback is the difficulty encountered for the control of porosity in the material, which seems a phase that inherently appears when using this technique. The control of the oxygen content (as metallic oxides existing concomitantly in the metallic powder) seems also to limit the possible massive use of this technique in the

Recently, another technique derived from the already mentioned powder-metallurgy has become a matter of interest. This technique is called "spark-plasma" and it consists of heating the metallic or graphitic mould, as well as the powder compact in case of conductive samples, by means of an electrical current that flows through it. This technique allows a fast processing of the materials but, nevertheless, it suffers from the same disadvantages of the

**3. Measurement and estimation of thermal properties in composites for** 

As already explained, there are several requirements for those materials considered for electronics. An ideal heat sink must extract the heat generated in excess in a given running

**2.1 Gas-pressure assisted infiltration** 

**2.2 Mechanically-assisted infiltration** 

industrial fabrication of composite materials.

**3.1 Property needs in materials for electronics** 

classical powder-metallurgy route.

**thermal management** 

**2.3 Powder-metallurgy** 

Thermal conductivity is measured by mainly two means. The simplest one consists of comparing the thermal conduction of the sample with a reference material by connecting the sections of both and establishing a thermal gradient. It is called the comparative stationary method and provides accurate and relatively fast measurements. Another more sophisticated method is based on the use of a laser flash, which measures the heat propagation in nonstationary conditions caused by the flash of a laser impacting the surface of the material.

The coefficient of thermal expansion is typically accessed through the use of a thermomechanical analyser, which subjects the sample to a thermal cycling over a certain range of temperature. The dimensions of the sample are followed in one, two or alternatively three axis. In fact, what is measured is the dimension change with the increase in temperature (units of ppm/K).

#### **3.3 Estimation (modelling) of thermal properties**

#### **3.3.1 Coefficient of thermal expansion**

A very simple and tentative model for the estimation of this property in composite materials consists of averaging over the volume fraction of the corresponding phases:

$$
\alpha = \alpha\_r V\_r + \alpha\_m \left(1 - V\_r\right) \tag{1}
$$

where the subscripts *m* and *r* denote matrix and reinforcement, respectively. This simple approach is called the linear rule of mixtures and offers a back-of-the-envelope calculation of what the coefficient of thermal expansion must approximately be.

More sophisticated treatments are all based on thermoelasticity theory (Clyne, 2000b). Schapery's model gives upper (+) and lower (-) bounds on the CTE. The specific expression for the former is:

$$\alpha^{(+)} = \alpha\_r + (\alpha\_m - \alpha\_r) \frac{K\_m^{\prime} \left( K\_r^{\prime} - K\_c^{\prime (-)} \right)}{K\_c^{(-)} \left( K\_r^{\prime} - K\_m^{\prime} \right)} \tag{2}$$

where *K'* refers to bulk modulus; ( ) ' *<sup>K</sup> <sup>c</sup>* <sup>−</sup> is Hashin and Shtrickman's lower bound to the bulk modulus of the composite, namely,

$$K\_c^{(-)} = K\_m^\prime + \frac{V\_r}{\frac{1}{K\_r^\prime - K\_m^\prime} + \frac{V\_m}{K\_m^\prime + \frac{4}{3}\mu\_m}}\tag{3}$$

SiC as Base of Composite Materials for Thermal Management 121

Nowadays it is easy to find many suppliers of silicon carbide in different forms (i.e. particles, fibers, sheets, rods, tubes) with a relatively huge variety of dimensions. The market of these products is related to abrasive or refractory applications. When speaking about fabrication of composite materials, different sources of silicon carbide, all finely divided (like particles or fibers), are mainly searched (Clyne, 2000a). Among all these forms of silicon carbide being used as reinforcements for composite fabrication, particles of different purity grades and shapes have been mostly used. The commonest particles are angular in shape (Fig. 2), although some have being processed with perfect spherical geometry. Though spherical shapes are always interesting for modelling purposes its use has been restricted due to its prohibitive price. SiC particles are mainly fabricated in two grades, differentiated by its colour: green powder for purities higher than 99% and black

(a) (b) Fig. 2. Scanning electron microscopy images of commercial particles of SiC of two different average size diameters: (a) 170 μm (corresponding to 100 mesh; SiC100) and (b) 17 μm

An important parameter of particulate systems is the relation between their average diameter and specific surface area, measured by means of a laser diffraction technique and gas adsorption, respectively. The importance of this correlation will be shown later on in

6

ρ

introduced to account deviations from sphericity, surface roughness and particle size

milling of SiC blocks and turns out to be especially important for the modelling of

*D*

ρ

*r*

typically takes values greater than unity for angular particles prepared by

<sup>=</sup> <sup>⋅</sup> (7)

is the density of SiC (with a nominal value of

is a geometrical factor

λ

*S* λ

Mathematically, these two intrinsic properties are related as follows:

3210 kg/m3), *Sr* is the specific surface area (m2/kg) and

**4. SiC-based composite materials for thermal management applications** 

**4.1 SiC reinforcements** 

powder for purities in the range 98%-99%.

(corresponding to 500 mesh; SiC500)

where *D* is the average particle diameter,

next sections.

distribution.

λ

different properties.

where μ*<sup>m</sup>* is the shear modulus of the matrix. The upper bound to the bulk modulus is obtained by interchanging the subscripts *m* and *r* everywhere in Eq. (3) which, when inserted in Eq. (2), gives the lower bound on the CTE.

#### **3.3.2 Thermal conductivity**

The thermal conductivity of composite materials containing thermally conductive inclusions has been extensively studied. One of the simplest analytical models that assume a nonidealized interface between matrix and reinforcement is that derived by Hasselman and Johnson for spherical particles in a pore-free infinite matrix (Clyne, 2000b):

$$K\_c = \frac{K\_m \left[ 2K\_m + K\_r^{eff} + 2V\_r \left( K\_r^{eff} - K\_m \right) \right]}{2K\_m + K\_r^{eff} - V\_r \left( K\_r^{eff} - K\_m \right)} \tag{4}$$

where *K* is the thermal conductivity, *eff K* is the effective thermal conductivity, *V* is the volume fraction, and the subscripts *c*, *m* and *r* refer to composite, matrix and reinforcement, respectively. This model has been proved to give accurate predictions when particles and matrix exhibit a low ratio of conductivities, which is the case for SiC particles and pure Al or many Al-based alloys. The effective thermal conductivity of particles *eff Kr* is defined as:

$$K\_r^{eff} = \frac{K\_r^{in}}{1 + \frac{2K\_r^{in}}{D \cdot h}} \tag{5}$$

where *in Kr* stands for the intrinsic thermal conductivity of the particles, and *D* and *h* are the average particle diameter and the interfacial thermal conductance, respectively.

The differential effective medium (DEM) scheme has been applied with success to model and interpret transport properties in different composite materials (Clyne, 2000b; Molina et al., 2008a; Molina et al., 2008b; Molina et al., 2009; Tavangar et al., 2007; Weber et al., 2010). Its predictive capacity is in many cases considerably superior to other available models in literature (see for example (Tavangar et al., 2007)). The leading integral equation of the DEM approach for the thermal conductivity of a multi-phase composite material is:

$$\int\_{K\_m}^{K\_c} \frac{dK}{K \sum\_i f\_i \frac{-\left(K - K\_{r\_i}^{eff}\right)}{\left(K - K\_{r\_i}^{eff}\right) \cdot P - K}} = -\ln\left(1 - V\_r\right) \tag{6}$$

where *Kc* is the thermal conductivity of the composite material, *fi* is the fraction of the *i* inclusion in the total amount of inclusions of the composite (hence, i*f*i=1) and *P* is the polarization factor of the inclusion. *<sup>i</sup> eff Kr* is the effective thermal conductivity of the *<sup>i</sup>* inclusion, which is related to its intrinsic thermal conductivity, *in Kr* , the matrix/inclusion interface thermal conductance *h*, and the diameter *D* of the inclusion by Eq. (5).

In general, the integral on the left hand side of Eq. (6) has no analytical solution and has to be solved numerically by means of appropriate mathematical software.

#### **4. SiC-based composite materials for thermal management applications**

#### **4.1 SiC reinforcements**

120 Silicon Carbide – Materials, Processing and Applications in Electronic Devices

obtained by interchanging the subscripts *m* and *r* everywhere in Eq. (3) which, when

The thermal conductivity of composite materials containing thermally conductive inclusions has been extensively studied. One of the simplest analytical models that assume a nonidealized interface between matrix and reinforcement is that derived by Hasselman and

2 2

*K K K VK K*

where *K* is the thermal conductivity, *eff K* is the effective thermal conductivity, *V* is the volume fraction, and the subscripts *c*, *m* and *r* refer to composite, matrix and reinforcement, respectively. This model has been proved to give accurate predictions when particles and matrix exhibit a low ratio of conductivities, which is the case for SiC particles and pure Al or many Al-based alloys. The effective thermal conductivity of

<sup>2</sup> <sup>1</sup>

where *in Kr* stands for the intrinsic thermal conductivity of the particles, and *D* and *h* are the

The differential effective medium (DEM) scheme has been applied with success to model and interpret transport properties in different composite materials (Clyne, 2000b; Molina et al., 2008a; Molina et al., 2008b; Molina et al., 2009; Tavangar et al., 2007; Weber et al., 2010). Its predictive capacity is in many cases considerably superior to other available models in literature (see for example (Tavangar et al., 2007)). The leading integral equation of the DEM

( )

− ⋅−

where *Kc* is the thermal conductivity of the composite material, *fi* is the fraction of the *i* inclusion in the total amount of inclusions of the composite (hence, i*f*i=1) and *P* is the

inclusion, which is related to its intrinsic thermal conductivity, *in Kr* , the matrix/inclusion

In general, the integral on the left hand side of Eq. (6) has no analytical solution and has to

*K K K f KK PK*

*<sup>r</sup> <sup>K</sup> eff r*

ln( ) 1 *<sup>c</sup>*

*dK <sup>V</sup>*

=− −

*eff Kr* is the effective thermal conductivity of the *<sup>i</sup>*

*i*

( )

− −

*i i eff r*

interface thermal conductance *h*, and the diameter *D* of the inclusion by Eq. (5).

be solved numerically by means of appropriate mathematical software.

*i*

<sup>+</sup> <sup>⋅</sup>

*<sup>K</sup> <sup>K</sup>*

=

average particle diameter and the interfacial thermal conductance, respectively.

approach for the thermal conductivity of a multi-phase composite material is:

*m*

*K*

polarization factor of the inclusion. *<sup>i</sup>*

*in eff <sup>r</sup> <sup>r</sup> in*

*K D h*

*r*

*c eff eff*

Johnson for spherical particles in a pore-free infinite matrix (Clyne, 2000b):

2

inserted in Eq. (2), gives the lower bound on the CTE.

*K*

*<sup>m</sup>* is the shear modulus of the matrix. The upper bound to the bulk modulus is

( )

++ − <sup>=</sup> +− − (4)

(5)

(6)

( )

*eff eff m m r rr m*

*m r rr m*

*K K VK K*

where μ

**3.3.2 Thermal conductivity** 

particles *eff Kr* is defined as:

Nowadays it is easy to find many suppliers of silicon carbide in different forms (i.e. particles, fibers, sheets, rods, tubes) with a relatively huge variety of dimensions. The market of these products is related to abrasive or refractory applications. When speaking about fabrication of composite materials, different sources of silicon carbide, all finely divided (like particles or fibers), are mainly searched (Clyne, 2000a). Among all these forms of silicon carbide being used as reinforcements for composite fabrication, particles of different purity grades and shapes have been mostly used. The commonest particles are angular in shape (Fig. 2), although some have being processed with perfect spherical geometry. Though spherical shapes are always interesting for modelling purposes its use has been restricted due to its prohibitive price. SiC particles are mainly fabricated in two grades, differentiated by its colour: green powder for purities higher than 99% and black powder for purities in the range 98%-99%.

Fig. 2. Scanning electron microscopy images of commercial particles of SiC of two different average size diameters: (a) 170 μm (corresponding to 100 mesh; SiC100) and (b) 17 μm (corresponding to 500 mesh; SiC500)

An important parameter of particulate systems is the relation between their average diameter and specific surface area, measured by means of a laser diffraction technique and gas adsorption, respectively. The importance of this correlation will be shown later on in next sections.

Mathematically, these two intrinsic properties are related as follows:

$$D = \frac{6\mathcal{X}}{\rho \cdot S\_r} \tag{7}$$

where *D* is the average particle diameter, ρ is the density of SiC (with a nominal value of 3210 kg/m3), *Sr* is the specific surface area (m2/kg) and λ is a geometrical factor introduced to account deviations from sphericity, surface roughness and particle size distribution. λ typically takes values greater than unity for angular particles prepared by milling of SiC blocks and turns out to be especially important for the modelling of different properties.

SiC as Base of Composite Materials for Thermal Management 123

(a) (b)

SiC particles Vr D (μm) TC (W/mK) CTE (ppm/K) SiC100 0.58 167 221 12.7 SiC180 0.58 86 209 13.2 SiC240 0.6 57 203 12.5 SiC320 0.59 37 204 12.9 SiC400 0.58 23 194 13.1 SiC500 0.55 17 193 13.4 SiC800 0.53 9 154 14.9

Fig. 3. Optical micrographs of cross sections of different samples of Al/SiC composites containing SiC particles of different average size diameters: (a) 17 μm (corresponding to 500

Table 1. Main characteristics of Al/SiC composites with monomodal distribution of particles; Vr is the particle volume fraction, D is the average size determined by laser

4a might be obtained from Eq. (4) or Eq. (6) with almost indistinguishable results.

diffraction, TC is the thermal conductivity (W/mK) and CTE refers to the thermal expansion

Modelling thermal conductivity in these composites is relatively simple. The two model schemes here reviewed are both applicable with similar results given that, as already explained, the phase contrast for aluminium and SiC is close to 1. In this sense, the plot in Fig.

If now we speculate about how thermal conductivity can be improved in these composites, we may think that the thermal conductivity of the SiC filler cannot be increased (for a given quality purity) and that the interface thermal conductance between Al and SiC is indeed of the order 108 W/m2K (in agreement with other experimental works and calculated data with the acoustic mismatch model (Molina et al., 2009). The largest potential comes from the metal, in improving the matrix conductivity to the value of pure aluminium (273 W/mK). In the experiments presented here, gas pressure infiltration was used to fabricate the composites. Seemingly, there was some chemical interaction between the metal and the quartz crucible during the time metal was molten prior to infiltration. The result of this

mesh; SiC500) and (b) 170 μm (corresponding to 100 mesh; SiC100)

coefficient

#### **4.2 Metal matrix composites with reinforcement of mono or multimodal distribution of SiC particles**

For years, the only materials able to mitigate the increasing demanding of heat removal in energy-related industrial applications have been composite materials made out of a proper combination of a metal and SiC particles.

Al/SiC composites have been extensively studied. Less studied materials are those with other metals such as copper or silver. We find only few references to those materials that point out their possible use in thermal management. Their potential as heat-dissipating materials is very high given the intrinsic properties of their constitutive elements. However, several problems arise when manufacturing these materials by liquid state processing routes. Estimates based on standard composite models indicate that the Cu/SiC system containing 50-60 vol.% SiC should yield materials with very good thermal properties: around 275 W/mK of thermal conductivity and 7-9 ppm/K of thermal expansion coefficient. Nevertheless, studies carried out on this system have demonstrated that those thermal properties are not achieved, mainly due to the detrimental reactivity at the metalceramic interface, which conducts to a solid solution of Si into the Cu matrix. An attempt to overcome the problem by protecting the SiC by an oxide layer has been demonstrated to be helpful but still not sufficient to attain the required properties (Narciso et al., 2006).

On its hand, the Ag/SiC system presents a problem of reactivity as well (Narciso et al., 1997, as cited in Molina et al., 2010). Ag dissolves a large amount of oxygen that can react with the SiC particles. The gas evolved in the reaction considerably reduces the metal/ceramic contact area and, hence, affects dramatically the thermal properties of the composite. The solution of oxidizing the SiC particles seems to improve, as in the case of Cu/SiC, the final properties of the material. However, for both systems, Cu/SiC and Ag/SiC, seemingly the only way to achieve the expected thermal properties by liquid state routes is to reduce the contact time between SiC particles and molten metal (details of the importance of the processing route will be given in following sections).

Given that in the Al/SiC system the problems related with reactivity are less accused, admissibly high thermal properties can be easily obtained. We will briefly summarize here two main kinds of materials obtainable when only SiC is used as reinforcement: composites based on a monomodal distribution of SiC particles and those based on bimodal distributions.

#### **4.2.1 Al/SiC with monomodal distribution of particles**

The traditional heat sinks in electronics, based on metallic combinations, promptly found a serious competitor in the Al/SiC family. These materials experimented a great impact on the industries and still nowadays represent the state-of-the-art in thermal management.

One of the most complete data collections on thermal properties of Al/SiC composites with monomodal distribution of particles can be accessed through (Arpon et al., 2003a; Arpon et al., 2003b; Molina et al., 2003a). The materials were fabricated by gas-pressure assisted infiltration of compacted SiC particles with molten Al at 750ºC. Metallographic studies give evidence of the proper distribution of particles in the metal and the absence of particle breaking, given the special care taken during the packing procedure (Fig. 3).

The thermal properties achieved by those composites have been reviewed in the following table (Table 1). It is clearly seen that the dependence of the thermal properties on the material characteristics is different for thermal conductivity and for the coefficient of thermal expansion. While the former depends strongly on the volume fraction and average size of the SiC particles, the latter is only dependent on the volume fraction of SiC.

**4.2 Metal matrix composites with reinforcement of mono or multimodal distribution of** 

For years, the only materials able to mitigate the increasing demanding of heat removal in energy-related industrial applications have been composite materials made out of a proper

Al/SiC composites have been extensively studied. Less studied materials are those with other metals such as copper or silver. We find only few references to those materials that point out their possible use in thermal management. Their potential as heat-dissipating materials is very high given the intrinsic properties of their constitutive elements. However, several problems arise when manufacturing these materials by liquid state processing routes. Estimates based on standard composite models indicate that the Cu/SiC system containing 50-60 vol.% SiC should yield materials with very good thermal properties: around 275 W/mK of thermal conductivity and 7-9 ppm/K of thermal expansion coefficient. Nevertheless, studies carried out on this system have demonstrated that those thermal properties are not achieved, mainly due to the detrimental reactivity at the metalceramic interface, which conducts to a solid solution of Si into the Cu matrix. An attempt to overcome the problem by protecting the SiC by an oxide layer has been demonstrated to be

helpful but still not sufficient to attain the required properties (Narciso et al., 2006).

On its hand, the Ag/SiC system presents a problem of reactivity as well (Narciso et al., 1997, as cited in Molina et al., 2010). Ag dissolves a large amount of oxygen that can react with the SiC particles. The gas evolved in the reaction considerably reduces the metal/ceramic contact area and, hence, affects dramatically the thermal properties of the composite. The solution of oxidizing the SiC particles seems to improve, as in the case of Cu/SiC, the final properties of the material. However, for both systems, Cu/SiC and Ag/SiC, seemingly the only way to achieve the expected thermal properties by liquid state routes is to reduce the contact time between SiC particles and molten metal (details of the importance of the

Given that in the Al/SiC system the problems related with reactivity are less accused, admissibly high thermal properties can be easily obtained. We will briefly summarize here two main kinds of materials obtainable when only SiC is used as reinforcement: composites based

The traditional heat sinks in electronics, based on metallic combinations, promptly found a serious competitor in the Al/SiC family. These materials experimented a great impact on the

One of the most complete data collections on thermal properties of Al/SiC composites with monomodal distribution of particles can be accessed through (Arpon et al., 2003a; Arpon et al., 2003b; Molina et al., 2003a). The materials were fabricated by gas-pressure assisted infiltration of compacted SiC particles with molten Al at 750ºC. Metallographic studies give evidence of the proper distribution of particles in the metal and the absence of particle

The thermal properties achieved by those composites have been reviewed in the following table (Table 1). It is clearly seen that the dependence of the thermal properties on the material characteristics is different for thermal conductivity and for the coefficient of thermal expansion. While the former depends strongly on the volume fraction and average

on a monomodal distribution of SiC particles and those based on bimodal distributions.

industries and still nowadays represent the state-of-the-art in thermal management.

breaking, given the special care taken during the packing procedure (Fig. 3).

size of the SiC particles, the latter is only dependent on the volume fraction of SiC.

**SiC particles** 

combination of a metal and SiC particles.

processing route will be given in following sections).

**4.2.1 Al/SiC with monomodal distribution of particles** 

Fig. 3. Optical micrographs of cross sections of different samples of Al/SiC composites containing SiC particles of different average size diameters: (a) 17 μm (corresponding to 500 mesh; SiC500) and (b) 170 μm (corresponding to 100 mesh; SiC100)


Table 1. Main characteristics of Al/SiC composites with monomodal distribution of particles; Vr is the particle volume fraction, D is the average size determined by laser diffraction, TC is the thermal conductivity (W/mK) and CTE refers to the thermal expansion coefficient

Modelling thermal conductivity in these composites is relatively simple. The two model schemes here reviewed are both applicable with similar results given that, as already explained, the phase contrast for aluminium and SiC is close to 1. In this sense, the plot in Fig. 4a might be obtained from Eq. (4) or Eq. (6) with almost indistinguishable results.

If now we speculate about how thermal conductivity can be improved in these composites, we may think that the thermal conductivity of the SiC filler cannot be increased (for a given quality purity) and that the interface thermal conductance between Al and SiC is indeed of the order 108 W/m2K (in agreement with other experimental works and calculated data with the acoustic mismatch model (Molina et al., 2009). The largest potential comes from the metal, in improving the matrix conductivity to the value of pure aluminium (273 W/mK). In the experiments presented here, gas pressure infiltration was used to fabricate the composites. Seemingly, there was some chemical interaction between the metal and the quartz crucible during the time metal was molten prior to infiltration. The result of this

SiC as Base of Composite Materials for Thermal Management 125

a bimodal mixture is considered (two different particle sizes), the following model with two

1 1 *<sup>r</sup> cp cp*

*<sup>V</sup> <sup>X</sup> X*

*r*

*V*

percentages up to that for which the maximum global compactness is reached.

0.45 0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9

particle volume fraction

<sup>=</sup> <sup>−</sup> <sup>+</sup>

*sp*

(8)

*<sup>X</sup>* <sup>=</sup> (9)

*V*

*cp*

*V*

where *Vr* is the total volume fraction; *Vcp* and *Vsp* are the volume fractions in compacts of only coarse and small particles, respectively; and *Xcp* is the fraction of coarse particles in the

Other mathematical schemes, like that proposed by Yu and Standish (Yu & Standish, 1987, as cited in Molina et al., 2002), make use of experimental information through an empirical parameter with adjustable value. Fig. 5 shows experimental results of packing obtained with mixtures of two largely different sizes of SiC (17 μm and 170 μm). Fig. 5 puts in clear evidence that the particle volume fraction of the compacts made from bimodal mixtures can be tailored by simply controlling the relative amount of large and small particles. Moreover, the experimental results for the particle volume fraction are rationalized using the simple model (Eq. (8) and Eq. (9)) that assumes that small particles can be easily accommodated in the free space left by large particles. Therefore, the local compactness of fine particles is nearly constant for coarse particle

*cp*

0 0.2 0.4 0.6 0.8 1 volume fraction of coarse particles

Fig. 5. Volume fraction of particles attained in packed preforms of a bimodal mixture of SiC formed by angular particles of 17 μm and 170 μm. The continuous lines correspond to the two branches of the simple geometrical model described by Eq. (8) and Eq. (9); the broken line refers to a semiempirical scheme proposed by (Yu & Standish, 1987, as cited in Molina

limits mathematically separated can be applied:

a. Fine particle end

b. Coarse particle end

powder mixture.

et al., 2002).

reaction was that metal was alloyed with Si and the matrix conductivity diminished down to a value as low as 185 W/mK (Molina et al., 2008b).

Fig. 4. Experimental results for Al/SiC composites containing SiC particles of different average size diameters: (a) thermal conductivity compared with predicted values obtained with the DEM scheme (the values taken for modelling are: *Km* = 185 W/mK, *in Kr* = 253 W/mK and *h*= 7.5 107 W/m2 K); and (b) coefficient of thermal expansion (α) versus volume fraction of reinforcement (the line corresponds to a fitting with equation α= -29.88*Vr* + 30.36)

The coefficient of thermal expansion of the different composites versus the SiC volume content is shown in Fig. 4b. All composite materials showed a low value of thermal expansion, increasingly lower when the SiC content is increased. The linear relation encountered for this property with the SiC volume fraction reinforces the conclusion that CTE is only dependent on the volume fraction of the different phases present, in qualitative agreement with most analysis of this property (Arpon et al., 2003a; Molina et al., 2003a), no matter the size, shape or size distribution of the particles.

#### **4.2.2 Al/SiC with bimodal distribution of particles**

For certain high-demanding electronic applications Al/SiC composites based on a monomodal distribution of SiC particles were unable to properly operate as admissible heat sinks. For those applications where the heat generated was in excess and/or the material had to accomplish with very restricted thermal expansion, new methods for increasing the volume fraction of SiC particles in the metal were developed.

It has been established that the minimum volume fraction needed for these composites is about 0.6. The logical reasoning to achieve high volume fractions of particles consists of mixing and packing particles of largely different sizes (size ratio >10). During the past few years diverse groups have been working in the ceramic particle packing of multimodal mixtures (Molina et al., 2002).

A very simple and intuitive model for the prediction of particle packing was presented and validated in (Molina et al., 2002) and the main features can be summarized as follows. When a bimodal mixture is considered (two different particle sizes), the following model with two limits mathematically separated can be applied:

a. Fine particle end

124 Silicon Carbide – Materials, Processing and Applications in Electronic Devices

reaction was that metal was alloyed with Si and the matrix conductivity diminished down

(a) (b)

For certain high-demanding electronic applications Al/SiC composites based on a monomodal distribution of SiC particles were unable to properly operate as admissible heat sinks. For those applications where the heat generated was in excess and/or the material had to accomplish with very restricted thermal expansion, new methods for increasing the

It has been established that the minimum volume fraction needed for these composites is about 0.6. The logical reasoning to achieve high volume fractions of particles consists of mixing and packing particles of largely different sizes (size ratio >10). During the past few years diverse groups have been working in the ceramic particle packing of multimodal

A very simple and intuitive model for the prediction of particle packing was presented and validated in (Molina et al., 2002) and the main features can be summarized as follows. When

Fig. 4. Experimental results for Al/SiC composites containing SiC particles of different average size diameters: (a) thermal conductivity compared with predicted values obtained with the DEM scheme (the values taken for modelling are: *Km* = 185 W/mK, *in Kr* = 253 W/mK and *h*= 7.5 107 W/m2 K); and (b) coefficient of thermal expansion (α) versus volume fraction of reinforcement (the line corresponds to a fitting with equation α= -29.88*Vr* + 30.36) The coefficient of thermal expansion of the different composites versus the SiC volume content is shown in Fig. 4b. All composite materials showed a low value of thermal expansion, increasingly lower when the SiC content is increased. The linear relation encountered for this property with the SiC volume fraction reinforces the conclusion that CTE is only dependent on the volume fraction of the different phases present, in qualitative agreement with most analysis of this property (Arpon et al., 2003a; Molina et al., 2003a), no

10

0.52 0.54 0.56 0.58 0.6 0.62 particle volume fraction

11

12

13

CTE (ppm/K)

14

15

16

to a value as low as 185 W/mK (Molina et al., 2008b).

140 160 180 200 220 240 exp thermal conductivity (W/mK)

matter the size, shape or size distribution of the particles.

volume fraction of SiC particles in the metal were developed.

**4.2.2 Al/SiC with bimodal distribution of particles** 

mixtures (Molina et al., 2002).

calc thermal conductivity (W/mK)

$$V\_r = \frac{1}{X\_{cp} + \frac{1 - X\_{cp}}{V\_{sp}}} \tag{8}$$

b. Coarse particle end

$$V\_r = \frac{V\_{cp}}{X\_{cp}}\tag{9}$$

where *Vr* is the total volume fraction; *Vcp* and *Vsp* are the volume fractions in compacts of only coarse and small particles, respectively; and *Xcp* is the fraction of coarse particles in the powder mixture.

Other mathematical schemes, like that proposed by Yu and Standish (Yu & Standish, 1987, as cited in Molina et al., 2002), make use of experimental information through an empirical parameter with adjustable value. Fig. 5 shows experimental results of packing obtained with mixtures of two largely different sizes of SiC (17 μm and 170 μm). Fig. 5 puts in clear evidence that the particle volume fraction of the compacts made from bimodal mixtures can be tailored by simply controlling the relative amount of large and small particles. Moreover, the experimental results for the particle volume fraction are rationalized using the simple model (Eq. (8) and Eq. (9)) that assumes that small particles can be easily accommodated in the free space left by large particles. Therefore, the local compactness of fine particles is nearly constant for coarse particle percentages up to that for which the maximum global compactness is reached.

Fig. 5. Volume fraction of particles attained in packed preforms of a bimodal mixture of SiC formed by angular particles of 17 μm and 170 μm. The continuous lines correspond to the two branches of the simple geometrical model described by Eq. (8) and Eq. (9); the broken line refers to a semiempirical scheme proposed by (Yu & Standish, 1987, as cited in Molina et al., 2002).

SiC as Base of Composite Materials for Thermal Management 127

The best results are obtained when the model takes into account that, instead of inserting in Eq. (5) the average particle diameter D measured by laser diffraction, the characteristic length scale of the finely divided powder might be better represented by a calculated value of D obtained from the specific surface area of the particles (Eq. (7)) (Molina et al., 2005). When considering bimodal mixtures, a proper length scale characteristic of the particle

<sup>6</sup> ' ' *cp sp*

*V'* is the volume fraction of a given particle size in the mixture; the subscripts *cp* and *sp* refer to coarse and small particles, respectively. Based on experimental measurements the values

Fig. 8a reports results for the coefficient of thermal expansion versus particle volume fraction for all Al/SiC composites presented in Table 1 and Table 2 containing either a single particle size or bimodal particle distributions. As shown in the figure the whole set of data can be satisfactorily accounted for by means of a linear fitting. As already pointed out in the former section, this indicates that what matters, as long as the CTE is concerned, is the global particle volume fraction, neither the particle size and shape nor the particle size

> 0 20 40 60 80 100 % coarse particles

Fig. 7. Thermal conductivity of Al/SiC composites obtained by gas pressure infiltration of aluminium into preforms of bimodal SiC mixtures (SiC100/SiC500) versus the percentage of coarse particles. Dots correspond to experimental results; the dashed lines are different calculations within the DEM scheme. The values taken for modelling are: *Km* = 185 W/mK,

DEM with parameters to fit all monomodals (Table 1) DEM with parameters to fit SiC100 and SiC500

DEM with averaged D

experimental

λ

ρ

deduced for the two particle types here considered are:

thermal conductivity (W/mK)

*in Kr* = 253 W/mK and *h*= 7.5 107 W/m2 K

used for the specific surface area are: *Scp*= 91 m2/kg and *Ssp*= 338 m2/kg.

*cp sp cp sp D VV S S*

 λ

 = +

λ

λ

*cp*=6.8 and

*S* with the volume fraction for

(10)

λ

*sp*=2.7; the values

reinforcement might be obtained by averaging the ratio

each present particle, as follows:

distribution (Arpon et al., 2003a).

of λ

For gas-pressure Al-infiltrated bimodal preforms, optical microscopy revealed that, up to a 60% of coarse particles, the SiC particles appear homogeneously distributed in the Al matrix, being the coarse particles embedded in a bed of small particles (Fig. 6a). For higher percentages of coarse particles, the spaces between the touching large particles were somewhat irregularly filled with the small particles (Fig. 6b).

Fig. 6. Optical micrographs of cross sections of different samples of Al/SiC composites containing a mixture of SiC particles of two largely different sizes (17 μm and 170 μm) in different proportions: (a) 67% coarse particles + 33% small particles; and (b) 75% coarse particles + 25% small particles, showing inhomogeneous filling

The main thermal properties of composite materials obtained by gas pressure infiltration of ceramic preforms containing a bimodal mixture of SiC particles (170 μm + 17 μm) with pure Al are gathered in Table 2.


Table 2. Main characteristics of Al/SiC composites with bimodal distribution of particles (SiC100/SiC500); Vr is the particle volume fraction, TC is the thermal conductivity (W/mK) and CTE refers to the coefficient of thermal expansion (ppm/K)

The experimental results of thermal conductivity for these composites are plotted in Fig. 7 versus the percentage of coarse particles. The results follow a trend similar to that of particle volume fraction (see Fig. 5) illustrating the close relationship between the two magnitudes. The figure shows as well the predictions offered by the DEM model, Eq. (6), for three different series of inputs (Molina et al., 2008b).

For gas-pressure Al-infiltrated bimodal preforms, optical microscopy revealed that, up to a 60% of coarse particles, the SiC particles appear homogeneously distributed in the Al matrix, being the coarse particles embedded in a bed of small particles (Fig. 6a). For higher percentages of coarse particles, the spaces between the touching large particles were

(a) (b)

The main thermal properties of composite materials obtained by gas pressure infiltration of ceramic preforms containing a bimodal mixture of SiC particles (170 μm + 17 μm) with pure

% of coarse particles Vr TC (W/mK) CTE (ppm/K)

25 0.62 215 10.8

50 0.69 220 9.0

67 0.74 228 7.8

75 0.72 225 8.4

Table 2. Main characteristics of Al/SiC composites with bimodal distribution of particles (SiC100/SiC500); Vr is the particle volume fraction, TC is the thermal conductivity (W/mK)

The experimental results of thermal conductivity for these composites are plotted in Fig. 7 versus the percentage of coarse particles. The results follow a trend similar to that of particle volume fraction (see Fig. 5) illustrating the close relationship between the two magnitudes. The figure shows as well the predictions offered by the DEM model, Eq. (6), for three

Fig. 6. Optical micrographs of cross sections of different samples of Al/SiC composites containing a mixture of SiC particles of two largely different sizes (17 μm and 170 μm) in different proportions: (a) 67% coarse particles + 33% small particles; and (b) 75% coarse

somewhat irregularly filled with the small particles (Fig. 6b).

particles + 25% small particles, showing inhomogeneous filling

and CTE refers to the coefficient of thermal expansion (ppm/K)

different series of inputs (Molina et al., 2008b).

Al are gathered in Table 2.

The best results are obtained when the model takes into account that, instead of inserting in Eq. (5) the average particle diameter D measured by laser diffraction, the characteristic length scale of the finely divided powder might be better represented by a calculated value of D obtained from the specific surface area of the particles (Eq. (7)) (Molina et al., 2005). When considering bimodal mixtures, a proper length scale characteristic of the particle reinforcement might be obtained by averaging the ratio λ *S* with the volume fraction for each present particle, as follows:

$$D = \frac{6}{\rho} \left| \frac{\mathcal{A}\_{cp}}{S\_{cp}} V'\_{cp} + \frac{\mathcal{A}\_{sp}}{S\_{sp}} V'\_{sp} \right| \tag{10}$$

*V'* is the volume fraction of a given particle size in the mixture; the subscripts *cp* and *sp* refer to coarse and small particles, respectively. Based on experimental measurements the values of λ deduced for the two particle types here considered are: λ*cp*=6.8 and λ*sp*=2.7; the values used for the specific surface area are: *Scp*= 91 m2/kg and *Ssp*= 338 m2/kg.

Fig. 8a reports results for the coefficient of thermal expansion versus particle volume fraction for all Al/SiC composites presented in Table 1 and Table 2 containing either a single particle size or bimodal particle distributions. As shown in the figure the whole set of data can be satisfactorily accounted for by means of a linear fitting. As already pointed out in the former section, this indicates that what matters, as long as the CTE is concerned, is the global particle volume fraction, neither the particle size and shape nor the particle size distribution (Arpon et al., 2003a).

Fig. 7. Thermal conductivity of Al/SiC composites obtained by gas pressure infiltration of aluminium into preforms of bimodal SiC mixtures (SiC100/SiC500) versus the percentage of coarse particles. Dots correspond to experimental results; the dashed lines are different calculations within the DEM scheme. The values taken for modelling are: *Km* = 185 W/mK, *in Kr* = 253 W/mK and *h*= 7.5 107 W/m2 K

SiC as Base of Composite Materials for Thermal Management 129

very low, given that interface resistance becomes very important for the small particle size here considered (16 μm). A different situation is found when mixtures of diamond-100 (170 μm) and SiC500 (16 μm) are considered, for which the maximum thermal conductivity is about 550 W/mK (that corresponds to a monomodal diamond particle distribution of 170 μm of average diameter). Fig. 9a also includes the calculation for a system in which SiC and

In (Molina et al., 2008a) powder mixtures containing 20, 40, 50, 60, 70, 80 and 90 vol.% of diamond (of about 200 μm of average diameter) were prepared by dry mixing with SiC (of same average size). Given the similarity in shape and size of the diamond and the SiC particles, the relative density of the preforms was in the range of 58 ± 1 vol.% for all

thermal conductivity (W/mK)

 (a) (b) Fig. 9. Thermal conductivity of aluminium-matrix composites containing different mixtures of diamond and SiC particles: (a) calculated values with the DEM scheme for three sets of mixtures; (b) experimental and calculated values with the DEM scheme for mixtures of powders of similar size (200 μm) for two intrinsic values of matrix thermal conductivity

Intrinsic thermal conductivity (W/mK) 259 1450

aluminium (W/m2K) 1.05 × 108 5 ×<sup>107</sup>

and interface thermal conductance with pure aluminium for SiC and diamond

Table 3. Parameters used in the calculations of Fig. 9 for the intrinsic thermal conductivity

The thermal conductivity of these composites was characterised and the results are gathered in Fig. 9b, along with the prediction obtained with the generalized differential effective medium scheme. The composites fabricated with this combination of ceramics exhibit high thermal conductivities for the whole range of ceramic proportions. Modelling in Fig. 9 has

Fig. 9b shows two predictive lines corresponding to different inputs for the intrinsic thermal conductivity of the metal. While for the SiC-rich mixture content end a thermal conductivity of the matrix of 185 is needed to fit experimental data, this value increases to the thermal conductivity of pure aluminium (237 W/mK) for those mixtures with predominant presence

0 0.2 0.4 0.6 0.8 1 diamond fraction of reinforcement

DEM with K(matrix)=185 W/mK DEM with K(matrix)=237 W/mK

SiC Diamond

experimental

diamond particles have the same average diameter (170 μm).

0 0.2 0.4 0.6 0.8 1 diamond fraction of reinforcement

Interface thermal conductance with pure

been developed within the parameters collected in Table 3.

SiC-100 + diamond-500 diamond-100 + SiC-500 SiC-100 + diamond-100

samples.

thermal conductivity (W/mK)

Fig. 8. Thermal expansion coefficient in the range 50-300ºC versus particle volume fraction for Al/SiC composites having either a single particle size (full circles) or bimodal particle distributions (empty circles): (a) fitting by a straight line of equation α= -33.20*Vr* + 32.16; (b) theoretical results predicted by different models

Different theoretical results for the coefficient of thermal expansion have been depicted in Fig. 8b for composites containing mono- and bimodal distributions of SiC particles. The present discrepancies between experimental results and predictions can be qualitatively understood by noting that those two models have been developed using thermoelasticity theory. In this sense, experimental results of CTE obtained at lower temperatures might be closer to the predictive values, given that plastic deformation becomes greater at higher temperatures. These results, in consequence, illustrate the failure of the thermoelasticity framework upon which most theories are based.

#### **4.3 Metal matrix composites with a hybrid mixture of reinforcement (SiC+ceramic) 4.3.1 Metal/SiC-diamond composites**

Being diamond a very interesting ceramic due to its superior thermal properties its use as particulate in metal matrix composites for thermal management applications has been largely evaluated. Many have been the composites fabricated with excellent thermal properties. However, these composites have no lack of some disadvantages: the price of diamond particles makes the material cost too high and machinability is very difficult or even impossible. In an attempt to overcome some of these problems and at the same time combine the unique properties of diamond and SiC together, a new material containing both types of ceramics was presented in (Molina et al., 2008a). The proposal consists of using as reinforcement a mixture of diamond and SiC particles of similar size. The preform is afterwards consolidated with Al by gas pressure infiltration. The aim of using this particular mixture of ceramics is to achieve a decrease in the material costs maintaining the thermal conductivity at a certain high value. In Fig. 9a it is shown the predicted property of thermal conductivity for three different combinations of SiC and diamond particles. As clearly shown, there is no big advantage in using a mixture of SiC100 (170 μm) and diamond-500 (16 μm) in respect to the use of monomodal SiC100 (170 μm) particles. Even when only the most conducting diamond phase is present, the thermal conductivity of the composite is still 128 Silicon Carbide – Materials, Processing and Applications in Electronic Devices

CTE (ppm/K)

 (a) (b) Fig. 8. Thermal expansion coefficient in the range 50-300ºC versus particle volume fraction for Al/SiC composites having either a single particle size (full circles) or bimodal particle distributions (empty circles): (a) fitting by a straight line of equation α= -33.20*Vr* + 32.16; (b)

Different theoretical results for the coefficient of thermal expansion have been depicted in Fig. 8b for composites containing mono- and bimodal distributions of SiC particles. The present discrepancies between experimental results and predictions can be qualitatively understood by noting that those two models have been developed using thermoelasticity theory. In this sense, experimental results of CTE obtained at lower temperatures might be closer to the predictive values, given that plastic deformation becomes greater at higher temperatures. These results, in consequence, illustrate the failure of the thermoelasticity

**4.3 Metal matrix composites with a hybrid mixture of reinforcement (SiC+ceramic)** 

Being diamond a very interesting ceramic due to its superior thermal properties its use as particulate in metal matrix composites for thermal management applications has been largely evaluated. Many have been the composites fabricated with excellent thermal properties. However, these composites have no lack of some disadvantages: the price of diamond particles makes the material cost too high and machinability is very difficult or even impossible. In an attempt to overcome some of these problems and at the same time combine the unique properties of diamond and SiC together, a new material containing both types of ceramics was presented in (Molina et al., 2008a). The proposal consists of using as reinforcement a mixture of diamond and SiC particles of similar size. The preform is afterwards consolidated with Al by gas pressure infiltration. The aim of using this particular mixture of ceramics is to achieve a decrease in the material costs maintaining the thermal conductivity at a certain high value. In Fig. 9a it is shown the predicted property of thermal conductivity for three different combinations of SiC and diamond particles. As clearly shown, there is no big advantage in using a mixture of SiC100 (170 μm) and diamond-500 (16 μm) in respect to the use of monomodal SiC100 (170 μm) particles. Even when only the most conducting diamond phase is present, the thermal conductivity of the composite is still

0.5 0.55 0.6 0.65 0.7 0.75 particle volume fraction

experimental monomodal experimental bimodal rule of mixtures Eq. (1) upper CTE Eq. (2) lower CTE Eq. (2)

CTE (ppm/K)

0.5 0.55 0.6 0.65 0.7 0.75 particle volume fraction

theoretical results predicted by different models

framework upon which most theories are based.

**4.3.1 Metal/SiC-diamond composites** 

experimental monomodal experimental bimodal

very low, given that interface resistance becomes very important for the small particle size here considered (16 μm). A different situation is found when mixtures of diamond-100 (170 μm) and SiC500 (16 μm) are considered, for which the maximum thermal conductivity is about 550 W/mK (that corresponds to a monomodal diamond particle distribution of 170 μm of average diameter). Fig. 9a also includes the calculation for a system in which SiC and diamond particles have the same average diameter (170 μm).

In (Molina et al., 2008a) powder mixtures containing 20, 40, 50, 60, 70, 80 and 90 vol.% of diamond (of about 200 μm of average diameter) were prepared by dry mixing with SiC (of same average size). Given the similarity in shape and size of the diamond and the SiC particles, the relative density of the preforms was in the range of 58 ± 1 vol.% for all samples.

Fig. 9. Thermal conductivity of aluminium-matrix composites containing different mixtures of diamond and SiC particles: (a) calculated values with the DEM scheme for three sets of mixtures; (b) experimental and calculated values with the DEM scheme for mixtures of powders of similar size (200 μm) for two intrinsic values of matrix thermal conductivity


 Table 3. Parameters used in the calculations of Fig. 9 for the intrinsic thermal conductivity and interface thermal conductance with pure aluminium for SiC and diamond

The thermal conductivity of these composites was characterised and the results are gathered in Fig. 9b, along with the prediction obtained with the generalized differential effective medium scheme. The composites fabricated with this combination of ceramics exhibit high thermal conductivities for the whole range of ceramic proportions. Modelling in Fig. 9 has been developed within the parameters collected in Table 3.

Fig. 9b shows two predictive lines corresponding to different inputs for the intrinsic thermal conductivity of the metal. While for the SiC-rich mixture content end a thermal conductivity of the matrix of 185 is needed to fit experimental data, this value increases to the thermal conductivity of pure aluminium (237 W/mK) for those mixtures with predominant presence

SiC as Base of Composite Materials for Thermal Management 131

Table 4 shows the most significant results of the thermal properties for some of these materials. These composites recently developed present exceptionally high values of thermal conductivity. The thermal properties are clearly anisotropic, given the fact mentioned before that graphite flakes are oriented in a plane, for which they exhibit the

Reinforcement Metal Vr CT (W/mK) CTE (ppm/K)

z: 65

z: 64

z: 11 xy: 7.0

z: 11 xy: 8.0

maximum thermal conductivity and the lowest CTE (xy-plane in Table 4).

60% graphite flakes + 40% SiC Al-12%Si 0.88 xy: 368

63% graphite flakes + 37% SiC Ag-3%Si 0.88 xy: 360

graphene planes, while the direction perpendicular to it is denoted by z

applications and represents a clear alternative candidate for heat sinking.

**materials for thermal management** 

ii. Liquid metal (surface tension, viscosity) iii. Liquid-solid interface (wettability, reactivity)

infiltration atmosphere)

**5.1 Threshold pressure for infiltration** 

fraction)

Table 4. Thermal properties of metal/SiC-graphite flakes composites. xy refers to the

Although the properties presented in Table 4 are very good, the authors of the patent (Narciso et al., 2007) have already encountered even more promising values when special conditions of infiltration are used. The thermal properties of these composites are currently being evaluated by means of different modelling schemes, conveniently adapted to account for both the anisotropic microstructure of the materials at the mesoscale and the anisotropy in the intrinsic thermal properties of the graphite flakes. Modelling on this system arouses special interest since it is a very cheap and machinable material which has attracted the interest for many

**5. Selection of processing conditions for fabrication of SiC-based composite** 

The thermal properties of composite materials are mainly determined by the intrinsic properties of their constituents and the characteristics of the matrix-reinforcement interface. Aside an appropriate selection of the constituents it is essential to control the processing conditions during fabrication of the material in order to generate a proper interface able to effectively transfer the heat across the different constituent phases. During fabrication of a composite

i. Ceramic particulate (average diameter, size distribution, shape, packed volume

iv. Experimental variables (maximum applied pressure, pressurization rate, temperature,

Next sections will focus on different aspects in regard to the most important parameters that mainly determine the thermal properties of SiC-based composite materials: wettabilityreactivity at the liquid-solid interface, maximum applied pressure and pressurization rate.

An outstanding technologically relevant parameter in composite materials processing is the threshold (*P0*), or minimum, pressure to achieve the entrance of the molten metal into the porous preform. Being essential for materials validation, its measurement is, however, not simple. One of the methods to get the threshold pressure of a given system is to infiltrate a

material by infiltration or squeeze casting some of these processing conditions concern:

of diamond particles. The reason behind this is that the thermal conductivity of the nominally pure aluminium matrix is influenced by take-up of some silicon from the silicon carbide. It was shown in (Molina et al., 2008b) that the intrinsic value of the thermal conductivity of pure aluminium in composites fabricated via gas-pressure infiltration might be as low as 185 W/mK, because of the presence of silicon in solid solution in combination with precipitated silicon phase in the matrix. Reactivity of liquid aluminium and SiC in the "as-received" condition seems unavoidable in gas-pressure infiltration, since the time elapsed during pressurization of the chamber and posterior solidification is of the order of some minutes, depending on the special characteristics of the equipment at hand. Decreasing as much as possible the infiltration temperature seems then to be a successful way to avoid metal-ceramic reactivity in SiC-based systems.

#### **4.3.2 Metal/SiC-graphite flakes composites**

A very recent family of composite materials has been developed and patented at the University of Alicante (Narciso et al., 2007; Prieto et al., 2008). The invention is concerned with a composite material with high thermal performance and low cost which has a layered structure achieved by proper combination of different components. The components of the material are three: 1) a phase mainly formed by graphite flakes (phase A); 2) a second phase (phase B) involving particles or fibers of a material which can act as a phase separator of phase A (phase B is a ceramic material preferably selected from the group of SiC, BN, AlN, TiB2, diamond and carbon fibers); and finally, 3) a third phase (phase C) formed by a metallic alloy. The three present phases must have good thermal properties, although their main function is different for each one: phase A (graphite flakes) is the principal responsible of the properties of the final material, phase B acts as a separator of the layers of phase A and phase C has to consolidate the preform.

The resultant layered structure of these composites is mainly due to the fact that graphite flakes naturally tend to lie on top of each other, especially when a given pressure is applied. It is in fact due to this tendency to get densely packed that, when only flakes are present, they almost leave no space between them and infiltration becomes an almost unfeasible task. The presence of another ceramic (phase B), like SiC particles, allows molten metal infiltration by keeping the graphite flakes separated. The feasibility of the fabrication procedure of these composites was demonstrated in (Prieto et al., 2008).

A representative illustration of the microstructures of these composites is given in Fig. 10.

Fig. 10. Micrographs of: (a) graphite flakes and (b) composite material obtained by infiltration with Al-12%Si of preforms obtained by mixing graphite flakes (60%) with SiC particles (40%)

of diamond particles. The reason behind this is that the thermal conductivity of the nominally pure aluminium matrix is influenced by take-up of some silicon from the silicon carbide. It was shown in (Molina et al., 2008b) that the intrinsic value of the thermal conductivity of pure aluminium in composites fabricated via gas-pressure infiltration might be as low as 185 W/mK, because of the presence of silicon in solid solution in combination with precipitated silicon phase in the matrix. Reactivity of liquid aluminium and SiC in the "as-received" condition seems unavoidable in gas-pressure infiltration, since the time elapsed during pressurization of the chamber and posterior solidification is of the order of some minutes, depending on the special characteristics of the equipment at hand. Decreasing as much as possible the infiltration temperature seems then to be a successful

A very recent family of composite materials has been developed and patented at the University of Alicante (Narciso et al., 2007; Prieto et al., 2008). The invention is concerned with a composite material with high thermal performance and low cost which has a layered structure achieved by proper combination of different components. The components of the material are three: 1) a phase mainly formed by graphite flakes (phase A); 2) a second phase (phase B) involving particles or fibers of a material which can act as a phase separator of phase A (phase B is a ceramic material preferably selected from the group of SiC, BN, AlN, TiB2, diamond and carbon fibers); and finally, 3) a third phase (phase C) formed by a metallic alloy. The three present phases must have good thermal properties, although their main function is different for each one: phase A (graphite flakes) is the principal responsible of the properties of the final material, phase B acts as a separator of the layers of phase A

The resultant layered structure of these composites is mainly due to the fact that graphite flakes naturally tend to lie on top of each other, especially when a given pressure is applied. It is in fact due to this tendency to get densely packed that, when only flakes are present, they almost leave no space between them and infiltration becomes an almost unfeasible task. The presence of another ceramic (phase B), like SiC particles, allows molten metal infiltration by keeping the graphite flakes separated. The feasibility of the fabrication

A representative illustration of the microstructures of these composites is given in Fig. 10.

(a) (b) Fig. 10. Micrographs of: (a) graphite flakes and (b) composite material obtained by infiltration with Al-12%Si of preforms obtained by mixing graphite flakes (60%) with SiC particles (40%)

procedure of these composites was demonstrated in (Prieto et al., 2008).

way to avoid metal-ceramic reactivity in SiC-based systems.

**4.3.2 Metal/SiC-graphite flakes composites** 

and phase C has to consolidate the preform.

Table 4 shows the most significant results of the thermal properties for some of these materials. These composites recently developed present exceptionally high values of thermal conductivity. The thermal properties are clearly anisotropic, given the fact mentioned before that graphite flakes are oriented in a plane, for which they exhibit the maximum thermal conductivity and the lowest CTE (xy-plane in Table 4).


Table 4. Thermal properties of metal/SiC-graphite flakes composites. xy refers to the graphene planes, while the direction perpendicular to it is denoted by z

Although the properties presented in Table 4 are very good, the authors of the patent (Narciso et al., 2007) have already encountered even more promising values when special conditions of infiltration are used. The thermal properties of these composites are currently being evaluated by means of different modelling schemes, conveniently adapted to account for both the anisotropic microstructure of the materials at the mesoscale and the anisotropy in the intrinsic thermal properties of the graphite flakes. Modelling on this system arouses special interest since it is a very cheap and machinable material which has attracted the interest for many applications and represents a clear alternative candidate for heat sinking.

#### **5. Selection of processing conditions for fabrication of SiC-based composite materials for thermal management**

The thermal properties of composite materials are mainly determined by the intrinsic properties of their constituents and the characteristics of the matrix-reinforcement interface. Aside an appropriate selection of the constituents it is essential to control the processing conditions during fabrication of the material in order to generate a proper interface able to effectively transfer the heat across the different constituent phases. During fabrication of a composite material by infiltration or squeeze casting some of these processing conditions concern:


Next sections will focus on different aspects in regard to the most important parameters that mainly determine the thermal properties of SiC-based composite materials: wettabilityreactivity at the liquid-solid interface, maximum applied pressure and pressurization rate.

#### **5.1 Threshold pressure for infiltration**

An outstanding technologically relevant parameter in composite materials processing is the threshold (*P0*), or minimum, pressure to achieve the entrance of the molten metal into the porous preform. Being essential for materials validation, its measurement is, however, not simple. One of the methods to get the threshold pressure of a given system is to infiltrate a preform at various applied pressures and measure, for a fixed time, the infiltrated height for each pressure (Garcia-Cordovilla et al., 1999, Molina et al., 2004; Molina et al, 2008; Piñero et al, 2008). Data are then analysed by means of Darcy's law:

$$h^2 = \frac{2k \cdot t}{\mu \cdot (1 - V\_r)} (P - P\_o) \tag{11}$$

SiC as Base of Composite Materials for Thermal Management 133

The most important conclusion is that the contact angle derived from a fitting of the experimental data (Fig. 11b) by means of Eq. (12) is the same for all cases studied. The infiltration behaviour of the different systems, governed by a unique contact angle, indicates that the metal/particle interface is in both cases the same. Instead of being a metal/SiC contact, there exists an interlayer of silica between both. The very thin silica layer that covers naturally the SiC particles seems to be thick enough to partly remain after reaction with the metal during infiltration at these low temperatures and relatively rapid infiltration kinetics. Another system with remarkable interest is Ag/SiC (Garcia-Cordovilla et al., 1999; Molina et al., 2003b). Silver is a metal with high capacity for dissolution of oxygen in the molten state. This oxygen can rapidly oxidize the SiC particles. This was observed to affect directly the threshold pressure of the system by increasing its value. The apparent contact angle derived from the data was 168º. The authors suggested that the gas evolved during the oxidation of

Determination of threshold pressures is often not sufficient to fully characterize wetting in infiltration processing. Intrinsic capillary parameters, characteristic of dynamic wetting of a discrete reinforcement, are not, per se, equal to those derived in near-static conditions (i.e. sessile drop measurements). Furthermore, preforms are invaded over a range of pressures that is governed by the complex internal geometry of open pores within the preform (Rodriguez-Guerrero et al., 2008). A more thorough characterization of wetting is obtained by the so-called drainage curves. These are plots of the metallic saturation (fraction of nonwetting fluid in the porous medium) versus the pressure difference between the fluid and the atmosphere in the pores. These drainage curves contain all information related to wetting of the porous preform by the non-wetting liquid. With the assumption that irreversibility effects (e.g. Haines jumps) and other inertial losses can be neglected, the work of immersion (*Wi*) can be calculated as the work necessary to fully infiltrate the preform (*W*) divided by the total preform/infiltrant interface created per unit volume of reinforcement:

( ) 1 *<sup>r</sup>*

θ

(13)

(14)

*W V PdS*

*Vr Vr*

*AV AV* − ⋅ = = ⋅ ⋅

where *P*, *S* and *Vr* are saturation, applied pressure and volume fraction of reinforcement, respectively; *Av* is the particle specific surface area per unit volume of preform. The contact

> cos *Wi lv* = ⋅ γ

Recently, a new technique was proposed for the direct measurement of capillary forces during the infiltration process of high-temperature melting non-wetting liquids into ceramic preforms. In essence, the equipment is a high-temperature analogue of mercury porosimetry. The device can track dynamically the volume of metal that is displaced during pressurization and hence allows obtaining in a single experiment the entire drainage curve characterizing capillarity in high-temperature infiltration of particles by molten metal (Bahraini et al., 2005; Bahraini et al., 2008; Molina et al., 2007a; Molina et al., 2008d). The technique was validated in an study of wetting of silicon carbide by pure aluminium and by aluminium-silicon eutectic

SiC reduced the contact area and, in consequence, wetting.

*i*

angle can be easily derived by making use of the following relationship:

alloy using drainage curves obtained during gas pressure infiltration at 750ºC.

*W*

**5.2 Drainage curves for gas-pressure infiltration** 

where *k* is the permeability of the porous solid, *t* is the infiltration time and μ the viscosity of the liquid metal. *P0* can be easily derived from plots of *h2* vs *P*.

Threshold pressure and contact angle are intimately correlated by means of the so-called capillary law:

$$P\_0 = 6\mathcal{A} \cdot \mathcal{Y}\_{lv} \cdot \cos\theta \frac{V\_r}{\left(1 - V\_r\right) \cdot D} = \mathcal{Y}\_{lv} \cdot \Sigma \cdot \cos\theta \tag{12}$$

being θ the contact angle and γ*lv* the surface tension of the molten metal at the infiltration temperature. The value of *P0* is clearly dependent on the wetting characteristics of the system and, hence, may be strongly affected by the reactive phenomena occurring at the interface between metal and substrate while the infiltration front moves over the substrate surface. The study of this parameter becomes especially interesting for those systems where infiltration front movement and reaction cannot be decoupled in time. A remarkable fact that has to be taken in consideration is that if infiltration occurs too rapidly, reaction could be prevented and the system may behave as non-reactive. A conclusive study regarding these points was presented in (Molina et al., 2007b; Tian et al., 2005), which discusses results for infiltration of pure Al and Al-12wt%Si into compacts of as-received and thermally oxidized SiC particles. The main results of this study are summarized in Fig. 11a.

Fig. 11. (a) Plots of the square of the infiltrated height *h2* as a function of applied pressure *P* for gas pressure infiltration at 700ºC of Al and Al-12%Si in preforms of SiC particles in the asreceived and oxidized conditions: Al/SiC500 (), Al-12%Si/SiC500 (), Al/SiC500ox (), Al-12%Si/SiC500ox (), Al/SiC400 (), Al-12%Si/SiC400 (), Al/SiC400ox () and Al-12%Si/SiCox (). The straight lines are linear fittings of experimental data; (b) Threshold pressure *P0* versus γlv for the different systems in (a). The line corresponds to a fitting with equation *P0*= 0.603γ*lv*+ 32.9 kPa

preform at various applied pressures and measure, for a fixed time, the infiltrated height for each pressure (Garcia-Cordovilla et al., 1999, Molina et al., 2004; Molina et al, 2008; Piñero et

> ( )( ) <sup>2</sup> <sup>2</sup> 1 *<sup>o</sup> r k t <sup>h</sup> P P*

Threshold pressure and contact angle are intimately correlated by means of the so-called

cos cos *<sup>r</sup> lv lv r*

 = ⋅Σ⋅ γ

P0 (kPa)

 (a) (b) Fig. 11. (a) Plots of the square of the infiltrated height *h2* as a function of applied pressure *P* for gas pressure infiltration at 700ºC of Al and Al-12%Si in preforms of SiC particles in the asreceived and oxidized conditions: Al/SiC500 (), Al-12%Si/SiC500 (), Al/SiC500ox (), Al-

12%Si/SiC500ox (), Al/SiC400 (), Al-12%Si/SiC400 (), Al/SiC400ox () and Al-12%Si/SiCox (). The straight lines are linear fittings of experimental data; (b) Threshold pressure *P0* versus γlv for the different systems in (a). The line corresponds to a fitting with

1

temperature. The value of *P0* is clearly dependent on the wetting characteristics of the system and, hence, may be strongly affected by the reactive phenomena occurring at the interface between metal and substrate while the infiltration front moves over the substrate surface. The study of this parameter becomes especially interesting for those systems where infiltration front movement and reaction cannot be decoupled in time. A remarkable fact that has to be taken in consideration is that if infiltration occurs too rapidly, reaction could be prevented and the system may behave as non-reactive. A conclusive study regarding these points was presented in (Molina et al., 2007b; Tian et al., 2005), which discusses results for infiltration of pure Al and Al-12wt%Si into compacts of as-received and thermally

θ

oxidized SiC particles. The main results of this study are summarized in Fig. 11a.

<sup>⋅</sup> = − ⋅ − (11)

θ − ⋅ (12)

> 700 900 1100 1300 1500 γlvΣ (kPa)

*lv* the surface tension of the molten metal at the infiltration

μ

the viscosity of

μ*V*

where *k* is the permeability of the porous solid, *t* is the infiltration time and

( ) <sup>0</sup> <sup>6</sup>

*<sup>V</sup> <sup>P</sup> V D* =⋅⋅

al, 2008). Data are then analysed by means of Darcy's law:

the liquid metal. *P0* can be easily derived from plots of *h2* vs *P*.

λ γ

γ

500 600 700 800 900 pressure (kPa)

+ 32.9 kPa

the contact angle and

h2 (mm2

equation *P0*= 0.603

γ*lv*

)

capillary law:

being θ The most important conclusion is that the contact angle derived from a fitting of the experimental data (Fig. 11b) by means of Eq. (12) is the same for all cases studied. The infiltration behaviour of the different systems, governed by a unique contact angle, indicates that the metal/particle interface is in both cases the same. Instead of being a metal/SiC contact, there exists an interlayer of silica between both. The very thin silica layer that covers naturally the SiC particles seems to be thick enough to partly remain after reaction with the metal during infiltration at these low temperatures and relatively rapid infiltration kinetics. Another system with remarkable interest is Ag/SiC (Garcia-Cordovilla et al., 1999; Molina et al., 2003b). Silver is a metal with high capacity for dissolution of oxygen in the molten state. This oxygen can rapidly oxidize the SiC particles. This was observed to affect directly the threshold pressure of the system by increasing its value. The apparent contact angle derived from the data was 168º. The authors suggested that the gas evolved during the oxidation of SiC reduced the contact area and, in consequence, wetting.

#### **5.2 Drainage curves for gas-pressure infiltration**

Determination of threshold pressures is often not sufficient to fully characterize wetting in infiltration processing. Intrinsic capillary parameters, characteristic of dynamic wetting of a discrete reinforcement, are not, per se, equal to those derived in near-static conditions (i.e. sessile drop measurements). Furthermore, preforms are invaded over a range of pressures that is governed by the complex internal geometry of open pores within the preform (Rodriguez-Guerrero et al., 2008). A more thorough characterization of wetting is obtained by the so-called drainage curves. These are plots of the metallic saturation (fraction of nonwetting fluid in the porous medium) versus the pressure difference between the fluid and the atmosphere in the pores. These drainage curves contain all information related to wetting of the porous preform by the non-wetting liquid. With the assumption that irreversibility effects (e.g. Haines jumps) and other inertial losses can be neglected, the work of immersion (*Wi*) can be calculated as the work necessary to fully infiltrate the preform (*W*) divided by the total preform/infiltrant interface created per unit volume of reinforcement:

$$\mathcal{W}\_i = \frac{\mathcal{W}}{A\_V \cdot V\_r} = \frac{\left(1 - V\_r\right) \cdot \oint PdS}{A\_V \cdot V\_r} \tag{13}$$

where *P*, *S* and *Vr* are saturation, applied pressure and volume fraction of reinforcement, respectively; *Av* is the particle specific surface area per unit volume of preform. The contact angle can be easily derived by making use of the following relationship:

$$\mathcal{W}\_i = \mathcal{Y}\_{lv} \cdot \cos \theta \tag{14}$$

Recently, a new technique was proposed for the direct measurement of capillary forces during the infiltration process of high-temperature melting non-wetting liquids into ceramic preforms. In essence, the equipment is a high-temperature analogue of mercury porosimetry. The device can track dynamically the volume of metal that is displaced during pressurization and hence allows obtaining in a single experiment the entire drainage curve characterizing capillarity in high-temperature infiltration of particles by molten metal (Bahraini et al., 2005; Bahraini et al., 2008; Molina et al., 2007a; Molina et al., 2008d). The technique was validated in an study of wetting of silicon carbide by pure aluminium and by aluminium-silicon eutectic alloy using drainage curves obtained during gas pressure infiltration at 750ºC.

SiC as Base of Composite Materials for Thermal Management 135

The curves of Fig. 13 show that interfacial reactions, which have proven in sessile-drop experiments to aid wetting, under forced pressure-driven infiltration can hinder infiltration of SiC preforms by aluminium-based melts. These effects can be due to the fact that chemical interactions can cause morphological changes at the solid/liquid interface. As a corollary, rapid pressure infiltration is preferable in processing metal matrix composites

It is interesting to compare the resulting materials processed by two different liquid-state routes, namely gas-pressure infiltration and squeeze casting, which make use of different pressures and pressurization rates (this having a direct implication on the contact time

In (Weber et al., 2010) it is presented a complete study of comparison of the different properties encountered for Al/SiC composites processed by these two fabrication techniques. In this work, bimodal powder mixtures of green quality SiC powders with average sizes of 170 μm and 17 μm, respectively, were used. A set of samples was processed by squeeze casting while other two sets were prepared by gas pressure-assisted infiltration at two largely different infiltration kinetics. Fig. 14a resumes the thermal conductivities for both series of composites together with modelling predictions using the DEM scheme.

featuring interfacial reactivity.

thermal conductivity (W/mK)

**5.3 Gas pressure infiltration vs squeeze casting** 

between molten metal and particles before metal is solidified).

0 0.2 0.4 0.6 0.8 fraction of coarse particles

SC GPI - fast GPI - slow

(a) (b)

For the squeeze cast samples, thermal conductivity was in between 225 and 235 W/mK with a slight tendency to increase with the amount of large particles. For the samples prepared by fast GPI, the thermal conductivity increased from around 200 W/mK for the composite containing only small particles with increasing fraction of large particles up to 230 W/mK. For the slow GPI samples, values increased from 160 to 205 W/mK with increasing fraction of large particles. For the modelling of thermal conductivity, different matrix conductivities have been taken into account. While for SC samples the matrix conductivity is that of pure

Fig. 14. (a) Thermal conductivity of the Al/SiC composites produced by infiltration of aluminium into preforms of mono- and bimodal SiC mixtures (SiC100/SiC500) versus the fraction of coarse particles. SC refers to squeeze casting and GPI refers to gas pressure infiltration. The lines correspond to calculations with the DEM scheme; (b) Coefficient of thermal expansion for the Al/SiC composites in (a) for temperatures of 25ºC and 125ºC

CTE (ppm/K)

0.5 0.55 0.6 0.65 0.7 0.75 particle volume fraction

GPI - fast at 25ºC GPI - fast at 125ºC SC at 25ºC SC at 125ºC

With relatively fast pressurization rates the drainage curves for a metal/SiC system that can be obtained are shown in Fig. 12 for SiC320 particles of about 37 μm of average diameter.

The shape of the curves is determined by the shape of particles in the preform. Any change of (i) the work of immersion, (ii) the particle volume fraction and/or (iii) the particle size (which is accounted for by *Av* parameter) will cause a predictable shift over the pressure axis. The values of contact angle derived from the drainage curves for different sizes of SiC particles with Al and Al-12%Si are in the range 110-113º. These values are fully consistent with measurements with the sessile drop method for the wetting of oxide-covered SiC by molten aluminium free of a surface layer of oxide. In these infiltration experiments the triple line is forced to move at a motion rate which is well above the "natural" rate dictated by reaction kinetics in the sessile drop method. Hence, infiltration and reaction processes are decoupled in time and the SiC surface is covered before reaction can take place at the interface.

Nevertheless, when pressurization rate is decreased, the interfacial reaction can take place concomitantly with the motion of the triple line and both phenomena may interact to provoque different behaviours in drainage curves. Fig. 13 shows drainage curves for the infiltration of SiC particles with molten Al and Al-Si eutectic at a reduced pressurization rate of 0.05MPa/s together with the curves obtained for the same systems at 0.13 MPa/s.

Fig. 12. Drainage curves of SiC320 infiltrated with Hg, Al and Al-12%Si at 750ºC

Fig. 13. Drainage curves at 750ºC of (a) SiC1000/Al and (b) SiC1000/Al-12%Si, measured at the two pressurization rates of 0.13 and 0.05 MPa/s

With relatively fast pressurization rates the drainage curves for a metal/SiC system that can be obtained are shown in Fig. 12 for SiC320 particles of about 37 μm of average diameter. The shape of the curves is determined by the shape of particles in the preform. Any change of (i) the work of immersion, (ii) the particle volume fraction and/or (iii) the particle size (which is accounted for by *Av* parameter) will cause a predictable shift over the pressure axis. The values of contact angle derived from the drainage curves for different sizes of SiC particles with Al and Al-12%Si are in the range 110-113º. These values are fully consistent with measurements with the sessile drop method for the wetting of oxide-covered SiC by molten aluminium free of a surface layer of oxide. In these infiltration experiments the triple line is forced to move at a motion rate which is well above the "natural" rate dictated by reaction kinetics in the sessile drop method. Hence, infiltration and reaction processes are decoupled in

Nevertheless, when pressurization rate is decreased, the interfacial reaction can take place concomitantly with the motion of the triple line and both phenomena may interact to provoque different behaviours in drainage curves. Fig. 13 shows drainage curves for the infiltration of SiC particles with molten Al and Al-Si eutectic at a reduced pressurization rate

> 0 0.5 1 1.5 2 pressure (MPa)

> > saturation

Fig. 13. Drainage curves at 750ºC of (a) SiC1000/Al and (b) SiC1000/Al-12%Si, measured at

0 0.2 0.4 0.6 0.8 1 1.2

> 0 2 4 6 8 10 12 pressure (MPa)

SiC1000/Al12Si (0.13 MPa/s) SiC1000/Al12Si (0.05 MPa/s)

Fig. 12. Drainage curves of SiC320 infiltrated with Hg, Al and Al-12%Si at 750ºC

SiC320/Hg SiC320/Al SiC320/Al12Si

time and the SiC surface is covered before reaction can take place at the interface.

of 0.05MPa/s together with the curves obtained for the same systems at 0.13 MPa/s.

0 0.2 0.4 0.6 0.8 1 1.2

saturation

0 2 4 6 8 10 12 pressure (MPa)

the two pressurization rates of 0.13 and 0.05 MPa/s

SiC1000/Al (0.13MPa/s) SiC1000/Al (0.05MPa/s)

0 0.2 0.4 0.6 0.8 1 1.2

saturation

The curves of Fig. 13 show that interfacial reactions, which have proven in sessile-drop experiments to aid wetting, under forced pressure-driven infiltration can hinder infiltration of SiC preforms by aluminium-based melts. These effects can be due to the fact that chemical interactions can cause morphological changes at the solid/liquid interface. As a corollary, rapid pressure infiltration is preferable in processing metal matrix composites featuring interfacial reactivity.

#### **5.3 Gas pressure infiltration vs squeeze casting**

It is interesting to compare the resulting materials processed by two different liquid-state routes, namely gas-pressure infiltration and squeeze casting, which make use of different pressures and pressurization rates (this having a direct implication on the contact time between molten metal and particles before metal is solidified).

In (Weber et al., 2010) it is presented a complete study of comparison of the different properties encountered for Al/SiC composites processed by these two fabrication techniques. In this work, bimodal powder mixtures of green quality SiC powders with average sizes of 170 μm and 17 μm, respectively, were used. A set of samples was processed by squeeze casting while other two sets were prepared by gas pressure-assisted infiltration at two largely different infiltration kinetics. Fig. 14a resumes the thermal conductivities for both series of composites together with modelling predictions using the DEM scheme.

Fig. 14. (a) Thermal conductivity of the Al/SiC composites produced by infiltration of aluminium into preforms of mono- and bimodal SiC mixtures (SiC100/SiC500) versus the fraction of coarse particles. SC refers to squeeze casting and GPI refers to gas pressure infiltration. The lines correspond to calculations with the DEM scheme; (b) Coefficient of thermal expansion for the Al/SiC composites in (a) for temperatures of 25ºC and 125ºC

For the squeeze cast samples, thermal conductivity was in between 225 and 235 W/mK with a slight tendency to increase with the amount of large particles. For the samples prepared by fast GPI, the thermal conductivity increased from around 200 W/mK for the composite containing only small particles with increasing fraction of large particles up to 230 W/mK. For the slow GPI samples, values increased from 160 to 205 W/mK with increasing fraction of large particles. For the modelling of thermal conductivity, different matrix conductivities have been taken into account. While for SC samples the matrix conductivity is that of pure

SiC as Base of Composite Materials for Thermal Management 137

recent paper (Molina et al., 2009) it has been demonstrated that a simple application of the Hasselman-Johnson model in a two-step procedure (which accounts for the presence of two types of inclusions, reinforcement particles and voids, and the metallic matrix) offers a good approximation of the experimental results of thermal conductivity obtained for Al-12%Si/SiC composite materials. Alternatively, the DEM model may be used as in (Molina et al., 2008a; Molina et al., 2008b) for accounting for the two types of inclusions (SiC particles and pores) at the time. Results of both models are equivalent since the phase contrast in the Al/SiC (or Al-Si/SiC) system is too low. It has been recently demonstrated (Tavangar et al., 2007) that the Hasselman-Johnson scheme increasingly offers inconsistent predictions for the thermal conductivity of composites as the effective phase contrast - ratio between effective thermal conductivity of reinforcement and matrix thermal conductivity - exceeds roughly

Several composite materials containing SiC as reinforcement, either single or combined with other ceramics, have been presented as serious candidates to cover the specific demand of heat dissipation for thermal management applications. Aside from the metal/SiC composites with monomodal distribution of SiC particles, which nowadays define the state of the art in materials for electronics, those derived from combinations of SiC with either SiC of another largely different size (bimodal mixtures) or other ceramics (hybrid mixtures with diamond or graphite flakes) present high values of thermal conductivity and coefficients of thermal expansion extremely low such as to represent the future generation of heat sinks for electronics. The use of these composites is mainly determined by the specific requirements for every application, taking into account not only the thermal properties but also density, isotropy or ease of machinability (when complex shapes are needed). The spectrum covered by the SiC-based composites aims to offer specific solutions for the different problems of heat dissipation encountered in the energy-related industries such as electronics or

This contribution emphasizes the fact that the choice of a proper fabrication processing is as important as a good selection of the constituents of the composite material. Being aluminium a very used metal for the fabrication of SiC-based composites, processing by liquid state routes must take into account the high reactivity between Al and SiC at the temperature of molten aluminium. In these sense, squeeze casting, which operates allowing very short contact times between metal and reinforcement, offers composites with the highest values of thermal conductivity. Several specific conditions should be taken into account in gas pressure infiltration to give appropriate materials with acceptable thermal properties. In any case, porosity has to be avoided because dramatically decreases the thermal conductivity of the materials. For this purpose, a certain minimum pressure that ensures complete saturation is needed along with a certain pressurization rate in order to force that infiltration and reactivity can be decoupled in time, since interfacial reaction can

The author acknowledges all those who have actively participated to the research presented in this contribution. Special thanks are given to M. Bahraini, L. Weber and A. Mortensen,

four.

**6. Conclusion** 

aeronautics.

hinder infiltration.

**7. Acknowledgement** 

aluminium (237 W/mK) due to the lack of time to react with the reinforcement, for the GPI samples values of 190 W/mK and 170 W/mK for GPI fast and GPI slow, respectively, have been used. Interestingly enough, the interface thermal conductance varies as well its value with the contact time corresponding to each processing technique. For SC and fast GPI the interface thermal conductance is found to be 1.4×108 W/m2K. For the slow GPI this parameter has a value which is about the half, most probably due to the abundant reaction product (Al4C3) at the interface (Weber et al., 2010).

The results of the CTE measurements are collected in Fig. 14b. The physical CTEs (measured in a range of ±5ºC around the indicated temperature) are given for the SC and the fast GPI samples only, yet for two temperatures of technical interest, i.e., 25ºC and 125ºC. The CTE decreases in general with increasing SiC volume fraction and is typically 1–1.5 ppm/K higher at 125ºC than at ambient temperature.

#### **5.4 Effect of porosity**

In a non-wetting system like Al/SiC infiltration of the metal into the open channels of the preform does not take place at a single, well-defined pressure but, as already seen, it rather takes place progressively with the applied pressure when this pressure exceeds a certain threshold (threshold pressure). In order to obtain a hundred percent filling of the porous space of the preform by the metal an infinitely large pressure, impossible to obtain in laboratory, would be needed. For a given infiltration pressure, therefore, defects at the contact area of particles will exist and porosity will hence be unavoidable.

Fig. 15. Plot of the thermal conductivity calculated with the two-step Hasselman-Johnson model versus that determined experimentally. The line represents the identity function. DEM scheme offers identical results

Porosity does affect the two main properties which are important in materials for thermal management and, hence, may limit its use for this application. Depending on the nature of both, metal and reinforcement, voids in the material may increase or decrease the coefficient of thermal expansion of the composite material, being this effect very dependent on the geometry of the pores. On the other hand, the presence of porosity does decrease strongly the thermal conductivity of any material, being monolithic or composite. The voids, present in the metallic phase, can be treated as inclusions of zero conductivity in the metal. In a recent paper (Molina et al., 2009) it has been demonstrated that a simple application of the Hasselman-Johnson model in a two-step procedure (which accounts for the presence of two types of inclusions, reinforcement particles and voids, and the metallic matrix) offers a good approximation of the experimental results of thermal conductivity obtained for Al-12%Si/SiC composite materials. Alternatively, the DEM model may be used as in (Molina et al., 2008a; Molina et al., 2008b) for accounting for the two types of inclusions (SiC particles and pores) at the time. Results of both models are equivalent since the phase contrast in the Al/SiC (or Al-Si/SiC) system is too low. It has been recently demonstrated (Tavangar et al., 2007) that the Hasselman-Johnson scheme increasingly offers inconsistent predictions for the thermal conductivity of composites as the effective phase contrast - ratio between effective thermal conductivity of reinforcement and matrix thermal conductivity - exceeds roughly four.

#### **6. Conclusion**

136 Silicon Carbide – Materials, Processing and Applications in Electronic Devices

aluminium (237 W/mK) due to the lack of time to react with the reinforcement, for the GPI samples values of 190 W/mK and 170 W/mK for GPI fast and GPI slow, respectively, have been used. Interestingly enough, the interface thermal conductance varies as well its value with the contact time corresponding to each processing technique. For SC and fast GPI the interface thermal conductance is found to be 1.4×108 W/m2K. For the slow GPI this parameter has a value which is about the half, most probably due to the abundant reaction

The results of the CTE measurements are collected in Fig. 14b. The physical CTEs (measured in a range of ±5ºC around the indicated temperature) are given for the SC and the fast GPI samples only, yet for two temperatures of technical interest, i.e., 25ºC and 125ºC. The CTE decreases in general with increasing SiC volume fraction and is typically 1–1.5 ppm/K

In a non-wetting system like Al/SiC infiltration of the metal into the open channels of the preform does not take place at a single, well-defined pressure but, as already seen, it rather takes place progressively with the applied pressure when this pressure exceeds a certain threshold (threshold pressure). In order to obtain a hundred percent filling of the porous space of the preform by the metal an infinitely large pressure, impossible to obtain in laboratory, would be needed. For a given infiltration pressure, therefore, defects at the

> 140 160 180 200 220 240 exp thermal conductivity (W/mK)

Fig. 15. Plot of the thermal conductivity calculated with the two-step Hasselman-Johnson model versus that determined experimentally. The line represents the identity function.

Porosity does affect the two main properties which are important in materials for thermal management and, hence, may limit its use for this application. Depending on the nature of both, metal and reinforcement, voids in the material may increase or decrease the coefficient of thermal expansion of the composite material, being this effect very dependent on the geometry of the pores. On the other hand, the presence of porosity does decrease strongly the thermal conductivity of any material, being monolithic or composite. The voids, present in the metallic phase, can be treated as inclusions of zero conductivity in the metal. In a

composites with zero nominal porosity

composites with porosity

contact area of particles will exist and porosity will hence be unavoidable.

140

160

180

calc thermal conductivity (W/mK)

DEM scheme offers identical results

200

220

240

product (Al4C3) at the interface (Weber et al., 2010).

higher at 125ºC than at ambient temperature.

**5.4 Effect of porosity** 

Several composite materials containing SiC as reinforcement, either single or combined with other ceramics, have been presented as serious candidates to cover the specific demand of heat dissipation for thermal management applications. Aside from the metal/SiC composites with monomodal distribution of SiC particles, which nowadays define the state of the art in materials for electronics, those derived from combinations of SiC with either SiC of another largely different size (bimodal mixtures) or other ceramics (hybrid mixtures with diamond or graphite flakes) present high values of thermal conductivity and coefficients of thermal expansion extremely low such as to represent the future generation of heat sinks for electronics. The use of these composites is mainly determined by the specific requirements for every application, taking into account not only the thermal properties but also density, isotropy or ease of machinability (when complex shapes are needed). The spectrum covered by the SiC-based composites aims to offer specific solutions for the different problems of heat dissipation encountered in the energy-related industries such as electronics or aeronautics.

This contribution emphasizes the fact that the choice of a proper fabrication processing is as important as a good selection of the constituents of the composite material. Being aluminium a very used metal for the fabrication of SiC-based composites, processing by liquid state routes must take into account the high reactivity between Al and SiC at the temperature of molten aluminium. In these sense, squeeze casting, which operates allowing very short contact times between metal and reinforcement, offers composites with the highest values of thermal conductivity. Several specific conditions should be taken into account in gas pressure infiltration to give appropriate materials with acceptable thermal properties. In any case, porosity has to be avoided because dramatically decreases the thermal conductivity of the materials. For this purpose, a certain minimum pressure that ensures complete saturation is needed along with a certain pressurization rate in order to force that infiltration and reactivity can be decoupled in time, since interfacial reaction can hinder infiltration.

#### **7. Acknowledgement**

The author acknowledges all those who have actively participated to the research presented in this contribution. Special thanks are given to M. Bahraini, L. Weber and A. Mortensen,

SiC as Base of Composite Materials for Thermal Management 139

Molina, J.M.; Rodriguez-Guerrero, A.; Bahraini, M.; Weber, L.; Narciso, F.; Rodriguez-

Molina, J.M.; Tian, J.T.; Garcia-Cordovilla, C.; Louis, E. & Narciso, F. (2007). Wettability in

Molina, J.M.; Rhême, M.; Carron, J. & Weber, L. (2008). Thermal conductivity of aluminium

Molina, J.M.; Narciso, J.; Weber, L.; Mortensen, A. & Louis, E. (2008). Thermal conductivity

Molina, J.M.; Bahraini, M.; Weber, L & Mortensen, A. (2008). Direct measurement of

Molina, J.M.; Prieto, R.; Narciso, J. & Louis, E. (2009). The effect of porosity on the thermal

Molina, J.M.; Narciso, J. & Louis, E. (2010). On the triple line in infiltration of liquid metals

Narciso, J.; Weber, L.; Molina, J.M.; Mortensen, A. & Louis, E. (2006). Reactivity and thermal

*Technology*, Vol.22, No.12, (February 2006), pp. 1464-1468, ISSN 0861-9786 Narciso, J.; Prieto, R.; Molina, J.M. & Louis, E. (2007). Production of composite materials

Piñero, E.; Molina, J.M.; Narciso, J. & Louis, E. (2008). Liquid metal infiltration into particle

Rodriguez-Guerrero, A; Molina, J.M.; Rodriguez-Reinoso, F.; Narciso, J. & Louis, E. (2008).

*Engineering A*, Vol.495, (November 2007), pp. 288-291, ISSN 0921-5093 Prieto, R.; Molina, J.M.; Narciso, J. & Louis, E. (2008). Fabrication and properties of graphite

Vol.59, (February 2008), pp. 11-14, ISSN 1359-6462

pp. 276-281, ISSN 0921-5093

*Science & Engineering A*, Vol.480, (July 2007), pp. 483-488, ISSN 0921-5093 Molina, J.M.; Prieto, R.; Duarte, M.; Narciso, J. & Louis, E. (2008). On the estimation of

*Materialia*, Vol.58, (October 2007), pp. 393-396, ISSN 1359-6462

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A1 2010)

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pressure infiltration of SiC and oxidized SiC particle compacts by molten Al and Al-12wt%Si alloy. *Journal of Materials Research*, Vol.22, No.8, (April 2007), pp. 2273-

matrix composites reinforced with mixtures of diamond and SiC particles. *Scripta* 

of Al-SiC composites with monomodal and bimodal particle distributions. *Materials* 

threshold pressures in infiltration of liquid metals into particle preforms. *Scripta* 

drainage curves in infiltration of SiC particle preforms: influence of interfacial reactivity. *Journal of Materials Science*, Vol.43, No.15 (April 2008), pp. 5061-5067,

conductivity of Al-12wt%Si/SiC composites. *Scripta Materialia*, Vol.60, (December

into porous preforms. *Scripta Materialia*, Vol.62, (March 2010), pp. 961-965, ISSN

behaviour of Cu-Si/SiC composites: effects of SiC oxidation. *Materials Science and* 

with high thermal conductivity. Spanish patent (P002700804 2007), European Application Patent (EP2130932-A1 2009), US Application Patent (US 20100143690-

compacts chemically and morphologically heterogeneous. *Materials Science &* 

flakes/metal composites for thermal management applications. *Scripta Materialia*,

Pore filling in graphite particle compacts infiltrated with Al-12wt%Si and Al-12wt%Si-1wt%Cu alloys. *Materials Science & Engineering A*, Vol.495, (January 2008),

from the École Polytechnique Fédérale de Lausanne (Switzerland). R. Arpón, R.A. Saravanan, C. García-Cordovilla, R. Prieto, J. Narciso and E. Louis, from the University of Alicante (Spain), are also gratefully acknowledged. J.M. Molina wants also to express his gratitude to the "Ministerio de Ciencia e Innovación" for a "Ramón y Cajal" contract.

#### **8. References**


from the École Polytechnique Fédérale de Lausanne (Switzerland). R. Arpón, R.A. Saravanan, C. García-Cordovilla, R. Prieto, J. Narciso and E. Louis, from the University of Alicante (Spain), are also gratefully acknowledged. J.M. Molina wants also to express his

Arpon, R.; Molina, J.M.; Saravanan, R.A.; Garcia-Cordovilla, C; Louis, E. & Narciso, J. (2003).

Arpon, R.; Molina, J.M.; Saravanan, R.A.; Garcia-Cordovilla, C; Louis, E. & Narciso, J. (2003).

Bahraini, M; Molina, J.M.; Kida, M.; Weber, L.; Narciso, J. & Mortensen, A. (2005).

*Opinion in Solid State & Materials Science*, Vol.9, pp. 196-201, ISSN 1359-0286 Bahraini, M; Molina, J.M.; Weber, L. & Mortensen, A. (2008). Direct measurement of

Clyne, T.W (2000). An introductory overview of MMC systems, types and developments, In:

Garcia-Cordovilla, C.; Louis, E. & Narciso, J. (1999). Pressure infiltration of packed ceramic

Molina, J.M.; Saravanan, R.A.; Arpon, R.; Narciso, J.; Garcia-Cordovilla, C. & Louis, E.

Molina, J.M.; Arpon, A.; Saravanan, R.A.; Garcia-Cordovilla, C.; Louis, E. & Narciso, J.

Molina, J.M.; Garcia-Cordovilla, C; Louis, E. & Narciso, J. (2003). Pressure infiltration of

Molina, J.M.; Arpon, R.; Saravanan, R.A.; Garcia-Cordovilla, C.; Louis, E. & Narciso, J.

Molina, J.M.; Piñero, E.; Narciso, J.; Garcia-Cordovilla, C. & Louis, E. (2005). Liquid metal

*Engineering A*, Vol.495, (January 2008), pp. 203-207, ISSN 0921-5093

Science, ISBN 0-080437214 (Volume 3), Oxford UK, United Kingdom Clyne, T.W (2000). Thermal and electrical conduction in MMCs, In: *Comprehensive Composite* 

Thermal expansion behaviour of aluminium/SiC composites with bimodal particle distributions. *Acta Materialia*, Vol.51, (January 2003), pp. 3145-3156, ISSN 1359-6454

Thermal expansion coefficient and thermal hysteresis of Al/SiC composites with bimodal particle distributions. *Materials Science Forum*, Vols.426-432, (July 2003), pp.

Measuring and tailoring capillary forces Turing liquid metal infiltration. *Current* 

drainage curves in infiltration of SiC particle preforms. *Materials Science &* 

*Comprehensive Composite Materials*, A. Kelly & C. Zweben (Eds.), 1-26, Elsevier

*Materials*, A. Kelly & C. Zweben (Eds.), 447-468, Elsevier Science, ISBN 0-080437214

particulates by liquid metals. *Acta Materialia*, Vol.47, No.18 (August 1999), pp. 4461-

(2002). Pressure infiltration of liquid aluminium into packed SiC particulares with a bimodal size distribution. *Acta Materialia*, Vol.50, No.2, (September 2001), pp. 247-

(2003). Thermal expansion coefficient and wear performance of aluminium/SiC composites with bimodal particle distributions. *Materials Science and Technology*,

silver into compacts of oxidized SiC. *Materials Science Forum*, Vols.426-432, (July

(2004). Threshold pressure for infiltration and particle specific surface area of particle compacts with bimodal size distributions. *Scripta Materialia*, Vol.51, (June

infiltration into compacts of ceramic particles with bimodal size distributions. *Current Opinion in Solid State & Materials Science*, Vol.9, pp. 202-210, ISSN 1359-0286

gratitude to the "Ministerio de Ciencia e Innovación" for a "Ramón y Cajal" contract.

**8. References** 

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4479, ISSN 1359-6454

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(Volume 3), Oxford UK, United Kingdom

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2003), pp. 2181-2186, ISSN 0255-5476

2004), pp. 623-627, ISSN 1359-6462


**6** 

*China* 

**Bulk Growth and Characterization of** 

Sublimation method was used to grow bulk SiC by J.A. Lely for the first time in 1955 (Lely, 1955). It was improved then by Tairov and Tsvetkov and became the most mature method for bulk SiC growth. In this chapter, we will introduce the growth of hexagonal SiC. Although the bulk growth method is well known and used widely, there are still plenty of

The growth of 4H-SiC is not as stable as that of 6H-SiC. That is to say the growth of 4H-SiC needs a harsh growth conditions. In order to grow high quality 4H polytype, the polytype

Although single crystals of SiC are commercially available, owing to the specific structures of SiC, there are still some structural defects, such as micropipes, mis-orientations, dislocations, stacking faults, basal plane dislocations, particle inclusions, precipitates and so on, which hinder its applications. So in this chapter we also introduce the recent progress in research of structural defects in 6H-SiC single crystals. Three kinds of typical structural defects in 6H-SiC single crystals were investigated. First, we describe the strain field of a micropipe by the theory of screw dislocation. Stress birefringence images from micropipes with different Burgers vectors have been simulated. The results are compared with polarized optical microscopic observations. Second, elementary screw dislocations were observed by back-reflection synchrotron radiation topography (BRSRT). Based on the reflection geometry, the image of an elementary screw dislocation was simulated. Elementary screw dislocation is a pure screw dislocation with Burger vector lc. Finally, Basal plane bending was detected by high resolution X-ray diffractometry (HRXRD) and

The observation and investigation of the structural defects helped us to understand their formation mechanisms. This makes it possible for us to further decrease or eventually

All the samples were grown by the sublimation method in our group. The crystal growth procedure has been described in detail elsewhere (Hu et al., 2006). The growth of 6H and 4H polytypes are mainly the same, except for temperature range, growth pressure, seed polarity

details which are different and unique for different groups.

transmission synchrotron white-beam x-ray topography (SWBXT).

transition of 4H-SiC single crystals had been studied.

**1. Introduction** 

eliminate them.

**2. Bulk growth** 

and also growth process.

**SiC Single Crystal** 

Lina Ning and Xiaobo Hu

*JiaXing University & Shandong University* 


### **Bulk Growth and Characterization of SiC Single Crystal**

Lina Ning and Xiaobo Hu *JiaXing University & Shandong University China* 

#### **1. Introduction**

140 Silicon Carbide – Materials, Processing and Applications in Electronic Devices

Tavangar, R.; Molina, J.M. & Weber, L. (2007). Assessing predictive schemes for thermal

Tian, J.T.; Molina, J.M.; Narciso, J.; Garcia-Cordovilla, C. & Louis, E. (2005). Pressure

Weber, L.; Sinicco, G. & Molina, J.M. (2010). Influence of processing route on electrical and

0022-2461

2461

conductivity against diamond-reinforced silver matrix composites at intermediate phase contrast. *Scripta Materialia*, Vol.56, (November 2006), pp. 357-360, ISSN 1359-6462

infiltration of Al and Al-12wt%Si alloy into compacts of SiC and oxidized SiC particles. *Journal of Materials Science*, Vol.40, (October 2004), pp. 2537-2540, ISSN

thermal conductivity of Al/SiC composites with bimodal particle distribution. *Journal of Materials Science*, Vol.45, No.8 (November 2009), pp. 2203-2209, ISSN 0022-

> Sublimation method was used to grow bulk SiC by J.A. Lely for the first time in 1955 (Lely, 1955). It was improved then by Tairov and Tsvetkov and became the most mature method for bulk SiC growth. In this chapter, we will introduce the growth of hexagonal SiC. Although the bulk growth method is well known and used widely, there are still plenty of details which are different and unique for different groups.

> The growth of 4H-SiC is not as stable as that of 6H-SiC. That is to say the growth of 4H-SiC needs a harsh growth conditions. In order to grow high quality 4H polytype, the polytype transition of 4H-SiC single crystals had been studied.

> Although single crystals of SiC are commercially available, owing to the specific structures of SiC, there are still some structural defects, such as micropipes, mis-orientations, dislocations, stacking faults, basal plane dislocations, particle inclusions, precipitates and so on, which hinder its applications. So in this chapter we also introduce the recent progress in research of structural defects in 6H-SiC single crystals. Three kinds of typical structural defects in 6H-SiC single crystals were investigated. First, we describe the strain field of a micropipe by the theory of screw dislocation. Stress birefringence images from micropipes with different Burgers vectors have been simulated. The results are compared with polarized optical microscopic observations. Second, elementary screw dislocations were observed by back-reflection synchrotron radiation topography (BRSRT). Based on the reflection geometry, the image of an elementary screw dislocation was simulated. Elementary screw dislocation is a pure screw dislocation with Burger vector lc. Finally, Basal plane bending was detected by high resolution X-ray diffractometry (HRXRD) and transmission synchrotron white-beam x-ray topography (SWBXT).

> The observation and investigation of the structural defects helped us to understand their formation mechanisms. This makes it possible for us to further decrease or eventually eliminate them.

#### **2. Bulk growth**

All the samples were grown by the sublimation method in our group. The crystal growth procedure has been described in detail elsewhere (Hu et al., 2006). The growth of 6H and 4H polytypes are mainly the same, except for temperature range, growth pressure, seed polarity and also growth process.

Bulk Growth and Characterization of SiC Single Crystal 143

Fig. 2. Micrograph of the as-grown surface showing the existence of 4H-SiC, 15R-SiC at two

A B

Fig. 3. Schematic diagram of one-dimensional Raman scanning route across the slit

the real line is the actual position of slit which is along the <11-20> direction.

In order to identify the polytype structures in the two areas with different morphologies, Raman spectroscopy were used. One-dimensional Raman scanning was done cross the slit in a range of 100 μm, as shown in Fig. 3.The dashed line represents the scanning path, and

The intensity ratio of folded transverse acoustic (FTA) mode of 15R-SiC (Raman shift at 172.3 cm-1) (Wang et al., 2004) and 4H-SiC (Raman shift at 204.99 cm-1) (Wang et al., 2004) was introduced. In Fig. 4, the horizontal coordinate is along the dashed line in Fig. 3, and the longitudinal coordinate is the intensity ratio. According to the intensity ratio, the scanning scope can be divided into three regions. In region A, the intensity ratio is much greater than

sides of the slit

#### **2.1 Growth of 4H-SiC**

During the sublimation growth process of 4H-SiC, other foreign polytypes nucleated easily since the stacking energies for different SiC polytypes are nearly same. Most of the researchers believed that, it is the growth temperature, the polarity and mis-orientation of the seed that influence the stability of polytypic structure during the growth. Schulze (Norbert et al., 1999) and Straubinger (Straubinger et al., 2001) used different polarity seeds to grow 4H-SiC and found that a stable 4H polytype could be obtained by using the seed with 4H C-face. Further research found that the off-axis C-face seeds with misorientation axis towrads the <11-20> direction are better (Rost et al., 2006) for 4H-SiC growth than other seeds. The defects density decreased with the increase of seed misorientation from C-face.

#### **2.2 Polytype transition of 4H-SiC**

In this chapter, 4H C-face seeds with an 8° mis-orientation towards [11-20] were used to grow 4H-SiC. In order to make out the relationship between the polytype of the as-grown crystal and the surface morphology, the morphology of as-grown surface and polytype transition of 4H-SiC single crystals had been studied by optical microscopy and Raman spectroscopy.

Fig. 1. The morphology of the facet of 4H-SiC

There are two growth mechanisms. Fig. 1 is the morphology of the facet of 4H-SiC. In this region, screw dislocation mechanism controls the growth process. Fig. 2 is the morphology of the area out of the facet. In this region, rough surface growth mechanism dominants. In Fig. 2, there are also two different morphologies. In area A, the growth steps are very fine. In area B, the surface is smooth. There is a slit between the two areas, which is not a scratch caused by machining or annealing after growth. Normally the slit is along the <11-20> direction and extends several or dozens of milli-meters on the as-grown surface.

During the sublimation growth process of 4H-SiC, other foreign polytypes nucleated easily since the stacking energies for different SiC polytypes are nearly same. Most of the researchers believed that, it is the growth temperature, the polarity and mis-orientation of the seed that influence the stability of polytypic structure during the growth. Schulze (Norbert et al., 1999) and Straubinger (Straubinger et al., 2001) used different polarity seeds to grow 4H-SiC and found that a stable 4H polytype could be obtained by using the seed with 4H C-face. Further research found that the off-axis C-face seeds with misorientation axis towrads the <11-20> direction are better (Rost et al., 2006) for 4H-SiC growth than other seeds. The defects density decreased with the increase of seed mis-

In this chapter, 4H C-face seeds with an 8° mis-orientation towards [11-20] were used to grow 4H-SiC. In order to make out the relationship between the polytype of the as-grown crystal and the surface morphology, the morphology of as-grown surface and polytype transition of 4H-SiC single crystals had been studied by optical microscopy and Raman

There are two growth mechanisms. Fig. 1 is the morphology of the facet of 4H-SiC. In this region, screw dislocation mechanism controls the growth process. Fig. 2 is the morphology of the area out of the facet. In this region, rough surface growth mechanism dominants. In Fig. 2, there are also two different morphologies. In area A, the growth steps are very fine. In area B, the surface is smooth. There is a slit between the two areas, which is not a scratch caused by machining or annealing after growth. Normally the slit is along the <11-20>

direction and extends several or dozens of milli-meters on the as-grown surface.

**2.1 Growth of 4H-SiC** 

orientation from C-face.

spectroscopy.

**2.2 Polytype transition of 4H-SiC** 

Fig. 1. The morphology of the facet of 4H-SiC

Fig. 2. Micrograph of the as-grown surface showing the existence of 4H-SiC, 15R-SiC at two sides of the slit

Fig. 3. Schematic diagram of one-dimensional Raman scanning route across the slit

In order to identify the polytype structures in the two areas with different morphologies, Raman spectroscopy were used. One-dimensional Raman scanning was done cross the slit in a range of 100 μm, as shown in Fig. 3.The dashed line represents the scanning path, and the real line is the actual position of slit which is along the <11-20> direction.

The intensity ratio of folded transverse acoustic (FTA) mode of 15R-SiC (Raman shift at 172.3 cm-1) (Wang et al., 2004) and 4H-SiC (Raman shift at 204.99 cm-1) (Wang et al., 2004) was introduced. In Fig. 4, the horizontal coordinate is along the dashed line in Fig. 3, and the longitudinal coordinate is the intensity ratio. According to the intensity ratio, the scanning scope can be divided into three regions. In region A, the intensity ratio is much greater than

Bulk Growth and Characterization of SiC Single Crystal 145

From Fig. 5c and 5d, 15R and 4H polytypes appear at the same time. The characteristic peak of 15R-SiC dominates at point C. Both the characteristic peaks of 15R and 4H-SiC are weak and the intensity of the background signal is strong at point D. That is to say, the phonon state density is irregular in this area. In other words, the Si-C di-atom stacking near slit is not completely disorder but contains short range order of 4H and

a b

c d

 Fig. 5. The Raman spectra at different points of one-dimensional Raman scanning, (a) region A, 15R-SiC; (b) region B, 4H-SiC; (c) point C 15R- and 4H-SiC; (d) point D 4H- and

In summary, the polytype transition is a process in which the stacking structure changes from long range order to short range order and then back to long range regular. The transition region in our observation is in a range of about 2-3μm. The slit is just the sign of

There are some structure defects in SiC single crystals which hinder its applications. For example, the micropipes increase leakage current and reduce the breakdown voltage of SiC devices (Neudeck & Powell, 1994; Wahab et al., 2000). All the samples used in this section

15R-SiC.

15R-SiC.

**2.3 Summary** 

the polytype transition.

**3. Characterizations** 

were 6H-SiC wafers grown by sublimation method.

one, so it is mainly 15R-SiC whose Raman spectrum is shown in Fig. 5a. In region B, the intensity ratio is much lower than one, so it is mainly 4H-SiC whose Raman spectrum is shown in Fig. 5b. Between the two regions, i.e. near the slit, the intensity ratio drops suddenly. Two points, C and D at a distance of 4μm, were chosen as reference points in this region. The corresponding Raman spectra are shown in Fig. 5c and d.

Fig. 4. The intensity ratio of FTA mode along the dashed line in Fig. 3.

one, so it is mainly 15R-SiC whose Raman spectrum is shown in Fig. 5a. In region B, the intensity ratio is much lower than one, so it is mainly 4H-SiC whose Raman spectrum is shown in Fig. 5b. Between the two regions, i.e. near the slit, the intensity ratio drops suddenly. Two points, C and D at a distance of 4μm, were chosen as reference points in this

B

C

D

region. The corresponding Raman spectra are shown in Fig. 5c and d.

A

Fig. 4. The intensity ratio of FTA mode along the dashed line in Fig. 3.

From Fig. 5c and 5d, 15R and 4H polytypes appear at the same time. The characteristic peak of 15R-SiC dominates at point C. Both the characteristic peaks of 15R and 4H-SiC are weak and the intensity of the background signal is strong at point D. That is to say, the phonon state density is irregular in this area. In other words, the Si-C di-atom stacking near slit is not completely disorder but contains short range order of 4H and 15R-SiC.

Fig. 5. The Raman spectra at different points of one-dimensional Raman scanning, (a) region A, 15R-SiC; (b) region B, 4H-SiC; (c) point C 15R- and 4H-SiC; (d) point D 4H- and 15R-SiC.

#### **2.3 Summary**

In summary, the polytype transition is a process in which the stacking structure changes from long range order to short range order and then back to long range regular. The transition region in our observation is in a range of about 2-3μm. The slit is just the sign of the polytype transition.

#### **3. Characterizations**

There are some structure defects in SiC single crystals which hinder its applications. For example, the micropipes increase leakage current and reduce the breakdown voltage of SiC devices (Neudeck & Powell, 1994; Wahab et al., 2000). All the samples used in this section were 6H-SiC wafers grown by sublimation method.

#### **3.1 Micropipes**

Hollow tubes called micropipes, which generally run along the c axis, are often found in sublimation grown SiC crystals. There has been much debate regarding the nature of micropipes and several models have been proposed to illuminate the formation mechanism of micropipes. One is based on Frank's theory, which interpreted the formation of micropipes as the stress relaxation of screw dislocations with large Burgers vectors (Frank, 1951). The diameter of micropipes depends on the Burgers vectors of screw dislocations:

$$D = \mu \mathbf{b}^2 \;/\; 4\pi\chi\tag{1}$$

Bulk Growth and Characterization of SiC Single Crystal 147

a b



MP1

d

MP2

Fig. 6. Microscopic images of two micropipes (MP1 and MP2). (a) A unique interference pattern observed by a polarizing optical microscope for MP1. (b) A bright-field optical microscopic image for MP1. (c) A unique interference pattern observed by a polarizing optical microscope for MP2. (d) A bright-field optical microscopic image for MP2. Images (a) and (b) are the same micropipe with a larger Burgers vector; images (c) and (d) are the same micropipe with a smaller Burgers vector. The insets in the upper right of (a) and (c) give the simulation of MP1 and MP2, respectively. The black spots that appear in the four images are

foreign particles on the lens.

c

Where D is the core diameter, μ the shear module, **b** the Burgers vector and *γ* the surface energy. The longer the Burgers vector, the larger is the diameter of the micropipes. The other model suggests that deposition or voids on the growth surface cause the generation of micropipes (Giocondi et al., 1997; Liu et al., 2005). It has been proposed that the large steps interact with unit screw dislocations and the heterogeneous phase to form the micropipe.

#### **3.1.1 Experimental observations**

Fig. 6a and 6c show the stress birefringence images of two typical micropipes with different diameters respectively. They look like butterflies with four bright wings, and have a dark core in the center. The wings' length varies with the diameter of micropipe. The wings' brightness was also not uniform from the center to the outside. The longer the distance from the center, the weaker is the brightness of the wings. Fig. 6b and 6d exhibit the bright field images of the two micripipes respectively. The open cores were visible distinctly in the centers of micropipes especially for the one with large diameter. When we rotated the sample, the birefringence pattern rotated simultaneously (as shown in Fig. 7).

#### **3.1.2 Theoretical explanations**

In this chapter we describe the strain field of a micropipe by the theory of screw dislocation. According to Frank's theory, micropipes are dislocations with large Burgers vectors. Therefore the strain field caused by the micropipes could be described by dislocation theory and stress birefringence image from a micropipe could be simulated. The existence of micropipes changes the crystal from uniaxial to biaxial crystal in the neighbour area of a micropipe. So the interference intensity near a micropipe should be written as follows:

$$I = \begin{cases} (A \;/\ r^2) \sin^2(2\theta - 2\alpha) & \text{when } r > r\_0 \\ 0 & \text{when } r < r\_0 \end{cases} \tag{2}$$

where r0 is the diameter of the micropipe, α is the angle between <2-1-10> direction and polarizer, A is constant which can be expressed as:

$$A = \frac{I\_0 \cdot \mu^2 \cdot b^2 \cdot n^6 \cdot \pi\_{44}^2 \cdot \Delta l^2 \cdot \cos^2 2\beta}{64\lambda^2} \tag{3}$$

When r>r0, the contour equation of the intensity curve can be obtained

$$r^2 = \frac{I\_0}{I} f^2 \sin^2(2\theta - 2\alpha) \mu m^2 \tag{4}$$

Hollow tubes called micropipes, which generally run along the c axis, are often found in sublimation grown SiC crystals. There has been much debate regarding the nature of micropipes and several models have been proposed to illuminate the formation mechanism of micropipes. One is based on Frank's theory, which interpreted the formation of micropipes as the stress relaxation of screw dislocations with large Burgers vectors (Frank, 1951). The diameter of micropipes depends on the Burgers vectors of screw dislocations:

> <sup>2</sup> *D* = μ**b** / 4πγ

Where D is the core diameter, μ the shear module, **b** the Burgers vector and *γ* the surface energy. The longer the Burgers vector, the larger is the diameter of the micropipes. The other model suggests that deposition or voids on the growth surface cause the generation of micropipes (Giocondi et al., 1997; Liu et al., 2005). It has been proposed that the large steps interact with unit screw dislocations and the heterogeneous phase to form the micropipe.

Fig. 6a and 6c show the stress birefringence images of two typical micropipes with different diameters respectively. They look like butterflies with four bright wings, and have a dark core in the center. The wings' length varies with the diameter of micropipe. The wings' brightness was also not uniform from the center to the outside. The longer the distance from the center, the weaker is the brightness of the wings. Fig. 6b and 6d exhibit the bright field images of the two micripipes respectively. The open cores were visible distinctly in the centers of micropipes especially for the one with large diameter. When we rotated the

In this chapter we describe the strain field of a micropipe by the theory of screw dislocation. According to Frank's theory, micropipes are dislocations with large Burgers vectors. Therefore the strain field caused by the micropipes could be described by dislocation theory and stress birefringence image from a micropipe could be simulated. The existence of micropipes changes the crystal from uniaxial to biaxial crystal in the neighbour area of a micropipe.

> ( / )sin (2 2 ) when 0 when *A r r r <sup>I</sup>*

where r0 is the diameter of the micropipe, α is the angle between <2-1-10> direction and

226 2 2 2

λ

π

64

2 22 <sup>0</sup> <sup>2</sup> sin (2 2 ) *<sup>I</sup> rf m <sup>I</sup>* = − θ αμ

2

θ α − > <sup>=</sup> <

sample, the birefringence pattern rotated simultaneously (as shown in Fig. 7).

So the interference intensity near a micropipe should be written as follows:

polarizer, A is constant which can be expressed as:

2 2

0 44

*I bn l <sup>A</sup>* μ

When r>r0, the contour equation of the intensity curve can be obtained

(1)

0 0

(2)

*r r*

β

(4)

⋅ ⋅ ⋅ ⋅ ⋅Δ ⋅ <sup>=</sup> (3)

cos 2

**3.1 Micropipes** 

**3.1.1 Experimental observations** 

**3.1.2 Theoretical explanations** 

Fig. 6. Microscopic images of two micropipes (MP1 and MP2). (a) A unique interference pattern observed by a polarizing optical microscope for MP1. (b) A bright-field optical microscopic image for MP1. (c) A unique interference pattern observed by a polarizing optical microscope for MP2. (d) A bright-field optical microscopic image for MP2. Images (a) and (b) are the same micropipe with a larger Burgers vector; images (c) and (d) are the same micropipe with a smaller Burgers vector. The insets in the upper right of (a) and (c) give the simulation of MP1 and MP2, respectively. The black spots that appear in the four images are foreign particles on the lens.

Bulk Growth and Characterization of SiC Single Crystal 149

Fig. 8 shows the microscopic images for the same area but in different growth stages of the same crystal. The micropipes' distribution proves that Fig. 8a and 8b, 8c and 8d are the same areas in different growth stages respectively. The diameter of the micropipe is increasing with the crystal growth which can be proved by the size of bright wings in the birefringence images. It means that the stress can be released through micropipes during cryatal growth. According to statistic of the densities of micropie along crystal growth, the micropipe density decreased with growth process for almost all samples, except one. That is to say, in case of optimizing growth conditions, micropipe density can be decreased and crystal

Fig. 8. Development of micropipes along growth direction, the red arrows represent the growth direction. Figure a and b belong to a same area; Fig. c and d belong to another same

D D

C C

E E

B

**3.1.3 Evolution of micropipes during growth** 

A A

a b

B

c d

quality can be improved.

area.

Fig. 7. Microscopic images of micropipe observed by a polarizing optical microscope with different α. The red and white arrows represent the directions of the polarizer and the <2-1- 10> direction, respectively. (a) α =0. (b) α =π/4.

From Eq. 4, we can get interference intensity contours with different *I0*/*I*, as shown in Fig. 6. The smaller the intensity of incident beam, the longer is the birefringence pattern's radius. In Fig. 6 the diameters of MP1 and MP2 are about 4.0μm and 0.66μm. According to Eq. 1 and Eq. 4, the lengths of the brightest wings (in case of *I*=*I0*) for the two micropipes could be calculated (Table 1). The observed and calculated values for these wings are nearly the same with two different micropipes. The insets in the upper rights of Fig. 6a and 6c give the simulation of MP1 and MP2 respectively. The simulation images are indeed a butterfly with four wings having a gradual changed intensity and a black core as same as the recorded images. However the four wings are not symmetrical in Fig. 6a. This may be caused by the off-orientation of the sample. The core of MP1 is not circular in Fig. 6b, which can not happen in on-axis sample for the consideration of energy. This indicates the off-axis of the sample surface.

From Eq. 4, it is known that the birefringence images rotated with different α. For example, if we rotate the sample for π/4 (α=π/4), the equal interference intensity contours rotated for π/4. This result fit well with the experimental results shown in Fig. 7, where the red and white arrows represent the directions of the polarizer and <2-1-10> direction respectively. A void is taken as a reference point in Fig. 7. In Fig. 7a, <2-1-10> direction is parallel to the polarizer, the bright wings make an angle of π/4 with <2-1-10> direction. In Fig. 7b, <2-1- 10> direction make an angle of π/4 with the polarizer, the bright wings make an angle of zero with <2-1-10> direction. We can conclude that the calculated rotation property also agreed with the experimental results.


Table 1. The observed and calculated wing lengths of MP1 and MP2 in case of *I*=*I0* 

Fig. 7. Microscopic images of micropipe observed by a polarizing optical microscope with different α. The red and white arrows represent the directions of the polarizer and the <2-1-

From Eq. 4, we can get interference intensity contours with different *I0*/*I*, as shown in Fig. 6. The smaller the intensity of incident beam, the longer is the birefringence pattern's radius. In Fig. 6 the diameters of MP1 and MP2 are about 4.0μm and 0.66μm. According to Eq. 1 and Eq. 4, the lengths of the brightest wings (in case of *I*=*I0*) for the two micropipes could be calculated (Table 1). The observed and calculated values for these wings are nearly the same with two different micropipes. The insets in the upper rights of Fig. 6a and 6c give the simulation of MP1 and MP2 respectively. The simulation images are indeed a butterfly with four wings having a gradual changed intensity and a black core as same as the recorded images. However the four wings are not symmetrical in Fig. 6a. This may be caused by the off-orientation of the sample. The core of MP1 is not circular in Fig. 6b, which can not happen in on-axis sample for the consideration of energy. This indicates the off-axis of the

From Eq. 4, it is known that the birefringence images rotated with different α. For example, if we rotate the sample for π/4 (α=π/4), the equal interference intensity contours rotated for π/4. This result fit well with the experimental results shown in Fig. 7, where the red and white arrows represent the directions of the polarizer and <2-1-10> direction respectively. A void is taken as a reference point in Fig. 7. In Fig. 7a, <2-1-10> direction is parallel to the polarizer, the bright wings make an angle of π/4 with <2-1-10> direction. In Fig. 7b, <2-1- 10> direction make an angle of π/4 with the polarizer, the bright wings make an angle of zero with <2-1-10> direction. We can conclude that the calculated rotation property also

MP1 4.00μm 22.2μm 21μm MP2 0.66μm 8.3μm 9μm

Table 1. The observed and calculated wing lengths of MP1 and MP2 in case of *I*=*I0* 

length of the brightest wing (r) Observed Calculated

10> direction, respectively. (a) α =0. (b) α =π/4.

a b

sample surface.

agreed with the experimental results.

MP Observed core diameter

(D)

#### **3.1.3 Evolution of micropipes during growth**

Fig. 8 shows the microscopic images for the same area but in different growth stages of the same crystal. The micropipes' distribution proves that Fig. 8a and 8b, 8c and 8d are the same areas in different growth stages respectively. The diameter of the micropipe is increasing with the crystal growth which can be proved by the size of bright wings in the birefringence images. It means that the stress can be released through micropipes during cryatal growth. According to statistic of the densities of micropie along crystal growth, the micropipe density decreased with growth process for almost all samples, except one. That is to say, in case of optimizing growth conditions, micropipe density can be decreased and crystal quality can be improved.

Fig. 8. Development of micropipes along growth direction, the red arrows represent the growth direction. Figure a and b belong to a same area; Fig. c and d belong to another same area.

Bulk Growth and Characterization of SiC Single Crystal 151

Fig. 10 shows the back-reflection synchrotron radiation topograph of SiC (0001) wafer with 000**30** reflection. From the topograph, many white dots with the same diameters of 26-28μm can be observed. As the simulation results in following paragraphs, these white dots correspond to elementary screw dislocations. Therefore, the density of elementary screw

Fig. 10. Back-reflection synchrotron radiation topograph of SiC wafer with 000**30** reflection The image of elementary screw dislocation can be simulated by ray-tracing method (Huang et al., 1999). As well known, for a screw dislocation along z axis, its displacement field can

> <sup>1</sup> ( / 2 )tan ( / ) *u b <sup>z</sup>* π

Here b is the Burgers vector of screw dislocation. y and x are the coordinate position of arbitrary point in distorted area. From Eq. 5, the position-dependent orientation of the (0001)

> (, ,) /( 4 ) (, ,) /( 4 ) ( , , ) 2 /( 4 )

= + =− + = +

Where r=(x2+y2)1/2. For the numerical simulation of the screw dislocation, the distorted lattice was divided into a set of small cubes of constant. All the cubes were assumed to have the same integrated diffraction density I0. The recording plane was also divided into a set of squares of constant area. Then the intensities from all the cubes were projected to the corresponding squares according to the traces of the diffracted beams. The sum of intensities each square received after the projection represents the local contrast level. Eventually, all the calculated intensity can be plotted as a gray-scale topograph to give the simulation of the

*n x y z by r b r n x y z bx r b r n xyz r b r*

π

2 2 2 1/2 2 2 2 1/2 2 2 2 1/2

π

π

 π

*y x* <sup>−</sup> = (5)

(6)

dislocation in this wafer was measured to be 1.56x104/cm2.

reflection plane can be expressed by the following equation.

*x y z*

be described as

screw dislocation image.

Fig. 9. Micropipes distribution along growth direction

#### **3.1.4 Summary**

In summary, the birefringence images of micropipes in 6H-SiC single crystals were observed by a polarization optical microscope. Based on the Frank's theory, the micropipes were treated as screw dislocations with huge Burgers vectors. Due to the strain caused by a micropipe, the SiC crystal in the neighbour area around a micropipe transferred from uniaxial into biaxial crystal. In the meanwhile, the refractive index ellipsoid was described by three principal refractive indexes and birefringence occurred. Based on above consideration, the birefringence images of micropipes with different Burgers vectors were simulated. The results agreed well with the observations. It confirms indirectly the Frank's theory that a micropipe is actually the super-screw dislocation with huge Burgers vector. With crystal growth, the micropipe density has a tendency of decrease and the diameter of micropipes can be enlarged for the stress release.

#### **3.2 Elementary screw dislocations**

Although the elementary screw dislocations did not seriously deteriorate the performance of device as micropipes, they prevent the realization of high-efficiency, reliable electronic devices (Lendenmann, 2001; Malhan et al., 2003; Neudeck et al., 1998).

In order to assess the density of elementary screw dislocation, back-reflection synchrotron radiation topograph of (0001) wafer was taken. In experimental setup, symmetric diffraction geometry with 000**30** reflection was used. The angle between incident beam and sample surface was 83°. In this case, the selected X-ray wavelength is 0.1nm. The distance between sample and film was 20cm. The illumination area is 1mm x 1mm.

**growth direction**

In summary, the birefringence images of micropipes in 6H-SiC single crystals were observed by a polarization optical microscope. Based on the Frank's theory, the micropipes were treated as screw dislocations with huge Burgers vectors. Due to the strain caused by a micropipe, the SiC crystal in the neighbour area around a micropipe transferred from uniaxial into biaxial crystal. In the meanwhile, the refractive index ellipsoid was described by three principal refractive indexes and birefringence occurred. Based on above consideration, the birefringence images of micropipes with different Burgers vectors were simulated. The results agreed well with the observations. It confirms indirectly the Frank's theory that a micropipe is actually the super-screw dislocation with huge Burgers vector. With crystal growth, the micropipe density has a tendency of decrease and the diameter of

Although the elementary screw dislocations did not seriously deteriorate the performance of device as micropipes, they prevent the realization of high-efficiency, reliable electronic

In order to assess the density of elementary screw dislocation, back-reflection synchrotron radiation topograph of (0001) wafer was taken. In experimental setup, symmetric diffraction geometry with 000**30** reflection was used. The angle between incident beam and sample surface was 83°. In this case, the selected X-ray wavelength is 0.1nm. The distance between

devices (Lendenmann, 2001; Malhan et al., 2003; Neudeck et al., 1998).

sample and film was 20cm. The illumination area is 1mm x 1mm.

**micropipe number**

**3.1.4 Summary** 

Fig. 9. Micropipes distribution along growth direction

micropipes can be enlarged for the stress release.

**3.2 Elementary screw dislocations** 

Fig. 10 shows the back-reflection synchrotron radiation topograph of SiC (0001) wafer with 000**30** reflection. From the topograph, many white dots with the same diameters of 26-28μm can be observed. As the simulation results in following paragraphs, these white dots correspond to elementary screw dislocations. Therefore, the density of elementary screw dislocation in this wafer was measured to be 1.56x104/cm2.

Fig. 10. Back-reflection synchrotron radiation topograph of SiC wafer with 000**30** reflection

The image of elementary screw dislocation can be simulated by ray-tracing method (Huang et al., 1999). As well known, for a screw dislocation along z axis, its displacement field can be described as

$$
\mu\_z = (b \,/\, 2\pi) \tan^{-1}(y \,/\, x) \tag{5}
$$

Here b is the Burgers vector of screw dislocation. y and x are the coordinate position of arbitrary point in distorted area. From Eq. 5, the position-dependent orientation of the (0001) reflection plane can be expressed by the following equation.

$$\begin{aligned} m\_x(\mathbf{x}, \mathbf{y}, z) &= by \;/\, r(b^2 + 4\pi^2 r^2)^{1/2} \\ m\_y(\mathbf{x}, \mathbf{y}, z) &= -b\mathbf{x} \;/\, r(b^2 + 4\pi^2 r^2)^{1/2} \\ m\_z(\mathbf{x}, \mathbf{y}, z) &= 2\pi r \;/\, (b^2 + 4\pi^2 r^2)^{1/2} \end{aligned} \tag{6}$$

Where r=(x2+y2)1/2. For the numerical simulation of the screw dislocation, the distorted lattice was divided into a set of small cubes of constant. All the cubes were assumed to have the same integrated diffraction density I0. The recording plane was also divided into a set of squares of constant area. Then the intensities from all the cubes were projected to the corresponding squares according to the traces of the diffracted beams. The sum of intensities each square received after the projection represents the local contrast level. Eventually, all the calculated intensity can be plotted as a gray-scale topograph to give the simulation of the screw dislocation image.

Bulk Growth and Characterization of SiC Single Crystal 153

samples were orientated with the (0001) surface perpendicular to the incident beam and the

Fig. 12 shows the plot of the relative ω006 rocking curve peak position as a function of the beam position across the diameters of a 2 inch wafer. The three groups of data in Fig. 12 were got from three different diameters of the same wafer. In case of precisely orientated crystal without any basal plane bending, ω is equal to Bragg angle. But the HRXRD test here is not the case. When the incident beam is located on the left of the center, the ω is larger than Bragg angle and the deviation of ω from Bragg angle is proportional to the distance between detected point and the center of the wafer. The farther the distance of the detected point from the center, the larger the deviation of surface from the basal plane. When the incident beam is located on the right of the center, the result is reversal, i.e. the ω is smaller than Bragg angle. The HRXRD experimental result implies that the (0001) basal plane in the

Fig. 12. Relative omega (Δω006) peak position as a function of the beam position across the diameter of a 2 inch 6H-SiC wafer. The three lines were got from three different diameters

The shape of the diffraction spots should be the same as that of footprint of X-ray source for a highly perfect crystal. In case of any lattice deformation, the diffraction spots for different reflections assume different shapes. Fig. 13 shows two transmission synchrotron topographs from two different samples. From this figure, it could be seen that the two samples have different distortion cases and each diffraction spot has its own shape in the two topographs. In Fig. 13a, all the diffraction spots are shrunk along the diffraction vector direction. In contrast, it seems that all the diffraction spots are stretched along the same line in Fig. 13b. No doubt, the two samples exist obviously structural imperfection. But is basal plane

topographs were recorded by Fuji film.

**3.3.1 Experimental results-HRXRD** 

sample is a concave face rather than a planar.

on the same wafer.

**3.3.2 Experimental results-SWBXT** 

bending which causes the distortion of the diffraction spots?

Fig. 11. The simulation images of screw dislocations with different Burgers vectors. (a). Elementary screw dislocation with Burgers vector 1c; (b). Screw dislocation with Burgers vector 2c. The image area is 100μm x l00μm.

Fig. 11a and 11b show the simulation images of an elementary screw dislocation with Burgers vector lc and a screw dislocation with Burgers vector 2c respectively. From the simulation images, the white dot diameter corresponding to an elementary screw dislocation with Burgers vector lc was measured to be 28μm. It is in well agreement with synchrotron observation. As for the screw dislocation with Burgers vector 2c, the corresponding white dot diameter from simulation was measured to be 39μm . Obviously, almost all the white dots in Fig. 10 correspond to elementary screw dislocations.

#### **3.3 Basal plane bending**

Recently, basal plane bending of SiC single crystals has attracted much attention (Lee et al., 2008; Seitz et al., 2006). In the case of basal plane bending, the normal orientation of the basal plane varies with the position from point to point. Basal plane bending causes serious lattice deformation and leads to the formation of low-angle boundaries. It was found that the degree of basal plane curvature in the facet region was less serious than that in the periphery region (Seitz et al., 2006). Therefore only the central part of a substrate can meet the requirements of device applications in the case of basal plane bending. For evaluating the crystal quality, <0001> orientated 6H-SiC samples were tested by HRXRD and SWBXT.

The HRXRD was conducted by XPERT-PRO diffractometer. The incident beam was adjusted by the beam conditioner of four Ge(022) collimated crystals so that the X-ray beam on the sample was accurately the Cu-Kα1(λ=1.54056Å) radiation. The symmetrical diffraction geometry has been used in the measurement. The slits for the incident beam and detector are 0.5mm × 4mm and two degree respectively. The tube voltage and tube current are 40kV and 40mA respectively.

Several samples were investigated by transmission synchrotron topography performed at the 4W1A beam line of Beijing Synchrotron Radiation Laboratory. In our experiment, the electron energy of storage ring was 2.2GeV and the beam current was 80-100mA. Transmission synchrotron topographs were taken by transmission Laue geometry. The samples were orientated with the (0001) surface perpendicular to the incident beam and the topographs were recorded by Fuji film.

#### **3.3.1 Experimental results-HRXRD**

152 Silicon Carbide – Materials, Processing and Applications in Electronic Devices

Fig. 11. The simulation images of screw dislocations with different Burgers vectors. (a). Elementary screw dislocation with Burgers vector 1c; (b). Screw dislocation with Burgers

almost all the white dots in Fig. 10 correspond to elementary screw dislocations.

Fig. 11a and 11b show the simulation images of an elementary screw dislocation with Burgers vector lc and a screw dislocation with Burgers vector 2c respectively. From the simulation images, the white dot diameter corresponding to an elementary screw dislocation with Burgers vector lc was measured to be 28μm. It is in well agreement with synchrotron observation. As for the screw dislocation with Burgers vector 2c, the corresponding white dot diameter from simulation was measured to be 39μm . Obviously,

Recently, basal plane bending of SiC single crystals has attracted much attention (Lee et al., 2008; Seitz et al., 2006). In the case of basal plane bending, the normal orientation of the basal plane varies with the position from point to point. Basal plane bending causes serious lattice deformation and leads to the formation of low-angle boundaries. It was found that the degree of basal plane curvature in the facet region was less serious than that in the periphery region (Seitz et al., 2006). Therefore only the central part of a substrate can meet the requirements of device applications in the case of basal plane bending. For evaluating the crystal quality, <0001> orientated 6H-SiC samples were tested by HRXRD and SWBXT. The HRXRD was conducted by XPERT-PRO diffractometer. The incident beam was adjusted by the beam conditioner of four Ge(022) collimated crystals so that the X-ray beam on the sample was accurately the Cu-Kα1(λ=1.54056Å) radiation. The symmetrical diffraction geometry has been used in the measurement. The slits for the incident beam and detector are 0.5mm × 4mm and two degree respectively. The tube voltage and tube current are 40kV

Several samples were investigated by transmission synchrotron topography performed at the 4W1A beam line of Beijing Synchrotron Radiation Laboratory. In our experiment, the electron energy of storage ring was 2.2GeV and the beam current was 80-100mA. Transmission synchrotron topographs were taken by transmission Laue geometry. The

vector 2c. The image area is 100μm x l00μm.

**3.3 Basal plane bending** 

and 40mA respectively.

Fig. 12 shows the plot of the relative ω006 rocking curve peak position as a function of the beam position across the diameters of a 2 inch wafer. The three groups of data in Fig. 12 were got from three different diameters of the same wafer. In case of precisely orientated crystal without any basal plane bending, ω is equal to Bragg angle. But the HRXRD test here is not the case. When the incident beam is located on the left of the center, the ω is larger than Bragg angle and the deviation of ω from Bragg angle is proportional to the distance between detected point and the center of the wafer. The farther the distance of the detected point from the center, the larger the deviation of surface from the basal plane. When the incident beam is located on the right of the center, the result is reversal, i.e. the ω is smaller than Bragg angle. The HRXRD experimental result implies that the (0001) basal plane in the sample is a concave face rather than a planar.

Fig. 12. Relative omega (Δω006) peak position as a function of the beam position across the diameter of a 2 inch 6H-SiC wafer. The three lines were got from three different diameters on the same wafer.

#### **3.3.2 Experimental results-SWBXT**

The shape of the diffraction spots should be the same as that of footprint of X-ray source for a highly perfect crystal. In case of any lattice deformation, the diffraction spots for different reflections assume different shapes. Fig. 13 shows two transmission synchrotron topographs from two different samples. From this figure, it could be seen that the two samples have different distortion cases and each diffraction spot has its own shape in the two topographs. In Fig. 13a, all the diffraction spots are shrunk along the diffraction vector direction. In contrast, it seems that all the diffraction spots are stretched along the same line in Fig. 13b. No doubt, the two samples exist obviously structural imperfection. But is basal plane bending which causes the distortion of the diffraction spots?

Bulk Growth and Characterization of SiC Single Crystal 155

If the sample surface is exactly the (0001) plane, the two Cartesian systems coincide. Otherwise there will be a rotation for X´, Y´, Z´ system using X, Y, Z system as reference coordinate. Based on the HRXRD measurement, it is believed that the (0001) plane after bending is a concave sphere with a radius of R and only the center of the 2 inch wafer is exactly the (0001) plane. Here the center of 2 inch wafer is taken as the origin of the X, Y, Z system. Therefore the position of the spherical center is located at (0, 0, R). The c axis for an arbitary (x, y, 0) point on the sample surface deviates from the <0001> direction in case of basal plane bending. In other words, the Z´ directional vector at (x, y, 0) could be described

> , 22 2 cos *<sup>y</sup>*

The directional vector from (0, 0, 0) to (x, y, 0) point could be written as (cosδ, sinδ, 0), where

In case of basal plane bending, for an arbitary point (x, y, 0) on sample surface, a new system X´, Y´, Z´ is established. Such system is unique and has exclusiveness. The new system X´, Y´, Z´ is got from the rotation of X, Y, Z system around a defined axis in XY plane whose directional vector is (sinδ, -cosδ, 0). So the base vector transformation relationship between

> cos cos sin cos sin cos cos sin cos sin ' cos sin cos cos sin cos sin cos sin sin

*i i j j k k*

+ − =− + − −

In one setup of our experiment, the X-ray is perpendicular to the sample surface and parallel to <000-1> at central point of sample, i.e. the positive plane of (0001) is facing to the incident beam. Here we define the Laue image of (0001) wafer in such setup as positive image. Similarly the Laue image of (0001) wafer is defined as negative image when the (000-1) Cface is facing to the incident beam. So the incident unit vector **g0** in positive image and the

> <sup>0</sup> **g** = −*k*

where **a\***, **b\*** and **c\*** are reciprocal space base vectors. In X´, Y´, Z´ system, they can be

\*\* \* 2 11 1 = ', = ' ', ' 3 3 *i ij k a a a c* **ab c** + =

 δδ

cos sin sin sin cos

β<sup>−</sup> <sup>=</sup>

2 2

*x x y* *x y R*

+ +

<sup>+</sup> , 2 2 sin *<sup>y</sup>*

2 2

 δ

 γ

δ γ

 δ γ

 δδ

\* \*\* **ga bc** =++ *hkl* (11)

δ= , 22 2

*R x y R*

+ +

<sup>+</sup> (8)

 δγ

 δγ

γ

(7)

(9)

(10)

(12)

cos

*x y*

γ=

as (cosα,cosβ,cosγ) in X, Y, Z coordinate system, where

22 2

cos

2 2

 γ

δ γ

diffraction vector **g** for hkl reflection can be expressed as:

δ γ

δδ

δ=

> δ

 δδ

+ +

*x x y R*

cos

α<sup>−</sup> <sup>=</sup>

the two systems can be derived:

'

'

expressed as follows:

Fig. 13. Synchrotron white-beam transmission images for two different samples under the same experimental conditions.

#### **3.3.3 Theory and simulation results for SWBXT**

In order to explore the relationship between the distortion of the diffraction spots and lattice imperfection, the shapes of Laue spots have been simulated based on the (0001) Si face concave sphere model.

We establish two Cartesian systems X, Y, Z at sample (X and Y are parallel to the vertical and the horizontal base line respectively, Z is opposite to the incident X-ray direction, as shown in Fig. 14), which stands for the spatial system and X´, Y´, Z´ (X´, Y´ and Z´ are parallel to <10-10>, <-12-10> and <0001> direction respectively), which stands for the crystallophysical system. The unit vectors for X, Y, Z and X´, Y´, Z´ systems are *<sup>i</sup>* , , *<sup>j</sup> <sup>k</sup>* and *<sup>i</sup>* ', ', ' *<sup>j</sup> <sup>k</sup>* respectively.

Fig. 14. Diffraction geometry of synchrotron white-beam topography in transmission mode. Where **g0** is the incident unit vector; g is the diffraction vector; Ф is the angel between **g** and **g0**.

 Fig. 13. Synchrotron white-beam transmission images for two different samples under the

In order to explore the relationship between the distortion of the diffraction spots and lattice imperfection, the shapes of Laue spots have been simulated based on the (0001) Si face

We establish two Cartesian systems X, Y, Z at sample (X and Y are parallel to the vertical and the horizontal base line respectively, Z is opposite to the incident X-ray direction, as shown in Fig. 14), which stands for the spatial system and X´, Y´, Z´ (X´, Y´ and Z´ are parallel to <10-10>, <-12-10> and <0001> direction respectively), which stands for the crystallophysical system. The unit vectors for X, Y, Z and X´, Y´, Z´ systems are *<sup>i</sup>* , , *<sup>j</sup> <sup>k</sup>*

Fig. 14. Diffraction geometry of synchrotron white-beam topography in transmission mode. Where **g0** is the incident unit vector; g is the diffraction vector; Ф is the angel between **g** and **g0**.

and

same experimental conditions.

concave sphere model.

*<sup>i</sup>* ', ', ' *<sup>j</sup> <sup>k</sup>* respectively.

**3.3.3 Theory and simulation results for SWBXT** 

a b

If the sample surface is exactly the (0001) plane, the two Cartesian systems coincide. Otherwise there will be a rotation for X´, Y´, Z´ system using X, Y, Z system as reference coordinate. Based on the HRXRD measurement, it is believed that the (0001) plane after bending is a concave sphere with a radius of R and only the center of the 2 inch wafer is exactly the (0001) plane. Here the center of 2 inch wafer is taken as the origin of the X, Y, Z system. Therefore the position of the spherical center is located at (0, 0, R). The c axis for an arbitary (x, y, 0) point on the sample surface deviates from the <0001> direction in case of basal plane bending. In other words, the Z´ directional vector at (x, y, 0) could be described as (cosα,cosβ,cosγ) in X, Y, Z coordinate system, where

$$\cos\alpha = \frac{-\mathbf{x}}{\sqrt{\mathbf{x}^2 + \mathbf{y}^2 + \mathbf{R}^2}}, \text{ } \cos\beta = \frac{-\mathbf{y}}{\sqrt{\mathbf{x}^2 + \mathbf{y}^2 + \mathbf{R}^2}}, \text{ } \cos\gamma = \frac{\mathbf{R}}{\sqrt{\mathbf{x}^2 + \mathbf{y}^2 + \mathbf{R}^2}}\tag{7}$$

The directional vector from (0, 0, 0) to (x, y, 0) point could be written as (cosδ, sinδ, 0), where

$$\cos \delta = \frac{\propto}{\sqrt{\mathbf{x}^2 + \mathbf{y}^2}}, \quad \sin \delta = \frac{y}{\sqrt{\mathbf{x}^2 + \mathbf{y}^2}} \tag{8}$$

In case of basal plane bending, for an arbitary point (x, y, 0) on sample surface, a new system X´, Y´, Z´ is established. Such system is unique and has exclusiveness. The new system X´, Y´, Z´ is got from the rotation of X, Y, Z system around a defined axis in XY plane whose directional vector is (sinδ, -cosδ, 0). So the base vector transformation relationship between the two systems can be derived:

$$
\begin{pmatrix}
\dot{i}^{\prime} \\
\dot{j}^{\prime} \\
k^{\prime}
\end{pmatrix} = \begin{pmatrix}
\cos^{2}\delta\cos\chi + \sin^{2}\delta & \cos\delta\sin\delta\cos\chi - \cos\delta\sin\delta & \cos\delta\sin\chi \\
\cos\delta\sin\delta\cos\chi - \cos\delta\sin\delta & \cos^{2}\delta + \sin^{2}\delta\cos\chi & \sin\delta\sin\chi \\
\end{pmatrix} \begin{pmatrix}
i \\
j \\
k
\end{pmatrix} \tag{9}
$$

In one setup of our experiment, the X-ray is perpendicular to the sample surface and parallel to <000-1> at central point of sample, i.e. the positive plane of (0001) is facing to the incident beam. Here we define the Laue image of (0001) wafer in such setup as positive image. Similarly the Laue image of (0001) wafer is defined as negative image when the (000-1) Cface is facing to the incident beam. So the incident unit vector **g0** in positive image and the diffraction vector **g** for hkl reflection can be expressed as:

$$\mathbf{g}\_0 = -\vec{k} \tag{10}$$

$$\mathbf{g} = h\mathbf{a}^\* + k\mathbf{b}^\* + l\mathbf{c}^\* \tag{11}$$

where **a\***, **b\*** and **c\*** are reciprocal space base vectors. In X´, Y´, Z´ system, they can be expressed as follows:

$$\mathbf{a}^\* = \frac{2}{\sqrt{3}a} \vec{i}^\prime, \mathbf{b}^\* = \frac{1}{\sqrt{3}a} \vec{i}^\prime + \frac{1}{a} \vec{j}^\prime, \mathbf{c}^\* = \frac{1}{c} \vec{k}^\prime \tag{12}$$

Bulk Growth and Characterization of SiC Single Crystal 157

<sup>2</sup> ( )cos sin sin sin cos 3 3

γ δ

> 2 2

− − =⋅ =⋅ <sup>−</sup> (16)

2

γ

 γ (15)

*a a a c*

So the distance between the diffraction spots with the center spot on the positive image for

<sup>2</sup> <sup>2</sup>

*BA B d D tg D A B* θ

According to Eq. 13 and Eq. 16, the exact position of the diffraction spots on the positive image for hkl reflection can be determined. Moreover, for an arbitrary (x, y, 0) point on

According to the descriptions above, for an arbitrary reflection, the corresponding diffraction spot shape could be simulated. It was found that the shapes of diffraction spots depended on the diffraction vector, the basal plane bending radius and incident beam direction. In simulation, a 4mm × 6mm illumination area was given and the positions for 20 points along the periphery of illumination area with 1mm interval were calculated for different reflections. Finally from one to its neighbor point was connected for each reflection and a series of Laue spots with distortion shapes were obtained. The simulation results are shown in Fig. 15a when a concave surface of (0001) wafer faces to the X-ray. The shapes for five typical areas of a (0001) wafer were simulated, i.e. center region O and four different quadrant regions A, B, C and D. It was found that the diffraction spots' distortion did not

The simulations for (000-1) convex face, i.e. negative image were shown in Fig. 15b and 15c. The two images correspond to different curvature radiuses. It was found that the distortions

In SWBXT experiment, the area of footprint of X-ray area was 4mm × 6mm and the sample holder had a small rotation around X axis. The simulation ignored the holder rotation and diffraction intensity variations of different reflections. The above ignorance has no effect on

Sample 1 and 2 were etched, for the purpose of knowing their polarity (Si face or C face). From the etching results, it was known that the illuminated lattice plane for sample 1 and 2 are (000-1) and (0001) respectively. According to HRXRD results, (0001) plane is concave and (000-1) plane is convex. Therefore the illuminated lattice plane for sample 1 and 2 are

Comparing the simulation results with the experimental observations, we can see obviously that Fig. 15b and Fig. 15a are nearly the same as Fig. 13a and Fig. 13b respectively. The main diffraction spots have the same distortion trend, which are shrunk and stretched along the diffraction directions respectively. When a convex lattice plane faces to x-ray source, its function is similar to a convex lens which make the X-ray focus and diffraction spots smaller. Similarly, the concave lattice face is like a concave lens, which make the X-ray

sample surface, its accurate positions for different reflections could be calculated.

*hk k l <sup>B</sup>*

δ

=− + <sup>−</sup> <sup>−</sup>

<sup>2</sup> <sup>222</sup> ( ) () () 3 3

*hk k l <sup>A</sup> a a a c*

= + ++

 

hkl reflection, *d*, can be expressed as follow:

where D is the distance between the sample and the film.

show remarkably difference for the five different areas.

distortion tendency of the Laue spots.

convex and concave respectively.

defocus and diffraction spots larger.

of the Laue spots became more serious with a smaller curvature radius.

where

In case of basal plane bending, the crystallophysical system, X´, Y´, Z´, varies with sample position continuously. For analysis convenience, the diffraction vector **g** could be divided into two parts, projection of **g** on XY plane, i.e. **g***f* and projection of **g** on **g0** direction. The following formula can be got in X, Y, Z system:

$$\begin{aligned} \mathbf{g}\_f &= \left[ (\frac{2h}{\sqrt{3}a} + \frac{k}{\sqrt{3}a}) (\cos^2 \delta \cos \gamma + \sin^2 \delta) + \frac{k}{a} (\sin \delta \cos \delta \cos \gamma - \sin \delta) \right] \\ &- \sin \delta \cos \delta) - \frac{l}{c} \cos \delta \sin \gamma \Big] \ddot{i} + \left\{ (\frac{2h}{\sqrt{3}a} + \frac{k}{\sqrt{3}a}) (\sin \delta \cos \delta \cos \gamma - \sin \delta) \right\} \\ &- \sin \delta \cos \delta) + \frac{k}{a} (\cos^2 \delta + \sin^2 \delta \cos \gamma) - \frac{l}{c} \sin \delta \sin \gamma \Big] \ddot{j} \end{aligned} \tag{13}$$

If the angle between **g** and **g0** is Ф, the diffraction angle θ can be written as follow according to their relationship in Fig. 14:

$$
\sin \theta = -\cos \Phi = -\frac{B}{\sqrt{A}}\tag{14}
$$

Fig. 15. The simulation results with conditions are as follows: light spot is 4mm × 6mm (the gray rectangle), D=10cm, a=0.3078nm, c=1.5117nm, x0∈[-2, 2], y0∈[-3, 3]. (a) concave plane, R=100cm. (b) convex plane, R=100cm. (c) convex plane, R=60cm.

where

156 Silicon Carbide – Materials, Processing and Applications in Electronic Devices

In case of basal plane bending, the crystallophysical system, X´, Y´, Z´, varies with sample position continuously. For analysis convenience, the diffraction vector **g** could be divided into two parts, projection of **g** on XY plane, i.e. **g***f* and projection of **g** on **g0** direction. The

2 2

γ

*h k k a a a <sup>l</sup> h k <sup>i</sup> c a a*

δ

<sup>2</sup> sin cos ) cos sin ( )(sin cos cos 3 3

− − ++ <sup>−</sup>

 δγ

If the angle between **g** and **g0** is Ф, the diffraction angle θ can be written as follow according

sin cos *<sup>B</sup>*

Fig. 15. The simulation results with conditions are as follows: light spot is 4mm × 6mm (the gray rectangle), D=10cm, a=0.3078nm, c=1.5117nm, x0∈[-2, 2], y0∈[-3, 3]. (a) concave plane,

R=100cm. (b) convex plane, R=100cm. (c) convex plane, R=60cm.

<sup>2</sup> ( )(cos cos sin ) (sin cos cos 3 3

=+ + + −

δ

 δδ

 δγ

*A*

δ δ

=− Φ=− (14)

γ

γ

2cm

Y

X

(13)

*k l <sup>j</sup>*

2 2

θ

 δ

 δ

sin cos ) (cos sin cos ) sin sin

− ++ −

γ

*a c*

following formula can be got in X, Y, Z system:

δδ

δδ

a b

c

*f*

**g**

to their relationship in Fig. 14:

$$\begin{cases} A = (\frac{2h}{\sqrt{3}a} + \frac{k}{\sqrt{3}a})^2 + (\frac{k}{a})^2 + (\frac{l}{c})^2 \\ B = -(\frac{2h}{\sqrt{3}a} + \frac{k}{\sqrt{3}a})\cos\delta\sin\gamma - \frac{k}{a}\sin\delta\sin\gamma - \frac{l}{c}\cos\gamma \end{cases} \tag{15}$$

So the distance between the diffraction spots with the center spot on the positive image for hkl reflection, *d*, can be expressed as follow:

$$d = D \cdot \text{tg} \, 2\theta = D \cdot \frac{-2B\sqrt{A - B^2}}{A - 2B^2} \tag{16}$$

where D is the distance between the sample and the film.

According to Eq. 13 and Eq. 16, the exact position of the diffraction spots on the positive image for hkl reflection can be determined. Moreover, for an arbitrary (x, y, 0) point on sample surface, its accurate positions for different reflections could be calculated.

According to the descriptions above, for an arbitrary reflection, the corresponding diffraction spot shape could be simulated. It was found that the shapes of diffraction spots depended on the diffraction vector, the basal plane bending radius and incident beam direction. In simulation, a 4mm × 6mm illumination area was given and the positions for 20 points along the periphery of illumination area with 1mm interval were calculated for different reflections. Finally from one to its neighbor point was connected for each reflection and a series of Laue spots with distortion shapes were obtained. The simulation results are shown in Fig. 15a when a concave surface of (0001) wafer faces to the X-ray. The shapes for five typical areas of a (0001) wafer were simulated, i.e. center region O and four different quadrant regions A, B, C and D. It was found that the diffraction spots' distortion did not show remarkably difference for the five different areas.

The simulations for (000-1) convex face, i.e. negative image were shown in Fig. 15b and 15c. The two images correspond to different curvature radiuses. It was found that the distortions of the Laue spots became more serious with a smaller curvature radius.

In SWBXT experiment, the area of footprint of X-ray area was 4mm × 6mm and the sample holder had a small rotation around X axis. The simulation ignored the holder rotation and diffraction intensity variations of different reflections. The above ignorance has no effect on distortion tendency of the Laue spots.

Sample 1 and 2 were etched, for the purpose of knowing their polarity (Si face or C face). From the etching results, it was known that the illuminated lattice plane for sample 1 and 2 are (000-1) and (0001) respectively. According to HRXRD results, (0001) plane is concave and (000-1) plane is convex. Therefore the illuminated lattice plane for sample 1 and 2 are convex and concave respectively.

Comparing the simulation results with the experimental observations, we can see obviously that Fig. 15b and Fig. 15a are nearly the same as Fig. 13a and Fig. 13b respectively. The main diffraction spots have the same distortion trend, which are shrunk and stretched along the diffraction directions respectively. When a convex lattice plane faces to x-ray source, its function is similar to a convex lens which make the X-ray focus and diffraction spots smaller. Similarly, the concave lattice face is like a concave lens, which make the X-ray defocus and diffraction spots larger.

Bulk Growth and Characterization of SiC Single Crystal 159

area. The insert of Fig. 16a is a microscopic image for <10-10> direction after etching. The white lines are low angle grain boundaries after etching. Fig. 16b stands for a wafer without basal plane bending. The boundary between the facet and the outside region disappeared. And the assembly of low angle grain bounbdaries along <10-10> direction disapppeared too. The stress for the whole wafer became more uniform. That is to say, the large number of

In this chapter, polytype transition mechanism during 4H-SiC growth, the nature of micropipe and the existence of basal plan bending has been proposed. Elementary screw dislocations were also detected by back-reflection synchrotron radiation topography. All the results obtained above helped us to optimize the growth condition and then improve the

This work was supported by National Basic Research Program of China under grant No. 2009CB930503 and No. 2011CB301904, Natural Science Foundation of China under grant

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grain boubdaries along <10-10> direction could be caused by basal plane bending.

**4. Conclusion** 

crystal quality.

**6. References** 

**5. Acknowledgment** 

No. 51021062 and 50802053.

Vol. 32, pp. 229-236.

#### **3.3.4 Discussions**

The HRXRD and SWBXT simulation results can confirm that basal plane bending exist in SiC single crystals. In SiC crystal growth experiments with different conditions, we found that the basal plane bending was caused mainly by the thermal mismatch between seed and holder which deteriorated the wafer's quality, i.e. increasing the density of low angle grain boundaries. Recently, the basal plane bending was eliminated by improving the seed attachment technique.

Fig. 16. Stress images for different wafers. The vertical directions <10-10>. (a) wafer with bending (The insert is a microscopic image of low angle grain boundaries after etching). (b) wafer without bending.

Fig. 16 are two stress images for two wafers grown with different conditions. The vertical direction is <10-10>. Fig. 16a stands for a wafer with basal plane bending. It can be seen obviously that there is a boundary between the center area (the facet) and the outside region. And a mass of low angle grain boundaries assembled along the <10-10> directions. The existance of grain boundaries deteriorated the crystal quality and reduced its usable area. The insert of Fig. 16a is a microscopic image for <10-10> direction after etching. The white lines are low angle grain boundaries after etching. Fig. 16b stands for a wafer without basal plane bending. The boundary between the facet and the outside region disappeared. And the assembly of low angle grain bounbdaries along <10-10> direction disapppeared too. The stress for the whole wafer became more uniform. That is to say, the large number of grain boubdaries along <10-10> direction could be caused by basal plane bending.

#### **4. Conclusion**

158 Silicon Carbide – Materials, Processing and Applications in Electronic Devices

The HRXRD and SWBXT simulation results can confirm that basal plane bending exist in SiC single crystals. In SiC crystal growth experiments with different conditions, we found that the basal plane bending was caused mainly by the thermal mismatch between seed and holder which deteriorated the wafer's quality, i.e. increasing the density of low angle grain boundaries. Recently, the basal plane bending was eliminated by improving the seed

Fig. 16. Stress images for different wafers. The vertical directions <10-10>. (a) wafer with bending (The insert is a microscopic image of low angle grain boundaries after etching). (b)

Fig. 16 are two stress images for two wafers grown with different conditions. The vertical direction is <10-10>. Fig. 16a stands for a wafer with basal plane bending. It can be seen obviously that there is a boundary between the center area (the facet) and the outside region. And a mass of low angle grain boundaries assembled along the <10-10> directions. The existance of grain boundaries deteriorated the crystal quality and reduced its usable

**3.3.4 Discussions** 

attachment technique.

a

b

wafer without bending.

In this chapter, polytype transition mechanism during 4H-SiC growth, the nature of micropipe and the existence of basal plan bending has been proposed. Elementary screw dislocations were also detected by back-reflection synchrotron radiation topography. All the results obtained above helped us to optimize the growth condition and then improve the crystal quality.

#### **5. Acknowledgment**

This work was supported by National Basic Research Program of China under grant No. 2009CB930503 and No. 2011CB301904, Natural Science Foundation of China under grant No. 51021062 and 50802053.

#### **6. References**


**7** 

*France* 

**SiC, from Amorphous to Nanosized Materials,** 

Silicon carbide materials are interesting because of their high thermal stability, high thermal conductivity, extreme hardness and good electrical properties. Some of these properties are directly related to the SiC structure that alternates the Si and C atom layers. SiC have applications as single crystal wafer (wide-gap semiconductor for high power device), as air, spacecraft and nuclear plant thermostructural composites because it is possible to prepare the materials in various forms (fibre, matrix and composite) from organic liquid or vapour precursors. Thus it is possible to adjust the crystallinity, from the amorphous to the crystalline state, including intermediate nanocrystalline state. The later state guaranties the optimal mechanical properties. Non-destructive Raman microspectrometry intrinsically probes the matter at the subnanoscale and offers a "bottom-up" approach that is especially efficient for the analysis of ill-crystallised and nanostructured materials. The great advantage of Raman spectroscopy is first to make possible the recording of series of spectrum by automatic mapping. However, because the Raman intensity depends on the polarisability tensor derivative, the scattered intensity – and the sensitivity - varies order of magnitude with the nature of the chemical bond. Comparison with transmission electron microscopy (TEM) is in general required to discriminate if the phonon coherence length is determined by the domain or the grain size. Both techniques are efficient to identify the

The properties of the materials are determined by their chemical bonds and the arrangement of the latter. The uniqueness of silicon carbide properties arises from the nature of the bond. Si-C bond as Si-O and Si-N ones are among the strongest chemical bonds in the matter (Bond dissociation energy > 350 KJ/mole). Consequently, this gives a very good chemical and thermal stability as well very high melting temperature, high mechanical properties and hardness. Silicon atoms form with C, N and O atoms the same tetrahedral coordination that allows very intimate mixture (oxycarbides, oxynitrides, etc.). Furthermore, a hydrogen atom can establish a bond with these oxygen, nitrogen and carbon atoms. This offers a large versatility of preparation routes, including polymerisation process. Consequently, because

different polytypes as well as the nature and degree of the disorder.

**1. Introduction** 

**2. About the chemistry** 

**the Exemple of SiC Fibres Issued of** 

**Polymer Precursors** 

*LADIR, CNRS – Université Pierre-et-Marie-Curie* 

Philippe Colomban


### **SiC, from Amorphous to Nanosized Materials, the Exemple of SiC Fibres Issued of Polymer Precursors**

Philippe Colomban *LADIR, CNRS – Université Pierre-et-Marie-Curie France* 

#### **1. Introduction**

160 Silicon Carbide – Materials, Processing and Applications in Electronic Devices

Wahab, Q. ; Ellison, A. ; Henry, A. ; Janzen, E. ; Hallin, C. ; Persio, J. D. & Martinez, R. (2000).

Neudeck, P. G. & Powell, J. A. (1994). Performance limiting micropipe defects in silicon

Frank, F. C. (1951). Capillary equilibria of dislocated crystals, *Acta Crystallographica*, Vol. 4,

Liu, J. L. ; Gao, J. Q. ; Cheng, J. K. ; Yang, J. F. & Qiao, G. J. (2005). Model for micropipe

Giocondi, J. ; Rohrer, G. S. ; Skowronski, M. ; Balakrishna, V. ; Augustine, G. ; Hobgood, H.

Neudeck, P. G. ; Huang, W. & Dudley, M. (1998). Breakdown degradation associated with

Lendenmann, H. ; Dahlquist, F. ; Johansson, N. ; Soderholm, R, ; Nilsson, P.A. ; Bergman, J.

Malhan, R.K. ; Nakamura, H. ; Onda, S. ; Nakamura, D. & Hara, K. (2003). Impact of SiC

Huang, X.R. ; Dudley, M. ; Vetter, W. M. ; Huang, W. ; Si,W. & Carter Jr, C.H. (1999)

*Material Science Forum*, VoI.. 353-356, pp. 727-730, ISSN 0255-5476.

*Crystal Growth*, Vol. 181, pp. 351–362, ISSN 0022-0248.

*Science Forum*, VoI. 433-436, pp.917-920, ISSN 0255-5476.

*Crystallography*, Vo1. 32, pp. 516-524, ISSN 0021-8898.

Vo1. 42, No. 12, pp. 2157-2164, ISSN 0038-1101.

ISSN 1077-3118.

No. 6, pp. 497–501.

pp. 2374–2377, ISSN 0167-577X.

3106.

Influence of epitaxial growth and substrate-induced defects on the breakdown of 4H–SiC Schottky diodes, *Applied Physics Letters*, Vol. 76, No. 19, pp. 2725–2727,

carbide wafers, *IEEE Electron Device Letters*, Vol. 15, No. 2, pp. 63–65, ISSN 0741-

formation in 6H-SiC single crystal by sublimation method, *Material Letters*, Vol. 59,

M. & Hopkins, R. H. (1997). An atomic force microscopy study of superdislocation/micropipe complexes on the 6H-SiC(0001) growth surface, *Journal of* 

elementary screw dislocations in 4H-SiC p+n junction rectifiers, *Solid-State Electron*,

P. & Skytt, P. (2001). Long term operation of 4.5kV PiN and 2.5kV JBS diodes,

structural defects on the degradation phenomenon of bipolar SiC devices, *Material* 

Superscrew dislocation contrast on synchrotron white-beam topographs: an accurate description of the direct dislocation image, *Journal of Appllied*  Silicon carbide materials are interesting because of their high thermal stability, high thermal conductivity, extreme hardness and good electrical properties. Some of these properties are directly related to the SiC structure that alternates the Si and C atom layers. SiC have applications as single crystal wafer (wide-gap semiconductor for high power device), as air, spacecraft and nuclear plant thermostructural composites because it is possible to prepare the materials in various forms (fibre, matrix and composite) from organic liquid or vapour precursors. Thus it is possible to adjust the crystallinity, from the amorphous to the crystalline state, including intermediate nanocrystalline state. The later state guaranties the optimal mechanical properties. Non-destructive Raman microspectrometry intrinsically probes the matter at the subnanoscale and offers a "bottom-up" approach that is especially efficient for the analysis of ill-crystallised and nanostructured materials. The great advantage of Raman spectroscopy is first to make possible the recording of series of spectrum by automatic mapping. However, because the Raman intensity depends on the polarisability tensor derivative, the scattered intensity – and the sensitivity - varies order of magnitude with the nature of the chemical bond. Comparison with transmission electron microscopy (TEM) is in general required to discriminate if the phonon coherence length is determined by the domain or the grain size. Both techniques are efficient to identify the different polytypes as well as the nature and degree of the disorder.

#### **2. About the chemistry**

The properties of the materials are determined by their chemical bonds and the arrangement of the latter. The uniqueness of silicon carbide properties arises from the nature of the bond. Si-C bond as Si-O and Si-N ones are among the strongest chemical bonds in the matter (Bond dissociation energy > 350 KJ/mole). Consequently, this gives a very good chemical and thermal stability as well very high melting temperature, high mechanical properties and hardness. Silicon atoms form with C, N and O atoms the same tetrahedral coordination that allows very intimate mixture (oxycarbides, oxynitrides, etc.). Furthermore, a hydrogen atom can establish a bond with these oxygen, nitrogen and carbon atoms. This offers a large versatility of preparation routes, including polymerisation process. Consequently, because

SiC, from Amorphous to Nanosized

enhancing the crystallisation process.

Whiting, 2011).

**3. Polytypes** 

diamond (Fayette et al., 1995; Bhargava et al., 1995).

Materials, the Exemple of SiC Fibres Issued of Polymer Precursors 163

in the porous performs (Greil, 1995; Parlier & Colomban, 1996; Lucke et al., 1997; Greil, 2000) and the technology was extended to multicomponent oxide precursors with the development of sol-gel routes (Colomban, 1989; Colomban & Wey, 1997; Colomban, 2005). A big problem was the achievement of the right stoichiometry: silicon excess was very detrimental because of the relatively low temperature melting of silicon; on the other hand, carbon excess, not detrimental from the thermomechanical point of view, led to a great reactivity to air and to high electrical conductivity (Chauvet et al., 1992a; idem, 1992b; Mouchon & Colomban, 1996). However, the polymer precursors are linear macromolecules (1D) but SiC synthesis requires a 3D crosslinking. This was first achieved by Si-O-Si bridges but the oxygen atoms react with carbon excess at ~1200-1300°C (Karlin & Colomban, 1997; idem, 1998). The use of gamma irradiation for the crosslinking allows approaching better the stoichiometry and the thermal stability of SiC materials issued from polymeric precursor was increased (Ischikawa et al., 1991; Yang et al., 1991; Torecki et al., 1991; idem, 1992; Ischikawa, 1995; Ischikawa et al., 1998). Residual hydrogen atoms evolve above 1000°C whereas the free carbon created by the destruction of the methyl groups reacted with the Si-O group with the evolution of CO gas and forming new Si-C bonds above 1300°C,

Alternative route was developed by US Sacks' group (Toreki et al., 1992; Sacks et al., 1998): they used high-molecular-weight PCS. The infusible PCS was prepared by pressure pyrolysis of polydimethylsilane and the fibres formed by the dry spinning of concentrated PCS-based polymer solutions which were then pyrolysed in an inert atmosphere at 1000 to 1200°C. The room temperature ultimate tensile strength ranges between 2.5 and 3.5 GPa as a function of the fibre grade with Young's modulus ranging between ~200 and 400 GPa, very close to the best properties achieved for bulk ceramics, films or crystals : ~430 GPa (Biswas et al., 2001; Dirras et al., 2004; Chung & Han, 2008). The axial room temperature thermal conductivity ranges between ~2-3 (oxygen rich, amorphous SiC) up to 50-60 W/mK for crystalline nearly stoichiometric SiC (Simon & Bunsell, 1984). The electrical conductivity from ~0.01 to 10 S.cm-1 is highly related to the carbon content (Chauvet et al., 1992 a & b; Mouchon & Colomban, 1996). The reduction of the oxygen content in the fibres made by irradiating PCS produced fibres ~35% stiffer than the first generation fibres. The 1400°C creep rates are slightly improved (Sha et al., 2004). Actually the thermal stability in air remains poor for the first and 2nd generation SiC fibres, ca. ~1100°C. The third generation stoichiometric fibres exhibit properties much closer to those of bulk SiC but the thermal stability in air remains much lower than that of oxide fibers (Mouchon & Colomban, 1995; Colomban, 1997; Baxter et al., 2000, Ruggles-Wrenn & Kutsal, 2010; Ruggles-Wrenn &

Polytypes are observed in a variety of covalent compounds where rotation along the covalent bond does not require a lot of energy. This often gives rise to more or less lamellar compounds with stacking faults along one direction: carbides (Feldmann et al., 1968; Salvador & Sherman, 1991; Choyke & Pensl, 1997), sulfides (CdS, ZnS, TiS2, ... (Kaflawi et al., 1969; Schneide & Kirby, 1972; Tronc et al., 1975; Moret & Huber, 1976; Lincot et al., 1997; Agrosi et al., 2009; Alvarez-Garcia et al., 2009; Chi et al., 2011), nitrides (Komatsu et al., 2010) but also some oxides (e.g. BaTiO3 perovskites (Wu et al., 2006; idem, 2009)) and even

silicon and carbon atoms form easily X-C and X-H bonds, a large variety of liquid or gaseous hybrid/organic precursors are available (Mc Diarmid, 1961; Fritz et al., 1965; Corriu & Lanneau, 1970; Lucke et al., 1997) and the control of their reactivity, viscosity/diffusivity dilution, etc. gives rise to a variety of preparation routes leading to monoliths, films, fibres, composites, crystal,…, from the amorphous state to the single crystal, including nanomaterials (Gough & Kern, 1967; Parlier & Colomban, 1996; Naslain, 2004).

The mix of atomic orbital led to an intermediate electric behaviour between that of carbon (a semi-metal) and silica (an insulator), the electronic gap is intermediate (2-3 eV) and the material is a semiconductor. Since the diffusion coefficient of oxygen atom in silica is very low (due to the very covalent character of the Si-O bond), the oxidation is blocked in a very large temperature range (except in water-rich atmosphere when volatile species are formed) that gives a good stability to Si(X)n compounds in air. The latter properties are searched for thermomechanical applications: the nanosized state combines the advantage of amorphous (homogeneity, lack of interface/phases) and crystalline (high density of bonds per volume unit) phases. Very high thermal conductivity contributes well to the unique properties of silicon carbide. Since nothing is perfect, the building of the SiC with a single type of bond makes that orientation disorder is possible and gives rise to two types of Si-C bilayer stacking. Their combination leads to series of structures: the polytypes and it is difficult to prepare materials without coexistence of the different phases. This behaviour is observed for all structures which are built up by corner-sharing tetrahedron. They can be regarded as consisting of stacked bi-layers.

The availability of volatile/liquid silanes led to the preparation of SiC materials in various forms (McDiarmid, 1961; Fritz et al., 1965; Gough & Kern, 1967; Learn & Khan, 1970; Corriu & Lanneau, 1970; Kumar & Litt, 1988; Schmidt et al., 1991): films/coatings (Rynders et al., 1991), fibres (a SiC coating is deposited on a carbon fibre core (Hurwitz et al., 1991; Tanaka et al., 1995; idem, 1996; Popovska et al., 1997), monoliths and fibre-reinforced composites (Yajima et al., 1980; Tanaka & Kurachi, 1988; Bouillon et al., 1991 a & b; Monthioux et al., 1990; idem, 1991; Delplancke et al., 1991; Lee & Yano, 2004). The growth rate was slow and for the preparation of thick monoliths or composites weeks are required with sometimes an intermediate machining of the parts in order to avoid the closure of the porosity that occurs at the sample surface, avoiding the completion of the core densification. This technology was used to prepare important parts of civil and military launch vehicles, missiles as well as aircraft engines (Parlier & Colomban, 1996; Mouchon & Colomban, 1996; Naslain, 2004) and extended to the preparation of other Si-based materials such as nitrides (Durham et al., 1991).

In the 80s Japanese groups developed liquids with appropriate viscosity (polycarbosilanes: PCS) as precursors for SiC fibre (Okamura et al., 1985). The difficulty concerned the production of a form of polycarbosilane which would have the "good" viscosity to be spun and then converted in small-diameter ceramic filaments. The small diameter (~10 µm) is required to permit the bending of the fibre during the weaving process and hence to prepare a variety of textile fabrics: satin, taffeta, etc. (Mouchon & Colomban, 1995; idem, 1996). It was found that very high molecular weight was not necessarily best and polymers with molecular weights of around 1500 were used for commercial production. Then the progress allowed preparing more complex compositions (Si/TiC, etc. (Stewart et al., 1991; Hasegawa et al., 1991; Burns et al., 1992; Hurwitz et al. 1993)) under more complex states (Tanaka et al., 1988; Langguth, 1995). The viscosity was adapted for an easy infiltration of the precursor

silicon and carbon atoms form easily X-C and X-H bonds, a large variety of liquid or gaseous hybrid/organic precursors are available (Mc Diarmid, 1961; Fritz et al., 1965; Corriu & Lanneau, 1970; Lucke et al., 1997) and the control of their reactivity, viscosity/diffusivity dilution, etc. gives rise to a variety of preparation routes leading to monoliths, films, fibres, composites, crystal,…, from the amorphous state to the single crystal, including

The mix of atomic orbital led to an intermediate electric behaviour between that of carbon (a semi-metal) and silica (an insulator), the electronic gap is intermediate (2-3 eV) and the material is a semiconductor. Since the diffusion coefficient of oxygen atom in silica is very low (due to the very covalent character of the Si-O bond), the oxidation is blocked in a very large temperature range (except in water-rich atmosphere when volatile species are formed) that gives a good stability to Si(X)n compounds in air. The latter properties are searched for thermomechanical applications: the nanosized state combines the advantage of amorphous (homogeneity, lack of interface/phases) and crystalline (high density of bonds per volume unit) phases. Very high thermal conductivity contributes well to the unique properties of silicon carbide. Since nothing is perfect, the building of the SiC with a single type of bond makes that orientation disorder is possible and gives rise to two types of Si-C bilayer stacking. Their combination leads to series of structures: the polytypes and it is difficult to prepare materials without coexistence of the different phases. This behaviour is observed for all structures which are built up by corner-sharing tetrahedron. They can be regarded as

The availability of volatile/liquid silanes led to the preparation of SiC materials in various forms (McDiarmid, 1961; Fritz et al., 1965; Gough & Kern, 1967; Learn & Khan, 1970; Corriu & Lanneau, 1970; Kumar & Litt, 1988; Schmidt et al., 1991): films/coatings (Rynders et al., 1991), fibres (a SiC coating is deposited on a carbon fibre core (Hurwitz et al., 1991; Tanaka et al., 1995; idem, 1996; Popovska et al., 1997), monoliths and fibre-reinforced composites (Yajima et al., 1980; Tanaka & Kurachi, 1988; Bouillon et al., 1991 a & b; Monthioux et al., 1990; idem, 1991; Delplancke et al., 1991; Lee & Yano, 2004). The growth rate was slow and for the preparation of thick monoliths or composites weeks are required with sometimes an intermediate machining of the parts in order to avoid the closure of the porosity that occurs at the sample surface, avoiding the completion of the core densification. This technology was used to prepare important parts of civil and military launch vehicles, missiles as well as aircraft engines (Parlier & Colomban, 1996; Mouchon & Colomban, 1996; Naslain, 2004) and extended to the preparation of other Si-based materials such as nitrides (Durham et al.,

In the 80s Japanese groups developed liquids with appropriate viscosity (polycarbosilanes: PCS) as precursors for SiC fibre (Okamura et al., 1985). The difficulty concerned the production of a form of polycarbosilane which would have the "good" viscosity to be spun and then converted in small-diameter ceramic filaments. The small diameter (~10 µm) is required to permit the bending of the fibre during the weaving process and hence to prepare a variety of textile fabrics: satin, taffeta, etc. (Mouchon & Colomban, 1995; idem, 1996). It was found that very high molecular weight was not necessarily best and polymers with molecular weights of around 1500 were used for commercial production. Then the progress allowed preparing more complex compositions (Si/TiC, etc. (Stewart et al., 1991; Hasegawa et al., 1991; Burns et al., 1992; Hurwitz et al. 1993)) under more complex states (Tanaka et al., 1988; Langguth, 1995). The viscosity was adapted for an easy infiltration of the precursor

nanomaterials (Gough & Kern, 1967; Parlier & Colomban, 1996; Naslain, 2004).

consisting of stacked bi-layers.

1991).

in the porous performs (Greil, 1995; Parlier & Colomban, 1996; Lucke et al., 1997; Greil, 2000) and the technology was extended to multicomponent oxide precursors with the development of sol-gel routes (Colomban, 1989; Colomban & Wey, 1997; Colomban, 2005). A big problem was the achievement of the right stoichiometry: silicon excess was very detrimental because of the relatively low temperature melting of silicon; on the other hand, carbon excess, not detrimental from the thermomechanical point of view, led to a great reactivity to air and to high electrical conductivity (Chauvet et al., 1992a; idem, 1992b; Mouchon & Colomban, 1996). However, the polymer precursors are linear macromolecules (1D) but SiC synthesis requires a 3D crosslinking. This was first achieved by Si-O-Si bridges but the oxygen atoms react with carbon excess at ~1200-1300°C (Karlin & Colomban, 1997; idem, 1998). The use of gamma irradiation for the crosslinking allows approaching better the stoichiometry and the thermal stability of SiC materials issued from polymeric precursor was increased (Ischikawa et al., 1991; Yang et al., 1991; Torecki et al., 1991; idem, 1992; Ischikawa, 1995; Ischikawa et al., 1998). Residual hydrogen atoms evolve above 1000°C whereas the free carbon created by the destruction of the methyl groups reacted with the Si-O group with the evolution of CO gas and forming new Si-C bonds above 1300°C, enhancing the crystallisation process.

Alternative route was developed by US Sacks' group (Toreki et al., 1992; Sacks et al., 1998): they used high-molecular-weight PCS. The infusible PCS was prepared by pressure pyrolysis of polydimethylsilane and the fibres formed by the dry spinning of concentrated PCS-based polymer solutions which were then pyrolysed in an inert atmosphere at 1000 to 1200°C.

The room temperature ultimate tensile strength ranges between 2.5 and 3.5 GPa as a function of the fibre grade with Young's modulus ranging between ~200 and 400 GPa, very close to the best properties achieved for bulk ceramics, films or crystals : ~430 GPa (Biswas et al., 2001; Dirras et al., 2004; Chung & Han, 2008). The axial room temperature thermal conductivity ranges between ~2-3 (oxygen rich, amorphous SiC) up to 50-60 W/mK for crystalline nearly stoichiometric SiC (Simon & Bunsell, 1984). The electrical conductivity from ~0.01 to 10 S.cm-1 is highly related to the carbon content (Chauvet et al., 1992 a & b; Mouchon & Colomban, 1996). The reduction of the oxygen content in the fibres made by irradiating PCS produced fibres ~35% stiffer than the first generation fibres. The 1400°C creep rates are slightly improved (Sha et al., 2004). Actually the thermal stability in air remains poor for the first and 2nd generation SiC fibres, ca. ~1100°C. The third generation stoichiometric fibres exhibit properties much closer to those of bulk SiC but the thermal stability in air remains much lower than that of oxide fibers (Mouchon & Colomban, 1995; Colomban, 1997; Baxter et al., 2000, Ruggles-Wrenn & Kutsal, 2010; Ruggles-Wrenn & Whiting, 2011).

#### **3. Polytypes**

Polytypes are observed in a variety of covalent compounds where rotation along the covalent bond does not require a lot of energy. This often gives rise to more or less lamellar compounds with stacking faults along one direction: carbides (Feldmann et al., 1968; Salvador & Sherman, 1991; Choyke & Pensl, 1997), sulfides (CdS, ZnS, TiS2, ... (Kaflawi et al., 1969; Schneide & Kirby, 1972; Tronc et al., 1975; Moret & Huber, 1976; Lincot et al., 1997; Agrosi et al., 2009; Alvarez-Garcia et al., 2009; Chi et al., 2011), nitrides (Komatsu et al., 2010) but also some oxides (e.g. BaTiO3 perovskites (Wu et al., 2006; idem, 2009)) and even diamond (Fayette et al., 1995; Bhargava et al., 1995).

SiC, from Amorphous to Nanosized

Producer Nippon

Grade NLM

Reticulation Si-O

Grain size/

Diameter /

nm

Si/C

Carbon

bond

Table 1. Small diameter SiC fibre generations.

Materials, the Exemple of SiC Fibres Issued of Polymer Precursors 165

the crystallization. The first problem to solve (Table 1) was the way to establish the bridge between the polymeric (Si-C)n chains: i) the first route (NLMTM Nippon Carbon fibre (Ishikawa, 1995)) is the thermal oxidation (Si-O-Si bridge) at relatively low temperature (~200°C), the resulting SiO2 content decreases from ~25 to ~10 wt% with improvements), ii) the second one is the electronic irradiation that allows forming Si-C bridges but leads to a carbon excess (C/Si ~1.4 in Hi-NicalonTM Nippon Carbon fibre (Berger et al; 1995; idem, 1999); alternatively the grafting of Ti or Zr alkoxide (Ti or Zr addition) leads to rather similar material but the fibres could be made with smaller diameter (UBE Industries TyrannoTM LOX-M, ZE and TE grade fibres (Berger et al., 1997; idem, 1999); iii) the optimization of the organic precursor and associated thermal treatments gives stoichiometric SiC fibre (SA3TM Ube Industries, SylramicTM Dow Corning Corp. Fibres and Hi-NicalonTM Type S (Lipowitz et al., 1995; Ishikawa et al., 1998; Berger et al., 1999; Bunsell & Piant, 2006). The high

temperature of the manufacture process leads to much larger grain sizes.

Ube Industries

Electron

stoichiometry 1.3 <1.3 <1.3 ~1 ~1 ~1

µm (+/- 3) 15 12 11 7.5 10 12

The first generations fibre microstructures consist of an amorphous ternary phase made of SiOxCy tetrahedra (Porte & Sartre, 1989) with x+y = 4, with ~1.4-1.7 nm SiC crystallites and ~5% of randomly oriented free carbon aggregates, 1 nm in size (NicalonTM 200 grade, x= 1.15). Carbon (002) lattice fringe images showed small stacks of two fringes of around 0.7 nm in size suggesting that the basic structural unit (BSU) was a face-to-face association of aromatic rings, called dicoronenes, in which the hydrogene-to-carbon atomic ratio is 0.5. Accordingly, a porosity level of 2% was present (Le Coustumer et al., 1995 a & b). Other studies proposed that the intergranular phase should be written as SiOxC1-x/2, which suggests that the composition varies continuously from SiC to SiO2 as the oxygen traces varied (Bodet et al., 1995). The removal of oxygen from the cross-linking process resulted in a stoichiometry closer to Si/C = 1 and an increase in size of the β-SiC grains which were in the range of 5 to 10 nm in commercial fibres. The TEM images show well ordered SiC

Ube Industries

irradiation Si-O bond Si-O

Nicalon Hi-Nicalon ZE,TE SA3 SYLRAMIC Hi-S

~<2 5-10 5-10 <50 <50 <50

Dow Corning Corp.

bond

Nippon Carbon

Electron irradiation

Generation 1st 2nd 3rd

Nippon Carbon

Electron irradiation

As sketched in **Figure 1**, SiC structures consist of alternate layers of Si and C atoms forming a bi-layer. These bi-layers are stacked together to form face-centre cubic unit-cell (cubic stacking = ABC-ABC-ABC-, the so-called zinc-blende type cell, to be abbreviated c-SiC) or closed-packed hexagonal system (hexagonal stacking = AB-AB-AB-, the so-called wurzite cell, to be abbreviated h-SiC). Two consecutive layers form a bilayer which is named "h" (h for hexagonal) if it is deduced from the one below by a simple translation. If not, when an additional 180° rotation (around the Si-C bond linking the bilayers) is necessary to get the superposition, the bilayer is named "k" (for "kubic"). The "k" stacking is the reference of β-SiC cubic symmetry, only. The infinite combination of h/c stacking sequences led to hundreds of different polytypes (Feldman et al., 1968; Choyke & Pensl, 1997).

Very similar structures are known for many compounds. Formation of polytypes arises because the energy required to change from one type to the other is very low. Consequently, different structures can be formed during the synthesis, simultaneously, especially for layer materials (CdS, SiC, TiS2, MoS2, BN, AlN, talc, micas, illites, perovskites, see references above) including MBE superlattices (Yano et al., 1995). Polytypes structure consists of close packed planes stacked in a sequence which corresponds neither to the face-centered cubic system nor the close-packed hexagonal system but to complex sequences associating both cubic and hexagonal stackings, ones such as = -ABABCABAB-, or –ABCAABAB A-, or - ABABCABBA-, etc.).

Fig. 1. Schematic diagrams of the (a) hexagonal, (b) cubic, (c,d) polytypes modifications and of the stacking fault disorder (e). SiC structures alternate layers of Si and C atoms to form a SiC bi-layer, AB or AC (e).

#### **4. From amorphous to crystalline materials**

The precursor route led to a rather progressive transformation of a more or less 1D organised framework to a 3D amorphous one and subsequent thermal treatments control

As sketched in **Figure 1**, SiC structures consist of alternate layers of Si and C atoms forming a bi-layer. These bi-layers are stacked together to form face-centre cubic unit-cell (cubic stacking = ABC-ABC-ABC-, the so-called zinc-blende type cell, to be abbreviated c-SiC) or closed-packed hexagonal system (hexagonal stacking = AB-AB-AB-, the so-called wurzite cell, to be abbreviated h-SiC). Two consecutive layers form a bilayer which is named "h" (h for hexagonal) if it is deduced from the one below by a simple translation. If not, when an additional 180° rotation (around the Si-C bond linking the bilayers) is necessary to get the superposition, the bilayer is named "k" (for "kubic"). The "k" stacking is the reference of β-SiC cubic symmetry, only. The infinite combination of h/c stacking sequences led to

Very similar structures are known for many compounds. Formation of polytypes arises because the energy required to change from one type to the other is very low. Consequently, different structures can be formed during the synthesis, simultaneously, especially for layer materials (CdS, SiC, TiS2, MoS2, BN, AlN, talc, micas, illites, perovskites, see references above) including MBE superlattices (Yano et al., 1995). Polytypes structure consists of close packed planes stacked in a sequence which corresponds neither to the face-centered cubic system nor the close-packed hexagonal system but to complex sequences associating both cubic and hexagonal stackings, ones such as = -ABABCABAB-, or –ABCAABAB A-, or -

Fig. 1. Schematic diagrams of the (a) hexagonal, (b) cubic, (c,d) polytypes modifications and of the stacking fault disorder (e). SiC structures alternate layers of Si and C atoms to form a

The precursor route led to a rather progressive transformation of a more or less 1D organised framework to a 3D amorphous one and subsequent thermal treatments control

hundreds of different polytypes (Feldman et al., 1968; Choyke & Pensl, 1997).

ABABCABBA-, etc.).

SiC bi-layer, AB or AC (e).

**4. From amorphous to crystalline materials** 

the crystallization. The first problem to solve (Table 1) was the way to establish the bridge between the polymeric (Si-C)n chains: i) the first route (NLMTM Nippon Carbon fibre (Ishikawa, 1995)) is the thermal oxidation (Si-O-Si bridge) at relatively low temperature (~200°C), the resulting SiO2 content decreases from ~25 to ~10 wt% with improvements), ii) the second one is the electronic irradiation that allows forming Si-C bridges but leads to a carbon excess (C/Si ~1.4 in Hi-NicalonTM Nippon Carbon fibre (Berger et al; 1995; idem, 1999); alternatively the grafting of Ti or Zr alkoxide (Ti or Zr addition) leads to rather similar material but the fibres could be made with smaller diameter (UBE Industries TyrannoTM LOX-M, ZE and TE grade fibres (Berger et al., 1997; idem, 1999); iii) the optimization of the organic precursor and associated thermal treatments gives stoichiometric SiC fibre (SA3TM Ube Industries, SylramicTM Dow Corning Corp. Fibres and Hi-NicalonTM Type S (Lipowitz et al., 1995; Ishikawa et al., 1998; Berger et al., 1999; Bunsell & Piant, 2006). The high temperature of the manufacture process leads to much larger grain sizes.


Table 1. Small diameter SiC fibre generations.

The first generations fibre microstructures consist of an amorphous ternary phase made of SiOxCy tetrahedra (Porte & Sartre, 1989) with x+y = 4, with ~1.4-1.7 nm SiC crystallites and ~5% of randomly oriented free carbon aggregates, 1 nm in size (NicalonTM 200 grade, x= 1.15). Carbon (002) lattice fringe images showed small stacks of two fringes of around 0.7 nm in size suggesting that the basic structural unit (BSU) was a face-to-face association of aromatic rings, called dicoronenes, in which the hydrogene-to-carbon atomic ratio is 0.5. Accordingly, a porosity level of 2% was present (Le Coustumer et al., 1995 a & b). Other studies proposed that the intergranular phase should be written as SiOxC1-x/2, which suggests that the composition varies continuously from SiC to SiO2 as the oxygen traces varied (Bodet et al., 1995). The removal of oxygen from the cross-linking process resulted in a stoichiometry closer to Si/C = 1 and an increase in size of the β-SiC grains which were in the range of 5 to 10 nm in commercial fibres. The TEM images show well ordered SiC

SiC, from Amorphous to Nanosized

Materials, the Exemple of SiC Fibres Issued of Polymer Precursors 167

(a) (b)

Fig. 2. a) Representative electron diffraction pattern recorded on SA3TM (Ube Industries Ltd,

Mazerolles); b) X-ray diffraction pattern recorded on powdered SA3TM fibre (the immersion

× 5

Hi-N

(a) (b)¶

Fig. 3. Representative spectra of the as-produced fibres (a) and after different thermal/chemical treatments in order to highlight the SiC fingerprint (b).

TE

Raman Intensity

× 10

ZE

400 800 1200 1600

Wavenumber / cm-1

850

960

790

1593 1370

see Table 1) fibre thermally treated at 1600°C under inert atmosphere (Courtesy, L.

in molten NaNO3 do not modify the pattern, (Havel & Colomban, 2005)).

[P63mc]

0006 0006

0114 0112 0112 0114

500 1000 1500 2000

Wavenumber / cm-1

970

1365 1595

796

**Sylramic**

**SA3**

**TE ZE**

**Hi-Nicalon**

**NLM-Nicalon**

Relative Raman Intensity

surrounded by highly disorderd/amorphous SiC interphase and free carbon grains (Monthioux et al., 1990; idem, 1991; Havel, 2004; Havel et al., 2007).

#### **5. How to identify the polytypes, the stacking disorder and the relative proportion of each polytypes?**

The challenge for the nanotechnologies, which is to achieve perfect control on nanoscale related properties, requires correlating the production conditions to the resulting nanostructure.

Transmission electron microscopy (darkfield and high resolution images, electronic diffraction, etc. (see e.g. Mirguet et al., 2009; Sciau et al., 2009)) is the most efficient technique to determine the grain size, the defaults (disorder, superstructures, amorphous interface, voids, etc.) but the technique is destructive, time-consuming and may modify the sample structure. Moreover the representativity of the samples is always poor.

Raman spectrometry is a very interesting technique to study nanomaterials since it investigates the matter at a sub-nanometer scale, i.e. the scale of the chemical bonds. The automatic mapping (best spatial resolution ~0.5 to 1 µm2 as a function of objective aperture and laser wavelength) allows a very representative view of the sample surface. Each Raman peak corresponds to a specific vibration (bending, stretching, librational, rotational and lattice modes) of a given chemical bond, and provides information (even on heterogeneous materials, e.g. composites) such as the phase nature and symmetry, distribution, residual stress,… (Colomban, 2002; Gouadec & Colomban, 2007). Since the Raman scattering efficiency depends on the polarisability of the electronic cloud, it can be very sensitive to light elements involved in covalent bonds (C, H, N, B, O, …), which is a valuable advantage, when compared to X-ray/electron-based techniques (EDS, micro-probe,…). In the case of coloured materials if the exciting laser energy is close to that of absorbing electronic levels, resonance Raman scattering occurs and the technique becomes a surface analysis in the range of ~20 to 100 nm in-depth penetration (also depending on the wavelength, (Gouadec & Colomban, 2007)). Then, the selection of a given wavelength allows probing specific layers. The main advantages compared to infrared spectrometry are that the laser in a Raman equipment can be focused down to ~0.5-1 µm2, allowing for imaging specific areas (Gouadec et al, 2001; Colomban, 2003; idem, 2005) and that Raman peaks are narrower that IR bands (Gouadec & Colomban, 2007 and references herein).

**Fig. 2a** shows the representative electronic diffraction pattern ([2-1-10] axis) of a SA3TM fibre thermally treated at 1600°C in inert atmosphere. Most of the Bragg spots correspond to 6H SiC (hexagonal P63mc space group), i.e. to the most simple polytype (Fig. 1). The diffuse scattering along the horizontal axe ([01-1l], arises from the stacking disorder of the SiC bilayer units. On the contrary, the disorder signature is weaker on the X-ray diffraction pattern (small polytype peak at d = 0.266 pm, **Fig. 2b).** However Bragg diffraction highlights the most crystalline part and sweeps the information on low crystalline (e.g. carbon) second phases. Fig. 3 shows the corresponding Raman spectra. For 1st and even 2nd generation fibres the Raman spectrum is dominated by the carbon doublet that overlaps the SiC Raman fingerprint. Specific thermal and chemical treatments are necessary to eliminate most of the carbon second phases and thus to have access to the Raman signal of the SiC phases (Havel & Colomban, 2005).

surrounded by highly disorderd/amorphous SiC interphase and free carbon grains

The challenge for the nanotechnologies, which is to achieve perfect control on nanoscale related properties, requires correlating the production conditions to the resulting

Transmission electron microscopy (darkfield and high resolution images, electronic diffraction, etc. (see e.g. Mirguet et al., 2009; Sciau et al., 2009)) is the most efficient technique to determine the grain size, the defaults (disorder, superstructures, amorphous interface, voids, etc.) but the technique is destructive, time-consuming and may modify the sample

Raman spectrometry is a very interesting technique to study nanomaterials since it investigates the matter at a sub-nanometer scale, i.e. the scale of the chemical bonds. The automatic mapping (best spatial resolution ~0.5 to 1 µm2 as a function of objective aperture and laser wavelength) allows a very representative view of the sample surface. Each Raman peak corresponds to a specific vibration (bending, stretching, librational, rotational and lattice modes) of a given chemical bond, and provides information (even on heterogeneous materials, e.g. composites) such as the phase nature and symmetry, distribution, residual stress,… (Colomban, 2002; Gouadec & Colomban, 2007). Since the Raman scattering efficiency depends on the polarisability of the electronic cloud, it can be very sensitive to light elements involved in covalent bonds (C, H, N, B, O, …), which is a valuable advantage, when compared to X-ray/electron-based techniques (EDS, micro-probe,…). In the case of coloured materials if the exciting laser energy is close to that of absorbing electronic levels, resonance Raman scattering occurs and the technique becomes a surface analysis in the range of ~20 to 100 nm in-depth penetration (also depending on the wavelength, (Gouadec & Colomban, 2007)). Then, the selection of a given wavelength allows probing specific layers. The main advantages compared to infrared spectrometry are that the laser in a Raman equipment can be focused down to ~0.5-1 µm2, allowing for imaging specific areas (Gouadec et al, 2001; Colomban, 2003; idem, 2005) and that Raman peaks are narrower that

**Fig. 2a** shows the representative electronic diffraction pattern ([2-1-10] axis) of a SA3TM fibre thermally treated at 1600°C in inert atmosphere. Most of the Bragg spots correspond to 6H SiC (hexagonal P63mc space group), i.e. to the most simple polytype (Fig. 1). The diffuse scattering along the horizontal axe ([01-1l], arises from the stacking disorder of the SiC bilayer units. On the contrary, the disorder signature is weaker on the X-ray diffraction pattern (small polytype peak at d = 0.266 pm, **Fig. 2b).** However Bragg diffraction highlights the most crystalline part and sweeps the information on low crystalline (e.g. carbon) second phases. Fig. 3 shows the corresponding Raman spectra. For 1st and even 2nd generation fibres the Raman spectrum is dominated by the carbon doublet that overlaps the SiC Raman fingerprint. Specific thermal and chemical treatments are necessary to eliminate most of the carbon second phases and thus to have access to the Raman signal of the SiC phases (Havel

**5. How to identify the polytypes, the stacking disorder and the relative** 

(Monthioux et al., 1990; idem, 1991; Havel, 2004; Havel et al., 2007).

structure. Moreover the representativity of the samples is always poor.

IR bands (Gouadec & Colomban, 2007 and references herein).

**proportion of each polytypes?** 

nanostructure.

& Colomban, 2005).

Fig. 2. a) Representative electron diffraction pattern recorded on SA3TM (Ube Industries Ltd, see Table 1) fibre thermally treated at 1600°C under inert atmosphere (Courtesy, L. Mazerolles); b) X-ray diffraction pattern recorded on powdered SA3TM fibre (the immersion in molten NaNO3 do not modify the pattern, (Havel & Colomban, 2005)).

Fig. 3. Representative spectra of the as-produced fibres (a) and after different thermal/chemical treatments in order to highlight the SiC fingerprint (b).

SiC, from Amorphous to Nanosized

(a)

Raman Intensity

Raman Intensity

NLM 1600°C 10h

 1600°C 1h + NaNO3 100h NLM

882

<sup>550</sup> <sup>513</sup> <sup>1117</sup> <sup>1714</sup>

500 1000 1500 2000

215

167

436 1715

Wavenumber / cm-1

Raman Intensity

872 954

794

770

702 <sup>569</sup> <sup>507</sup>

(c)

fibre (c) and for very amorphous SiC zone are shown.

1143

1363

768

969 796

Materials, the Exemple of SiC Fibres Issued of Polymer Precursors 169

The Raman spectrum of well crystallised SiC phases is observed between 600 and 1000 cm-1 (Feldman et al., 1968; Nakashima et al., 1986; idem, 1987; idem, 2000; Nakashima & Hangyo, 1991; Nakashima & Harima, 1997; Okimura et al., 1987; Tomita et al., 2000; Hundhausen et al., 2008,). The main Raman peaks centred at 795 and 966 cm-1 correspond to the transverse (TO) and longitudinal (LO) optic modes respectively of the (polar) cubic 3C phase, also called β SiC. Any other definite stacking sequence is called α-SiC and displays either hexagonal or rhombohedral lattice symmetry. Polytypes in the α-SiC structure induce the formation of satellite peaks around 766 cm-1 and of additional features between the TO and LO modes (Figs 5 & 6). However, the TO mode is twice degenerated; while TO1 is centred at 796 cm-1, TO2 is a function of the "h" layers concentration in the structure. A linear variation of 0.296 cm-1/% has been demonstrated (Salvador & Sherman, 1991; Feldman et al., 1968).

> 1620 1590 1523

> > 1582

1506

1380

(b)

200 400 600 800

Wavenumber / cm-1

Fig. 5. Representative Raman spectra recorded for NLMTM Nicalon fibres thermally and chemically treated (a,b). Detail on the disorder-activated acoustic modes observed for ZETM

The main effect of the disorder is the break of the symmetry rules that excludes the Raman activity of the vibrational, optical and acoustical, modes (phonons) of the whole Brillouin

477 438 344

(e)

Raman Intensity

ZE 1600°C 10 h

644 591

300 600 900 1200

α α α

TO

Wavenumber / cm-1

amorphous

LO

Fig. 4. Variations of a) the ~1320 cm-1 Raman peak area (A1320) and b) its wavenumber shift across the diameter of a NLMTM fibre polished section, as-received (dot) and after a chemical attack (triangle) eliminating the carbon phase; a comparison of the variation of the "carbon rate" (Raman peaks surfaces ratio A1598 / A795(C/SiC)) along the diameter of SA3TM (c) and SylramicTM fibres section (d) (λ= 632 nm, P= 0.5 mW, t= 60s).

Raman peaks attribution of the disordered carbons present in SiC fibres has been previously discussed (Karlin & Colomban, 1997; idem, 1998; Gouadec et al., 1998). Pure diamond (sp3 C-C bonds) and graphite (in plane sp2 C=C bond) have sharp stretching mode peaks at 1331 and 1581 cm-1 respectively. The two main bands of amorphous carbons are then assigned to diamond-like (D band for diamond and disorder) and graphite-like (G band for graphite) entities. Because diamond Raman scattering cross-section is much lower than that of graphite (∼10-2), a weak Csp 3-Csp 3 stretching mode is expected. Actually, given the small size of carbon moieties and the strong light absorption of black carbons the contribution of the chemical bonds located near their surface will be enlarged (resonance Raman, the Raman wavenumbers shift with used laser wavelength, see in (Gouadec & Colomban, 2007)). The D band corresponds to vibration modes involving Csp 3-Csp 2/sp 3 bonds also called sp2/3. This band presents a strong resonant character, evidenced by a high dependence of the intensity and position on wavelength. Additional components below 1300 cm-1 arise from hydrogenated carbons and those intermediate between D and G bands have been assigned to oxidised and special carbon phases (Karlin & Colomban, 1997; idem, 1998; Colomban et al., 2002). The wavenumber of the sp3 carbon bond (D peak) measures the aromaticity degree (aromaticity is a function of the "strength and extension size" of the π electronic clouds and thus also function of the crystal order) and hence is directly related to the electric properties of the material (Mouchon & Colomban, 1996). This value depends directly on the thermal treatment temperature history and hence is also related to the mechanical properties, see details in (Gouadec & Colomban, 2001; Colomban, 2003).

The plot of the carbon fingerprint parameters recorded across the fibre section diameter (on fracture) shows the very anisotropic carbon distribution (Fig. 4). Chemical treatments eliminate the carbon in the analysed SiC volume and hence allow a better study of the SiC phases (Havel & Colomban, 2005).

Fig. 4. Variations of a) the ~1320 cm-1 Raman peak area (A1320) and b) its wavenumber shift across the diameter of a NLMTM fibre polished section, as-received (dot) and after a chemical attack (triangle) eliminating the carbon phase; a comparison of the variation of the "carbon rate" (Raman peaks surfaces ratio A1598 / A795(C/SiC)) along the diameter of SA3TM (c) and

Raman peaks attribution of the disordered carbons present in SiC fibres has been previously discussed (Karlin & Colomban, 1997; idem, 1998; Gouadec et al., 1998). Pure diamond (sp3 C-C bonds) and graphite (in plane sp2 C=C bond) have sharp stretching mode peaks at 1331 and 1581 cm-1 respectively. The two main bands of amorphous carbons are then assigned to diamond-like (D band for diamond and disorder) and graphite-like (G band for graphite) entities. Because diamond Raman scattering cross-section is much lower than that of

of carbon moieties and the strong light absorption of black carbons the contribution of the chemical bonds located near their surface will be enlarged (resonance Raman, the Raman wavenumbers shift with used laser wavelength, see in (Gouadec & Colomban, 2007)). The D

band presents a strong resonant character, evidenced by a high dependence of the intensity and position on wavelength. Additional components below 1300 cm-1 arise from hydrogenated carbons and those intermediate between D and G bands have been assigned to oxidised and special carbon phases (Karlin & Colomban, 1997; idem, 1998; Colomban et al., 2002). The wavenumber of the sp3 carbon bond (D peak) measures the aromaticity degree (aromaticity is a function of the "strength and extension size" of the π electronic clouds and thus also function of the crystal order) and hence is directly related to the electric properties of the material (Mouchon & Colomban, 1996). This value depends directly on the thermal treatment temperature history and hence is also related to the mechanical

The plot of the carbon fingerprint parameters recorded across the fibre section diameter (on fracture) shows the very anisotropic carbon distribution (Fig. 4). Chemical treatments eliminate the carbon in the analysed SiC volume and hence allow a better study of the SiC

3 stretching mode is expected. Actually, given the small size

3 bonds also called sp2/3. This

3-Csp 2/sp

SylramicTM fibres section (d) (λ= 632 nm, P= 0.5 mW, t= 60s).

3-Csp

properties, see details in (Gouadec & Colomban, 2001; Colomban, 2003).

band corresponds to vibration modes involving Csp

graphite (∼10-2), a weak Csp

phases (Havel & Colomban, 2005).

The Raman spectrum of well crystallised SiC phases is observed between 600 and 1000 cm-1 (Feldman et al., 1968; Nakashima et al., 1986; idem, 1987; idem, 2000; Nakashima & Hangyo, 1991; Nakashima & Harima, 1997; Okimura et al., 1987; Tomita et al., 2000; Hundhausen et al., 2008,). The main Raman peaks centred at 795 and 966 cm-1 correspond to the transverse (TO) and longitudinal (LO) optic modes respectively of the (polar) cubic 3C phase, also called β SiC. Any other definite stacking sequence is called α-SiC and displays either hexagonal or rhombohedral lattice symmetry. Polytypes in the α-SiC structure induce the formation of satellite peaks around 766 cm-1 and of additional features between the TO and LO modes (Figs 5 & 6). However, the TO mode is twice degenerated; while TO1 is centred at 796 cm-1, TO2 is a function of the "h" layers concentration in the structure. A linear variation of 0.296 cm-1/% has been demonstrated (Salvador & Sherman, 1991; Feldman et al., 1968).

Fig. 5. Representative Raman spectra recorded for NLMTM Nicalon fibres thermally and chemically treated (a,b). Detail on the disorder-activated acoustic modes observed for ZETM fibre (c) and for very amorphous SiC zone are shown.

The main effect of the disorder is the break of the symmetry rules that excludes the Raman activity of the vibrational, optical and acoustical, modes (phonons) of the whole Brillouin

SiC, from Amorphous to Nanosized

795 cm-1 band to 3C-SiC polytypes.

Materials, the Exemple of SiC Fibres Issued of Polymer Precursors 171

Fig. 7. a) Raman spectra recorded every 2µm along a line from the centre of a SCS-6

the contribution of the disordered activated modes is low or even not detected.

Furthermore the latter group is dominated by the broad bands of the amorphous SiC.

TextronTM fibre (L= 532nm, 1mW, 120s/spectrum); b) representative spectra of the pure SiC (III) zone; the different components have been fitted with Gaussian or Lorentzian lines: the broad 740 and 894 cm-1 bands correspond to amorphous SiC, the 767 cm-1 to 6H-SiC and the

The apparition of disordered activated acoustic phonon in the Raman spectrum is not surprising in compounds with large stacking disorder (Chi et al., 2011). Additional multiphonon features are not excluded. However, many Raman studies of such materials have been made using exciting laser line leading to a resonance spectrum, simpler, in which

Very similar features are observed for SiC materials prepared by Chemical Vapour Infiltration. The Raman spectra of the SiC coating deposited on a small diameter (~7µm) carbon fibre core to obtain the SCS-6 TextronTM fibre, a ~120 µm thick fibre used to reinforce metal matrix consist in features where the acoustic phonon intensity becomes stronger than the optical ones.

Because of the different laser line absorption, Rayleigh confocal imaging allows to have very interesting image of the heterogeneous material (Colomban & Havel, 2002; Colomban, 2003; Havel & Colomban, 2003; idem, 2004; idem, 2005; idem, 2006). Fig. 8 shows representative spectra recorded on the deposit obtained around the fibres of a textile perform. In order to

zone: only zone centre modes give rise to a Raman activity. Because the wavenumber of these modes shift with wavevector value, they give broad asymmetric bands. Fig. 6 illustrates the apparition of satellite peaks because the step-by-step Brillouin Zone folding associated to the formation of polytypes. On the contrary, stacking disorder lead to a projection of the vibrational density of state on the vertical energy axis and broad asymmetric bands are observed.

Fig. 6. a) Sketch of the folding of the original phonon Brillouin zone in the stretching LO/TO mode region along the stacking axis of the reference cubic symmetry by factor 2 (2H polytype), 4 (4H) and 6 (6H). b) Satellite peak wavenumbers for series of polytypes (after Nakashima & Harima, 1997).

The comparison of the Figures 2a (Diffraction & diffuse scattering) and 2b (Raman scattering) points out the very different sensitivity of these two methods. Fig. 4 compares the Raman spectra of the different generation SiC fibres, with carbon excess ranging from ~20 wt% (1st generation) to less than 1 wt% (3rd generation). A small wavenumber shift may be associated to the change of the exciting wavelength. Another important point is that for coloured materials, the interaction between laser light and matter must be very strong and hence the light absorption. This may have detrimental effect (local heating – and thermal induced wavenumber shift – (Colomban, 2002), oxidation and phase transition (Gouadec et al., 2001) in the lack of attention but this also controls the penetration depth of the laser light: the penetration can be limited to a few (tenths of) nanometers (Gouadec & Colomban, 2007).

Figs 5 to 9 give examples of the variety of Raman signatures observed on SiC materials issued of the organic precursor routes.

The narrow peaks pattern of crystalline polytypes is obvious and assignments are univocal with the comprehensive work of Nakashima (Nakashima et al., 1986; idem, 1987; Nakashima &Harima, 1997), see Fig. 6. The most stringent new features are the very broad bands observed at ~730 and 870 cm-1 and the structured pattern below 600 cm-1. The first feature corresponds to the amorphous silicon carbide and the second one to the acoustic modes rendered active because of the very poor crystallinity of the fibre.

zone: only zone centre modes give rise to a Raman activity. Because the wavenumber of these modes shift with wavevector value, they give broad asymmetric bands. Fig. 6 illustrates the apparition of satellite peaks because the step-by-step Brillouin Zone folding associated to the formation of polytypes. On the contrary, stacking disorder lead to a projection of the vibrational density of state on the vertical energy axis and broad

(a) (b)

Wavenumber / cm-1

0,0 0,2 0,4 0,6 0,8 1,0

Reduced wave vector

33R 6H 3C 6H

15R

3C 21R

π/c

LO

TO

33R

4H 21R 15R

 Raman calculation

6H 4H

6H 21R

Fig. 6. a) Sketch of the folding of the original phonon Brillouin zone in the stretching LO/TO

The comparison of the Figures 2a (Diffraction & diffuse scattering) and 2b (Raman scattering) points out the very different sensitivity of these two methods. Fig. 4 compares the Raman spectra of the different generation SiC fibres, with carbon excess ranging from ~20 wt% (1st generation) to less than 1 wt% (3rd generation). A small wavenumber shift may be associated to the change of the exciting wavelength. Another important point is that for coloured materials, the interaction between laser light and matter must be very strong and hence the light absorption. This may have detrimental effect (local heating – and thermal induced wavenumber shift – (Colomban, 2002), oxidation and phase transition (Gouadec et al., 2001) in the lack of attention but this also controls the penetration depth of the laser light: the penetration can be limited to a few (tenths of)

Figs 5 to 9 give examples of the variety of Raman signatures observed on SiC materials

The narrow peaks pattern of crystalline polytypes is obvious and assignments are univocal with the comprehensive work of Nakashima (Nakashima et al., 1986; idem, 1987; Nakashima &Harima, 1997), see Fig. 6. The most stringent new features are the very broad bands observed at ~730 and 870 cm-1 and the structured pattern below 600 cm-1. The first feature corresponds to the amorphous silicon carbide and the second one to the acoustic

modes rendered active because of the very poor crystallinity of the fibre.

mode region along the stacking axis of the reference cubic symmetry by factor 2 (2H polytype), 4 (4H) and 6 (6H). b) Satellite peak wavenumbers for series of polytypes (after

asymmetric bands are observed.

Nakashima & Harima, 1997).

nanometers (Gouadec & Colomban, 2007).

issued of the organic precursor routes.

Fig. 7. a) Raman spectra recorded every 2µm along a line from the centre of a SCS-6 TextronTM fibre (L= 532nm, 1mW, 120s/spectrum); b) representative spectra of the pure SiC (III) zone; the different components have been fitted with Gaussian or Lorentzian lines: the broad 740 and 894 cm-1 bands correspond to amorphous SiC, the 767 cm-1 to 6H-SiC and the 795 cm-1 band to 3C-SiC polytypes.

The apparition of disordered activated acoustic phonon in the Raman spectrum is not surprising in compounds with large stacking disorder (Chi et al., 2011). Additional multiphonon features are not excluded. However, many Raman studies of such materials have been made using exciting laser line leading to a resonance spectrum, simpler, in which the contribution of the disordered activated modes is low or even not detected.

Very similar features are observed for SiC materials prepared by Chemical Vapour Infiltration. The Raman spectra of the SiC coating deposited on a small diameter (~7µm) carbon fibre core to obtain the SCS-6 TextronTM fibre, a ~120 µm thick fibre used to reinforce metal matrix consist in features where the acoustic phonon intensity becomes stronger than the optical ones. Furthermore the latter group is dominated by the broad bands of the amorphous SiC.

Because of the different laser line absorption, Rayleigh confocal imaging allows to have very interesting image of the heterogeneous material (Colomban & Havel, 2002; Colomban, 2003; Havel & Colomban, 2003; idem, 2004; idem, 2005; idem, 2006). Fig. 8 shows representative spectra recorded on the deposit obtained around the fibres of a textile perform. In order to

SiC, from Amorphous to Nanosized

(a)

100

(b)

Distance (µm)

4

6 8 10

+ 4 %

hydrostatic pressure (see Table 2).

2 4 6 8 <sup>10</sup> <sup>2</sup>

Distance (µm)


2

Materials, the Exemple of SiC Fibres Issued of Polymer Precursors 173

up-deformation of the fibre matter close to the edges resulting from the pyramidal shape of the Vickers indentor is obvious. The residual stress is calculated using the experimental relationship previously established under pressure (Salvador & Sherman, 1991; Olego et al., 1982). The amorphization is obvious at the center of the indented area with the relative increase of the intensity of the 760-923 cm-1 doublet and the decrease of the TO/LO doublet; note, the up-shift of the TO mode from 796 to 807 cm-1. Similar information can be extracted from the D carbon band using the relationship established by Gouadec & Colomban, 2001.

ν (cm-1) P (GPa) ν (cm-1) P (GPa)

(c) 400 800 1200 1600

(c') 400 800 1200 1600

777

807 923 969

<sup>759</sup> <sup>548</sup> <sup>447</sup> <sup>339</sup>

Wavenumber / cm-1

Fig. 9. (a,b) Rayleigh images of the Vickers indented area on the mixed SiC+C II region of a

representative spectra (step: 0.1µm) recorded at the core (c') and the periphery (c) of the indented area; the fitting of the different component allows calculating the residual

SCS-6 TextronTM fibre (100x100 spectra, 3s/Spectrum, 10-6 mW, l = 532 nm); c,c')

<sup>898</sup> <sup>796</sup> 771 <sup>761</sup> <sup>549</sup> 443 331

969

< <sup>262</sup> > <sup>1605</sup> <sup>1508</sup>

1526 1604

1369

< <sup>314</sup> >

1351

Extérieur

Peak Out of the indented area At the tip position

TO 796 ± 2 0 **807** ± **6 3** ± **2**  LO 969 ± 2 0 969 ± 4 3 +- 2 D 1351± 3 0 1369± 4 3± **1**

Table 2. Comparison between the TO/LO peak wavenumbers measured at the tip and out of the 50 g Vickers indented area on SCS-6 TextronTM fibre, mixed SiC-C zone II (see Fig. 7a).

optimise the thermomechanical properties of the composite a first coating of the SiC fibre with BN has been made. The spectra show the 3C (narrow peak at 799 and 968 cm-1), 6H (786 cm-1), 8H or 15R (768 cm-1) as well the broad and strong contribution of amorphous SiC (optical modes at 750 & 900 cm-1 and acoustic modes at 450 cm-1 with shoulder at 380 and 530 cm-1). Traces of carbon (1350-1595 cm-1 doublet) are also observed. We assign the broad Gaussian peaks at ~ 700 cm-1 and ~ 882 cm-1 to the amorphous SiC. Indeed, the position of the band at ca 882 cm-1 is exactly between the two optical modes at a wavenumber of (796+969) / 2 = 882.5 cm-1. Dkaki et al. (Dkaki et al., 2001) already assigned the band at ca. 740 cm-1 to the amorphous SiC phase.

Fig. 8. Optical photomicrograph (a) and Rayleigh image (b) of a SiC (BN coated) fibre reinforced–SiC matrix composite. Examples of SiC spectra are given in c). Polytypes are evidenced by 786 (4H) and 768 (6H) cm-1 TO modes. The fingerprints of 3C (799 cm-1) and amorphous (900 cm-1 broad band) SiC are also present.

When classically used, a Raman spectrometer is built to avoid the elastic (Rayleigh) scattering which is much more intense (× 106) than the inelastic one (Raman) and masks it. However, the Rayleigh signal contains useful information (volume of interaction and dielectric constant) that can be recorded in only few seconds, giving rise to topological and/or chemical maps (a high resolution Raman image requires tenths of hours!). The combination of Rayleigh image and Raman scattering is very interesting to study indentation figures (Colomban & Havel, 2002). Rayleigh scattering gives image of the topology mixed with information on the chemical composition through the variation of the optical index. Fig. 9 presents the Rayleigh image of the Vickers indented zone of the mixed SiC+C region (zone II) of a SCS-6 polished section (see Fig. 7). The automatic XY mapping has been performed with an objective with an Z axis extension of the focus volume sufficiently large to be bigger than the indentation depth. Thus, a 3D view is obtained. The

optimise the thermomechanical properties of the composite a first coating of the SiC fibre with BN has been made. The spectra show the 3C (narrow peak at 799 and 968 cm-1), 6H (786 cm-1), 8H or 15R (768 cm-1) as well the broad and strong contribution of amorphous SiC (optical modes at 750 & 900 cm-1 and acoustic modes at 450 cm-1 with shoulder at 380 and 530 cm-1). Traces of carbon (1350-1595 cm-1 doublet) are also observed. We assign the broad Gaussian peaks at ~ 700 cm-1 and ~ 882 cm-1 to the amorphous SiC. Indeed, the position of the band at ca 882 cm-1 is exactly between the two optical modes at a wavenumber of (796+969) / 2 = 882.5 cm-1. Dkaki et al. (Dkaki et al., 2001) already assigned the band at ca.

(c) 300 600 900 1200 1500 1800

<sup>968</sup> <sup>900</sup>

786 799

768

750 530 <sup>450</sup> <sup>378</sup>

Wavenumber / cm-1

60 µm (3)

1351 1593

1525

(2)

*SiC*

740 cm-1 to the amorphous SiC phase.

(a)

10 µm

Fibre

(b)

amorphous (900 cm-1 broad band) SiC are also present.

Fig. 8. Optical photomicrograph (a) and Rayleigh image (b) of a SiC (BN coated) fibre reinforced–SiC matrix composite. Examples of SiC spectra are given in c). Polytypes are evidenced by 786 (4H) and 768 (6H) cm-1 TO modes. The fingerprints of 3C (799 cm-1) and

When classically used, a Raman spectrometer is built to avoid the elastic (Rayleigh) scattering which is much more intense (× 106) than the inelastic one (Raman) and masks it. However, the Rayleigh signal contains useful information (volume of interaction and dielectric constant) that can be recorded in only few seconds, giving rise to topological and/or chemical maps (a high resolution Raman image requires tenths of hours!). The combination of Rayleigh image and Raman scattering is very interesting to study indentation figures (Colomban & Havel, 2002). Rayleigh scattering gives image of the topology mixed with information on the chemical composition through the variation of the optical index. Fig. 9 presents the Rayleigh image of the Vickers indented zone of the mixed SiC+C region (zone II) of a SCS-6 polished section (see Fig. 7). The automatic XY mapping has been performed with an objective with an Z axis extension of the focus volume sufficiently large to be bigger than the indentation depth. Thus, a 3D view is obtained. The

SiC

BN

up-deformation of the fibre matter close to the edges resulting from the pyramidal shape of the Vickers indentor is obvious. The residual stress is calculated using the experimental relationship previously established under pressure (Salvador & Sherman, 1991; Olego et al., 1982). The amorphization is obvious at the center of the indented area with the relative increase of the intensity of the 760-923 cm-1 doublet and the decrease of the TO/LO doublet; note, the up-shift of the TO mode from 796 to 807 cm-1. Similar information can be extracted from the D carbon band using the relationship established by Gouadec & Colomban, 2001.


Table 2. Comparison between the TO/LO peak wavenumbers measured at the tip and out of the 50 g Vickers indented area on SCS-6 TextronTM fibre, mixed SiC-C zone II (see Fig. 7a).

Fig. 9. (a,b) Rayleigh images of the Vickers indented area on the mixed SiC+C II region of a SCS-6 TextronTM fibre (100x100 spectra, 3s/Spectrum, 10-6 mW, l = 532 nm); c,c') representative spectra (step: 0.1µm) recorded at the core (c') and the periphery (c) of the indented area; the fitting of the different component allows calculating the residual hydrostatic pressure (see Table 2).

SiC, from Amorphous to Nanosized

1981; Gouadec & Colomban, 2007).

al., 1993; Kosacki et al., 2002).

with

Materials, the Exemple of SiC Fibres Issued of Polymer Precursors 175

(Nemanich et al., 1981) and then popularised Parayantal and Pollack (Parayantal & Pollack, 1984). A comprehensive description for non-specialist has been given in our previous work (Gouadec & Colomban, 2007). It can be briefly explained as follows. In "large" crystals, phonons propagate "to infinity" and because of the momentum selection rule the first order Raman spectrum only consists of "q=0" phonon modes, i.e. the centre of the Brillouin Zone (Fig. 6). However, since crystalline perfection is destroyed by impurities or lattice disorder, including at the surface where atoms environment is singular, the phonon function of polycrystals is spatially confined. This results in an exploration of the wavevectors space and subsequent wavenumber shifts and band broadening. Another effect is the possible activation of "symmetry forbidden" modes. This is linked to the Brillouin zone folding as illustrated in Fig. 6. In the 6H polytype structure, the zone is folded three times at the Γ centre point and the reduced wave vectors that can be observed are at q = 0, 0.33, 0.67 and 1 (Feldman et al., 1968; Nakashima et al., 1987; Nakashima & Harima, 1997). The Raman line broadening can be described by the (linear) dependence of its half width upon the inverse grain size, as reported previously for many nanocrystalline materials including CeO2

(Kosacki et al., 2002), BN (Nemanich et al., 1981), Si (Richter et al., 1981), etc.

In equation (1), the SCM describes the crystalline quality by introducing a parameter L0, the coherence length, which is the average extension of the material homogeneity region. Noting q the wave vector expressed in units of π/a (a being the lattice unit-cell parameter) and Γ0 the half width of Raman peaks for the ordered reference structure, the intensity I( ν ) at the wavenumber ν is then given by equation (2). (Richter et al., 1981; Nemanich et al.,

The exponential function represents a Gaussian spatial correlation and ν (q) is the mode dispersion function, which can be deduced from neutron scattering measurements or from calculations often based on a rigid-model structure (Parayanthal & Pollak, 1984; Weber et

> 0 2 2 q 0 0

While the one dimensional disorder (in the stacking direction) leads to the polytypes formation, a complete disorder induces the total folding of the Brillouin zone and the apparition of a very broad Raman signal (density of state spectrum, e.g. Fig. 9c). The phonon

The dispersion curve can be modelled with the Eq. 2-4 (Parayanthal & Pollak, 1984). Our 6H reference corresponds to coefficients A and B of respectively 3.18 × 105 and 1.38 × 1010 for TO

> ( 0) 1 <sup>2</sup>

[ ]

*q*

<sup>2</sup> ν( ) *q A AB q* = + −× − π (1 cos( ) 0 ≤ q ≤ 1 (2)

( ) <sup>2</sup>

(1)

ν−ν +

Γ

<sup>2</sup> *<sup>q</sup> <sup>A</sup>* <sup>=</sup> = ×ν (3)

( )

*BZ k qq L dq II e*

16

<sup>=</sup> ×− × <sup>−</sup> ×π

ν × ×

q 1

=

confinement is observed for small grains in a well crystallized state.

and 4.72 × 105 and 8.52 × 1010 for LO modes (Havel & Colomban, 2004).

( ) =

2 2 2 0 0 2

Fig. 10. TEM photomicrographs showing the carbon slabs in 1600°C thermally treated SA3 fibre (a,b) and the extension of the polytypes in thermally treated NLM 202TM (c) and SA3TM (d) fibres. The progressive transition between crystalline layers and amorphous zone is shown in (d) (Courtesy, L. Mazerolles).

#### **6. Microstructure and defects**

Fig. 10 shows representative high resolution Transmission Electron Microscopy (TEM) images recorded on thermally treated NLM 202 NicalonTM and SA3TM fibres (Table 1). Structural studies of SiC nanocrystals were carried out on fragments of fibres deposited on a copper grid after crushing in an agate mortar (Havel, 2004; Havel et al., 2007). In SA3 TM fibre the carbon phase appears to be well organized, graphitic, according to the narrow doublet of the Raman spectra (Fig. 3a). The interplane spacing is 0.33 pm. The stacking sequence of SiC bilayers is clear in Fig. 10c & d, because the contrast jump relative to the Bragg peak shifts. The domain sizes along the stacking direction might rich 3-4 nm. Figure 10c shows a typical HRTEM image of a nanocrystal with a size of 15 nm along its longest axis consisting of two regions corresponding to the α and β phases. The stacking faults, which are clearly seen on the micrograph, show no periodicity along the c axis of the hexagonal structure. Stacking faults can be considered as a perturbation of the β-SiC 3C stacking sequence so that the α phase can be seen as a sequence of β-SiC domains of various sizes ranging from 0.2 to 5 nm. The progressive transition between crystalline domains explains the variety of Raman fingerprint. There is a good agreement between Raman and TEM data.

#### **7. Quantitative extraction of the (micro)structural information present in the Raman spectrum**

For the decomposition of the SiC Raman peaks we used the spatial correlation model (SCM), which was established by Richter et al. (Richter et al., 1981), and by Nemanich et al. (Nemanich et al., 1981) and then popularised Parayantal and Pollack (Parayantal & Pollack, 1984). A comprehensive description for non-specialist has been given in our previous work (Gouadec & Colomban, 2007). It can be briefly explained as follows. In "large" crystals, phonons propagate "to infinity" and because of the momentum selection rule the first order Raman spectrum only consists of "q=0" phonon modes, i.e. the centre of the Brillouin Zone (Fig. 6). However, since crystalline perfection is destroyed by impurities or lattice disorder, including at the surface where atoms environment is singular, the phonon function of polycrystals is spatially confined. This results in an exploration of the wavevectors space and subsequent wavenumber shifts and band broadening. Another effect is the possible activation of "symmetry forbidden" modes. This is linked to the Brillouin zone folding as illustrated in Fig. 6. In the 6H polytype structure, the zone is folded three times at the Γ centre point and the reduced wave vectors that can be observed are at q = 0, 0.33, 0.67 and 1 (Feldman et al., 1968; Nakashima et al., 1987; Nakashima & Harima, 1997). The Raman line broadening can be described by the (linear) dependence of its half width upon the inverse grain size, as reported previously for many nanocrystalline materials including CeO2 (Kosacki et al., 2002), BN (Nemanich et al., 1981), Si (Richter et al., 1981), etc.

In equation (1), the SCM describes the crystalline quality by introducing a parameter L0, the coherence length, which is the average extension of the material homogeneity region. Noting q the wave vector expressed in units of π/a (a being the lattice unit-cell parameter) and Γ0 the half width of Raman peaks for the ordered reference structure, the intensity I( ν ) at the wavenumber ν is then given by equation (2). (Richter et al., 1981; Nemanich et al., 1981; Gouadec & Colomban, 2007).

The exponential function represents a Gaussian spatial correlation and ν (q) is the mode dispersion function, which can be deduced from neutron scattering measurements or from calculations often based on a rigid-model structure (Parayanthal & Pollak, 1984; Weber et al., 1993; Kosacki et al., 2002).

$$I(\overline{\mathbf{v}}) = I\_0 \times \int\_{q=0}^{q=1} e^{-\frac{k\_{\overline{K}}^2 \times \left(q-q\_0\right)^2 \times L\_0^{-2}}{16 \times \pi^2}} \times \frac{d\eta}{\left[\nabla - \nabla(q)\right]^2 + \left(\frac{\Gamma\_0}{2}\right)^2} \tag{1}$$

While the one dimensional disorder (in the stacking direction) leads to the polytypes formation, a complete disorder induces the total folding of the Brillouin zone and the apparition of a very broad Raman signal (density of state spectrum, e.g. Fig. 9c). The phonon confinement is observed for small grains in a well crystallized state.

The dispersion curve can be modelled with the Eq. 2-4 (Parayanthal & Pollak, 1984). Our 6H reference corresponds to coefficients A and B of respectively 3.18 × 105 and 1.38 × 1010 for TO and 4.72 × 105 and 8.52 × 1010 for LO modes (Havel & Colomban, 2004).

$$\overline{\mathbf{v}(q)} = \sqrt{A + \sqrt{A^2 - B \times (1 - \cos(\pi q))}} \quad 0 \le q \le 1 \tag{2}$$

with

174 Silicon Carbide – Materials, Processing and Applications in Electronic Devices

Fig. 10. TEM photomicrographs showing the carbon slabs in 1600°C thermally treated SA3 fibre (a,b) and the extension of the polytypes in thermally treated NLM 202TM (c) and SA3TM (d) fibres. The progressive transition between crystalline layers and amorphous zone is shown in (d)

Fig. 10 shows representative high resolution Transmission Electron Microscopy (TEM) images recorded on thermally treated NLM 202 NicalonTM and SA3TM fibres (Table 1). Structural studies of SiC nanocrystals were carried out on fragments of fibres deposited on a copper grid after crushing in an agate mortar (Havel, 2004; Havel et al., 2007). In SA3 TM fibre the carbon phase appears to be well organized, graphitic, according to the narrow doublet of the Raman spectra (Fig. 3a). The interplane spacing is 0.33 pm. The stacking sequence of SiC bilayers is clear in Fig. 10c & d, because the contrast jump relative to the Bragg peak shifts. The domain sizes along the stacking direction might rich 3-4 nm. Figure 10c shows a typical HRTEM image of a nanocrystal with a size of 15 nm along its longest axis consisting of two regions corresponding to the α and β phases. The stacking faults, which are clearly seen on the micrograph, show no periodicity along the c axis of the hexagonal structure. Stacking faults can be considered as a perturbation of the β-SiC 3C stacking sequence so that the α phase can be seen as a sequence of β-SiC domains of various sizes ranging from 0.2 to 5 nm. The progressive transition between crystalline domains explains the variety of Raman fingerprint.

**7. Quantitative extraction of the (micro)structural information present in the** 

For the decomposition of the SiC Raman peaks we used the spatial correlation model (SCM), which was established by Richter et al. (Richter et al., 1981), and by Nemanich et al.

(a) (c)

(b) (d)

There is a good agreement between Raman and TEM data.

(Courtesy, L. Mazerolles).

**Raman spectrum** 

**6. Microstructure and defects** 

$$A = \frac{1}{2} \times \overline{\mathbf{v}}\_{\cdot (q=0)}^2 \tag{3}$$

and

$$B = \frac{1}{2} \times \overline{\mathbf{v}}\_{\left(\!\!\!q^{\text{-}1}\right)}^{2} \times \left(\overline{\mathbf{v}}\_{\left(\!\!\!\!q^{\text{-}0}\right)}^{2} - \overline{\mathbf{v}}\_{\left(\!\!\!\!\!\!T^{-1}\right)}^{2}\right) \tag{4}$$

SiC, from Amorphous to Nanosized

12 20 - 22

(c) (b)

3 6 9 12

Distance (μm)

3 6 9 12

Distance (µm) (e)

(a) 3 6 9 12

3

3

(d)

3

6

9

12

6

9

12

6

9

Materials, the Exemple of SiC Fibres Issued of Polymer Precursors 177

analysed, which is much more time-consuming than the acquisition itself. This is why automatic decomposition software must be developed (Havel et al., 2004; Gouadec et al., 2011).

 12,6 - 14 11,2 - 12,6 9,8 - 11,2 8,4 - 9,8 7 - 8,4 5,6 - 7 4,2 - 5,6 2,8 - 4,2 1,4 - 2,8

3

Fig. 11. Raman maps of the TO SiC (a) and D C stretching mode intensity (b) and D wavenumber (c-top) recorded on the section of a SA3TM fibre (30x30 spectra, 0.5µm step, x100 objective, λ = 632 nm). The c-bottom image is a calculation, see text. Evolution of the TO and D band intensity after a thermal treatment at 1600°C is shown in d) and e).

Because of their interesting thermal and mechanical properties, SiC composites (SiC fibres + SiC matrix) find numerous applications in the aerospace industry and new ones are expected in fusion ITER plant (Roubin et al., 2005). However, their expensive cost has to be balanced with a long lifetime, which is not yet achieved. To increase their lifetime, we first have to understand their behaviour under chemical and mechanical stresses, and thus, to characterize their nanostructure. In this section, we focus on the SiC fibres, which are analysed across their section. Indeed, this approach allows observing the chemical variations that may exist between the fibre's core and surface. Fig. 11 shows Raman maps

6

9

12

3 6 9 12

I D (u.a.) 16,6 - 18 15,1 - 16,6 13,6 - 15,1 12,2 - 13,6 11 - 12.2 9,3 - 11 8 - 9,3 6,5 - 8 5 - 6,5 3,5 - 5

Distance (µm)

I D (u.a.)

I TO (u.a.)

The SCM has been used to determine the size and structure of SiC nanocrystals extracted from annealed SiC fibre. The Raman spectra of the NLM fibres annealed 1h and 10h are shown in Fig 5. The SiC Raman signature, is composed of the 2 optical TO and LO modes. A satellite at 768 cm-1 indicates the presence of the 6H-SiC polytype (Fig. 6). The most interesting parameter in this SiC signature is the strong asymmetry of the LO peak at ~ 969 cm-1 (see also Fig. 7). The TO peak is much less asymmetric and centred at 796 cm-1. The elementary peaks obtained from the decomposition of the experimental spectrum are shown in Fig. 5 and the adjustment parameters (position, q0 and L0) are summarized in Table 3. Note that the accuracy on the calculated reduced wavevector, q0, is increased for the LO mode because its dispersion curve explores a wider wavenumber range (838-972 cm-1) than the TO mode (767-797 cm-1).


Table 3. Peak fitting parameters of the TO and LO peaks of SiC calculated from the Raman spectra of the NLM fibres annealed 1h and 10h at 1600°C and annealed 1h then corroded 100h in NaNO3 (Havel & Colomban, 2005).

For the fibre annealed for 1h, the L0 parameters of both TO and LO peaks show a confinement dimension in the range of 2.5 to 7 nm, in good agreement with the TEM image. After 10h annealing, the TO and LO peaks become sharper and more intense, indicating an increase in the size of the nanocrystals. This is confirmed by the L0 parameter, which gives a confinement dimension slightly higher, between 3 and 8 nm, according to the polytype domain size (Fig. 10).

#### **8. Raman imaging**

Raman imaging is very powerful, especially for heterogeneous materials but its rise is limited because of a lack of real control on the x, y, z spatial resolution (changing the diameter of confocal hole allows however some possibility) and of the huge recording time required (the spectrometer has often to be used during night time). However, a precise study of the laser shape, can improve the control on the resolution and since the CCD detectors are more and more sensitive, Raman images will now require more reasonable acquisition time (hours!). Note, that once the image is recorded, the set of spectra (also called hyperspectrum) has to be

( 1) ( 0) ( 1) ( ) <sup>1</sup> 2 22

The SCM has been used to determine the size and structure of SiC nanocrystals extracted from annealed SiC fibre. The Raman spectra of the NLM fibres annealed 1h and 10h are shown in Fig 5. The SiC Raman signature, is composed of the 2 optical TO and LO modes. A satellite at 768 cm-1 indicates the presence of the 6H-SiC polytype (Fig. 6). The most interesting parameter in this SiC signature is the strong asymmetry of the LO peak at ~ 969 cm-1 (see also Fig. 7). The TO peak is much less asymmetric and centred at 796 cm-1. The elementary peaks obtained from the decomposition of the experimental spectrum are shown in Fig. 5 and the adjustment parameters (position, q0 and L0) are summarized in Table 3. Note that the accuracy on the calculated reduced wavevector, q0, is increased for the LO mode because its dispersion curve explores a wider wavenumber range (838-972 cm-1) than

Peak Parameter 1h 10h 1h + corroded

ν (cm-1) 961.7 969.5 954.5 q0 0.18 ± 0.03 0.00 ± 0.07 0.26 ± 0.01 L0 (nm) 2.9 ± 0.4 3.8 ± 0.9 5.2 ± 0.5

Table 3. Peak fitting parameters of the TO and LO peaks of SiC calculated from the Raman spectra of the NLM fibres annealed 1h and 10h at 1600°C and annealed 1h then corroded

For the fibre annealed for 1h, the L0 parameters of both TO and LO peaks show a confinement dimension in the range of 2.5 to 7 nm, in good agreement with the TEM image. After 10h annealing, the TO and LO peaks become sharper and more intense, indicating an increase in the size of the nanocrystals. This is confirmed by the L0 parameter, which gives a confinement dimension slightly higher, between 3 and 8 nm, according to the polytype

Raman imaging is very powerful, especially for heterogeneous materials but its rise is limited because of a lack of real control on the x, y, z spatial resolution (changing the diameter of confocal hole allows however some possibility) and of the huge recording time required (the spectrometer has often to be used during night time). However, a precise study of the laser shape, can improve the control on the resolution and since the CCD detectors are more and more sensitive, Raman images will now require more reasonable acquisition time (hours!). Note, that once the image is recorded, the set of spectra (also called hyperspectrum) has to be

ν (cm-1) 796.8 795.6 794.2 ±<sup>2</sup> q0 0.22 ± 0.02 0.26 ± 0.01 0.30 ± 0.01 L0 (nm) 5.6 ± 1.5 6.5 ± 1.2 5.6 ± 0.6

*B* = ×ν × ν −ν *q qq* = == (4)

2

and

TO

LO

the TO mode (767-797 cm-1).

100h in NaNO3 (Havel & Colomban, 2005).

domain size (Fig. 10).

**8. Raman imaging** 

analysed, which is much more time-consuming than the acquisition itself. This is why automatic decomposition software must be developed (Havel et al., 2004; Gouadec et al., 2011).

Fig. 11. Raman maps of the TO SiC (a) and D C stretching mode intensity (b) and D wavenumber (c-top) recorded on the section of a SA3TM fibre (30x30 spectra, 0.5µm step, x100 objective, λ = 632 nm). The c-bottom image is a calculation, see text. Evolution of the TO and D band intensity after a thermal treatment at 1600°C is shown in d) and e).

Because of their interesting thermal and mechanical properties, SiC composites (SiC fibres + SiC matrix) find numerous applications in the aerospace industry and new ones are expected in fusion ITER plant (Roubin et al., 2005). However, their expensive cost has to be balanced with a long lifetime, which is not yet achieved. To increase their lifetime, we first have to understand their behaviour under chemical and mechanical stresses, and thus, to characterize their nanostructure. In this section, we focus on the SiC fibres, which are analysed across their section. Indeed, this approach allows observing the chemical variations that may exist between the fibre's core and surface. Fig. 11 shows Raman maps

SiC, from Amorphous to Nanosized

section.

sintering steps, etc.).

**10. References** 

**9. Acknowledgments** 

311, 4784-4790.

Materials, the Exemple of SiC Fibres Issued of Polymer Precursors 179

σRupture (GPa) 3,5 - 3,7 3,3 - 3,5 3,0 - 3,3 2,8 - 3,0 2,6 - 2,8 2,4 - 2,6 2,2 - 2,4 2,0 - 2,2

3 6 9 12

Distance (μm)

Fig. 11. Raman map of calculated ultimate tensile strength of the SiC zones in a SA3TM fibre

"Smart Raman images" in this section bring a lot of interesting information. First, there is a huge difference between the fibre's core and surface with a radial gradient of physical properties as function of the fibre' producer and additional treatments. Second, the maximum tolerable strain is observed in the fibre's core, where the carbon species are the smallest (~ 1.5 nm). The core/skin differences are due to the elaboration process (spinning,

The author thanks Drs Havel, Karlin, Gouadec, Mazerolles and Parlier for their very

Agrosi, G., Tempesta, G., Capitani, G.C., Scandale, E. & Siche, D. (2009). Multi-analytical

Alvarez-Garcia, J., Barcones, B., Perez-Rodriguez, A., Romano-Rodriguez, A., Morante, J.R.,

Aoki, M., Miyazaki, M. & Nishiguchi, T. (2009). TEM Observation of the polytype

Baxter D., Bellosi, A. & Monteverde, F. (2000). Oxidation and burner rig corrosion of liquid

Berger, M.-H., Hochet, N. & Bunsell, A.R. (1995) Microstructure and thermomechanical stability of low-oxygen Nicalon fibers, *J. Microsc.-Oxford*, 177[3], 230-241. Berger, M.-H., Hochet, N. & Bunsell, A.R. (1997). Microstrucure evolution of the latest

Berger, M.-H., Hochet, N. & Bunsell A.R. (1999). Properties and microstructure of small-

Bhargava, S., Bist, H.D. & Sahli, S., (1995). Diamond polytypes in the chemical vapor

polymorphic CuInC2 (C= Se,S), *Phys. Rev. B*, 71, 054303.

Parts 1 & 2, *Mater. Sci. Forum*, 600-603, 365-368.

*Microsc*.-*Oxford* 185 (Part 2), 243-258.

phase sintered SiC, *J. Eur. Ceram. Soc*., 20, 367-382.

& M.-H. Berger, Marcel-Dekker Inc., New-York.

deposited diamond films, *Appl. Phys. Lett.*, 67, 1706-1708.

study of syntactic coalescence of polytypes in a 6H-SiC sample, *J. Crystal Growth*,

Janotti, A., Wei, S.-H. & Scheer, R., (2005). Vibrational and crystalline properties of

transformation of Bulk SiC Ingot, in Silicon Carbide and Related Materials 2007,

generation of small-diameter SiC-based fibers tested at high temperature, *J.* 

diameter SiC-based fibers ch. 6, pp 231-290 in *Fine Ceramic Fibers*, Ed. A.R. Bunsell

3

valuable contributions to the study of SiC materials.

6

9

12

of the Tyranno SA3TM (Ube Industry) fibre polished sections: a full spectrum is recorded each 0.5 µm (the hyperspectrum) and after computation, Raman parameters are extracted and mapped. Figures 11a & b consider the intensity variation of the TO SiC and D carbon peaks (see also Fig. 4); this later line is assigned to the vibrations of peculiar carbon moieties, which are thought to be located at the edges of the sp2 carbon grains (Fig. 10a). Fig. 11c (top) shows the wavenumber shift of the later D band. In this particular case, the wavenumber shift represents the aromaticity of the carbon species. It has been reported that this parameter also depends on the residual strain as is shown in equation 5 (Gouadec & Colomban, 2001).

$$
\Delta \overline{\nu}\_{\text{D}} = \begin{array}{c} \text{10 } cm^{-1} \end{array} / \text{GPa} \tag{5}
$$

The radial anisotropy results from the fibre preparation process: the fibre is heated from outside and the departure of the H and C excess takes place at the fibre surface. Consequently, because of the thermodynamic rules, the temperature of the fibre surface is higher than that of the core, that keep C and H excess. After thermal treatment at 1600°C a better homogeneity is achieved. Obviously, the specific microstructures of the different fibre grades can be analysed using a "simpler" and faster diameter line-scan (Fig. 4).

The first maps (Figs 10a, b & c-top), representing the distribution of a simple Raman parameter, may be of limited physical interest. However, it can be translated (through models) to a property' map (Colomban, 2003). The resulting image as exempled in (Fig. 11cbottom) gives the distribution of physical parameters; we call it a "Smart image".

For instance, the size of short-range ordered vibrational units in carbon moieties can be deduced from the Raman parameters. It is based on the ratio of the intensity, I, of the two main carbon Raman peaks (ID/IG), as first proposed by Tiunstra & Koenig, 1970.

$$\mathbf{I\_D / I\_G = C\_l / Sg} \tag{6}$$

with the grain size Sg in nm and the constant C = 44 for 5145.5 nm laser excitation; this formula works well for relatively large grains (>2 nm). A new model (7) takes into account the Raman efficiency, d, of the D1340 with respect to that of G1600, as well as R, the ratio of atoms on the surface of each grain with respect to the bulk, et the surface thickness and Lg, the coherent length (~ the grain size of Tuinstra and Koenig model). Assuming a spherical shape of all grains the following equation can be proposed (Colomban et al., 2001).

$$d \times R = d \times \left[ \left( 1 - \frac{2 \times e\_t}{L\_g} \right)^{-3} - 1 \right] \tag{7}$$

This model has been used to calculate the carbon grains size distribution in SA3TM fibre's cross sections. We observe that the intensity ratio is much higher in the core than near the surface and the carbon grain size appears approximately 2-3 times smaller on the fibre's core than on its periphery because the thermal gradient during the process.

The Raman data can be translated through equation 5 to a map of the maximum tolerable strain (Colomban, 2003). The resulting image (Fig. 12) clearly evidences that the fibre's mechanical properties are better (~ 3.5 GPa) in the core than near the surface (~ 2 GPa).

Fig. 11. Raman map of calculated ultimate tensile strength of the SiC zones in a SA3TM fibre section.

"Smart Raman images" in this section bring a lot of interesting information. First, there is a huge difference between the fibre's core and surface with a radial gradient of physical properties as function of the fibre' producer and additional treatments. Second, the maximum tolerable strain is observed in the fibre's core, where the carbon species are the smallest (~ 1.5 nm). The core/skin differences are due to the elaboration process (spinning, sintering steps, etc.).

#### **9. Acknowledgments**

The author thanks Drs Havel, Karlin, Gouadec, Mazerolles and Parlier for their very valuable contributions to the study of SiC materials.

#### **10. References**

178 Silicon Carbide – Materials, Processing and Applications in Electronic Devices

of the Tyranno SA3TM (Ube Industry) fibre polished sections: a full spectrum is recorded each 0.5 µm (the hyperspectrum) and after computation, Raman parameters are extracted and mapped. Figures 11a & b consider the intensity variation of the TO SiC and D carbon peaks (see also Fig. 4); this later line is assigned to the vibrations of peculiar carbon moieties, which are thought to be located at the edges of the sp2 carbon grains (Fig. 10a). Fig. 11c (top) shows the wavenumber shift of the later D band. In this particular case, the wavenumber shift represents the aromaticity of the carbon species. It has been reported that this parameter also depends on the residual strain as is shown in equation 5

1

The radial anisotropy results from the fibre preparation process: the fibre is heated from outside and the departure of the H and C excess takes place at the fibre surface. Consequently, because of the thermodynamic rules, the temperature of the fibre surface is higher than that of the core, that keep C and H excess. After thermal treatment at 1600°C a better homogeneity is achieved. Obviously, the specific microstructures of the different fibre

The first maps (Figs 10a, b & c-top), representing the distribution of a simple Raman parameter, may be of limited physical interest. However, it can be translated (through models) to a property' map (Colomban, 2003). The resulting image as exempled in (Fig. 11c-

For instance, the size of short-range ordered vibrational units in carbon moieties can be deduced from the Raman parameters. It is based on the ratio of the intensity, I, of the two

with the grain size Sg in nm and the constant C = 44 for 5145.5 nm laser excitation; this formula works well for relatively large grains (>2 nm). A new model (7) takes into account the Raman efficiency, d, of the D1340 with respect to that of G1600, as well as R, the ratio of atoms on the surface of each grain with respect to the bulk, et the surface thickness and Lg, the coherent length (~ the grain size of Tuinstra and Koenig model). Assuming a spherical shape of all

> 3 <sup>2</sup> 1 1 *<sup>t</sup> g*

*L* <sup>−</sup> <sup>×</sup> × ≈× − −

This model has been used to calculate the carbon grains size distribution in SA3TM fibre's cross sections. We observe that the intensity ratio is much higher in the core than near the surface and the carbon grain size appears approximately 2-3 times smaller on the fibre's core

The Raman data can be translated through equation 5 to a map of the maximum tolerable strain (Colomban, 2003). The resulting image (Fig. 12) clearly evidences that the fibre's mechanical properties are better (~ 3.5 GPa) in the core than near the surface (~ 2 GPa).

*<sup>D</sup>* 10 / *cm GPa* <sup>−</sup> Δ = (5)

DG l I /I C /S = g (6)

(7)

ν

grades can be analysed using a "simpler" and faster diameter line-scan (Fig. 4).

bottom) gives the distribution of physical parameters; we call it a "Smart image".

main carbon Raman peaks (ID/IG), as first proposed by Tiunstra & Koenig, 1970.

*<sup>e</sup> dR d*

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electrical properties during heat treatment of SiC fiber precursor, *Composite Sci. &* 

Characterization of ceramic composites and of their constituents – Precursors,

properties and r.f.–microwave conductivity of SiC (and/or mullite) fibre reinforced


**0**

**8**

*St. Petersburg*

1,2,3,4,5*Russia* <sup>6</sup>*Republic of Korea*

**Micropipe Reactions in Bulk SiC Growth**

<sup>1</sup>*Institute of Problems of Mechanical Engineering, RAS, St. Petersburg*

<sup>3</sup>*Department of Theory of Elasticity, St. Petersburg State University,*

<sup>2</sup>*Department of Physics of Materials Strength and Plasticity, St. Petersburg State*

<sup>6</sup>*X-ray Imaging Center, Department of Materials Science and Engineering, Pohang*

Structural defects in silicon carbide (SiC) single crystals such as dislocations, micropipes, inclusions, etc., have been investigated by different methods, including x-ray diffraction topography (Huang et al., 1999), visible light and scanning electron microscopies (SEM) (Epelbaum & Hofmann, 2001; Kamata et al., 2000), AFM and TEM (Yakimova et al., 2005). In particular, defects were imaged in polarized light (Ma, 2006) or made visible in electron beam-induced current and electroluminescence images (Wang et al., 2005). Their morphology has been classified and examined well enough. However, the correlation between structure and morphology still remains an important issue, in which a direct correspondence is complicated by transformation behaviors of structural defects. For example, micropipes superscrew dislocations with hollow cores (Frank, 1951; Huang et al., 1999) — can dissociate into full-core dislocations (Epelbaum & Hofmann, 2001; Kamata et al., 2000; Yakimova et al., 2005) and react with each other (Gutkin et al., 2009a; Ma, 2006) or with foreign polytype

Recent developments have stimulated the progress in defect studies. The push was the production of high-quality crystals (Müller et al., 2006; Nakamura et al., 2004). For example, 4*H*-SiC with micropipe densities as low as 0.7 cm−<sup>2</sup> is commercially available; and the growth of the epitaxial layers with a dislocation density < 10 cm−<sup>2</sup> has been demonstrated (Müller et al., 2006). Such low defect densities are very suitable for x-ray imaging techniques, whose development is pulled by the advent of synchrotron radiation (SR) sources. The combination of synchrotron x-ray topography and optical microscopy succeeded in shedding light on the elucidation of the origin and transformation of dislocations and stacking faults (Tsuchida et al., 2007). The highly coherent beams allowed to analyze dislocation types and structures (Nakamura et al., 2007; Wierzchowski et al., 2007), the Burgers vectors senses and

**1. Introduction**

inclusions (Gutkin et al., 2006; Ohtani et al., 2006).

M. Yu. Gutkin,1,2,3 T. S. Argunova,4,6 V. G. Kohn,<sup>5</sup>

<sup>4</sup>*Ioffe Physical-Technical Institute, RAS, St. Petersburg* <sup>5</sup>*National Research Center 'Kurchatov Institute', Moscow*

*University of Science and Technology, Pohang*

A. G. Sheinerman1 and J. H. Je<sup>6</sup>

*Polytechnical University, St. Petersburg*


### **Micropipe Reactions in Bulk SiC Growth**

M. Yu. Gutkin,1,2,3 T. S. Argunova,4,6 V. G. Kohn,<sup>5</sup> A. G. Sheinerman1 and J. H. Je<sup>6</sup> <sup>1</sup>*Institute of Problems of Mechanical Engineering, RAS, St. Petersburg* <sup>2</sup>*Department of Physics of Materials Strength and Plasticity, St. Petersburg State Polytechnical University, St. Petersburg* <sup>3</sup>*Department of Theory of Elasticity, St. Petersburg State University, St. Petersburg* <sup>4</sup>*Ioffe Physical-Technical Institute, RAS, St. Petersburg* <sup>5</sup>*National Research Center 'Kurchatov Institute', Moscow* <sup>6</sup>*X-ray Imaging Center, Department of Materials Science and Engineering, Pohang University of Science and Technology, Pohang* 1,2,3,4,5*Russia* <sup>6</sup>*Republic of Korea*

#### **1. Introduction**

186 Silicon Carbide – Materials, Processing and Applications in Electronic Devices

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Tanaka, T. Tamari, N. Kondoh, I. & Iwasa M., (1996). Fabrication and mechanical properties

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Toreki, W., Batich, C.D. & Choi, G.J. (1991). High molecular weight polycarbosilane as a precursor to oxygen free SiC fibers, *Abtr. Paper Am. Chem. Soc*., 202, 360-POLY Toreki, W.M., Batich, C.D., Sacks, M.D., Saleem, M., Choi, G.J. & Morrone, A.A. (1992).

Yajima, S., Okamura, K., Tanaka, J. & Hayase, T. (1980). Synthesis of aluminium composite

Yang, Y.M., Liu, X.W., Tan, Z.L., Yang, S.J., Lu, Y. & Feng, C.X. (1991). Synthesis of SiC fiber

Yano, M., Utatsu, T., Iwai, Y. & Inoue, F. (1995). A Raman scatering study on the interface

Weber, W.H., Hass, K.C. & McBride, J.R. (1993). Raman study of CeO2 – 2nd order scattering, lazttice dynamics and particle size effects, *Phys. Rev. B,* 48[1], 178-185. Wu, Y.-C., Wang, S.-F. & Lu, H.-Y. (2006). Stacking Faults and Stacking Fault Energy of

Wu,Y.-C., Wang, S.-F. & Chen, S.-H. (2009). Microstructural Investigation of Ba(Ti(1-x)Mnx)O3 Ceramics with 6H- and 12R-polytypes, *J. Am. Ceram. Soc.,* 92, 2099-2108.

thermomechanical stability, *Comp. Sci. Techn. Eng*., 1351[2], 145-159. Tronc, E., Moret, R. & Legendre, J.J. & Huber, M. (1975). Refinement of polytypes structure

12R Ti8S12*. Acta Crystallogr. Section B-Structure Sci.*, 31, 2800-2804.

organo-silicon precursor polymer, *J. Mater. Sci*., 15, 2130-2131.

molecular-beam epitaxy*. J. Cryst. Growth,* 150 [1-4], 868-873.

Hexagonal Barium Titanate, *J. Am. Ceram. Soc*., 89, 3778-3787.

polycarbosilane, *J. Ceram.* Soc. *Jpn*, 103, 1-5.

spectra of SiC, *Phys. Rev. B*, 62, 12896-12901.

*Mater. Sci*., 26[19], 5167-5170.

of polycarbosilane, *J. Ceram. Soc. Jpn*, 104, 454-457.

dimensional Tyranno fiber–reinforced SiC composites by repeated infiltration of

of 3-dimensional Tyranno fiber reinforced SiC composites by repeated infiltration

Selective resonance effect of the folded longitudinal phonon modes in the Raman

Polymer-derived silicon-carbide fibres with low-oxygen content and improved

reinforced with continuous SiC Fiber obtained from the precursor fiber of an

with low oxygen content and high tensile strength using a polyblend precursor, *J.* 

sharpness of INAS/ALSB/GASB/ALSB polytypes superlattices grown by

Structural defects in silicon carbide (SiC) single crystals such as dislocations, micropipes, inclusions, etc., have been investigated by different methods, including x-ray diffraction topography (Huang et al., 1999), visible light and scanning electron microscopies (SEM) (Epelbaum & Hofmann, 2001; Kamata et al., 2000), AFM and TEM (Yakimova et al., 2005). In particular, defects were imaged in polarized light (Ma, 2006) or made visible in electron beam-induced current and electroluminescence images (Wang et al., 2005). Their morphology has been classified and examined well enough. However, the correlation between structure and morphology still remains an important issue, in which a direct correspondence is complicated by transformation behaviors of structural defects. For example, micropipes superscrew dislocations with hollow cores (Frank, 1951; Huang et al., 1999) — can dissociate into full-core dislocations (Epelbaum & Hofmann, 2001; Kamata et al., 2000; Yakimova et al., 2005) and react with each other (Gutkin et al., 2009a; Ma, 2006) or with foreign polytype inclusions (Gutkin et al., 2006; Ohtani et al., 2006).

Recent developments have stimulated the progress in defect studies. The push was the production of high-quality crystals (Müller et al., 2006; Nakamura et al., 2004). For example, 4*H*-SiC with micropipe densities as low as 0.7 cm−<sup>2</sup> is commercially available; and the growth of the epitaxial layers with a dislocation density < 10 cm−<sup>2</sup> has been demonstrated (Müller et al., 2006). Such low defect densities are very suitable for x-ray imaging techniques, whose development is pulled by the advent of synchrotron radiation (SR) sources. The combination of synchrotron x-ray topography and optical microscopy succeeded in shedding light on the elucidation of the origin and transformation of dislocations and stacking faults (Tsuchida et al., 2007). The highly coherent beams allowed to analyze dislocation types and structures (Nakamura et al., 2007; Wierzchowski et al., 2007), the Burgers vectors senses and

Spectrum Effective size, *μ*m Divergence, *μ*rad Source-sample

Micropipe Reactions in Bulk SiC Growth 189

Sensitivity Matrix size, px View field, (H) CCD-sample

Source 6–40 keV 160(H) × 60(V) 5(H) × 2(V) 34 m

Table 1. Source and detector attributes for x-ray imaging

vectors **b**<sup>1</sup> and **b**2, respectively.

lead to their gradual healing.

**2. Samples and techniques**

down to ≈ 0.4 mm thick.

contrast and bragg-diffraction imaging.

Detector 14 bit 1600(H) × 1200(V) 4 mm–280 *μ*m 5 cm–1 m

during the crystal growth (Gutkin et al., 2008). This 'contact-free' reaction between two micropipes, MP1 and MP2, as illustrated in Fig. 1(b), is different with a 'contact' reaction [Fig. 1(a)]. Here MP1 and MP2 contain opposite-sign superscrew dislocations with Burgers

In the 'contact' reaction, the elastic attraction of the two opposite dislocations induces the gradual shift of the two micropipes to each other during the crystal growth, resulting in the formation of a new micropipe MP3 containing a new superscrew dislocation with the sum Burgers vector **b**<sup>3</sup> = **b**<sup>1</sup> + **b**2, *b*<sup>3</sup> < (*b*1, *b*2), where *bi* is the Burgers vector magnitude, *i* = 1, 2, 3. As the micropipe radius is in the quadratic dependence on its Burgers vector magnitude (Frank, 1951), the profit of this reaction is evident: instead of two micropipes we get only one with a much smaller radius. In the special case of *b*<sup>3</sup> = *b*0, where *b*<sup>0</sup> is the Burgers vector

In case of a contact-free interaction micropipe MP1 emits a full-core dislocation half-loop D, which expands by gliding, reaches the surface of micropipe MP2 and reacts with its dislocation. The corresponding dislocation reactions are described by equations: **b**<sup>1</sup> − **b**<sup>0</sup> = **b**<sup>3</sup> and **b**<sup>2</sup> + **b**<sup>0</sup> = **b**4, where **b**<sup>3</sup> and **b**<sup>4</sup> are the Burgers vectors of micropipes MP1 and MP2, respectively. This reaction explains the radii reduction of both micropipes by the emission of the full-core dislocation in MP1 and its absorption in MP2. Strong reduction in the radii can

Reaction between micropipes is always a positive process in view of their elimination during the crystal growth. Therefore, one should better understand the mechanisms of reactions and the factors stimulating such reactions. In our studies, micropipes are assumed to be screw dislocations with hollow cores (Huang et al., 1999), as made certain by combining phase

SiC crystals were grown by the sublimation sandwich method. In this technique Si-C vapor species brought from the source (polycrystalline SiC powder) are sublimated on the seed (a crystalline SiC wafer). The source and the seed are separated by a small distance and put into the growth container with an axial temperature gradient. To improve the quality of SiC crystals, a tantalum container was used (Vodakov et al., 1997). The container was filled with Ar (the Ar pressure: 80 mbar). The growth temperature was 2180◦ C, and the growth rate was 0.5 mm <sup>×</sup> <sup>h</sup>−1. Polytype inclusions were studied by using n-type crystals N-doped, with a donor concentration 2 <sup>×</sup> 1018 cm−3. They contained B to a concentration (1–2) <sup>×</sup> 1017 cm−3. Besides, doping of SiC by Al to a concentration of approximately (2–7) <sup>×</sup> 1017 cm−<sup>3</sup> occurred because of the presence of Al in the polycrystalline SiC source. The samples were on-axis wafers cut perpendicular to the [0001] growth direction and axial-cut slices along the growth direction obtained from 4*H* and 6*H* boules. The wafers were polished from the both sides

magnitude of the elemental full-core dislocation, micropipe MP3 is normally healed.

Fig. 1. Sketch of the contact (a) and contact-free (b) reactions between micropipes MP1 and MP2 in a longitudinal section of growing SiC crystal. (a) The micropipes contain superscrew dislocations with opposite Burgers vectors **b**<sup>1</sup> and **b**2. The micropipes meet each other and react, forming a new micropipe MP3 that contains a superscrew dislocation with the sum Burgers vector **b**3=**b**1+**b**2. (b) The micropipes contain superscrew dislocations with opposite Burgers vectors **b**<sup>1</sup> and **b**2. Micropipe MP1 emits a half-loop of full-core dislocation D with Burgers vector **b**0. As a result, the Burgers vector of MP1 changes from **b**<sup>1</sup> to **b**3=**b**1-**b**0, and the radius of MP1 decreases. Dislocation D glides from MP1 to MP2; the frontal (top) segment of D is absorbed by MP2. Micropipe MP2 changes its Burgers vector from **b**<sup>2</sup> to **b**4=**b**2+**b**0, and, as a consequence, also decreases its radius.

magnitudes (Chen et al., 2008; Nakamura et al., 2008), and the propagation and distribution of threading dislocations (Kamata et al., 2009) in detail .

A decisive advantage of third generation SR sources is the availability of phase contrast imaging which has a strong potential for studying hollow defects in SiC. To image objects with relatively small cross sections, such as micropipes, high temporal coherence is not necessary; and the spatial coherence required is directly yielded by SR source. In this work, we briefly survey the results of white beam phase contrast imaging to investigate the reactions of micropipes in SiC. We also give a short review of their experimental characterization, theoretical modeling, and computer simulation. The improvement of the crystal quality enabled us to develop our research from the collective effects in dense groups of micropipes to remote interactions between distant micropipes. The morphology of individual micropipe, which was not resolvable by diffraction topography, has been examined by phase-contrast imaging. The computer simulation of phase contrast images allowed us to determine the cross-section sizes of micropipes (Kohn et al., 2007).

In our experimental studies, different transformations and reactions between micropipes in SiC crystals have been documented: ramification of a dislocated micropipe into two smaller ones (Gutkin et al., 2002); bundling and merging that led to the generation of new micropipes or annihilation of initial ones (Gutkin et al., 2003a;b); and interaction of micropipes with foreign polytype inclusions (Gutkin et al., 2006) followed by agglomeration and coalescence of micropipes into pores (Gutkin et al., 2009b).

Theoretical analyses of micropipes interactions show that micropipe split happens if the splitting dislocation overcomes the pipe attraction zone and the crystal surface attraction zone; bundling and twisting of dislocation dipoles arise when two micropipes are under strong stress fields from dense groups of other micropipes; micropipes are attracted by foreign polytype inclusion stress fields, initiating the nucleation and growth of pore on the inclusion. When micropipes come in contact with each other [Fig. 1(a)], strong interactions occur. Such interactions are expected to become less probable for low micropipe densities. In the meanwhile, remote elastic interactions between dislocations were detected and known to govern the propagation of elementary screw dislocations (Nakamura et al., 2008). In our study we experimentally measured the variation in cross-sections of two neighboring micropipes and revealed that they reduced their diameters (approximately by half) one after another 2 Will-be-set-by-IN-TECH

(b)

**b2**

**b0** D

**b1**

MP2

**b4**

**b3**

MP1

MP3

Fig. 1. Sketch of the contact (a) and contact-free (b) reactions between micropipes MP1 and MP2 in a longitudinal section of growing SiC crystal. (a) The micropipes contain superscrew dislocations with opposite Burgers vectors **b**<sup>1</sup> and **b**2. The micropipes meet each other and react, forming a new micropipe MP3 that contains a superscrew dislocation with the sum Burgers vector **b**3=**b**1+**b**2. (b) The micropipes contain superscrew dislocations with opposite Burgers vectors **b**<sup>1</sup> and **b**2. Micropipe MP1 emits a half-loop of full-core dislocation D with Burgers vector **b**0. As a result, the Burgers vector of MP1 changes from **b**<sup>1</sup> to **b**3=**b**1-**b**0, and the radius of MP1 decreases. Dislocation D glides from MP1 to MP2; the frontal (top) segment of D is absorbed by MP2. Micropipe MP2 changes its Burgers vector from **b**<sup>2</sup> to

magnitudes (Chen et al., 2008; Nakamura et al., 2008), and the propagation and distribution

A decisive advantage of third generation SR sources is the availability of phase contrast imaging which has a strong potential for studying hollow defects in SiC. To image objects with relatively small cross sections, such as micropipes, high temporal coherence is not necessary; and the spatial coherence required is directly yielded by SR source. In this work, we briefly survey the results of white beam phase contrast imaging to investigate the reactions of micropipes in SiC. We also give a short review of their experimental characterization, theoretical modeling, and computer simulation. The improvement of the crystal quality enabled us to develop our research from the collective effects in dense groups of micropipes to remote interactions between distant micropipes. The morphology of individual micropipe, which was not resolvable by diffraction topography, has been examined by phase-contrast imaging. The computer simulation of phase contrast images allowed us to determine the

In our experimental studies, different transformations and reactions between micropipes in SiC crystals have been documented: ramification of a dislocated micropipe into two smaller ones (Gutkin et al., 2002); bundling and merging that led to the generation of new micropipes or annihilation of initial ones (Gutkin et al., 2003a;b); and interaction of micropipes with foreign polytype inclusions (Gutkin et al., 2006) followed by agglomeration and coalescence

Theoretical analyses of micropipes interactions show that micropipe split happens if the splitting dislocation overcomes the pipe attraction zone and the crystal surface attraction zone; bundling and twisting of dislocation dipoles arise when two micropipes are under strong stress fields from dense groups of other micropipes; micropipes are attracted by foreign polytype inclusion stress fields, initiating the nucleation and growth of pore on the inclusion. When micropipes come in contact with each other [Fig. 1(a)], strong interactions occur. Such interactions are expected to become less probable for low micropipe densities. In the meanwhile, remote elastic interactions between dislocations were detected and known to govern the propagation of elementary screw dislocations (Nakamura et al., 2008). In our study we experimentally measured the variation in cross-sections of two neighboring micropipes and revealed that they reduced their diameters (approximately by half) one after another

**b3**

**b**4=**b**2+**b**0, and, as a consequence, also decreases its radius.

of threading dislocations (Kamata et al., 2009) in detail .

cross-section sizes of micropipes (Kohn et al., 2007).

of micropipes into pores (Gutkin et al., 2009b).

**b2**

**b1**

MP2

(a)

MP1


Table 1. Source and detector attributes for x-ray imaging

during the crystal growth (Gutkin et al., 2008). This 'contact-free' reaction between two micropipes, MP1 and MP2, as illustrated in Fig. 1(b), is different with a 'contact' reaction [Fig. 1(a)]. Here MP1 and MP2 contain opposite-sign superscrew dislocations with Burgers vectors **b**<sup>1</sup> and **b**2, respectively.

In the 'contact' reaction, the elastic attraction of the two opposite dislocations induces the gradual shift of the two micropipes to each other during the crystal growth, resulting in the formation of a new micropipe MP3 containing a new superscrew dislocation with the sum Burgers vector **b**<sup>3</sup> = **b**<sup>1</sup> + **b**2, *b*<sup>3</sup> < (*b*1, *b*2), where *bi* is the Burgers vector magnitude, *i* = 1, 2, 3. As the micropipe radius is in the quadratic dependence on its Burgers vector magnitude (Frank, 1951), the profit of this reaction is evident: instead of two micropipes we get only one with a much smaller radius. In the special case of *b*<sup>3</sup> = *b*0, where *b*<sup>0</sup> is the Burgers vector magnitude of the elemental full-core dislocation, micropipe MP3 is normally healed.

In case of a contact-free interaction micropipe MP1 emits a full-core dislocation half-loop D, which expands by gliding, reaches the surface of micropipe MP2 and reacts with its dislocation. The corresponding dislocation reactions are described by equations: **b**<sup>1</sup> − **b**<sup>0</sup> = **b**<sup>3</sup> and **b**<sup>2</sup> + **b**<sup>0</sup> = **b**4, where **b**<sup>3</sup> and **b**<sup>4</sup> are the Burgers vectors of micropipes MP1 and MP2, respectively. This reaction explains the radii reduction of both micropipes by the emission of the full-core dislocation in MP1 and its absorption in MP2. Strong reduction in the radii can lead to their gradual healing.

Reaction between micropipes is always a positive process in view of their elimination during the crystal growth. Therefore, one should better understand the mechanisms of reactions and the factors stimulating such reactions. In our studies, micropipes are assumed to be screw dislocations with hollow cores (Huang et al., 1999), as made certain by combining phase contrast and bragg-diffraction imaging.

#### **2. Samples and techniques**

SiC crystals were grown by the sublimation sandwich method. In this technique Si-C vapor species brought from the source (polycrystalline SiC powder) are sublimated on the seed (a crystalline SiC wafer). The source and the seed are separated by a small distance and put into the growth container with an axial temperature gradient. To improve the quality of SiC crystals, a tantalum container was used (Vodakov et al., 1997). The container was filled with Ar (the Ar pressure: 80 mbar). The growth temperature was 2180◦ C, and the growth rate was 0.5 mm <sup>×</sup> <sup>h</sup>−1. Polytype inclusions were studied by using n-type crystals N-doped, with a donor concentration 2 <sup>×</sup> 1018 cm−3. They contained B to a concentration (1–2) <sup>×</sup> 1017 cm−3. Besides, doping of SiC by Al to a concentration of approximately (2–7) <sup>×</sup> 1017 cm−<sup>3</sup> occurred because of the presence of Al in the polycrystalline SiC source. The samples were on-axis wafers cut perpendicular to the [0001] growth direction and axial-cut slices along the growth direction obtained from 4*H* and 6*H* boules. The wafers were polished from the both sides down to ≈ 0.4 mm thick.

as

respectively.

where *Wc* <sup>≈</sup> *Gb*<sup>2</sup>

+ *Gb*<sup>0</sup> 2*π*

to the latter relation for Δ*W* yields:

Δ*W* = *b*0*τ*<sup>0</sup>

 1 + ln

+ *Gb*<sup>2</sup> 0 4*π*

*b*<sup>1</sup> − *b*<sup>0</sup>

 *<sup>x</sup>* <sup>−</sup> *<sup>r</sup>*<sup>2</sup> 1 *x* + *r*2 2 *<sup>d</sup>* <sup>−</sup> *<sup>x</sup>* <sup>−</sup> *<sup>r</sup>*<sup>2</sup>

> *<sup>x</sup>*<sup>2</sup> <sup>−</sup> *<sup>r</sup>*<sup>2</sup> 1

the emitted dislocation, situated in between the micropipes.

second one strongly. The first barrier has the height of about 1.5*Gb*<sup>2</sup>

*<sup>x</sup>* <sup>−</sup> *<sup>b</sup>*<sup>2</sup>

*d* − *x* + *b*0 *<sup>x</sup>* <sup>−</sup> *<sup>b</sup>*0*<sup>x</sup> <sup>x</sup>*<sup>2</sup> <sup>−</sup> *<sup>r</sup>*<sup>2</sup> 1

The energy Δ*W* associated with dislocation emission is given by Δ*W* = *<sup>x</sup>*−*b*<sup>0</sup>

*F* (*d* � *r*1,*r*2) ≈ *b*0*τyz* (1)

<sup>0</sup>/(4*π*) is the dislocation core energy (Hirth & Lothe, 1982). Substitution of (1)

2*b*<sup>1</sup> *b*0

ln *<sup>r</sup>*<sup>1</sup> *x* + 2*b*<sup>2</sup> *b*0

where *G* is the shear modulus. In brackets of formula (1), the first and second terms correspond to the interactions of the emitted dislocation with dislocations within micropipes MP1 and MP2, respectively; the third-fourth and fifth-sixth terms correspond to the image force (Gutkin & Sheinerman, 2002; Pirouz, 1998) exerted by the surface of MP1 and MP2,

Micropipe Reactions in Bulk SiC Growth 191

2 *d* − *r*<sup>1</sup>

(*<sup>d</sup>* <sup>−</sup> *<sup>x</sup>*)<sup>2</sup> <sup>−</sup> *<sup>r</sup>*<sup>2</sup>

In the following calculations, we will use the Frank relation (Frank, 1951) *ri* = *Gb*<sup>2</sup>

micropipe dislocations and on the level of thermal shear stress *τ*<sup>0</sup> [Fig. 2(b,c)].

*<sup>b</sup>*0*r*1(*<sup>d</sup>* <sup>−</sup> *<sup>x</sup>*)<sup>2</sup> <sup>+</sup>

between the Burgers vectors magnitudes *bi* and micropipe radii *ri*, where *γ* is the surface energy. Numerical evaluation of Δ*W* for the case of growing 4*H*-SiC crystal with *G* = 165 GPa, *<sup>γ</sup>*/*<sup>G</sup>* <sup>=</sup> 1.4 · <sup>10</sup>−<sup>3</sup> nm (Si et al., 1997) and equilibrium micropipes [for which the Frank relation (Frank, 1951) is valid] shows that Δ*W* depends primarily on the Burgers vectors of

Let us first consider the case when *τ*<sup>0</sup> = 0 [Fig. 2(b)]. As is seen, the dislocation exchange is most energetically favorable if the Burgers vectors **b**<sup>1</sup> and **b**<sup>2</sup> are opposite in sign. At the same time, to move from one micropipe to the other, the emitted dislocation must overcome an energetic barrier. If the Burgers vectors of the two micropipes are of the same sign, the emitted dislocation must overcome two energetic barriers on its way from one micropipe to the other. In this case, the possibility for the dislocation exchange between these micropipes is governed by the difference of the Burgers vector magnitudes. If (*b*<sup>1</sup> − *b*2) < 3*b*0, then we have: Δ*W* > 0, and the dislocation exchange is impossible. If (*b*<sup>1</sup> − *b*<sup>2</sup> ≥ 3*b*0), then the dislocation reaction can occur if the emitted dislocation is able to overcome the two energetic barriers. The presence of two energetic barriers results in the appearance of an equilibrium position for

Figure 2(c) shows the case where micropipes initially have the same Burgers vectors, equal in magnitude to 7*b*0, and the dislocation emission occurs under the action of a thermal shear stress *τ*0. One can see that the stress *τ*<sup>0</sup> reduces the energetic barriers for the dislocation exchange. In the range of stress values from 10 to 100 MPa, which are characteristic for bulk SiC growth (Ma et al., 2003; Müller et al., 2000), the first barrier decreases weakly while the

length, which for a 4*H*-SiC crystal with *<sup>G</sup>* <sup>=</sup> 165 GPa and *<sup>b</sup>*<sup>0</sup> <sup>=</sup> 1 nm gives <sup>≈</sup> 0.48*Gb*<sup>2</sup>

125 eV per unit distance *l* ≈ 0.252 nm (Dudley et al., 2003) between basal atomic planes. This value is obviously very high that is not surprising due to the model of an infinite medium considered within the classical theory of linear elasticity. Moreover, in reality, the dislocation

2  <sup>−</sup> *<sup>b</sup>*<sup>0</sup> *d* − *x* +

*b*0(*d* − *x*) (*<sup>d</sup>* <sup>−</sup> *<sup>x</sup>*)<sup>2</sup> <sup>−</sup> *<sup>r</sup>*<sup>2</sup>

> ln *<sup>d</sup> d* − *x*

 .

<sup>0</sup>/*π* per unit dislocation

<sup>0</sup>*l* ≈

2

 ,

*<sup>r</sup>*<sup>1</sup> *F*(*x*)*dx* + *Wc*,

(2)

*<sup>i</sup>* /(8*π*2*γ*)

X-ray imaging experiments were performed on the 7B2 X-ray Microscopy beamline at the Pohang Light Source (PLS) in Pohang, Korea. The source was the 7B2 bending magnet port of the PLS storage ring. Unmonochromatized ('white') beam was propagated through polished beryllium window of 2 mm thick and then through a specimen with no optical elements in between. Passing through a CdWO4 scintillator crystal of 200 *μ*m thick, the X-ray beam was converted to visible lights, which were then reflected from a mirror (a polished silicon wafer) and directed to a detector with a charge coupled device (CCD) matrix. The source and the detector attributes are listed in table 1. Prior to recording, the visible light image was magnified by a lens system with the magnification 1 × – 50 ×. Under a low magnification [for example, by using 1500 *μ*m (H) view field] the overall defect density and distribution were visualized. The ≈ 300 *μ*m (H) view field provided a very useful enlargement for the examination of micropipes. Optical micrographs were taken on a Zeiss universal microscope equipped with a CCD. Scanning electron microscopy was done on a JEOL JSM-6330F FESEM operating at 12 kV. Photoluminescence (PL) images of polytype inclusions were taken with the PL microscope in visible as well as ultraviolet lights under the magnifications of 50× – 200×.

#### **3. Contact-free reactions between micropipes**

#### **3.1 Model**

Let us turn back to Fig. 1(b) sketching the contact-free reaction between two micropipes. Direct experimental justifications of this mechanism has not been provided up to now. However, using computer simulation of phase contrast images (Kohn et al., 2007), we have demonstrated the correlated reduction in the radii of two remote micropipes in SiC (Gutkin et al., 2008). As shown below, this effect indirectly supports our model.

The first stage of the contact-free reaction is the split of a dislocation from a micropipe at the crystal growth front. Recently the possibility of such a split event has been analyzed within a three-dimensional model (Gutkin & Sheinerman, 2004). Here we consider a simplified two-dimensional model of a contact-free reaction between two parallel micropipes. Fig. 2 shows micropipes with circular cross sections of the radii *r*<sup>1</sup> and *r*<sup>2</sup> that contain screw dislocations with the Burgers vectors **b**<sup>1</sup> and **b**2, respectively. The distance between the micropipe axes is denoted as *d*. Let the first micropipe emits a screw full-core dislocation with the Burgers vector **b**<sup>0</sup> [Fig. 2(a)]. We also assume that a shear stress *τ*<sup>0</sup> = *τ*<sup>0</sup> *yz* associated with thermal stresses appearing during the growth of SiC acts in the region between the examined micropipes and far from their surfaces. To analyze the possibility of the emission, we can use the corresponding variation Δ*W* on the total energy of the system. It is calculated (per unit dislocation length) using the previous results (Gutkin & Sheinerman, 2002; Gutkin et al., 2009c) for the stresses and energies of dislocations lying in an isotropic medium with two cylindrical voids. However, in the case of interest, when *d* � *r*1,*r*2, it is sufficient to separately consider the effects of the two voids on the shear stress as well as on the image force exerted by the micropipe surfaces on the emitted dislocation and the forces of dislocation interaction. In this approximation, the thermal shear stress *τyz* acting on the emitted dislocation in between the micropipes, taken with account for the stress concentration near their surfaces, is *τyz* = *τ*0[1 + *r*<sup>2</sup> <sup>1</sup>/*x*<sup>2</sup> <sup>+</sup> *<sup>r</sup>*<sup>2</sup> <sup>2</sup>/(*<sup>d</sup>* <sup>−</sup> *<sup>x</sup>*)2], where *<sup>x</sup>* is the coordinate of the emitted dislocation. The second and third terms in brackets reflect the effects of the first and second void (Thölén, 1970), respectively, in the limiting case *d* � *r*1,*r*<sup>2</sup> when the mutual influence of the voids is negligible. The total elastic force acting on the emitted dislocation (per its unit length) follows

$$\begin{split} F\left(d \gg r\_1, r\_2\right) &\approx b\_0 \mathbf{r}\_{yz} \\ + \frac{G b\_0}{2\pi} \left\{ \frac{b\_1 - b\_0}{\mathbf{x}} - \frac{b\_2}{d - \mathbf{x}} + \frac{b\_0}{\mathbf{x}} - \frac{b\_0 \mathbf{x}}{\mathbf{x}^2 - r\_1^2} - \frac{b\_0}{d - \mathbf{x}} + \frac{b\_0 (d - \mathbf{x})}{(d - \mathbf{x})^2 - r\_2^2} \right\}, \end{split} \tag{1}$$

where *G* is the shear modulus. In brackets of formula (1), the first and second terms correspond to the interactions of the emitted dislocation with dislocations within micropipes MP1 and MP2, respectively; the third-fourth and fifth-sixth terms correspond to the image force (Gutkin & Sheinerman, 2002; Pirouz, 1998) exerted by the surface of MP1 and MP2, respectively.

The energy Δ*W* associated with dislocation emission is given by Δ*W* = *<sup>x</sup>*−*b*<sup>0</sup> *<sup>r</sup>*<sup>1</sup> *F*(*x*)*dx* + *Wc*, where *Wc* <sup>≈</sup> *Gb*<sup>2</sup> <sup>0</sup>/(4*π*) is the dislocation core energy (Hirth & Lothe, 1982). Substitution of (1) to the latter relation for Δ*W* yields:

$$
\Delta W = b\_0 \pi^0 \left( \mathbf{x} - \frac{r\_1^2}{\mathbf{x}} + \frac{r\_2^2}{d - \mathbf{x}} - \frac{r\_2^2}{d - r\_1} \right) \tag{2}
$$

$$
+ \frac{Gb\_0^2}{4\pi} \left\{ 1 + \ln \frac{(\mathbf{x}^2 - r\_1^2) \left[ (d - \mathbf{x})^2 - r\_2^2 \right]}{b\_0 r\_1 (d - \mathbf{x})^2} + \frac{2b\_1}{b\_0} \ln \frac{r\_1}{\mathbf{x}} + \frac{2b\_2}{b\_0} \ln \frac{d}{d - \mathbf{x}} \right\}.
$$

In the following calculations, we will use the Frank relation (Frank, 1951) *ri* = *Gb*<sup>2</sup> *<sup>i</sup>* /(8*π*2*γ*) between the Burgers vectors magnitudes *bi* and micropipe radii *ri*, where *γ* is the surface energy. Numerical evaluation of Δ*W* for the case of growing 4*H*-SiC crystal with *G* = 165 GPa, *<sup>γ</sup>*/*<sup>G</sup>* <sup>=</sup> 1.4 · <sup>10</sup>−<sup>3</sup> nm (Si et al., 1997) and equilibrium micropipes [for which the Frank relation (Frank, 1951) is valid] shows that Δ*W* depends primarily on the Burgers vectors of micropipe dislocations and on the level of thermal shear stress *τ*<sup>0</sup> [Fig. 2(b,c)].

Let us first consider the case when *τ*<sup>0</sup> = 0 [Fig. 2(b)]. As is seen, the dislocation exchange is most energetically favorable if the Burgers vectors **b**<sup>1</sup> and **b**<sup>2</sup> are opposite in sign. At the same time, to move from one micropipe to the other, the emitted dislocation must overcome an energetic barrier. If the Burgers vectors of the two micropipes are of the same sign, the emitted dislocation must overcome two energetic barriers on its way from one micropipe to the other. In this case, the possibility for the dislocation exchange between these micropipes is governed by the difference of the Burgers vector magnitudes. If (*b*<sup>1</sup> − *b*2) < 3*b*0, then we have: Δ*W* > 0, and the dislocation exchange is impossible. If (*b*<sup>1</sup> − *b*<sup>2</sup> ≥ 3*b*0), then the dislocation reaction can occur if the emitted dislocation is able to overcome the two energetic barriers. The presence of two energetic barriers results in the appearance of an equilibrium position for the emitted dislocation, situated in between the micropipes.

Figure 2(c) shows the case where micropipes initially have the same Burgers vectors, equal in magnitude to 7*b*0, and the dislocation emission occurs under the action of a thermal shear stress *τ*0. One can see that the stress *τ*<sup>0</sup> reduces the energetic barriers for the dislocation exchange. In the range of stress values from 10 to 100 MPa, which are characteristic for bulk SiC growth (Ma et al., 2003; Müller et al., 2000), the first barrier decreases weakly while the second one strongly. The first barrier has the height of about 1.5*Gb*<sup>2</sup> <sup>0</sup>/*π* per unit dislocation length, which for a 4*H*-SiC crystal with *<sup>G</sup>* <sup>=</sup> 165 GPa and *<sup>b</sup>*<sup>0</sup> <sup>=</sup> 1 nm gives <sup>≈</sup> 0.48*Gb*<sup>2</sup> <sup>0</sup>*l* ≈ 125 eV per unit distance *l* ≈ 0.252 nm (Dudley et al., 2003) between basal atomic planes. This value is obviously very high that is not surprising due to the model of an infinite medium considered within the classical theory of linear elasticity. Moreover, in reality, the dislocation

as

4 Will-be-set-by-IN-TECH

X-ray imaging experiments were performed on the 7B2 X-ray Microscopy beamline at the Pohang Light Source (PLS) in Pohang, Korea. The source was the 7B2 bending magnet port of the PLS storage ring. Unmonochromatized ('white') beam was propagated through polished beryllium window of 2 mm thick and then through a specimen with no optical elements in between. Passing through a CdWO4 scintillator crystal of 200 *μ*m thick, the X-ray beam was converted to visible lights, which were then reflected from a mirror (a polished silicon wafer) and directed to a detector with a charge coupled device (CCD) matrix. The source and the detector attributes are listed in table 1. Prior to recording, the visible light image was magnified by a lens system with the magnification 1 × – 50 ×. Under a low magnification [for example, by using 1500 *μ*m (H) view field] the overall defect density and distribution were visualized. The ≈ 300 *μ*m (H) view field provided a very useful enlargement for the examination of micropipes. Optical micrographs were taken on a Zeiss universal microscope equipped with a CCD. Scanning electron microscopy was done on a JEOL JSM-6330F FESEM operating at 12 kV. Photoluminescence (PL) images of polytype inclusions were taken with the PL microscope in visible as well as ultraviolet lights under the magnifications of 50× – 200×.

Let us turn back to Fig. 1(b) sketching the contact-free reaction between two micropipes. Direct experimental justifications of this mechanism has not been provided up to now. However, using computer simulation of phase contrast images (Kohn et al., 2007), we have demonstrated the correlated reduction in the radii of two remote micropipes in SiC

The first stage of the contact-free reaction is the split of a dislocation from a micropipe at the crystal growth front. Recently the possibility of such a split event has been analyzed within a three-dimensional model (Gutkin & Sheinerman, 2004). Here we consider a simplified two-dimensional model of a contact-free reaction between two parallel micropipes. Fig. 2 shows micropipes with circular cross sections of the radii *r*<sup>1</sup> and *r*<sup>2</sup> that contain screw dislocations with the Burgers vectors **b**<sup>1</sup> and **b**2, respectively. The distance between the micropipe axes is denoted as *d*. Let the first micropipe emits a screw full-core dislocation with

thermal stresses appearing during the growth of SiC acts in the region between the examined micropipes and far from their surfaces. To analyze the possibility of the emission, we can use the corresponding variation Δ*W* on the total energy of the system. It is calculated (per unit dislocation length) using the previous results (Gutkin & Sheinerman, 2002; Gutkin et al., 2009c) for the stresses and energies of dislocations lying in an isotropic medium with two cylindrical voids. However, in the case of interest, when *d* � *r*1,*r*2, it is sufficient to separately consider the effects of the two voids on the shear stress as well as on the image force exerted by the micropipe surfaces on the emitted dislocation and the forces of dislocation interaction. In this approximation, the thermal shear stress *τyz* acting on the emitted dislocation in between the micropipes, taken with account for the stress concentration near their surfaces,

The second and third terms in brackets reflect the effects of the first and second void (Thölén, 1970), respectively, in the limiting case *d* � *r*1,*r*<sup>2</sup> when the mutual influence of the voids is negligible. The total elastic force acting on the emitted dislocation (per its unit length) follows

<sup>2</sup>/(*<sup>d</sup>* <sup>−</sup> *<sup>x</sup>*)2], where *<sup>x</sup>* is the coordinate of the emitted dislocation.

*yz* associated with

(Gutkin et al., 2008). As shown below, this effect indirectly supports our model.

the Burgers vector **b**<sup>0</sup> [Fig. 2(a)]. We also assume that a shear stress *τ*<sup>0</sup> = *τ*<sup>0</sup>

**3. Contact-free reactions between micropipes**

**3.1 Model**

is *τyz* = *τ*0[1 + *r*<sup>2</sup>

<sup>1</sup>/*x*<sup>2</sup> <sup>+</sup> *<sup>r</sup>*<sup>2</sup>

100 200 300 400 500 0

MP1

MP2

100 200 300 400

200 300 400

(b)

Micropipe Reactions in Bulk SiC Growth 193

Fig. 3. (a) Variation in cross-section sizes along the axes of MP1 and MP2 from the group of micropipes (squares – transverse and circles – longitudinal diameters, respectively); (b) phase contrast image of the group (the growth direction is from left to right); (c) optical micrograph in transmission light of MP2 lying remotely from two micropipes in contact.

group and the optical micrograph of the remote micropipe MP2 are demonstrated in (b) and

For all sample-to-detector distances and for different points along the axis of micropipes, the intensity profiles normal to the axis were measured. To determine the characteristic sizes of the micropipe cross sections in different points along the micropipe axis, we applied a computer simulation (Kohn et al., 2007) of the measured intensity profiles, assuming that these sections can have variations in longitudinal (along the beam) and transverse (across the beam) sizes. For every micropipe cross section under investigation, the computer program calculated many profiles for various possible section sizes on the base of Kirchhoff propagation (Kohn et al., 2007) to find the profile, which gives the best fit to the experimental profile registered for this section. The coincidence allowed us to determine both the longitudinal and transverse sizes of the section. We found that the micropipes had elliptical cross sections extended in transverse direction. The transverse and longitudinal diameters of micropipes MP1 and MP2 are presented in Fig. 3(a) versus the distance along the pipe axes increasing in the growth direction. It is seen that, with growth, the transverse size of MP1 reduces from 7.4 to 2.1 *μ*m. At the same time, the transverse size of the MP2 reduces from 4.1 to 1.6 *μ*m. In contrast, the longitudinal diameters remain almost the same and of the order of 0.8 *μ*m for the MP1 and 0.5 *μ*m for the MP2. In the correlated decrease of MP1 and MP2 cross section sizes in Fig. 3(b) several features are apparent. A remarkable decrease of the MP1 cross section size occurs in the distance interval from 74 to 132 *μ*m while the transverse diameter of MP2 drastically decreases later in the distance interval from 314 to 345 *μ*m. In addition, a rapid decrease of the transverse diameter of MP1 happens in the distance interval from 393 to

458 *μ*m when the transverse diameter of MP2 remains almost invariable.

We explain the changes in the cross sections of the two neighboring micropipes by the contact-free reaction between them. Experimental data in Fig. 3(a, b) tend to confirm the reaction schematically shown in Fig. 1(b). Most likely, during the rapid decrease of its cross section area MP1 emits a full-core dislocation moving towards MP2 and finally absorbed by

50 μ m

50 μm

MP2

MP2

MP1

Distance along pipe, μm

(a) (c)

it.

<sup>8</sup>Section size<sup>μ</sup> <sup>m</sup>

(c), respectively.

MP1

MP2

Fig. 2. A model of contact-free reaction between two micropipes realized through screw dislocation exchange. Micropipe MP1 emits a dislocation with the Burgers vector **b**0, which moves to micropipe MP2 and is absorbed by it (a). Dependences of the energy Δ*W* associated with the emission of a dislocation by a micropipe near a second micropipe on the normalized dislocation coordinate *<sup>x</sup>*/*r*<sup>1</sup> for *<sup>d</sup>*/*r*<sup>1</sup> <sup>=</sup> 20 and *<sup>b</sup>*1/*b*<sup>0</sup> <sup>=</sup> 7. (b) *<sup>τ</sup>*<sup>0</sup> <sup>=</sup> 0 and *<sup>b</sup>*2/*b*<sup>0</sup> <sup>=</sup> <sup>−</sup>7, <sup>−</sup>5, <sup>−</sup>2, 2, 5, 7 (from bottom to top). (c) *b*2/*b*<sup>0</sup> = 7 and *τ*<sup>0</sup> = 0, 10, 50, and 100 MPa. The energy Δ*W* is given in units of *Gb*<sup>2</sup> <sup>0</sup>/4*π*, the stress values are given at the curves in MPa.

emission is expected to occur within a rather thin subsurface layer under the growth front where the conditions can be very far from equilibrium due to high temperature and surface effects. The height of the second barrier is approximately five times higher at *τ*<sup>0</sup> = 0 but it falls down to <sup>≈</sup> 0.16*Gb*<sup>2</sup> <sup>0</sup>*<sup>l</sup>* at *<sup>τ</sup>*<sup>0</sup> <sup>=</sup> 100 MPa. The equilibrium position of the emitted dislocation increases from <sup>≈</sup> <sup>9</sup>*r*<sup>1</sup> at *<sup>τ</sup>*<sup>0</sup> <sup>=</sup> 0 to <sup>≈</sup> <sup>17</sup>*r*<sup>1</sup> at *<sup>τ</sup>*<sup>0</sup> <sup>=</sup> 100 MPa. One can conclude that thermal shear stress greatly promotes dislocation transfer and makes it possible even in the case of micropipes having large Burgers vectors of the same sign.

#### **3.2 Correlated reduction in micropipe cross sections in SiC growth**

To observe micropipe cross-sections at different distances from the surface of a grown crystal, we prepared a special sample, which was axial-cut slice along the growth direction (0001) obtained from 4*H*-SiC boule. So micropipes located almost parallel to the growth axis were nearly parallel to the surface. Micropipes grouped along the boundaries of foreign polytype inclusions (6*H* and 12*R*) which appeared at ≈ 1 cm distance from the seed/boule interface. Below the inclusions over the area of 1 cm2 micropipes were undetectable. The sample (rotated to have a horizontal position of the micropipe axis for better edge enhancement in a more coherent vertical direction) was sequentially placed at different distances from the detector. We obtained nine images for the distances from 5 to 45 cm starting with the first image registered at 5 cm from the sample. Three micropipes forming a group were examined: two in contact and the third lying remotely. The variation in cross-section sizes along the axes of MP1 and MP2 from the group are shown in Fig. 3(a), while phase contrast image of the 6 Will-be-set-by-IN-TECH

5 10 15 *x/r1*

τ = 0

10

50

100

5 10 15 *x/r1*

0 -20 -40 -60

0

(b)

Δ*W*




Fig. 2. A model of contact-free reaction between two micropipes realized through screw dislocation exchange. Micropipe MP1 emits a dislocation with the Burgers vector **b**0, which moves to micropipe MP2 and is absorbed by it (a). Dependences of the energy Δ*W* associated with the emission of a dislocation by a micropipe near a second micropipe on the normalized dislocation coordinate *<sup>x</sup>*/*r*<sup>1</sup> for *<sup>d</sup>*/*r*<sup>1</sup> <sup>=</sup> 20 and *<sup>b</sup>*1/*b*<sup>0</sup> <sup>=</sup> 7. (b) *<sup>τ</sup>*<sup>0</sup> <sup>=</sup> 0 and *<sup>b</sup>*2/*b*<sup>0</sup> <sup>=</sup> <sup>−</sup>7, <sup>−</sup>5, <sup>−</sup>2, 2, 5, 7 (from bottom to top). (c) *b*2/*b*<sup>0</sup> = 7 and *τ*<sup>0</sup> = 0, 10, 50, and 100 MPa. The energy Δ*W* is

<sup>0</sup>/4*π*, the stress values are given at the curves in MPa. emission is expected to occur within a rather thin subsurface layer under the growth front where the conditions can be very far from equilibrium due to high temperature and surface effects. The height of the second barrier is approximately five times higher at *τ*<sup>0</sup> = 0 but it

increases from <sup>≈</sup> <sup>9</sup>*r*<sup>1</sup> at *<sup>τ</sup>*<sup>0</sup> <sup>=</sup> 0 to <sup>≈</sup> <sup>17</sup>*r*<sup>1</sup> at *<sup>τ</sup>*<sup>0</sup> <sup>=</sup> 100 MPa. One can conclude that thermal shear stress greatly promotes dislocation transfer and makes it possible even in the case of

To observe micropipe cross-sections at different distances from the surface of a grown crystal, we prepared a special sample, which was axial-cut slice along the growth direction (0001) obtained from 4*H*-SiC boule. So micropipes located almost parallel to the growth axis were nearly parallel to the surface. Micropipes grouped along the boundaries of foreign polytype inclusions (6*H* and 12*R*) which appeared at ≈ 1 cm distance from the seed/boule interface. Below the inclusions over the area of 1 cm2 micropipes were undetectable. The sample (rotated to have a horizontal position of the micropipe axis for better edge enhancement in a more coherent vertical direction) was sequentially placed at different distances from the detector. We obtained nine images for the distances from 5 to 45 cm starting with the first image registered at 5 cm from the sample. Three micropipes forming a group were examined: two in contact and the third lying remotely. The variation in cross-section sizes along the axes of MP1 and MP2 from the group are shown in Fig. 3(a), while phase contrast image of the

<sup>0</sup>*<sup>l</sup>* at *<sup>τ</sup>*<sup>0</sup> <sup>=</sup> 100 MPa. The equilibrium position of the emitted dislocation

Δ*W*

*y*

*x*

**b**2

MP2

(a) (c)

micropipes having large Burgers vectors of the same sign.

**3.2 Correlated reduction in micropipe cross sections in SiC growth**

*r*2

MP1

**b**1-**b**<sup>0</sup>

**b**0

*d*

given in units of *Gb*<sup>2</sup>

falls down to <sup>≈</sup> 0.16*Gb*<sup>2</sup>

*r*1

Fig. 3. (a) Variation in cross-section sizes along the axes of MP1 and MP2 from the group of micropipes (squares – transverse and circles – longitudinal diameters, respectively); (b) phase contrast image of the group (the growth direction is from left to right); (c) optical micrograph in transmission light of MP2 lying remotely from two micropipes in contact.

group and the optical micrograph of the remote micropipe MP2 are demonstrated in (b) and (c), respectively.

For all sample-to-detector distances and for different points along the axis of micropipes, the intensity profiles normal to the axis were measured. To determine the characteristic sizes of the micropipe cross sections in different points along the micropipe axis, we applied a computer simulation (Kohn et al., 2007) of the measured intensity profiles, assuming that these sections can have variations in longitudinal (along the beam) and transverse (across the beam) sizes. For every micropipe cross section under investigation, the computer program calculated many profiles for various possible section sizes on the base of Kirchhoff propagation (Kohn et al., 2007) to find the profile, which gives the best fit to the experimental profile registered for this section. The coincidence allowed us to determine both the longitudinal and transverse sizes of the section. We found that the micropipes had elliptical cross sections extended in transverse direction. The transverse and longitudinal diameters of micropipes MP1 and MP2 are presented in Fig. 3(a) versus the distance along the pipe axes increasing in the growth direction. It is seen that, with growth, the transverse size of MP1 reduces from 7.4 to 2.1 *μ*m. At the same time, the transverse size of the MP2 reduces from 4.1 to 1.6 *μ*m. In contrast, the longitudinal diameters remain almost the same and of the order of 0.8 *μ*m for the MP1 and 0.5 *μ*m for the MP2. In the correlated decrease of MP1 and MP2 cross section sizes in Fig. 3(b) several features are apparent. A remarkable decrease of the MP1 cross section size occurs in the distance interval from 74 to 132 *μ*m while the transverse diameter of MP2 drastically decreases later in the distance interval from 314 to 345 *μ*m. In addition, a rapid decrease of the transverse diameter of MP1 happens in the distance interval from 393 to 458 *μ*m when the transverse diameter of MP2 remains almost invariable.

We explain the changes in the cross sections of the two neighboring micropipes by the contact-free reaction between them. Experimental data in Fig. 3(a, b) tend to confirm the reaction schematically shown in Fig. 1(b). Most likely, during the rapid decrease of its cross section area MP1 emits a full-core dislocation moving towards MP2 and finally absorbed by it.

(a) (b)

micropipe split is shown in Fig. 5(a). It is presented in units of *Gb*<sup>2</sup>

*<sup>r</sup>*<sup>1</sup> <sup>=</sup> *<sup>r</sup>*1/*r*0, *<sup>r</sup>*<sup>2</sup> <sup>=</sup> *<sup>r</sup>*2/*r*0, *<sup>b</sup>*<sup>1</sup> <sup>=</sup> *<sup>b</sup>*1/*b*0, and *<sup>κ</sup>* <sup>=</sup> <sup>8</sup>*π*2*γr*0/(*Gb*<sup>2</sup>

Fig. 5. (a) The dependences of Δ*W* [in units of *Gb*<sup>2</sup>

01 2 3 4 5 *<sup>d</sup>*/*r*<sup>0</sup> *b1*/*b2*

between the micropipe axes, for the following values of parameters: (*<sup>r</sup>*<sup>1</sup> = 0.05, *<sup>r</sup>*<sup>2</sup> <sup>=</sup> *<sup>b</sup>*<sup>1</sup> = 0.5, *<sup>κ</sup>* = 3), (*<sup>r</sup>*<sup>1</sup> = 0.3, *<sup>r</sup>*<sup>2</sup> = 0.45, *<sup>b</sup>*<sup>1</sup> = 0.4, *<sup>κ</sup>* = 3), (*<sup>r</sup>*<sup>1</sup> <sup>=</sup> *<sup>r</sup>*<sup>2</sup> <sup>=</sup> *<sup>b</sup>*<sup>1</sup> = 0.5, *<sup>κ</sup>*=1), (*<sup>r</sup>*<sup>1</sup> = 0.05, *<sup>r</sup>*<sup>2</sup> <sup>=</sup> *<sup>b</sup>*<sup>1</sup> = 0.5, *<sup>κ</sup>* = 1), (*<sup>r</sup>*<sup>1</sup> = 0.3, *<sup>r</sup>*<sup>2</sup> <sup>=</sup> *<sup>b</sup>*<sup>1</sup> = 0.8, *<sup>κ</sup>* = 3), and (*<sup>r</sup>*<sup>1</sup> = 0.6, *<sup>r</sup>*<sup>2</sup> = 0.9, *<sup>b</sup>*<sup>1</sup> = 0.4, *<sup>κ</sup>* = 3), from bottom to top. (b) The system state diagram in the coordinate space (*b*1/*b*2, *r*1/*r*2). The curves separate parameter regions I and III, where both attraction area and unstable equilibrium position exist for two micropipes, from parameter region II, where the micropipes repulse at any distance.

Micropipe Reactions in Bulk SiC Growth 195

The crystal is modeled as an isotropic medium with the shear modulus *G* and specific surface energy *γ*. Let the radius and the Burgers vector of the micropipe prior to the split be *r*<sup>0</sup> and **b**<sup>0</sup> = *b*0**e***<sup>z</sup>* while the radii and the Burgers vectors of two micropipes generated due to the split be *r*1, *r*<sup>2</sup> and **b**<sup>1</sup> = *b*1**e***z*, **b**<sup>2</sup> = *b*2**e***z*, respectively. The distance between the micropipe axes is denoted by *d* while that between the micropipe free surfaces is designated by *h* (*h*=*d* -*r*<sup>1</sup> -*r*2). We suppose that the micropipe ramification is possible if the energy of two growing ramifying micropipe segments (per their unit length) is smaller than the energy of the original micropipe (per its unit length). Also, we assume that the micropipe ramification requires the repulsion of the ramifying segments. To find the conditions for the split we have calculated the energy change due to the split of a micropipe into two contacting ones and the interaction force between two parallel micropipes (Gutkin et al., 2002).The energy Δ*W* resulting from the

normalized distance *d*/*r*<sup>0</sup> between the micropipe axes for different values of the parameters

monotonously decreases with *d* or has a maximum. In the first case, the micropipes formed due to the split repulse at any distance. If the curve Δ*W* has a maximum, the micropipes repulse at any distance greater than some critical distance *dc* and attract each other at distances smaller than *dc*. In this case, the micropipes separation requires overcoming an energetic

It is important to note that the reverse process of the micropipe merging may follow the micropipe split. Indeed, the split may be possible only on account of the reduction in the total micropipe surface area. If the micropipes formed due to the split stay in contact, they are energetically favored to coalesce and produce a single micropipe with a radius close enough to the equilibrium one. In this case, the split and following coalescence of the micropipes results only in a decrease in the micropipe radius, that is, in its partial overgrowth. We suppose that the merging of the micropipe segments generated after the split does not occur if these


barrier.


0

0.5

1

Δ*W*

II

III

I

0 1 2 34 5

<sup>0</sup>/(4*π*) in dependence on the

<sup>0</sup>). As is seen in Fig. 5(a), Δ*W* either

<sup>0</sup>/(4*π*)] on the normalized distance *d*/*r*<sup>0</sup>

0

1

2

3

4

5

*r*1/*r*<sup>2</sup>

For a new possible mechanism of the contact-free reactions between micropipes, our calculations have demonstrated that, depending on the signs of the micropipe Burgers vectors (prior to dislocation exchange between micropipes), the moving dislocation must overcome one or two energetic barriers. In the case where the initial micropipe Burgers vectors are of the same sign, the dislocation exchange can happen only if the difference between the micropipe Burgers vector magnitudes is large enough (not less than three magnitudes of the elementary Burgers vector). The energetic barrier(s) that the dislocation has to surmount on its way from one micropipe to the other can supposedly be overcome under the growth front where the conditions can be very far from equilibrium due to high temperature and surface effects. Correlated reduction in micropipe cross-sections indirectly supports our suggestion that micropipes can interact each other without a direct contact, by the proposed mechanism.

#### **4. Elastic interaction and split of micropipes**

#### **4.1 Ramification of micropipes**

Three imaging techniques: SEM, optical microscopy, and x-ray phase contrast imaging were applied to study the split of micropipes. The SiC samples were on-axis wafers cut perpendicular to the [0001] growth direction, and the ends of screw dislocations with Burgers vector aligned along the [0001] axis were visible on the etched (0001) surface. A typical SEM image of a ramified dislocation with a hollow core is shown in Fig. 4(a), and Fig. 4(b) is a transmission light image of the same configuration. However, SEM is insensitive and light microscopy is limitedly suited for the detection of micropipes in the wafer interior. By using the phase contrast imaging [Fig. 4(c)] ramified micropipes were clearly detected in the bulk, and the numbers of single and ramified ones within each view field were calculated. It appeared that the density of nearby single dislocations as well as the presence of dislocation boundaries did not influence the number of ramified micropipes. Their distribution over the wafer area was almost homogeneous with an average density of two per each view field, the latter being 0.6 <sup>×</sup> 0.4 mm2.

Let us determine when a dislocated micropipe is favorable to split into a pair of parallel micropipes with smaller radii and Burgers vectors. For the sake of simplicity, we focus on the case when the angle between ramifying segments of the micropipe "tree" is small enough to allow one to model these segments as a pair of parallel micropipes extending through the entire crystal.

8 Will-be-set-by-IN-TECH

Fig. 4. (a) SEM image of a ramified micropipe; (b) transmission light microscopy image of the

For a new possible mechanism of the contact-free reactions between micropipes, our calculations have demonstrated that, depending on the signs of the micropipe Burgers vectors (prior to dislocation exchange between micropipes), the moving dislocation must overcome one or two energetic barriers. In the case where the initial micropipe Burgers vectors are of the same sign, the dislocation exchange can happen only if the difference between the micropipe Burgers vector magnitudes is large enough (not less than three magnitudes of the elementary Burgers vector). The energetic barrier(s) that the dislocation has to surmount on its way from one micropipe to the other can supposedly be overcome under the growth front where the conditions can be very far from equilibrium due to high temperature and surface effects. Correlated reduction in micropipe cross-sections indirectly supports our suggestion that micropipes can interact each other without a direct contact, by the proposed mechanism.

Three imaging techniques: SEM, optical microscopy, and x-ray phase contrast imaging were applied to study the split of micropipes. The SiC samples were on-axis wafers cut perpendicular to the [0001] growth direction, and the ends of screw dislocations with Burgers vector aligned along the [0001] axis were visible on the etched (0001) surface. A typical SEM image of a ramified dislocation with a hollow core is shown in Fig. 4(a), and Fig. 4(b) is a transmission light image of the same configuration. However, SEM is insensitive and light microscopy is limitedly suited for the detection of micropipes in the wafer interior. By using the phase contrast imaging [Fig. 4(c)] ramified micropipes were clearly detected in the bulk, and the numbers of single and ramified ones within each view field were calculated. It appeared that the density of nearby single dislocations as well as the presence of dislocation boundaries did not influence the number of ramified micropipes. Their distribution over the wafer area was almost homogeneous with an average density of two per each view field, the

Let us determine when a dislocated micropipe is favorable to split into a pair of parallel micropipes with smaller radii and Burgers vectors. For the sake of simplicity, we focus on the case when the angle between ramifying segments of the micropipe "tree" is small enough to allow one to model these segments as a pair of parallel micropipes extending through the

30 μm

(c) X-rays

(a) SEM (b) Optics

same micropipe; (c) SR phase-contrast image of another ramified configuration.

**4. Elastic interaction and split of micropipes**

**4.1 Ramification of micropipes**

latter being 0.6 <sup>×</sup> 0.4 mm2.

entire crystal.

10 μm

Fig. 5. (a) The dependences of Δ*W* [in units of *Gb*<sup>2</sup> <sup>0</sup>/(4*π*)] on the normalized distance *d*/*r*<sup>0</sup> between the micropipe axes, for the following values of parameters: (*<sup>r</sup>*<sup>1</sup> = 0.05, *<sup>r</sup>*<sup>2</sup> <sup>=</sup> *<sup>b</sup>*<sup>1</sup> = 0.5, *<sup>κ</sup>* = 3), (*<sup>r</sup>*<sup>1</sup> = 0.3, *<sup>r</sup>*<sup>2</sup> = 0.45, *<sup>b</sup>*<sup>1</sup> = 0.4, *<sup>κ</sup>* = 3), (*<sup>r</sup>*<sup>1</sup> <sup>=</sup> *<sup>r</sup>*<sup>2</sup> <sup>=</sup> *<sup>b</sup>*<sup>1</sup> = 0.5, *<sup>κ</sup>*=1), (*<sup>r</sup>*<sup>1</sup> = 0.05, *<sup>r</sup>*<sup>2</sup> <sup>=</sup> *<sup>b</sup>*<sup>1</sup> = 0.5, *<sup>κ</sup>* = 1), (*<sup>r</sup>*<sup>1</sup> = 0.3, *<sup>r</sup>*<sup>2</sup> <sup>=</sup> *<sup>b</sup>*<sup>1</sup> = 0.8, *<sup>κ</sup>* = 3), and (*<sup>r</sup>*<sup>1</sup> = 0.6, *<sup>r</sup>*<sup>2</sup> = 0.9, *<sup>b</sup>*<sup>1</sup> = 0.4, *<sup>κ</sup>* = 3), from bottom to top. (b) The system state diagram in the coordinate space (*b*1/*b*2, *r*1/*r*2). The curves separate parameter regions I and III, where both attraction area and unstable equilibrium position exist for two micropipes, from parameter region II, where the micropipes repulse at any distance.

The crystal is modeled as an isotropic medium with the shear modulus *G* and specific surface energy *γ*. Let the radius and the Burgers vector of the micropipe prior to the split be *r*<sup>0</sup> and **b**<sup>0</sup> = *b*0**e***<sup>z</sup>* while the radii and the Burgers vectors of two micropipes generated due to the split be *r*1, *r*<sup>2</sup> and **b**<sup>1</sup> = *b*1**e***z*, **b**<sup>2</sup> = *b*2**e***z*, respectively. The distance between the micropipe axes is denoted by *d* while that between the micropipe free surfaces is designated by *h* (*h*=*d* -*r*<sup>1</sup> -*r*2). We suppose that the micropipe ramification is possible if the energy of two growing ramifying micropipe segments (per their unit length) is smaller than the energy of the original micropipe (per its unit length). Also, we assume that the micropipe ramification requires the repulsion of the ramifying segments. To find the conditions for the split we have calculated the energy change due to the split of a micropipe into two contacting ones and the interaction force between two parallel micropipes (Gutkin et al., 2002).The energy Δ*W* resulting from the micropipe split is shown in Fig. 5(a). It is presented in units of *Gb*<sup>2</sup> <sup>0</sup>/(4*π*) in dependence on the normalized distance *d*/*r*<sup>0</sup> between the micropipe axes for different values of the parameters *<sup>r</sup>*<sup>1</sup> <sup>=</sup> *<sup>r</sup>*1/*r*0, *<sup>r</sup>*<sup>2</sup> <sup>=</sup> *<sup>r</sup>*2/*r*0, *<sup>b</sup>*<sup>1</sup> <sup>=</sup> *<sup>b</sup>*1/*b*0, and *<sup>κ</sup>* <sup>=</sup> <sup>8</sup>*π*2*γr*0/(*Gb*<sup>2</sup> <sup>0</sup>). As is seen in Fig. 5(a), Δ*W* either monotonously decreases with *d* or has a maximum. In the first case, the micropipes formed due to the split repulse at any distance. If the curve Δ*W* has a maximum, the micropipes repulse at any distance greater than some critical distance *dc* and attract each other at distances smaller than *dc*. In this case, the micropipes separation requires overcoming an energetic barrier.

It is important to note that the reverse process of the micropipe merging may follow the micropipe split. Indeed, the split may be possible only on account of the reduction in the total micropipe surface area. If the micropipes formed due to the split stay in contact, they are energetically favored to coalesce and produce a single micropipe with a radius close enough to the equilibrium one. In this case, the split and following coalescence of the micropipes results only in a decrease in the micropipe radius, that is, in its partial overgrowth. We suppose that the merging of the micropipe segments generated after the split does not occur if these

*z*

30 μm

(a)

segments.

520

560

*y*

<sup>60</sup> *<sup>x</sup>*

**b**=+3

600

100

*mk***a***<sup>k</sup>* <sup>=</sup> *Gbk*

<sup>2</sup>*<sup>π</sup>* ∑ *i*� *k bi* 

140

Fig. 7. SR phase-contrast image of semi-loops resulting from macropipes twisting (a); coalescence of micropipes with equal magnitudes of Burgers vectors results in the

annihilation of the subsurface micropipe segments (b, c). The coalescing micropipes come to each other along the shortest way (b) or twist (c). For the units see the caption to Fig. 6.

performed a computer simulation of micropipe evolution (Gutkin et al., 2003a;b). For computer modeling, a simple computer code has been elaborated to simulate 2D dynamics of pipes within Newton's approach. We considered the lateral motion of subsurface micropipe segments. The equations of the motion of subsurface micropipe segments had the form:

*h*2/*r*<sup>2</sup>

where *k* denotes the number of a specified micropipes, *i* denotes the numbers of other micropipes, **a***<sup>k</sup>* is the micropipe segment acceleration, *mk* is its effective mass, *Rk* is its radius, *G* is the shear modulus, *bk* is the projection of the micropipe dislocation Burgers vector onto the direction of the dislocation line, *h* is the height of subsurface micropipe segments, *γ* is the specific surface energy, *rik* is the distance between the *i*th and *k*th micropipes, **e***ik* is the unit vector directed from the *i*th to the *k*th micropipe, and **e***<sup>k</sup>* is the unit vector whose direction coincides with the direction of the lateral micropipe motion. The first term on the right-hand side of formula (3) describes the total force of the interaction of the *k*-th micropipe with other micropipes, while the second term specifies the force of surface tension related to the steps appearing on micropipe cylindrical surfaces during lateral displacements of micropipe

As a result of the simulation, various reactions between the subsurface micropipe segments were observed. It has been shown that the reaction of micropipe coalescence gives rise to the generation of new micropipes with smaller diameters and Burgers vectors or annihilation of initial micropipes (see Figs. 6, 7), which leads to diminishing their average density. Using the results of 2D simulation, we reconstructed some typical defect configurations in a 3D space. They may be subdivided into planar and twisted micropipe configurations. The planar configurations arise when the interacting pair of micropipes has incomparable diameters or is located far (at the distance of more than about 5 average micropipe diameters) from other

*ik* + 1 − 1

(b) (c)

**b**=-3 200

Micropipe Reactions in Bulk SiC Growth 197

100

*z*

0

200 <sup>100</sup> *<sup>x</sup>* <sup>300</sup>

**b**=+2

<sup>400</sup> *<sup>y</sup>*

**b**=-2

**e***ik* − 4*γRk***e***k*, (3)

segments repulse as soon as they have been formed. As is shown above [see Fig. 5(a)], the micropipes may either repulse at any distance or repulse at distances *d* greater than the critical distance *dc* and attract each other at *d* < *dc* . The ramification of the micropipe segments (not followed by their coalescence) is possible if they repulse at any distance or the critical distance *dc* [and the corresponding energy barrier *W*(*d* = *dc*) − *W*(*d* = *r*<sup>1</sup> + *r*<sup>2</sup> + *a*) that the micropipes have to overcome to go outside of the attraction area] is small enough.

Now let us determine the parameter region where the ramifying micropipe segments (modeled as a pair of parallel micropipes) repulse at any distance. This parameter region is shown in Fig. 5(b) that depicts the system state diagram in the coordinate space (*b*1/*b*2, *r*1/*r*2). The upper and lower curves separate regions I and III, where the micropipes attract each other at short distances while they repel each other at long distances, and the corresponding critical distance *hc* = *dc* -*r*<sup>1</sup> -*r*<sup>2</sup> between the micropipe free surfaces exists, from region II, where the micropipes repulse at any distance. As is seen, an attraction area may exist for two same-sign micropipes if *b*1/*b*<sup>2</sup> and *r*1/*r*<sup>2</sup> differ by more than 15%–25%.

The parameter region where the micropipe ramification does not require overcoming an energetic barrier is given by the intersection of the corresponding parameter regions shown in Fig. 5(a, b). Such a ramification is possible if the micropipes are of the same sign, the radius of the original micropipe exceeds the equilibrium one, the total micropipe surface area reduces due to the ramification, and the radii of the ramifying micropipes are approximately in the same ratio as the magnitudes of their dislocation Burgers vectors.

#### **4.2 Merging and twisting of micropipes**

Many morphologies of twisted and coalesced micropipes have been observed experimentally in SiC crystals by means of x-ray phase contrast imaging. The examples of twisted configurations are shown in Figs. 6(a) and 7(a). To explain these phenomena, we have

Fig. 6. SR phase-contrast image of micropipe twisting (a); coalescence of micropipes with different magnitudes of Burgers vectors results in the generation of a new micropipe segment (b, c). The coalescing micropipes come to each other along the shortest way (b) or twist (c). The Burgers vectors are shown in units of *c*, which is the lattice parameter in the growth direction. The coordinates *x* and *y* are given in units of *Gc*2/(8*π*2*γ*). The length of micropipes (along the *z* axes) is in arbitrary units that depend on the growth rate.

10 Will-be-set-by-IN-TECH

segments repulse as soon as they have been formed. As is shown above [see Fig. 5(a)], the micropipes may either repulse at any distance or repulse at distances *d* greater than the critical distance *dc* and attract each other at *d* < *dc* . The ramification of the micropipe segments (not followed by their coalescence) is possible if they repulse at any distance or the critical distance *dc* [and the corresponding energy barrier *W*(*d* = *dc*) − *W*(*d* = *r*<sup>1</sup> + *r*<sup>2</sup> + *a*) that the micropipes

Now let us determine the parameter region where the ramifying micropipe segments (modeled as a pair of parallel micropipes) repulse at any distance. This parameter region is shown in Fig. 5(b) that depicts the system state diagram in the coordinate space (*b*1/*b*2, *r*1/*r*2). The upper and lower curves separate regions I and III, where the micropipes attract each other at short distances while they repel each other at long distances, and the corresponding critical distance *hc* = *dc* -*r*<sup>1</sup> -*r*<sup>2</sup> between the micropipe free surfaces exists, from region II, where the micropipes repulse at any distance. As is seen, an attraction area may exist for two same-sign

The parameter region where the micropipe ramification does not require overcoming an energetic barrier is given by the intersection of the corresponding parameter regions shown in Fig. 5(a, b). Such a ramification is possible if the micropipes are of the same sign, the radius of the original micropipe exceeds the equilibrium one, the total micropipe surface area reduces due to the ramification, and the radii of the ramifying micropipes are approximately in the

Many morphologies of twisted and coalesced micropipes have been observed experimentally in SiC crystals by means of x-ray phase contrast imaging. The examples of twisted configurations are shown in Figs. 6(a) and 7(a). To explain these phenomena, we have

400

600

*z* 500

**b**=+6

*<sup>y</sup>* <sup>600</sup> <sup>300</sup>

**b**=+3

<sup>400</sup> *<sup>x</sup>*

**b**=-2

have to overcome to go outside of the attraction area] is small enough.

micropipes if *b*1/*b*<sup>2</sup> and *r*1/*r*<sup>2</sup> differ by more than 15%–25%.

same ratio as the magnitudes of their dislocation Burgers vectors.

200

Fig. 6. SR phase-contrast image of micropipe twisting (a); coalescence of micropipes with different magnitudes of Burgers vectors results in the generation of a new micropipe segment (b, c). The coalescing micropipes come to each other along the shortest way (b) or twist (c). The Burgers vectors are shown in units of *c*, which is the lattice parameter in the growth direction. The coordinates *x* and *y* are given in units of *Gc*2/(8*π*2*γ*). The length of

micropipes (along the *z* axes) is in arbitrary units that depend on the growth rate.

150

(a) (b) (c)

*x*

100 0

50

100

150

*z*

150

*y*

200 250

**b**=-2

**4.2 Merging and twisting of micropipes**

30 μm

Fig. 7. SR phase-contrast image of semi-loops resulting from macropipes twisting (a); coalescence of micropipes with equal magnitudes of Burgers vectors results in the annihilation of the subsurface micropipe segments (b, c). The coalescing micropipes come to each other along the shortest way (b) or twist (c). For the units see the caption to Fig. 6.

performed a computer simulation of micropipe evolution (Gutkin et al., 2003a;b). For computer modeling, a simple computer code has been elaborated to simulate 2D dynamics of pipes within Newton's approach. We considered the lateral motion of subsurface micropipe segments. The equations of the motion of subsurface micropipe segments had the form:

$$m\_k \mathbf{a}\_k = \frac{Gb\_k}{2\pi} \sum\_{i \neq k} b\_i \left(\sqrt{h^2/r\_{ik}^2 + 1} - 1\right) \mathbf{e}\_{ik} - 4\gamma R\_k \mathbf{e}\_{k\prime} \tag{3}$$

where *k* denotes the number of a specified micropipes, *i* denotes the numbers of other micropipes, **a***<sup>k</sup>* is the micropipe segment acceleration, *mk* is its effective mass, *Rk* is its radius, *G* is the shear modulus, *bk* is the projection of the micropipe dislocation Burgers vector onto the direction of the dislocation line, *h* is the height of subsurface micropipe segments, *γ* is the specific surface energy, *rik* is the distance between the *i*th and *k*th micropipes, **e***ik* is the unit vector directed from the *i*th to the *k*th micropipe, and **e***<sup>k</sup>* is the unit vector whose direction coincides with the direction of the lateral micropipe motion. The first term on the right-hand side of formula (3) describes the total force of the interaction of the *k*-th micropipe with other micropipes, while the second term specifies the force of surface tension related to the steps appearing on micropipe cylindrical surfaces during lateral displacements of micropipe segments.

As a result of the simulation, various reactions between the subsurface micropipe segments were observed. It has been shown that the reaction of micropipe coalescence gives rise to the generation of new micropipes with smaller diameters and Burgers vectors or annihilation of initial micropipes (see Figs. 6, 7), which leads to diminishing their average density. Using the results of 2D simulation, we reconstructed some typical defect configurations in a 3D space. They may be subdivided into planar and twisted micropipe configurations. The planar configurations arise when the interacting pair of micropipes has incomparable diameters or is located far (at the distance of more than about 5 average micropipe diameters) from other

(a) 100 μm

density in the neighboring regions.

propagate along the inclusion boundaries.

of absorbed micropipes.

scintillator.

MP1

**5.2 Pore growth by micropipe absorption at foreign polytype boundaries**

MP2

Micropipe Reactions in Bulk SiC Growth 199

MP4

Fig. 9. Representative phase contrast images among the sequences of the images registered while rotating the sample, (a)–(c) show the same region as Fig. 8, the inset in (c) displays the image of twisted micropipe recorded at another place in the same sample, and the growth direction is indicated in (a) by an arrow. The elongated white spot is a defect of the

bundles at the inclusion boundaries. This phenomenon was observed throughout this crystal and other similar crystals. The gathering of micropipes is followed by the reduction of their

The observations were interpreted based on the following model (Gutkin et al., 2006). At the boundaries of the other polytypes inclusions the lattice mismatch should exist that gives rise to essential elastic deformation, whose orientational constituent relaxes with the formation of micropipes. At the sites of micropipe accumulation, micropipes elastically interact, which leads to the merge of several micropipes with the generation of cavities along the inclusion boundaries. As a result, the misfit stresses completely relax. Due to the action of image forces, the free surfaces of the cavities thus formed attract new micropipes and, absorbing them,

In the previous section we outlined the results of the elastic interaction of micropipes with polytype inclusions. In this section the processes of micropipe accumulation and their coalescence into a pore is discussed. The pores generated in this way may grow at the expense

We have observed that pores of different sizes and shapes are always present at the boundaries of foreign polytype inclusions in SiC samples under study. Figure 10 illustrates the representative morphology of a typical pore in a 4*H*-SiC wafer. Comparison of the phase-contrast image [Fig. 10(a)] with the PL image [Fig. 10(b)] clearly shows that pores are located along the inclusion boundaries as sketched in Fig. 10(c). The slit pore (1) surrounds one of the inclusion edges, while tubular pores (2)–(5) are located at the inclusion corners. Pore shape reflects a stage in its development. The pore nucleation is initiated as a tube form by initial accumulation of some micropipes near the inclusion boundary. In the process of sequential attraction and absorption of new micropipes, the pore shape changes and step by

Images of another wafer cut of the same 4*H*-SiC boule are shown in Fig. 11. The SEM image [(Fig. 11(a)] represents etch pits of not only pores, but also micropipes, which appear as faceted pits on the top of the tubes. We see that pores are produced by agglomeration of micropipes. The PL dark green image displayed in the inset to (a) represents a 21*R*-SiC inclusion in the 4*H*-SiC wafer. [At room temperature, n-type 6*H* and 4*H* polytypes containing N and B show yellow and light green PL, respectively, while Al activated luminescence for rombohedral 21*R* polytype taken at 77 K is dark green (Saparin et al., 1997).] The marked pores are located at

step transforms into a slit, which can then propagate along the inclusion boundary.

MP3

MP5 (b) (c)

micropipes. The twisted configurations like double spirals form if the interacting micropipes have comparable diameters and are located within dense groups of other micropipes.

#### **5. Role of micropipes in the formation of pores at foreign polytype boundaries**

#### **5.1 Interaction of micropipes with polytype inclusions**

SR phase contrast imaging, optical and scanning electron microscopies, and color photoluminescence have been used to study the interaction of micropipes with foreign polytype inclusions in 4*H*-SiC bulk crystals. The boules had been grown on carbon-terminated faces of the 6*H*-SiC seeds by the sublimation sandwich method in Ar atmosphere and in the presence of Sn vapor. The Sn vapor promotes the transformation of the polytype of the substrate into 4*H*-SiC (Vodakov et al., 1997). Several wafers were cut from 4*H*-SiC boules. One wafer, 0.4 mm thick and misoriented 8◦ away from the basal plane, was further cut into 0.5 mm wide bars. X-ray experiment was performed in two regimes: (1) via the translation of the wafer to map micropipe distributions over the area and (2) via the rotation of the bar samples to reveal the spatial orientations of macro- and micropores. In the latter case, the rotation axis was perpendicular to the beam and parallel to the long edges of the bar. The rotation interval was 180◦ with a 2◦ step. The images were recorded in a step by step sequence.

Figure 8(a) shows SEM image of a typical pore located at the boundary of a foreign polytype inclusion. The pore uncovers a slit on a molten KOH treated surface. Figure 8(b) displays the illumination of the inclusion itself excited by an ultraviolet light at room temperature. When the inclusion is located close to the wafer surface, its polytype can be easily identified by the color of PL. In low N doped samples at room temperature, 6*H* polytype inclusions have yellow PLs (Saparin et al., 1997). A sketch of the inclusion, pore, and micropipes is shown in Fig. 8(c).

For the purposes of the model, it is important to find a way by which micropipes accumulate at the inclusions. Figure 9 shows several representative phase-contrast images registered while rotating the sample in the SR beam. The sample had the shape of a bar. In the image, a relatively thick micropipe [indicated as MP1 on Fig. 9(b)] follows the growth direction, while the much thinner (and therefore much more mobile) MP2 inclines towards the inclusion boundary. On the other hand, the thick MP3 also bends towards the inclusion, and its surface becomes steplike. MP4 revolves about MP5, which follows the growth direction. The inset in (c) displays twisted micropipes turning to another inclusion of 6*H*-SiC in the same crystal.

Earlier, the reactions of micropipes — twisting and bundling — were discussed in terms of the stress fields from the other surrounding micropipes. (Gutkin et al., 2003a;b). However, in this study, stress fields seem to result from the inclusions. The remarkable deviation from the growth direction, the transformation of shape, and the reactions of micropipes prove that they are strongly influenced by the inclusions. Attracted by the inclusions, micropipes collect into

Fig. 8. (a) SEM image of the pore. (b) PL image of the inclusion. (c) Sketch of the inclusion, the pore, and the micropipes.

12 Will-be-set-by-IN-TECH

micropipes. The twisted configurations like double spirals form if the interacting micropipes have comparable diameters and are located within dense groups of other micropipes.

SR phase contrast imaging, optical and scanning electron microscopies, and color photoluminescence have been used to study the interaction of micropipes with foreign polytype inclusions in 4*H*-SiC bulk crystals. The boules had been grown on carbon-terminated faces of the 6*H*-SiC seeds by the sublimation sandwich method in Ar atmosphere and in the presence of Sn vapor. The Sn vapor promotes the transformation of the polytype of the substrate into 4*H*-SiC (Vodakov et al., 1997). Several wafers were cut from 4*H*-SiC boules. One wafer, 0.4 mm thick and misoriented 8◦ away from the basal plane, was further cut into 0.5 mm wide bars. X-ray experiment was performed in two regimes: (1) via the translation of the wafer to map micropipe distributions over the area and (2) via the rotation of the bar samples to reveal the spatial orientations of macro- and micropores. In the latter case, the rotation axis was perpendicular to the beam and parallel to the long edges of the bar. The rotation interval

Figure 8(a) shows SEM image of a typical pore located at the boundary of a foreign polytype inclusion. The pore uncovers a slit on a molten KOH treated surface. Figure 8(b) displays the illumination of the inclusion itself excited by an ultraviolet light at room temperature. When the inclusion is located close to the wafer surface, its polytype can be easily identified by the color of PL. In low N doped samples at room temperature, 6*H* polytype inclusions have yellow PLs (Saparin et al., 1997). A sketch of the inclusion, pore, and micropipes is shown in

For the purposes of the model, it is important to find a way by which micropipes accumulate at the inclusions. Figure 9 shows several representative phase-contrast images registered while rotating the sample in the SR beam. The sample had the shape of a bar. In the image, a relatively thick micropipe [indicated as MP1 on Fig. 9(b)] follows the growth direction, while the much thinner (and therefore much more mobile) MP2 inclines towards the inclusion boundary. On the other hand, the thick MP3 also bends towards the inclusion, and its surface becomes steplike. MP4 revolves about MP5, which follows the growth direction. The inset in (c) displays twisted micropipes turning to another inclusion of 6*H*-SiC in the same crystal. Earlier, the reactions of micropipes — twisting and bundling — were discussed in terms of the stress fields from the other surrounding micropipes. (Gutkin et al., 2003a;b). However, in this study, stress fields seem to result from the inclusions. The remarkable deviation from the growth direction, the transformation of shape, and the reactions of micropipes prove that they are strongly influenced by the inclusions. Attracted by the inclusions, micropipes collect into

(b) PhL

Fig. 8. (a) SEM image of the pore. (b) PL image of the inclusion. (c) Sketch of the inclusion,

Inclusion

(c) Sketch

Micropipes

Pore

**5. Role of micropipes in the formation of pores at foreign polytype boundaries**

was 180◦ with a 2◦ step. The images were recorded in a step by step sequence.

50 μm

**5.1 Interaction of micropipes with polytype inclusions**

Fig. 8(c).

40 μm

(a) SEM

the pore, and the micropipes.

Fig. 9. Representative phase contrast images among the sequences of the images registered while rotating the sample, (a)–(c) show the same region as Fig. 8, the inset in (c) displays the image of twisted micropipe recorded at another place in the same sample, and the growth direction is indicated in (a) by an arrow. The elongated white spot is a defect of the scintillator.

bundles at the inclusion boundaries. This phenomenon was observed throughout this crystal and other similar crystals. The gathering of micropipes is followed by the reduction of their density in the neighboring regions.

The observations were interpreted based on the following model (Gutkin et al., 2006). At the boundaries of the other polytypes inclusions the lattice mismatch should exist that gives rise to essential elastic deformation, whose orientational constituent relaxes with the formation of micropipes. At the sites of micropipe accumulation, micropipes elastically interact, which leads to the merge of several micropipes with the generation of cavities along the inclusion boundaries. As a result, the misfit stresses completely relax. Due to the action of image forces, the free surfaces of the cavities thus formed attract new micropipes and, absorbing them, propagate along the inclusion boundaries.

#### **5.2 Pore growth by micropipe absorption at foreign polytype boundaries**

In the previous section we outlined the results of the elastic interaction of micropipes with polytype inclusions. In this section the processes of micropipe accumulation and their coalescence into a pore is discussed. The pores generated in this way may grow at the expense of absorbed micropipes.

We have observed that pores of different sizes and shapes are always present at the boundaries of foreign polytype inclusions in SiC samples under study. Figure 10 illustrates the representative morphology of a typical pore in a 4*H*-SiC wafer. Comparison of the phase-contrast image [Fig. 10(a)] with the PL image [Fig. 10(b)] clearly shows that pores are located along the inclusion boundaries as sketched in Fig. 10(c). The slit pore (1) surrounds one of the inclusion edges, while tubular pores (2)–(5) are located at the inclusion corners. Pore shape reflects a stage in its development. The pore nucleation is initiated as a tube form by initial accumulation of some micropipes near the inclusion boundary. In the process of sequential attraction and absorption of new micropipes, the pore shape changes and step by step transforms into a slit, which can then propagate along the inclusion boundary.

Images of another wafer cut of the same 4*H*-SiC boule are shown in Fig. 11. The SEM image [(Fig. 11(a)] represents etch pits of not only pores, but also micropipes, which appear as faceted pits on the top of the tubes. We see that pores are produced by agglomeration of micropipes. The PL dark green image displayed in the inset to (a) represents a 21*R*-SiC inclusion in the 4*H*-SiC wafer. [At room temperature, n-type 6*H* and 4*H* polytypes containing N and B show yellow and light green PL, respectively, while Al activated luminescence for rombohedral 21*R* polytype taken at 77 K is dark green (Saparin et al., 1997).] The marked pores are located at

Matrix Matrix

Micropipes Pore

Inclusion Inclusion

Micropipe Reactions in Bulk SiC Growth 201

(a) (b)

(c) (d)

micropipes.

Micropipes Micropipes

Inclusion Inclusion

Fig. 12. Scheme of nucleation and extension of a pore at the inclusion/matrix interface through agglomeration of micropipes. (a) Micropipes are attracted to their equilibrium positions at a corner of the inclusion. (b) The first micropipe occupies its equilibrium position at the corner; the others come closer to it. (c) Some micropipes are agglomerated at the corner and form a pore; the others are attracted both to the corner and to the free surface of the pore.

(d) The pore propagates along the inclusion/matrix interface by absorption of close

pore size becomes so large that the inclusion stops to attract new micropipes.

the inclusion and the free surface of the first micropipe is stronger than the repulsion force between micropipe dislocations, and so the second micropipe merges with the first one. Some of such micropipes, which have been attracted to this corner [Fig. 12(c)], agglomerate and form a pore. After the pore has been formed, some other micropipes move to the same equilibrium position at the inclusion boundary and are absorbed by the pore [Fig. 12(d)], resulting in the pore growth and the change of the dislocation charge accumulated at the boundary. This process continues until the pore occupies the entire inclusion facet or until the

To analyze the conditions at which pore growth along a foreign polytype inclusion at the expense of micropipes absorbed is favored, we suggest a two-dimensional (2D) model of the inclusion, pore and micropipes. Within the model, the inclusion is infinitely long and has a rectangular cross-section (Fig. 13). The long inclusion axis (*z*-axis) is oriented along the crystal growth direction while the inclusion cross-section occupies the region (*x*<sup>1</sup> < *x* < *x*2, *y*<sup>1</sup> < *y* < 0). The mismatch of the matrix and the inclusion crystal lattices is characterized by the inclusion plastic distortions *βxz* and *βyz* (Gutkin et al., 2006). The inclusion/matrix interface contains an elliptic pore, and mobile micropipes lie nearby. The pore is assumed to grow at the expense of micropipes absorbed (Fig. 12). For definiteness, we suppose that the pore is symmetric with respect to the upper inclusion facet *y*=0. The pore semiaxes are denoted as *p* and *q*, and the pore surface is defined by the equation *x*2/*p*<sup>2</sup> + *y*2/*q*<sup>2</sup> = 1.

Fig. 10. Pores and micropipes at the boundary of 6*H*-SiC inclusion in 4*H*-SiC wafer. (a) SR phase-contrast image. (b) PL image. (c) The sketch outlines the inclusion and the pores as indicated by the black and white arrows, respectively. The number 1 points to a slit pore and the numbers 2–5 to tubular pores.

the edge of the left (concave) inclusion as defined in Fig. 11(c). The pores spread over the inclusion boundary and propagate deeply inside the wafer. The phase-contrast image [Fig. 4(b)] also reveals that the pores are produced through the coalescence of micropipes. The observed micropipes remarkably deviate from the growth direction, which we attribute to the interaction of micropipes with the polytype inclusion.

Mapping with a lower magnification revealed a significant reduction in micropipe density nearby to the pores, which can be explained by the absorption of micropipes by the pores.

The following scenario for pore growth is suggested, as is illustrated by the sketch in Fig. 12. At the beginning, a few neighboring micropipes are attracted to an inclusion with no pore to accommodate the orientation mismatch between the inclusion and the matrix crystalline lattices [Fig. 12(a)] (Gutkin et al., 2006; 2009b). This orientation mismatch is described mathematically through the components of the inclusion plastic distortions (Gutkin et al., 2006). In the case of two nonvanishing plastic distortion components, micropipes are attracted to a corner of the inclusion [Figs. 12(a) and 12(b)], where they have an equilibrium position (Gutkin et al., 2006; 2009b). Let the first micropipe occupy its equilibrium position at this corner [Fig. 12(b)]. Then another micropipe, containing a dislocation of the same sign as the first micropipe, is attracted by the inclusion to the same equilibrium position. If the inclusion is "powerful" enough (that is the plastic distortions are large), the attraction force exerted by

Fig. 11. Agglomeration of micropipes into the pores at the boundary of a 21*R*-SiC inclusion in the 4*H*-SiC wafer. (a) SEM image of the pore. Inset shows PL image of the 21*R*-SiC inclusion. (b) SR phase-contrast image reveals merging of micropipes into slit pores in the wafer interior. (c) Sketch of the inclusion and the pores.

14 Will-be-set-by-IN-TECH

Fig. 10. Pores and micropipes at the boundary of 6*H*-SiC inclusion in 4*H*-SiC wafer. (a) SR phase-contrast image. (b) PL image. (c) The sketch outlines the inclusion and the pores as indicated by the black and white arrows, respectively. The number 1 points to a slit pore and

the edge of the left (concave) inclusion as defined in Fig. 11(c). The pores spread over the inclusion boundary and propagate deeply inside the wafer. The phase-contrast image [Fig. 4(b)] also reveals that the pores are produced through the coalescence of micropipes. The observed micropipes remarkably deviate from the growth direction, which we attribute to the

Mapping with a lower magnification revealed a significant reduction in micropipe density nearby to the pores, which can be explained by the absorption of micropipes by the pores. The following scenario for pore growth is suggested, as is illustrated by the sketch in Fig. 12. At the beginning, a few neighboring micropipes are attracted to an inclusion with no pore to accommodate the orientation mismatch between the inclusion and the matrix crystalline lattices [Fig. 12(a)] (Gutkin et al., 2006; 2009b). This orientation mismatch is described mathematically through the components of the inclusion plastic distortions (Gutkin et al., 2006). In the case of two nonvanishing plastic distortion components, micropipes are attracted to a corner of the inclusion [Figs. 12(a) and 12(b)], where they have an equilibrium position (Gutkin et al., 2006; 2009b). Let the first micropipe occupy its equilibrium position at this corner [Fig. 12(b)]. Then another micropipe, containing a dislocation of the same sign as the first micropipe, is attracted by the inclusion to the same equilibrium position. If the inclusion is "powerful" enough (that is the plastic distortions are large), the attraction force exerted by

(b) (c)

Fig. 11. Agglomeration of micropipes into the pores at the boundary of a 21*R*-SiC inclusion in the 4*H*-SiC wafer. (a) SEM image of the pore. Inset shows PL image of the 21*R*-SiC inclusion. (b) SR phase-contrast image reveals merging of micropipes into slit pores in the wafer

50 μm

**2**

**3**

interaction of micropipes with the polytype inclusion.

30 μm

interior. (c) Sketch of the inclusion and the pores.

**4**

the numbers 2–5 to tubular pores.

100 μ m

Tube

**1** (b)

**4**

Inclusion Slit

Inclusion

Pores

**2**

**3**

**1**

(a) (c)

100 μ m

30 μm

(a)

**5**

Fig. 12. Scheme of nucleation and extension of a pore at the inclusion/matrix interface through agglomeration of micropipes. (a) Micropipes are attracted to their equilibrium positions at a corner of the inclusion. (b) The first micropipe occupies its equilibrium position at the corner; the others come closer to it. (c) Some micropipes are agglomerated at the corner and form a pore; the others are attracted both to the corner and to the free surface of the pore. (d) The pore propagates along the inclusion/matrix interface by absorption of close micropipes.

the inclusion and the free surface of the first micropipe is stronger than the repulsion force between micropipe dislocations, and so the second micropipe merges with the first one. Some of such micropipes, which have been attracted to this corner [Fig. 12(c)], agglomerate and form a pore. After the pore has been formed, some other micropipes move to the same equilibrium position at the inclusion boundary and are absorbed by the pore [Fig. 12(d)], resulting in the pore growth and the change of the dislocation charge accumulated at the boundary. This process continues until the pore occupies the entire inclusion facet or until the pore size becomes so large that the inclusion stops to attract new micropipes.

To analyze the conditions at which pore growth along a foreign polytype inclusion at the expense of micropipes absorbed is favored, we suggest a two-dimensional (2D) model of the inclusion, pore and micropipes. Within the model, the inclusion is infinitely long and has a rectangular cross-section (Fig. 13). The long inclusion axis (*z*-axis) is oriented along the crystal growth direction while the inclusion cross-section occupies the region (*x*<sup>1</sup> < *x* < *x*2, *y*<sup>1</sup> < *y* < 0). The mismatch of the matrix and the inclusion crystal lattices is characterized by the inclusion plastic distortions *βxz* and *βyz* (Gutkin et al., 2006). The inclusion/matrix interface contains an elliptic pore, and mobile micropipes lie nearby. The pore is assumed to grow at the expense of micropipes absorbed (Fig. 12). For definiteness, we suppose that the pore is symmetric with respect to the upper inclusion facet *y*=0. The pore semiaxes are denoted as *p* and *q*, and the pore surface is defined by the equation *x*2/*p*<sup>2</sup> + *y*2/*q*<sup>2</sup> = 1.


20 0 20 *xp*/1000*c*


20 0 20 *xp*/1000*c*


Fig. 15. Vector fields of the force **F** exerted by a 4*H*-SiC inclusion (containing a pore on its boundary) in a 6*H*-SiC matrix on a mobile micropipe with the magnitude 4*c* of the

dislocation Burgers vector, for *<sup>β</sup>xz* <sup>=</sup> *<sup>β</sup>yz* <sup>=</sup> <sup>5</sup> <sup>×</sup> <sup>10</sup>−3. (a) One micropipe lies at the inclusion corner, and another one is attracted to the same place. (b) 35 micropipes merge into the pore, which still attracts new micropipes. (c) 70 micropipes merge into the pore, and the latter starts to repulse new micropipes. (d) Figure (c) in a smaller scale. The arrows show the force

Consider pore growth in the case of equal plastic distortions *βxz* = *βyz* = *β*. Figures 14(a) and 14(b) show the final pore configurations when *β* is very small and very large, respectively. If *<sup>β</sup>* is very small (here we take *<sup>β</sup>* <sup>=</sup> <sup>5</sup> <sup>×</sup> <sup>10</sup>−4), only one micropipe is attracted to its equilibrium position at the inclusion corner [Fig. 14(a)]. The following micropipes attracted to the inclusion boundary will come to new equilibrium positions at the inclusion boundary far away from the corner. As a result, micropipes do not merge into a larger pore. In contrast, if *β* is very large (here *β* = 0.05), the following micropipes come first to the corner and further to the growing pore. In this case, the pore can occupy the whole inclusion facet, which is

The process of pore growth in the intermediate case (here *<sup>β</sup>* <sup>=</sup> <sup>5</sup> <sup>×</sup> <sup>10</sup>−3) is shown step by step in Fig. 15. Initially, the first micropipe is attracted to its equilibrium position at the inclusion corner [Fig. 15(a)]. Then new micropipes are attracted to the same equilibrium position and merge, thereby forming a pore. When the pore is not too large, the value of inclusion plastic distortion is sufficient for the pore to attract new micropipes. This case is illustrated in Fig. 15(b), which shows the force vector field (acting on micropipes) around the pore that has absorbed 35 micropipes. However, the situation drastically changes when the pore size becomes large enough [Fig. 15(c)]. Although in this situation a micropipe attraction region still exists near the pore surface, the force on the micropipe is repulsive at some distance from the pore, and the micropipe cannot approach the pore. Under the action of the force field, the micropipe has to round the pore and come to a new equilibrium position at the inclusion boundary far from the pore. The presence of a new equilibrium position for new micropipes

Thus, the analysis of the forces exerted on micropipes by the inclusion and elliptic pore has shown that the pore attracts micropipes until their number reaches a critical value. After that, the micropipes absorbed by the pore produce a repulsion zone for new micropipes, and pore growth stops. The critical pore size is determined by the values of inclusion plastic distortions. At their small values, isolated micropipes form at the inclusion/matrix interface; at medium values micropipes coalesce to form a pore of a certain size; at large values the pore occupies

20 0 20 *xp*/1000*c*



(d) re-scaled (c)

*xp*/1000*c*


*yp*/1000*c*

(c) 70 micropipes

0

20

Micropipe Reactions in Bulk SiC Growth 203

*yp*/1000*c*

(b) 35 micropipes

directions, and their length is proportional to the force magnitude.

is clearly seen in Fig. 15(d), which represents Fig. 15(c) in a smaller scale.

0

20

*yp*/1000*c*

(a) 1 micropipe

illustrated in Fig. 14(b).

the whole inclusion boundary.

0

20

*yp*/1000*c*

Fig. 13. Elliptic pore at the inclusion boundary and a mobile micropipe nearby.

Fig. 14. Vector fields of the force **F** exerted by a 4*H*-SiC inclusion (containing a pore on its boundary) in a 6*H*-SiC matrix on a mobile micropipe with the magnitude 4*c* of the dislocation Burgers vector. (a) The inclusion plastic distortion components are equal and very small, *<sup>β</sup>xz* <sup>=</sup> *<sup>β</sup>yz* <sup>=</sup> <sup>5</sup> <sup>×</sup> <sup>10</sup>−4, and the inclusion contains only one micropipe at the corner. (b) The inclusion plastic distortion components are equal and very large, *βxz* = *βyz* = 0.05, and the inclusion contains a dislocated elliptic pore which is produced by the coalescence of 306 micropipes and occupies the whole inclusion facet. The arrows show the force directions, and their length is proportional to the force magnitude.

For simplicity, in the following analysis we presume that all micropipes attracted to the inclusion boundary have the same Burgers vectors **b** and the same radii *R*<sup>0</sup> (Fig. 13). The micropipe radius *R*<sup>0</sup> is supposed to be related to its Burgers vector magnitude *b* by the Frank relation (Frank, 1951) *R*<sup>0</sup> = *Gb*2/(8*π*2*γ*), where *G* is the shear modulus and *γ* is the specific surface energy. Also, the pore is assumed to grow in such a way that one of its semiaxes *q* is constant and equal to the micropipe radius *R*<sup>0</sup> (*q* = *R*0), while the other semiaxis *p* increases. The volume of the elliptic pore is supposed to be equal to the total volume of the micropipes that merge to form the pore. The free volume conservation equation *πpq* = *NπR*<sup>2</sup> <sup>0</sup> (where *N* is the number of micropipes agglomerated into the pore) along with the relation *q* = *R*<sup>0</sup> gives the following expression for the larger pore semiaxis *p*: *p* = *NR*0.

To analyze the conditions for pore growth, we have calculated the force **F** = *Fx***e***<sup>x</sup>* + *Fy***e***<sup>y</sup>* exerted on a micropipe by the inclusion containing the pore. To do so, we have neglected the short-range effect of the micropipe free surface and considered the micropipe as a screw dislocation with the Burgers vector **b** and coordinates (*xp*, *yp*) (Fig. 13). The inclusion stress field has been calculated by integrating the stresses of virtual screw dislocations distributed over inclusion facets, with the density determined by the value of the corresponding component of inclusion plastic distortion. To account for the influence of the elliptic pore, we have used the solution for a screw dislocation near an elliptic pore (Zhang & Li, 1991) in the calculation of the stress field of an individual virtual dislocation. The same solution was used to separately account for micropipe attraction to the free surface of the elliptic pore. The calculation scheme used to cast the quantities *Fx* and *Fy* is described in (Gutkin et al., 2009b). As an example, in the following analysis, we consider a 4*H*-SiC inclusion in the 6*H*-SiC matrix. We assume that the inclusion has the square cross-section with the facet dimension of 200 *μ*m and put *<sup>γ</sup>*/*<sup>G</sup>* <sup>=</sup> 1.4 <sup>×</sup> <sup>10</sup>−<sup>3</sup> nm (Si et al., 1997). The magnitude of the micropipe dislocation Burgers vector is chosen to take the values of 4*c*, where *c* ≈ 1 nm is the 4*H*-SiC lattice parameter (Goldberg et al., 2001).

16 Will-be-set-by-IN-TECH


Fig. 14. Vector fields of the force **F** exerted by a 4*H*-SiC inclusion (containing a pore on its boundary) in a 6*H*-SiC matrix on a mobile micropipe with the magnitude 4*c* of the dislocation Burgers vector. (a) The inclusion plastic distortion components are equal and very small, *<sup>β</sup>xz* <sup>=</sup> *<sup>β</sup>yz* <sup>=</sup> <sup>5</sup> <sup>×</sup> <sup>10</sup>−4, and the inclusion contains only one micropipe at the corner. (b) The inclusion plastic distortion components are equal and very large,

*βxz* = *βyz* = 0.05, and the inclusion contains a dislocated elliptic pore which is produced by the coalescence of 306 micropipes and occupies the whole inclusion facet. The arrows show

For simplicity, in the following analysis we presume that all micropipes attracted to the inclusion boundary have the same Burgers vectors **b** and the same radii *R*<sup>0</sup> (Fig. 13). The micropipe radius *R*<sup>0</sup> is supposed to be related to its Burgers vector magnitude *b* by the Frank relation (Frank, 1951) *R*<sup>0</sup> = *Gb*2/(8*π*2*γ*), where *G* is the shear modulus and *γ* is the specific surface energy. Also, the pore is assumed to grow in such a way that one of its semiaxes *q* is constant and equal to the micropipe radius *R*<sup>0</sup> (*q* = *R*0), while the other semiaxis *p* increases. The volume of the elliptic pore is supposed to be equal to the total volume of the micropipes

is the number of micropipes agglomerated into the pore) along with the relation *q* = *R*<sup>0</sup> gives

To analyze the conditions for pore growth, we have calculated the force **F** = *Fx***e***<sup>x</sup>* + *Fy***e***<sup>y</sup>* exerted on a micropipe by the inclusion containing the pore. To do so, we have neglected the short-range effect of the micropipe free surface and considered the micropipe as a screw dislocation with the Burgers vector **b** and coordinates (*xp*, *yp*) (Fig. 13). The inclusion stress field has been calculated by integrating the stresses of virtual screw dislocations distributed over inclusion facets, with the density determined by the value of the corresponding component of inclusion plastic distortion. To account for the influence of the elliptic pore, we have used the solution for a screw dislocation near an elliptic pore (Zhang & Li, 1991) in the calculation of the stress field of an individual virtual dislocation. The same solution was used to separately account for micropipe attraction to the free surface of the elliptic pore. The calculation scheme used to cast the quantities *Fx* and *Fy* is described in (Gutkin et al., 2009b). As an example, in the following analysis, we consider a 4*H*-SiC inclusion in the 6*H*-SiC matrix. We assume that the inclusion has the square cross-section with the facet dimension of 200 *μ*m and put *<sup>γ</sup>*/*<sup>G</sup>* <sup>=</sup> 1.4 <sup>×</sup> <sup>10</sup>−<sup>3</sup> nm (Si et al., 1997). The magnitude of the micropipe dislocation Burgers vector is chosen to take the values of 4*c*, where *c* ≈ 1 nm is the 4*H*-SiC lattice

*yp*/1000*c*

(a) (b) *xp*/1000*c*



<sup>0</sup> (where *N*


0

*yp*/1000*c*


*2R0*

Fig. 13. Elliptic pore at the inclusion boundary and a mobile micropipe nearby.

the force directions, and their length is proportional to the force magnitude.

that merge to form the pore. The free volume conservation equation *πpq* = *NπR*<sup>2</sup>

the following expression for the larger pore semiaxis *p*: *p* = *NR*0.

Micropipe

**b**

*y*

*yp*

*q*

*-q*

*x1 -p p x2 xp x*

Inclusion Matrix

Pore

*y1*

parameter (Goldberg et al., 2001).

Fig. 15. Vector fields of the force **F** exerted by a 4*H*-SiC inclusion (containing a pore on its boundary) in a 6*H*-SiC matrix on a mobile micropipe with the magnitude 4*c* of the dislocation Burgers vector, for *<sup>β</sup>xz* <sup>=</sup> *<sup>β</sup>yz* <sup>=</sup> <sup>5</sup> <sup>×</sup> <sup>10</sup>−3. (a) One micropipe lies at the inclusion corner, and another one is attracted to the same place. (b) 35 micropipes merge into the pore, which still attracts new micropipes. (c) 70 micropipes merge into the pore, and the latter starts to repulse new micropipes. (d) Figure (c) in a smaller scale. The arrows show the force directions, and their length is proportional to the force magnitude.

Consider pore growth in the case of equal plastic distortions *βxz* = *βyz* = *β*. Figures 14(a) and 14(b) show the final pore configurations when *β* is very small and very large, respectively. If *<sup>β</sup>* is very small (here we take *<sup>β</sup>* <sup>=</sup> <sup>5</sup> <sup>×</sup> <sup>10</sup>−4), only one micropipe is attracted to its equilibrium position at the inclusion corner [Fig. 14(a)]. The following micropipes attracted to the inclusion boundary will come to new equilibrium positions at the inclusion boundary far away from the corner. As a result, micropipes do not merge into a larger pore. In contrast, if *β* is very large (here *β* = 0.05), the following micropipes come first to the corner and further to the growing pore. In this case, the pore can occupy the whole inclusion facet, which is illustrated in Fig. 14(b).

The process of pore growth in the intermediate case (here *<sup>β</sup>* <sup>=</sup> <sup>5</sup> <sup>×</sup> <sup>10</sup>−3) is shown step by step in Fig. 15. Initially, the first micropipe is attracted to its equilibrium position at the inclusion corner [Fig. 15(a)]. Then new micropipes are attracted to the same equilibrium position and merge, thereby forming a pore. When the pore is not too large, the value of inclusion plastic distortion is sufficient for the pore to attract new micropipes. This case is illustrated in Fig. 15(b), which shows the force vector field (acting on micropipes) around the pore that has absorbed 35 micropipes. However, the situation drastically changes when the pore size becomes large enough [Fig. 15(c)]. Although in this situation a micropipe attraction region still exists near the pore surface, the force on the micropipe is repulsive at some distance from the pore, and the micropipe cannot approach the pore. Under the action of the force field, the micropipe has to round the pore and come to a new equilibrium position at the inclusion boundary far from the pore. The presence of a new equilibrium position for new micropipes is clearly seen in Fig. 15(d), which represents Fig. 15(c) in a smaller scale.

Thus, the analysis of the forces exerted on micropipes by the inclusion and elliptic pore has shown that the pore attracts micropipes until their number reaches a critical value. After that, the micropipes absorbed by the pore produce a repulsion zone for new micropipes, and pore growth stops. The critical pore size is determined by the values of inclusion plastic distortions. At their small values, isolated micropipes form at the inclusion/matrix interface; at medium values micropipes coalesce to form a pore of a certain size; at large values the pore occupies the whole inclusion boundary.

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Mokhov, E. N. (2009). Micropipe absorption mechanism of pore growth at foreign polytype boundaries in SiC crystals. *J. Appl. Phys.*, Vol. 106, 123515 (7 pp.), ISSN

micropipe-related pure superscrew dislocations in SiC. *Appl. Phys. Lett.*, Vol. 74,

dislocations via thick 4*H*-SiC epitaxial overgrowth. *Jpn. J. Appl. Phys.*, Vol. 39,

and spatial distribution of threading edge dislocations in 4*H*-SiC epilayers by high-resolution topography. *J. Cryst. Growth*, Vol. 311, 1416–1422, ISSN: 0022-0248. Kohn, V. G.; Argunova, T. S.; Je, J.-H. (2007). Study of micropipe structure in SiC by x-ray phase contrast imaging. *Appl. Phys. Lett.*, Vol. 91, 171901 (3 pp.), ISSN 0003-6951. Ma, R.-H.; Zhang, H.; DudleyM.; Prasad, V. (2003). Thermal system design and dislocation

reduction for growth of wide band gap crystals: : application to SiC growth. *J. Cryst.*

Jenny, J. R.; Malta, D.; Carter Jr., C. H. (2000). The status of SiC bulk growth from an industrial point of view. *J. Cryst. Growth*, Vol. 211, No. 1–4, 325–332, ISSN: 0022-0248.

#### **6. Summary**

We have briefly reviewed our recent experimental and theoretical studies of collective behavior of micropipes during the bulk SiC growth. The micropipes grow up with the propagation of the crystal growth front and come into reactions with each other as well as with other structural imperfections like foreign polytype inclusions and pores. The reactions between micropipes are either contact-free or contact. A contact-free reaction occurs when one micropipe emits a full-core dislocation, while another micropipe accepts it. We have theoretically described the conditions necessary for such a reaction and provided its indirect experimental evidence. As to contact reactions, we have experimentally documented different transformations and reactions between micropipes in SiC crystal, such as ramification of a dislocated micropipe into two smaller ones, bundling and merging that led to the generation of new micropipes or annihilation of initial ones, interaction of micropipes with foreign polytype inclusions followed by agglomeration and coalescence of micropipes into pores. Theoretical analyses of each configuration have shown that micropipe split happens if the splitting dislocation overcomes the pipe attraction zone and the crystal surface attraction zone. Bundles and twisted dislocation dipoles arise when two micropipes are under strong influence of the stress fields from dense groups of other micropipes. Foreign polytype inclusions attract micropipes due to the action of inclusion stress fields. The micropipe absorption by a pore that has been nucleated at the boundary of inclusion depends on the inclusion distortion. The pore growth stops when the pore absorbs a critical amount of micropipes or occupies the whole inclusion boundary. The general issue is that any kind of the above reactions is quite desired because they always lead to micropipe healing and/or cleaning the corresponding crystal areas from micropipes. Moreover, the contact-free reactions can be treated as a mechanism of thermal stress relaxation, while the micropipe interaction with foreign polytype inclusions and accumulation on their boundaries is a mechanism of misfit stress accommodation.

#### **7. Acknowledgements**

This work was supported by the Creative Research Initiatives (Functional X-ray Imaging) of MEST/NRF of Korea. Support of the Russian Foundation of Basic Research (Grant No 10-02-00047-a) is also acknowledged.

#### **8. References**


18 Will-be-set-by-IN-TECH

We have briefly reviewed our recent experimental and theoretical studies of collective behavior of micropipes during the bulk SiC growth. The micropipes grow up with the propagation of the crystal growth front and come into reactions with each other as well as with other structural imperfections like foreign polytype inclusions and pores. The reactions between micropipes are either contact-free or contact. A contact-free reaction occurs when one micropipe emits a full-core dislocation, while another micropipe accepts it. We have theoretically described the conditions necessary for such a reaction and provided its indirect experimental evidence. As to contact reactions, we have experimentally documented different transformations and reactions between micropipes in SiC crystal, such as ramification of a dislocated micropipe into two smaller ones, bundling and merging that led to the generation of new micropipes or annihilation of initial ones, interaction of micropipes with foreign polytype inclusions followed by agglomeration and coalescence of micropipes into pores. Theoretical analyses of each configuration have shown that micropipe split happens if the splitting dislocation overcomes the pipe attraction zone and the crystal surface attraction zone. Bundles and twisted dislocation dipoles arise when two micropipes are under strong influence of the stress fields from dense groups of other micropipes. Foreign polytype inclusions attract micropipes due to the action of inclusion stress fields. The micropipe absorption by a pore that has been nucleated at the boundary of inclusion depends on the inclusion distortion. The pore growth stops when the pore absorbs a critical amount of micropipes or occupies the whole inclusion boundary. The general issue is that any kind of the above reactions is quite desired because they always lead to micropipe healing and/or cleaning the corresponding crystal areas from micropipes. Moreover, the contact-free reactions can be treated as a mechanism of thermal stress relaxation, while the micropipe interaction with foreign polytype inclusions and accumulation on their boundaries is a mechanism of misfit stress accommodation.

This work was supported by the Creative Research Initiatives (Functional X-ray Imaging) of MEST/NRF of Korea. Support of the Russian Foundation of Basic Research (Grant No

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Epelbaum, B. M. & Hofmann, D. (2001). On the mechanisms of micropipe and macrodefect

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synchrotron white beam X-ray topographic images of micropipes in 4*H*-SiC and determination of their dislocation senses. *J. Electron. Mater.*, Vol. 37, No. 5, 713–720,

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**6. Summary**

**7. Acknowledgements**

**8. References**

10-02-00047-a) is also acknowledged.

ISSN: 0361-5235.

ISSN: 0022-0248.

ISSN: 0108-7673.

Vol. 36, No. 10A, A30–36, ISSN 0022-3727.


**9** 

*India* 

**Thermal Oxidation of Silicon Carbide (SiC) –** 

*Central Electronics Engineering Research Institute (CEERI)/ Council of Scientific and* 

The thin thermally grown SiO2 plays a unique role in device fabrication of Si-VLSI Technology. The well established growth mechanisms and continuous research to grow high quality SiO2 on Si substrate has to lead the development of planner-Technology and permits the fabrication of well defined diffused or ion-implanted junctions of precisely controllable dimensions. Among the all wide bandgap semiconductors, Silicon Carbide (SiC) is the only compound semiconductor which can be thermally oxidized in the form of SiO2, similar to the silicon growth mechanism. This means that the devices which can be easily fabricated on Si substrate (Power MOSFET, IGBT, MOS controlled thyristor etc.) can also be fabricated on SiC substrate. Moreover, a good knowledge of SiO2/Si interface has been established and has to lead great progress in Silicon-Technology that can be directly

Similar to the Silicon-Technology, high quality thin SiO2 is most demanded gate oxide from the SiC based semiconductor industries to reduce the cost and process steps in device fabrication. Various oxidation processes has been adopted such as dry oxidation [1], wet oxidation [2], chemical vapour deposition (CVD) [3], and pyrogenic oxidation [4-6] in order to achieve the most suitable process to realize the SiC-based MOS structures. To develop the basic growth mechanism of SiO2 on SiC surfaces apart from the Si growth mechanisms, worldwide numbers of researchers are intensively working on the above specified problems. Since SiC is a compound material of Si and C atoms, that is why the role of C atoms during the thermal growth of SiO2 has been observed to be very crucial. Several studies [7-9] confirm the presence of C species in the thermally grown oxide, which directly affect the interface as well as dielectric properties of metal-oxide-semiconductor structures [10]. For this reason, rigorous studies on electrical behavior of thermally grown SiO2 on SiC play a fundamental role in the understanding and control of electrical characteristics of SiCbased devices. It has been reported that the growth rate of SiC polytypes is much lower than that of Si [11-13]. The rate of reaction on the surface of SiC is much slower than that of Si under the same oxidation conditions. In case of SiC, another unique phenomenon has been observed that the oxidation of SiC is a face terminated oxidation, means the both polar faces (Si and C face) have different oxidation rates [14-15]. These oxidation rates are also depend on the crystal orientation of SiC and polytypes i.e. Silicon carbide shows an anisotropic

**1. Introduction** 

oxidation nature.

applied to development of SiC-Technology.

**Experimentally Observed Facts** 

Sanjeev Kumar Gupta and Jamil Akhtar

*Industrial Research (CSIR)* 


### **Thermal Oxidation of Silicon Carbide (SiC) – Experimentally Observed Facts**

Sanjeev Kumar Gupta and Jamil Akhtar

*Central Electronics Engineering Research Institute (CEERI)/ Council of Scientific and Industrial Research (CSIR) India* 

#### **1. Introduction**

20 Will-be-set-by-IN-TECH

206 Silicon Carbide – Materials, Processing and Applications in Electronic Devices

Müller, St. G.; Brady,M. F.; Burk, A. A.; Hobgood, H. McD; Jenny, J. R.; Leonard, R. T.;

Nakamura, D.; Yamaguchi, S.; Gunjishima, I.; Hirose, Y.; Kimoto T. (2007). Topographic study

Nakamura, D.; Yamaguchi, S.; Hirose, Y.; Tani, T.; Takatori, K.; Kajiwara, K.; Kimoto T.

Ohtani, N.; Katsuno, M.; Tsuge, H.; Fujimoto, T.; Nakabayashi, M.; Yashiro, H.; Sawamura, M.;

Pirouz, P. (1998). On micropipes and nanopipes in SiC and GaN. *Philos. Mag. A*, Vol. 78, No. 3,

Saparin, G. V.; Obyden, S. K.; Ivannikov, P. V.; Shishkin, E. B.; Mokhov, E. N.; Roenkov, A. D.;

Si, W.; Dudley,M.; Glass, R.; Tsvetkov, V.; Carter Jr., C. (1997). Hollow-core screw dislocations

Thölén, A. R. (1970). The stress field of a pile-up of screw dislocations at a cylindrical inclusion.

Tsuchida, H.; Kamata, I.; Nagano M. (2007). Investigation of defect formation in 4*H*-SiC

Vodakov, Yu. A.; Roenkov, A. D.; Ramm, M. G.; Mokhov, E. N.; Makarov, Yu. N. (1997). Use of

Wang, Y.; Ali, G. N.; Mikhov,M. K.; Vaidyanathan, V.; Skromme, B. J.; Raghothamachar, B.;

Wierzchowski,W.; Wieteska, K.; Balcer, T.; Malinowska, A.; Graeff,W.; Hofman,W. (2007).

Yakimova, R.; Vouroutzis, N.; Syväjärvi, M.; Stoemenos, J. (2005). Morphological features

Zhang, T-Y. & Li, J. C. M. (1991). Image forces and shielding effects of a screw dislocation near a finite-length crack. *Mater. Sci. and Eng. A*, Vol. 142, No. 1, 35-39, ISSN: 0921-5093.

layers. *Phys. Status Solidi B*, Vol. 202, 177–200, ISSN: 1521-3951.

diodes. *J. Appl. Phys.*, Vol. 97, 013540 (10 pp.), ISSN 0021-8979.

Vol. 430, 1009–1012, ISSN: 0028-0836.

*Growth*, Vol. 286, 55–60, ISSN: 0022-0248.

*Scanning*, Vol. 19, 269–274, ISSN: 1932-8745.

*Acta Metall.*, Vol. 18, No. 4, 445–455, ISSN: 1359-6454

(7 pp.), ISSN 0021-8979.

727–736, ISSN: 1478-6435.

128–133, ISSN: 0361-5235.

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1359–1363, ISSN: 0232-1300.

0021-8979.

*J. Cryst. Growth*, Vol. 304, 57–63, ISSN: 0022-0248.

Malta, D. P.; Powell, A. R.; Sumakeris, J. J.; Tsvetkov, V. F.; Carter Jr., C. H. (2006). Large area SiC substrates and epitaxial layers for high power semiconductor devices - An industrial perspective. *Superlattices Microst.*, Vol. 40, 195–200, ISSN: 0749-6036. Nakamura, D.; Gunjishima, I.; Yamaguchi, S.; Ito, T.; Okamoto, A.; Kondo, H.; Onda, S.;

Takatori K. (2004). Ultrahigh-quality silicon carbide single crystals. *Let. Nature*,

of dislocation structure in hexagonal SiC single crystals with low dislocation density.

(2008). Direct determination of Burgers vector sense and magnitude of elementary dislocations by synchrotron white x-ray topography. *J. Appl. Phys.*, Vol. 103, 013510

Aigo, T.; Hoshino T. (2006). Propagation behavior of threading dislocations during physical vapor transport growth of silicon carbide (SiC) single crystals. *J. Cryst.*

Hofmann, D. H. (1997). Three-Dimensional Studies of SiC Polytype Transformations.

in 6*H*-SiC single crystals: A test of Frank's theory. *J. Electron. Maters.*, Vol. 26, No. 3,

epitaxial growth by X-ray topography and defect selective etching. *J. Cryst. Growth*,

Ta-container for sublimation growth and doping of SiC bulk crystals and epitaxial

Dudley,M. (2005). Correlation between morphological defects, electron beam-induced current imaging, and the electrical properties of 4*H*-SiC Schottky

Observation of individual dislocations in 6*H* and 4*H*-SiC by means of back-reflection methods of X-ray diffraction topography. *Cryst. Res. Technol.*, Vol. 42, No. 12,

related to micropipe closing in 4*H*-SiC. *J. Appl. Phys.*, Vol. 98, 034905 (6 pp.), ISSN

The thin thermally grown SiO2 plays a unique role in device fabrication of Si-VLSI Technology. The well established growth mechanisms and continuous research to grow high quality SiO2 on Si substrate has to lead the development of planner-Technology and permits the fabrication of well defined diffused or ion-implanted junctions of precisely controllable dimensions. Among the all wide bandgap semiconductors, Silicon Carbide (SiC) is the only compound semiconductor which can be thermally oxidized in the form of SiO2, similar to the silicon growth mechanism. This means that the devices which can be easily fabricated on Si substrate (Power MOSFET, IGBT, MOS controlled thyristor etc.) can also be fabricated on SiC substrate. Moreover, a good knowledge of SiO2/Si interface has been established and has to lead great progress in Silicon-Technology that can be directly applied to development of SiC-Technology.

Similar to the Silicon-Technology, high quality thin SiO2 is most demanded gate oxide from the SiC based semiconductor industries to reduce the cost and process steps in device fabrication. Various oxidation processes has been adopted such as dry oxidation [1], wet oxidation [2], chemical vapour deposition (CVD) [3], and pyrogenic oxidation [4-6] in order to achieve the most suitable process to realize the SiC-based MOS structures. To develop the basic growth mechanism of SiO2 on SiC surfaces apart from the Si growth mechanisms, worldwide numbers of researchers are intensively working on the above specified problems. Since SiC is a compound material of Si and C atoms, that is why the role of C atoms during the thermal growth of SiO2 has been observed to be very crucial. Several studies [7-9] confirm the presence of C species in the thermally grown oxide, which directly affect the interface as well as dielectric properties of metal-oxide-semiconductor structures [10]. For this reason, rigorous studies on electrical behavior of thermally grown SiO2 on SiC play a fundamental role in the understanding and control of electrical characteristics of SiCbased devices. It has been reported that the growth rate of SiC polytypes is much lower than that of Si [11-13]. The rate of reaction on the surface of SiC is much slower than that of Si under the same oxidation conditions. In case of SiC, another unique phenomenon has been observed that the oxidation of SiC is a face terminated oxidation, means the both polar faces (Si and C face) have different oxidation rates [14-15]. These oxidation rates are also depend on the crystal orientation of SiC and polytypes i.e. Silicon carbide shows an anisotropic oxidation nature.

Thermal Oxidation of Silicon Carbide (SiC) – Experimentally Observed Facts 209

(a)

(b) Fig. 1. (a) Schematic details of 4H-SiC substrate which was used and (b) A 2″ diameter 4H-SiC wafer hold by tweezers showing optical transparency by looking at carrier holder

through the wafer

### **2. Specification of used 4H-SiC substrate**

The availability of the right kind of material has put a restriction for the fabrication of semiconductor devices. There are limited sources where single crystalline SiC substrate is available. At present, the most known firm is M/s CREE Research Inc USA, which is known worldwide for the supply of basic SiC substrates in 2″ or larger diameter sizes. In this reported work n-type 4H-SiC material was the obvious selection with maximum possible epitaxy layer (50 µm) on Si-face with lowest possible doping. Accordingly, CREE Research Inc. USA supplied the following structure on a 2" diameter wafer. Figure 1 (a) shows the schematic details of used 4H-SiC substrate and (b) shows the 2″ wafer hold by tweezers showing optical transparency by looking at carrier holder through the wafer.

#### **3. Kinetics of thermal oxidation**

#### **3.1 Thermal oxidation setup**

Thermal oxidation is the proficient process in VLSI technology which is generally carried out in oxidation furnace (or diffusion furnace, since oxidation is basically based on the diffusion mechanism of oxidizing agent) that provides the sufficient heat needed to elevate the oxidizing ambient temperature. The furnace which was used for thermal growth of SiO2 on 4H-SiC is typically consisted of:


The heating assembly usually consists of several heating coils that control the temperature around the furnace quartz tube. There are three different zones in the quartz tube i.e. left, right and center. The temperature of both end zones (left and right) was fixed at 4000C±500C throughout the process. For the ramp up and ramp down of furnace temperature, there are three digital control systems for all three zones. The furnace consists of two different gas pipe lines, one is for N2 gas and other is for dry/wet O2 gas. To control the gas flow, there are MATHESON'S gas flow controllers. A quartz bubbler has been used to generate the steam using highly pure DI-water. There is a temperature controller called heating mental to control the temperature of bubbler. Wet oxygen as well as dry oxygen or dry nitrogen has been passed through a quartz nozzle to the quartz furnace tube.

#### **3.2 Sample preparation**

The cleaning procedure, which is generally used in Si-Technology, has been adopted for this work. All chemicals used in wet-chemical procedure were MOS grade. The wafers were treated for all three major chemical cleaning procedures i.e. Degreasing, RCA and Piranha. Degreasing has three conjugative cleaning steps. First, the wafers were dipped in 1, 1, 1- Trichloroethane (TCE) and boiled for ten minutes to remove the grease on the surface of wafers. Second, the wafers were dipped in acetone and boiled for ten minutes, to remove

The availability of the right kind of material has put a restriction for the fabrication of semiconductor devices. There are limited sources where single crystalline SiC substrate is available. At present, the most known firm is M/s CREE Research Inc USA, which is known worldwide for the supply of basic SiC substrates in 2″ or larger diameter sizes. In this reported work n-type 4H-SiC material was the obvious selection with maximum possible epitaxy layer (50 µm) on Si-face with lowest possible doping. Accordingly, CREE Research Inc. USA supplied the following structure on a 2" diameter wafer. Figure 1 (a) shows the schematic details of used 4H-SiC substrate and (b) shows the 2″ wafer hold by tweezers showing optical transparency by looking at carrier holder through the

Thermal oxidation is the proficient process in VLSI technology which is generally carried out in oxidation furnace (or diffusion furnace, since oxidation is basically based on the diffusion mechanism of oxidizing agent) that provides the sufficient heat needed to elevate the oxidizing ambient temperature. The furnace which was used for thermal growth of SiO2

5. a system of gas flow meter for monitoring involved gases into and out of the process

6. a loading station used for loading (or unloading) wafers into (or from) the process tubes

The heating assembly usually consists of several heating coils that control the temperature around the furnace quartz tube. There are three different zones in the quartz tube i.e. left, right and center. The temperature of both end zones (left and right) was fixed at 4000C±500C throughout the process. For the ramp up and ramp down of furnace temperature, there are three digital control systems for all three zones. The furnace consists of two different gas pipe lines, one is for N2 gas and other is for dry/wet O2 gas. To control the gas flow, there are MATHESON'S gas flow controllers. A quartz bubbler has been used to generate the steam using highly pure DI-water. There is a temperature controller called heating mental to control the temperature of bubbler. Wet oxygen as well as dry oxygen or dry nitrogen has

The cleaning procedure, which is generally used in Si-Technology, has been adopted for this work. All chemicals used in wet-chemical procedure were MOS grade. The wafers were treated for all three major chemical cleaning procedures i.e. Degreasing, RCA and Piranha. Degreasing has three conjugative cleaning steps. First, the wafers were dipped in 1, 1, 1- Trichloroethane (TCE) and boiled for ten minutes to remove the grease on the surface of wafers. Second, the wafers were dipped in acetone and boiled for ten minutes, to remove

3. a fused quartz horizontal process tubes where the wafers undergo oxidation

4. a digital temperature controller and measurement system

been passed through a quartz nozzle to the quartz furnace tube.

**2. Specification of used 4H-SiC substrate** 

**3. Kinetics of thermal oxidation** 

on 4H-SiC is typically consisted of:

1. a fool proof cabinet 2. a heating assembly

tubes and

as shown in figure 2.

**3.2 Sample preparation** 

**3.1 Thermal oxidation setup** 

wafer.

(a)

Fig. 1. (a) Schematic details of 4H-SiC substrate which was used and (b) A 2″ diameter 4H-SiC wafer hold by tweezers showing optical transparency by looking at carrier holder through the wafer

Thermal Oxidation of Silicon Carbide (SiC) – Experimentally Observed Facts 211

and diffusion take place at the surface of substrate. This diffusion mechanism is resulted into a vast variation in oxidation rate. In the experiment of wet oxidation the temperature of quartz bubbler (filled with DI water) is always kept at constant 850C. 0.4 LPM (liter per minutes) flow of wet molecular oxygen has been maintained in the helical path through out the process tube. While in the experiment of dry oxidation, a continuous flow of constant dry oxygen is maintained throughout the process. The samples of each group were loaded and unloaded at 8000C in the 1.9 LPM flow of nitrogen for different time as described above, the ramp up and

The thickness of thermally grown oxide on both terminating faces was experimentally captured by ellipsometry technique followed by DAKTEK surface profiler verification.

Room Temperature

Wet/dry Oxidation at 10000C, 10500C, 11100C, 11500C

Time 0.5 H to 6H with step 0.5H

Unload {8000C}

In ellipsometry technique a polarized coherent beam of light is reflected off the oxide surface at some angle. In this experiment, He-Ne Laser (6328 Å), was used as a source. The monochromatic light passes through a polarizing prism, which results in linearly polarized light. The polarization of light is changed by the reflection so it is now elliptically polarized. The reflected polarized light is then passed through another prism which is rotating about the axis of the light and finally onto a photodetector. This light is now reflected off of the sample which we wish to study. The reflected light intensity is measured as a function of polarization angle. By comparing the incident and reflected intensity and the change in the polarization angle, the film thickness was estimated. The output of the photodetector is displayed on a computer monitor. The principle of operation of an ellipsometer is illustrated

The profiler has sharply, pointed, conical diamond with a rounded tip stylus, resting lightly on the surface, is traversed slowly across it, and the up and down movement of the stylus relative to a suitable datum are magnified and recorded on a base representing the distance traversed, a graph representing the cross-section will be obtained. Figure 5 shows the schematic diagram of surface profiler. Figure 6 (a) shows a sharp step on the oxidized surface which has been realized by photolithography. Figure 6 (b) shows the experimentally

by the schematic drawing of the ellipsometer shown in the figure 4 below.

ramp down temperature of furnace 50C/min as shown in figure 3.

Fig. 3. Process flow of wet thermal oxidation

**3.4 Determination of oxide thickness** 

Load {8000C}

**3.4.1 Basic principle of ellipsometry** 

**3.4.2 Basic principle of surface profiler** 

measured thickness of test sample.

Fig. 2. Schematic diagram of horizontal oxidation furnace

light metal ions. Third, the wafers were dipped in methanol and boiled for ten minutes. Then the wafers were rinsed in de-ionized (DI) water. Subsequently, the standard Radio Corporation of America (RCA) cleaning procedure was followed. This process consisted of two stages, which is termed as standard cleaning-1 (SC-1) and SC-2. In SC-1, the wafers were dipped in high pH alkaline mixture (NH4OH, H2O2 and DI-water) in the ratio of (1:1:5) at some temperature for 10 minutes. There are three main purpose of SC-1: (1) to remove the organic substances on the 4H-SiC wafer surface due to wet oxidation effect, (2) to expose the surface so that any trace metals can be desorbed, and (3) to enable hydrous oxide film to form and dissolve continuously. After SC-1, the wafers were thoroughly ringed in DI-water and then dipped in 10% hydrofluoric (HF) acid for one minute to etch off any remaining SiO2 (native oxide). The SC-2 consisted of a mixture of (HCl, H2O2 and DI-water) in the ratio of (1:1:6). The wafers were dipped in the mixture for 10 minutes at some temperature followed by thoroughly ringed in DI-water and native oxide removal using 10% HF solution. The SC-2 cleaning process could able to dissolve alkali ions, water insoluble hydro oxide compounds and any dual trace metals that was unable to disrobe by SC-1. The last cleaning treatment is known as Piranha cleaning. The piranha solution consisted of a mixture of (H2SO4 and H2O2) in the ratio of (7:1). Then wafers are dipped in this solution for 15 minutes to remove any heavy metal resident on the wafer surface. Finally, the wafers were thoroughly rinsed in DI- water which, is followed by 10% HF dip.

#### **3.3 Oxidation methodology**

Thermal oxidation process was divided into six groups of different temperature range starting from 10500C to 11500C for different oxidation time i.e. 30, 60, 90, 120, 150 and180 minutes. The both oxidizing ambient (steam and dry) had been tried to analyze the exact behavior of thermal oxidation on both faces of 4H-SiC. The wafers were placed in quartz glassware known as boats, which are supported by fused silica paddles inside the process tube of the center zone. A boat can contain many wafers. The oxidizing agent comes with the contact of wafers and diffusion take place at the surface of substrate. This diffusion mechanism is resulted into a vast variation in oxidation rate. In the experiment of wet oxidation the temperature of quartz bubbler (filled with DI water) is always kept at constant 850C. 0.4 LPM (liter per minutes) flow of wet molecular oxygen has been maintained in the helical path through out the process tube. While in the experiment of dry oxidation, a continuous flow of constant dry oxygen is maintained throughout the process. The samples of each group were loaded and unloaded at 8000C in the 1.9 LPM flow of nitrogen for different time as described above, the ramp up and ramp down temperature of furnace 50C/min as shown in figure 3.

Fig. 3. Process flow of wet thermal oxidation

#### **3.4 Determination of oxide thickness**

210 Silicon Carbide – Materials, Processing and Applications in Electronic Devices

light metal ions. Third, the wafers were dipped in methanol and boiled for ten minutes. Then the wafers were rinsed in de-ionized (DI) water. Subsequently, the standard Radio Corporation of America (RCA) cleaning procedure was followed. This process consisted of two stages, which is termed as standard cleaning-1 (SC-1) and SC-2. In SC-1, the wafers were dipped in high pH alkaline mixture (NH4OH, H2O2 and DI-water) in the ratio of (1:1:5) at some temperature for 10 minutes. There are three main purpose of SC-1: (1) to remove the organic substances on the 4H-SiC wafer surface due to wet oxidation effect, (2) to expose the surface so that any trace metals can be desorbed, and (3) to enable hydrous oxide film to form and dissolve continuously. After SC-1, the wafers were thoroughly ringed in DI-water and then dipped in 10% hydrofluoric (HF) acid for one minute to etch off any remaining SiO2 (native oxide). The SC-2 consisted of a mixture of (HCl, H2O2 and DI-water) in the ratio of (1:1:6). The wafers were dipped in the mixture for 10 minutes at some temperature followed by thoroughly ringed in DI-water and native oxide removal using 10% HF solution. The SC-2 cleaning process could able to dissolve alkali ions, water insoluble hydro oxide compounds and any dual trace metals that was unable to disrobe by SC-1. The last cleaning treatment is known as Piranha cleaning. The piranha solution consisted of a mixture of (H2SO4 and H2O2) in the ratio of (7:1). Then wafers are dipped in this solution for 15 minutes to remove any heavy metal resident on the wafer surface. Finally, the wafers

Thermal oxidation process was divided into six groups of different temperature range starting from 10500C to 11500C for different oxidation time i.e. 30, 60, 90, 120, 150 and180 minutes. The both oxidizing ambient (steam and dry) had been tried to analyze the exact behavior of thermal oxidation on both faces of 4H-SiC. The wafers were placed in quartz glassware known as boats, which are supported by fused silica paddles inside the process tube of the center zone. A boat can contain many wafers. The oxidizing agent comes with the contact of wafers

Fig. 2. Schematic diagram of horizontal oxidation furnace

were thoroughly rinsed in DI- water which, is followed by 10% HF dip.

**3.3 Oxidation methodology** 

The thickness of thermally grown oxide on both terminating faces was experimentally captured by ellipsometry technique followed by DAKTEK surface profiler verification.

#### **3.4.1 Basic principle of ellipsometry**

In ellipsometry technique a polarized coherent beam of light is reflected off the oxide surface at some angle. In this experiment, He-Ne Laser (6328 Å), was used as a source. The monochromatic light passes through a polarizing prism, which results in linearly polarized light. The polarization of light is changed by the reflection so it is now elliptically polarized. The reflected polarized light is then passed through another prism which is rotating about the axis of the light and finally onto a photodetector. This light is now reflected off of the sample which we wish to study. The reflected light intensity is measured as a function of polarization angle. By comparing the incident and reflected intensity and the change in the polarization angle, the film thickness was estimated. The output of the photodetector is displayed on a computer monitor. The principle of operation of an ellipsometer is illustrated by the schematic drawing of the ellipsometer shown in the figure 4 below.

#### **3.4.2 Basic principle of surface profiler**

The profiler has sharply, pointed, conical diamond with a rounded tip stylus, resting lightly on the surface, is traversed slowly across it, and the up and down movement of the stylus relative to a suitable datum are magnified and recorded on a base representing the distance traversed, a graph representing the cross-section will be obtained. Figure 5 shows the schematic diagram of surface profiler. Figure 6 (a) shows a sharp step on the oxidized surface which has been realized by photolithography. Figure 6 (b) shows the experimentally measured thickness of test sample.

Thermal Oxidation of Silicon Carbide (SiC) – Experimentally Observed Facts 213

(a) (b) Fig. 6. (a) Oxide step on 4H-SiC (b) Oxide thickness measurements using surface profiler

The measured oxide thickness was plotted as a function of oxidation time, which is shown

The thermal oxidation growth mechanism of SiC is described by same rules as Si, which is well explained by Deal and Grove [16] with some modifications. Finally, the growth rate equation (linear-parabolic) is the same as explained for Si-oxidation. During thermal oxidation of silicon carbide most of the excess carbon is believed to be removed from the interface through the formation of CO2, which diffuses through the oxide and is thereafter released from the sample surface. However, some of the carbon can remain within the oxide and form carbon clusters or graphitic regions. Such regions near the SiO2/SiC are expected to be electrically active and could be responsible for the interface states [17]. The process of SiC thermal oxidation can be divided into three steps. First, the oxidation of the SiC surface occurs through the interaction of an oxygen atom into the chemical bond of a SiC molecule. This oxygen insertion creates a Si-O-C species, which then splits into a CO molecule and a Si atom with a dangling bond. These CO molecules diffuse through the oxide of the oxide surface and react with an oxygen atom, creating CO2. Second, the Si atom reacts with oxygen atoms, which are at the SiC surface in the initial oxidation or diffuses through the oxide to the oxide SiC interface, forming SiO2. These

> 2 2

SiC O CO Si CO O CO

+ → + →

+→+

Si 2O SiO

Contrary to the relatively simple oxidation of Si, there are five major steps in the thermal

in figure 7 and 8. The measured thickness was verified by surface profiler also.

**4. Basic growth mechanism of 4H-SiC** 

three processes can be summarized by the following reactions:

1. transport of molecular oxygen gas to the oxide surface

2. in-diffusion of oxygen through the oxide film 3. reactions with SiC at the oxide/SiC interface

oxidation of SiC.

Fig. 4. Schematic drawing of an ellipsometer

Fig. 5. Schematic drawing of surface profiler

Fig. 4. Schematic drawing of an ellipsometer

Fig. 5. Schematic drawing of surface profiler

Fig. 6. (a) Oxide step on 4H-SiC (b) Oxide thickness measurements using surface profiler

The measured oxide thickness was plotted as a function of oxidation time, which is shown in figure 7 and 8. The measured thickness was verified by surface profiler also.

#### **4. Basic growth mechanism of 4H-SiC**

The thermal oxidation growth mechanism of SiC is described by same rules as Si, which is well explained by Deal and Grove [16] with some modifications. Finally, the growth rate equation (linear-parabolic) is the same as explained for Si-oxidation. During thermal oxidation of silicon carbide most of the excess carbon is believed to be removed from the interface through the formation of CO2, which diffuses through the oxide and is thereafter released from the sample surface. However, some of the carbon can remain within the oxide and form carbon clusters or graphitic regions. Such regions near the SiO2/SiC are expected to be electrically active and could be responsible for the interface states [17]. The process of SiC thermal oxidation can be divided into three steps. First, the oxidation of the SiC surface occurs through the interaction of an oxygen atom into the chemical bond of a SiC molecule. This oxygen insertion creates a Si-O-C species, which then splits into a CO molecule and a Si atom with a dangling bond. These CO molecules diffuse through the oxide of the oxide surface and react with an oxygen atom, creating CO2. Second, the Si atom reacts with oxygen atoms, which are at the SiC surface in the initial oxidation or diffuses through the oxide to the oxide SiC interface, forming SiO2. These three processes can be summarized by the following reactions:

$$\begin{array}{rcl} \text{SiC} + \text{O} & \rightarrow & \text{CO} + \text{Si} \\ \text{CO} + \text{O} & \rightarrow & \text{CO}\_2 \\ \text{Si} + 2\text{O} & \rightarrow & \text{SiO}\_2 \end{array}$$

Contrary to the relatively simple oxidation of Si, there are five major steps in the thermal oxidation of SiC.


Thermal Oxidation of Silicon Carbide (SiC) – Experimentally Observed Facts 215

Fig. 8. Growth of thermal oxide on C-face There are two limiting case of equation 2

1. For long oxidation time i.e. thick oxidation Equation 2 becomes

This relation is called parabolic law and B is called parabolic rate constant. This limiting case is diffusion controlled case because diffusion flux becomes small in comparison to the substrate surface reaction flux. Here the rate of oxidation is limited by the availability of oxidant at the Si

> <sup>0</sup> ( ) *<sup>B</sup> X t A* = +τ

This relation is called linear law and the quantity B/A is called the linear rate constant because in this case enough oxidant is transported across the oxide layer, and the oxidation

Wet thermal oxidation of the C-face of 4H-SiC is systematically slower than that of Si for identical conditions of temperature, pressure and time. Since the oxidation rate has been

rich interface as well as C rich interface, which is controlled by the diffusion process.

2. For short oxidation time i.e. thin oxide equation 2 can be written as

rate is controlled by concentration of oxidant at the surface [21].

<sup>2</sup> *X Bt* <sup>0</sup> = (3)

(4)

4. Out-diffusion of product gases (e.g., CO2) through the oxide film and

5. removals of product gases away from the oxide surface.

The last two steps are not involved in the oxidation of Si. The oxidation of SiC is about one order of magnitude slower than that of Si under the same conditions. The first and last steps are rapid and are not rate-controlling steps. But among the remaining steps, the ratecontrolling step is still uncertain as discussed in several articles [12]. It has been reported in various research papers that the thermal growth kinetics of SiC is governed by linear parabolic law of Deal and Grove, as derived for Silicon [12] [18-20].

$$\left|X\_0\right|^2 + AX\_0 = B\left(t + \tau\right) \tag{1}$$

Where, X denotes the oxide thickness and t is oxidation time. The quantity τ corresponds to a shift in the time coordinate that correct for the presence of the initial layer of oxide thickness and A and B are constants. The above equation is a quadratic equation. The solution of equation can be written as

$$\frac{X\_0}{A/2} = \left(1 + \frac{t+\pi}{A^2/4B}\right)^{1/2} - 1\tag{2}$$

In order to observe the experiment more precise, four numbers of samples were oxidized at same temperature for same oxidation time. All obtained values of thickness are statistically plotted as the function of oxidation time, which is shown in figure 7 (Si-face) and Figure 8 (C-face).

Fig. 7. Growth of thermal oxide on Si-face

The last two steps are not involved in the oxidation of Si. The oxidation of SiC is about one order of magnitude slower than that of Si under the same conditions. The first and last steps are rapid and are not rate-controlling steps. But among the remaining steps, the ratecontrolling step is still uncertain as discussed in several articles [12]. It has been reported in various research papers that the thermal growth kinetics of SiC is governed by linear

( ) <sup>2</sup> *X AX B t* 0 0 + =+

Where, X denotes the oxide thickness and t is oxidation time. The quantity τ corresponds to a shift in the time coordinate that correct for the presence of the initial layer of oxide thickness and A and B are constants. The above equation is a quadratic equation. The

> +τ

In order to observe the experiment more precise, four numbers of samples were oxidized at same temperature for same oxidation time. All obtained values of thickness are statistically plotted as

=+ − 

/ 2 / 4 *X t A A B*

the function of oxidation time, which is shown in figure 7 (Si-face) and Figure 8 (C-face).

τ

1/2

<sup>2</sup> 1 1

(1)

(2)

4. Out-diffusion of product gases (e.g., CO2) through the oxide film and

5. removals of product gases away from the oxide surface.

parabolic law of Deal and Grove, as derived for Silicon [12] [18-20].

0

solution of equation can be written as

Fig. 7. Growth of thermal oxide on Si-face

Fig. 8. Growth of thermal oxide on C-face

There are two limiting case of equation 2

1. For long oxidation time i.e. thick oxidation Equation 2 becomes

$$\left|X\_0\right|^2 = Bt\tag{3}$$

This relation is called parabolic law and B is called parabolic rate constant. This limiting case is diffusion controlled case because diffusion flux becomes small in comparison to the substrate surface reaction flux. Here the rate of oxidation is limited by the availability of oxidant at the Si rich interface as well as C rich interface, which is controlled by the diffusion process.

2. For short oxidation time i.e. thin oxide equation 2 can be written as

$$X\_0 = \frac{B}{A}(t+\tau) \tag{4}$$

This relation is called linear law and the quantity B/A is called the linear rate constant because in this case enough oxidant is transported across the oxide layer, and the oxidation rate is controlled by concentration of oxidant at the surface [21].

Wet thermal oxidation of the C-face of 4H-SiC is systematically slower than that of Si for identical conditions of temperature, pressure and time. Since the oxidation rate has been

Thermal Oxidation of Silicon Carbide (SiC) – Experimentally Observed Facts 217

 Fig. 10. (a) Plots of oxide growth profile on Si-face by wet oxidation, (b) by dry oxidation, (c)

The growth rate multiplication factor (GRMF) on both terminating faces has been calculated as a function of oxidizing ambient (dry and wet). It was observed that in case of dry oxidation GRMF is found in the range of 4-6, means in case of dry oxidation C-face oxidize 4 to 6 times faster than that of Si-face. In the similar way for wet oxidation this GRMF is found in the range of 8-12, means in case of wet oxidation C-face oxidize 8 to 12 times faster than that of Si-face. Figure 11 shows the experimentally measured GRMF in both oxidizing

wet oxidation on C-face and (d) dry oxidation on C-face

ambient.

shown to depend only feebly on the polytypes for the Si-face and not at all for the C-face. It is realistic to believe that although there may be small quantitative differences between the oxidation processes of different polytypes along the perpendicular directions to the bilayer stacking units. The main processes involved in oxidation are diffusion, interface reaction rates and so on, should be largely analogous, and so it is practical to discuss oxidations mechanisms without paying special attention to the polytypes. Figure 9 shows the quantitative oxide thickness up to 6 hours after analyzing the growth dynamic as explained above at 11100C. A number of oxidation experiments have been repeated in order to verify the previously obtained results. Wet and dry thermal oxidations have been performed separately at the different temperature. Figure 10 (a, b, c and d) shows the experimentally measured thermal oxide thickness at the different temperature as explained above by the method of wet and dry oxidation on Si as well as C-face. In both cases (dry and wet), a face terminated behavior has been observed means C-face always oxidized faster than that of Siface under same oxidation condition. This discrepancy in growth rate is termed as growth rate multiplication factor (GRMF), means how much oxidation on C-face is faster than that of Si-face. A very simple equation has been formulated by just dividing the oxide thickness on C-face to oxide thickness on Si-face (equation 5).

$$GRMF = \frac{X\_0 \Big|\_{C-f\_{\text{fice}}}}{X\_0 \Big|\_{Si-f\_{\text{fice}}}} \tag{5}$$

Fig. 9. Experimental growth of wet thermal oxide on both terminating face

shown to depend only feebly on the polytypes for the Si-face and not at all for the C-face. It is realistic to believe that although there may be small quantitative differences between the oxidation processes of different polytypes along the perpendicular directions to the bilayer stacking units. The main processes involved in oxidation are diffusion, interface reaction rates and so on, should be largely analogous, and so it is practical to discuss oxidations mechanisms without paying special attention to the polytypes. Figure 9 shows the quantitative oxide thickness up to 6 hours after analyzing the growth dynamic as explained above at 11100C. A number of oxidation experiments have been repeated in order to verify the previously obtained results. Wet and dry thermal oxidations have been performed separately at the different temperature. Figure 10 (a, b, c and d) shows the experimentally measured thermal oxide thickness at the different temperature as explained above by the method of wet and dry oxidation on Si as well as C-face. In both cases (dry and wet), a face terminated behavior has been observed means C-face always oxidized faster than that of Siface under same oxidation condition. This discrepancy in growth rate is termed as growth rate multiplication factor (GRMF), means how much oxidation on C-face is faster than that of Si-face. A very simple equation has been formulated by just dividing the oxide thickness

> 0 0

*X*

*X*

*GRMF*

Fig. 9. Experimental growth of wet thermal oxide on both terminating face

*C face Si face*

= (5)

− −

on C-face to oxide thickness on Si-face (equation 5).

Fig. 10. (a) Plots of oxide growth profile on Si-face by wet oxidation, (b) by dry oxidation, (c) wet oxidation on C-face and (d) dry oxidation on C-face

The growth rate multiplication factor (GRMF) on both terminating faces has been calculated as a function of oxidizing ambient (dry and wet). It was observed that in case of dry oxidation GRMF is found in the range of 4-6, means in case of dry oxidation C-face oxidize 4 to 6 times faster than that of Si-face. In the similar way for wet oxidation this GRMF is found in the range of 8-12, means in case of wet oxidation C-face oxidize 8 to 12 times faster than that of Si-face. Figure 11 shows the experimentally measured GRMF in both oxidizing ambient.

Thermal Oxidation of Silicon Carbide (SiC) – Experimentally Observed Facts 219

Fig. 12. (a) Plots of face terminated wet oxidation growth rate at 10000C, (b) at 10500C, (c) at

11100C and (d) at 11500C

Fig. 11. Determination of growth rate multiplication factor between both terminating faces by the method of wet and dry oxidation process

#### **5. Determination of average growth rates**

We have applied the Deal and Grove oxidation model to the relations between oxide thickness X and oxidation time t. The quantitative values of the linear parameters B/A and parabolic parameter B in the Deal–Grove equation has been used by fitting to the calculated curve to the observed values in the entire thickness range. The fits are in general good at all of the oxidation temperatures. However, to observe the growth rate behavior for both terminating faces, the grown oxide is divided by its oxidation time. We have derived the oxidation rates dX0/dt as a function of oxide thickness for dry as well as wet oxidation on both terminating faces. Since we are calculating the growth rate of all samples after each successive experiment that's why we are calling it average growth rate.

$$
\left. \frac{dX\_0}{dt} \right|\_{sample1} \Rightarrow Average \frac{dX\_0}{dt} \bigg|\_{sample1} \tag{6}
$$

Figure 12 (a, b, c and d) shows the values of dX0/dt as a function of oxide thickness (grown by the method of wet oxidation) at various oxidation temperatures. We have successfully obtained the values of the oxidation rate even in the thin oxide thickness range of less than 10 nm by these experiments. Figure 13 (a, b, c and d) shows the values of dX0/dt as a function of oxide thickness (grown by the method of wet oxidation) at various oxidation

Fig. 11. Determination of growth rate multiplication factor between both terminating faces

We have applied the Deal and Grove oxidation model to the relations between oxide thickness X and oxidation time t. The quantitative values of the linear parameters B/A and parabolic parameter B in the Deal–Grove equation has been used by fitting to the calculated curve to the observed values in the entire thickness range. The fits are in general good at all of the oxidation temperatures. However, to observe the growth rate behavior for both terminating faces, the grown oxide is divided by its oxidation time. We have derived the oxidation rates dX0/dt as a function of oxide thickness for dry as well as wet oxidation on both terminating faces. Since we are calculating the growth rate of all samples after each

0 0

*dX dX Average dt dt*

*sample*1 1 *sample*

Figure 12 (a, b, c and d) shows the values of dX0/dt as a function of oxide thickness (grown by the method of wet oxidation) at various oxidation temperatures. We have successfully obtained the values of the oxidation rate even in the thin oxide thickness range of less than 10 nm by these experiments. Figure 13 (a, b, c and d) shows the values of dX0/dt as a function of oxide thickness (grown by the method of wet oxidation) at various oxidation

(6)

successive experiment that's why we are calling it average growth rate.

by the method of wet and dry oxidation process

**5. Determination of average growth rates** 

Fig. 12. (a) Plots of face terminated wet oxidation growth rate at 10000C, (b) at 10500C, (c) at 11100C and (d) at 11500C

Thermal Oxidation of Silicon Carbide (SiC) – Experimentally Observed Facts 221

temperatures. Initial oxide growth rate of 19, 24, 35, 67 nm/h (on Si-face) while 180, 220, 357, 374 nm/h (on C-face) have been calculated at 10000C, 10500C, 11100C and 11500C respectively. Similarly, thermal oxide growth for dry oxidation has been found to be 12, 17, 25, 42 nm/h (on Si-face) while 44.5, 81, 113, 157 nm/h (on C-face) have been calculated at 10000C, 10500C, 11100C and 11500C respectively. However, in the smaller thickness range, the values of dX0/dt are not constant but increases with decreasing oxide thickness, i.e., the oxide growth rate enhancement occur at any temperature in this study in both case (Si-face and C-face). It is evident from the above data that the nature of growth rate is parabolic for all cases and initial average growth rate for wet oxidation is faster than that for dry oxidation. C-face is having the higher growth rate than that of Si-face at each oxidation temperature in both oxidations ambient. Figure 14 show the face terminated growth rate, revealing that the average growth rates of dry and wet oxide on Si-face is slower than that of

Fig. 14. Plots of oxidizing ambient terminated growth rate in wet oxidation and (b) in dry

Thermal oxide growth rate constants have been determined by fitting the experimentally measured curve to the measurement made by Deal and Grove (as explained above) of oxide thickness as a function of oxidation time at various oxidation temperatures. In this experiment dry and wet thermal oxidation has been performed (as explained in section 2.3) at10000C, 10500C, 11100C and 11500C for different oxidation time. In each individual experiment, the value of τ has been fixed to zero for all temperature range. A plot of oxide thickness (X0) versus t/X0 from equation 1 should yield a straight line with intercept –A and slope B. Figure 15 (a) and Figure 15 (b) shows the X0 versus t/X0 plots of wet oxidation on Si-face (figure a) and C-face (figure b) of 4H-SiC. It has been observed that the absolute value of A increasing with decreasing oxidation temperature. At the same condition, the slope of the plots increases with increasing temperature. Measured values of these constants

C-face.

oxidation

**6. Determination of rate constants** 

from the figure 15 are listed in table 1.

Fig. 13. (a) Plots of face terminated dry oxidation growth rate at 10000C, (b) at 10500C, (c) at 11100C and (d) at 11500C

Fig. 13. (a) Plots of face terminated dry oxidation growth rate at 10000C, (b) at 10500C, (c) at

11100C and (d) at 11500C

temperatures. Initial oxide growth rate of 19, 24, 35, 67 nm/h (on Si-face) while 180, 220, 357, 374 nm/h (on C-face) have been calculated at 10000C, 10500C, 11100C and 11500C respectively. Similarly, thermal oxide growth for dry oxidation has been found to be 12, 17, 25, 42 nm/h (on Si-face) while 44.5, 81, 113, 157 nm/h (on C-face) have been calculated at 10000C, 10500C, 11100C and 11500C respectively. However, in the smaller thickness range, the values of dX0/dt are not constant but increases with decreasing oxide thickness, i.e., the oxide growth rate enhancement occur at any temperature in this study in both case (Si-face and C-face). It is evident from the above data that the nature of growth rate is parabolic for all cases and initial average growth rate for wet oxidation is faster than that for dry oxidation. C-face is having the higher growth rate than that of Si-face at each oxidation temperature in both oxidations ambient. Figure 14 show the face terminated growth rate, revealing that the average growth rates of dry and wet oxide on Si-face is slower than that of C-face.

Fig. 14. Plots of oxidizing ambient terminated growth rate in wet oxidation and (b) in dry oxidation

#### **6. Determination of rate constants**

Thermal oxide growth rate constants have been determined by fitting the experimentally measured curve to the measurement made by Deal and Grove (as explained above) of oxide thickness as a function of oxidation time at various oxidation temperatures. In this experiment dry and wet thermal oxidation has been performed (as explained in section 2.3) at10000C, 10500C, 11100C and 11500C for different oxidation time. In each individual experiment, the value of τ has been fixed to zero for all temperature range. A plot of oxide thickness (X0) versus t/X0 from equation 1 should yield a straight line with intercept –A and slope B. Figure 15 (a) and Figure 15 (b) shows the X0 versus t/X0 plots of wet oxidation on Si-face (figure a) and C-face (figure b) of 4H-SiC. It has been observed that the absolute value of A increasing with decreasing oxidation temperature. At the same condition, the slope of the plots increases with increasing temperature. Measured values of these constants from the figure 15 are listed in table 1.

Thermal Oxidation of Silicon Carbide (SiC) – Experimentally Observed Facts 223

Figure 16 (a) and 2.16 (b) are the again X0 and t/X0 for face terminated (Si-face and C-Face) oxidation in dry ambient at different oxidation time. The plots are straight line again (as shown in figure 16) with intercept –A and slope B. The measured linear as well as parabolic

Fig. 16. (a) Experimentally measured curve of X0 versus t/X0 for dry oxidation on Si-face

rates constant are listed in table 2.

and (b) on C-face

Fig. 15. (a) Experimentally measured curve of X0 versus t/X0 for wet oxidation on Si-face and (b) on C-face

Fig. 15. (a) Experimentally measured curve of X0 versus t/X0 for wet oxidation on Si-face

and (b) on C-face

Figure 16 (a) and 2.16 (b) are the again X0 and t/X0 for face terminated (Si-face and C-Face) oxidation in dry ambient at different oxidation time. The plots are straight line again (as shown in figure 16) with intercept –A and slope B. The measured linear as well as parabolic rates constant are listed in table 2.

Fig. 16. (a) Experimentally measured curve of X0 versus t/X0 for dry oxidation on Si-face and (b) on C-face

Thermal Oxidation of Silicon Carbide (SiC) – Experimentally Observed Facts 225

Where, K is the rate constant for the reaction, Z is a proportionality constant that varies from one reaction to another, Ea is the activation energy for the reaction, R is the ideal gas

The Arrhenius equation can be used to determine the activation energy for a reaction.

ln( ) ln( ) *Ea K Z*

<sup>1</sup> ln( ) ln( ) *Ea K Z R T*

According to this equation, a plot of ln (K) versus 1/T should give a straight line with a

Figure 17 (a) and (b) shows the straight line tendency of linear rate constant (B/A) with 1/T. Using above equation activation energy has been calculated on both faces of 4H-SiC for wet oxidation as well as dry oxidation and are listed in table 3. Similarly, using parabolic rate constant the rate constants are plotted with 1/T (figure 18 (a) and (b)) and the activation

The linear rate constants B/A show the apparent activation energy of 2.81 eV (dry oxidation on Si-face), 2.274 eV (dry oxidation on C-face), 2.677 eV (wet oxidation on Si-face) and 2.131 eV (wet Oxidation C-face). Similarly parabolic rate constant B show the apparent activation energy of 2.86 eV (dry oxidation on Si-face), 2.0261 eV (dry oxidation on C-face), 2.505 eV (wet oxidation on Si-face) and 1.539 eV (wet Oxidation C-face). It has been found that the activation energy of C-face in both oxidations ambient is always less than that of Si-face, which clearly indicates a face terminated mechanism. Hence different oxidation rates on both faces of 4H-SiC, may be attributed to different activation energies found at both faces.

> C-face (Dry oxidation)

constant (B/A) 2.81 eV 2.274 eV 2.677eV 2.131 eV

constant (B) 2.86 eV 2.0261 eV 2.505 eV 1.539 eV

Table 3. Experimentally measured value of Activation Energy (Ea) in linear region and

slope of - Ea/R, from which the value of activation energy can easily be determined.

energy on both terminating faces has been calculated and presented in table 3.

Si-face (Dry oxidation)

constant in joules per mole kelvin, and T is the temperature in kelvin.

Taking the natural logarithm of both sides of the equation we get

This equation is then to fit as the equation for a straight line.

**Activation energy (Ea)** 

From linear rate

parabolic region

From parabolic rate

*Ea K Ze RT* −

= (7)

*RT* = − (8)

*Y mX C* = + (9)

=− + (10)

Si-face (Wet oxidation)

C-face (Wet oxidation)


Table 1. Experimentally measured Parabolic Rate Constant (B)


Table 2. Experimentally measured Linear Rate Constant (B/A)

#### **7. Determination of activation energy**

The rate of any reaction depends on the temperature at which it is run. As the temperature increases, the molecules move faster, and therefore, they collide more frequently to each other. As a result of these collisions, the molecules also carried more kinetic energy. Thus, the proportion of collisions that can overcome the activation energy for the reaction increases with temperature. The only way to explain the relationship between temperature and the rate of a reaction is to assume that the rate constant depends on the temperature at which the reaction is run. In 1889, Swedish scientist Svante Arrhenius showed that the relationship between temperature and the rate constant of a reaction. Arrhenius's research was a follow up of the theories of reaction rate by Serbian physicist Nebojsa Lekovic. Activation energy may also be defined as the minimum energy required to start a chemical reaction. The activation energy of a reaction is usually denoted by *Ea*, and given in units of kilojoules per mole or in eV.

Temperature (0C) 1000 1050 1110 1050

(Dry oxidation) 0.0000748 0.0001035 0.0003021 0.0006130

(Dry oxidation) 0.00309 0.00568 0.01251 0.01711

(Wet oxidation) 0.000158 0.00033088 0.0008830 0.00120

(Wet oxidation) 0.02571 0.06825 0.11303 0.14207

Temperature (0C) 1000 1050 1110 1050

(Dry oxidation) 0.01533 0.02728 0.14081 0.58161

(Dry oxidation) 0.05072 0.11643 0.34992 0.93078

(Wet oxidation) 0.01022 0.02916 0.10441 0.88499

(Wet oxidation) 0.04887 0.14882 0.40398 0.61975

The rate of any reaction depends on the temperature at which it is run. As the temperature increases, the molecules move faster, and therefore, they collide more frequently to each other. As a result of these collisions, the molecules also carried more kinetic energy. Thus, the proportion of collisions that can overcome the activation energy for the reaction increases with temperature. The only way to explain the relationship between temperature and the rate of a reaction is to assume that the rate constant depends on the temperature at which the reaction is run. In 1889, Swedish scientist Svante Arrhenius showed that the relationship between temperature and the rate constant of a reaction. Arrhenius's research was a follow up of the theories of reaction rate by Serbian physicist Nebojsa Lekovic. Activation energy may also be defined as the minimum energy required to start a chemical reaction. The activation energy of a reaction is usually denoted by *Ea*, and given in units of

Table 1. Experimentally measured Parabolic Rate Constant (B)

Table 2. Experimentally measured Linear Rate Constant (B/A)

**7. Determination of activation energy** 

kilojoules per mole or in eV.

Si-face

C-face

Si-face

C-face

Si-face

C-face

Si-face

C-face

$$K = \mathcal{Z}e^{-\frac{E\_s}{RT}}\tag{7}$$

Where, K is the rate constant for the reaction, Z is a proportionality constant that varies from one reaction to another, Ea is the activation energy for the reaction, R is the ideal gas constant in joules per mole kelvin, and T is the temperature in kelvin.

The Arrhenius equation can be used to determine the activation energy for a reaction. Taking the natural logarithm of both sides of the equation we get

$$\ln(K) = \ln(Z) - \frac{E\_a}{RT} \tag{8}$$

This equation is then to fit as the equation for a straight line.

$$Y = mX + \mathbb{C} \tag{9}$$

$$\ln(K) = -\frac{Ea}{R}\left(\frac{1}{T}\right) + \ln(Z) \tag{10}$$

According to this equation, a plot of ln (K) versus 1/T should give a straight line with a slope of - Ea/R, from which the value of activation energy can easily be determined.

Figure 17 (a) and (b) shows the straight line tendency of linear rate constant (B/A) with 1/T. Using above equation activation energy has been calculated on both faces of 4H-SiC for wet oxidation as well as dry oxidation and are listed in table 3. Similarly, using parabolic rate constant the rate constants are plotted with 1/T (figure 18 (a) and (b)) and the activation energy on both terminating faces has been calculated and presented in table 3.

The linear rate constants B/A show the apparent activation energy of 2.81 eV (dry oxidation on Si-face), 2.274 eV (dry oxidation on C-face), 2.677 eV (wet oxidation on Si-face) and 2.131 eV (wet Oxidation C-face). Similarly parabolic rate constant B show the apparent activation energy of 2.86 eV (dry oxidation on Si-face), 2.0261 eV (dry oxidation on C-face), 2.505 eV (wet oxidation on Si-face) and 1.539 eV (wet Oxidation C-face). It has been found that the activation energy of C-face in both oxidations ambient is always less than that of Si-face, which clearly indicates a face terminated mechanism. Hence different oxidation rates on both faces of 4H-SiC, may be attributed to different activation energies found at both faces.


Table 3. Experimentally measured value of Activation Energy (Ea) in linear region and parabolic region

Thermal Oxidation of Silicon Carbide (SiC) – Experimentally Observed Facts 227

Fig. 18. (a) Parabolic rate constant (B) as a function of 1/T for oxidation in wet ambient and

(b) in dry ambient. Calculated activation energy is shown in their respective plots

Fig. 17. (a) Linear rate constant (B/A) as a function of 1/T for oxidation in wet ambient and (b) in dry ambient. Calculated activation energy is shown in their respective plots

Fig. 17. (a) Linear rate constant (B/A) as a function of 1/T for oxidation in wet ambient and

(b) in dry ambient. Calculated activation energy is shown in their respective plots

Fig. 18. (a) Parabolic rate constant (B) as a function of 1/T for oxidation in wet ambient and (b) in dry ambient. Calculated activation energy is shown in their respective plots

Thermal Oxidation of Silicon Carbide (SiC) – Experimentally Observed Facts 229

[4] P. T. Lai, J. P. Xu, H. P. Wu, C. L. Chen, "Interface properties and reliability of SiO2

[5] M. Meakawa, A. Kawasuso, Z. Q. Chen, M. Yoshikawa, R. Suzuki, T. Ohdaria,

[6] C. Zetterling, M. Ostling, C. I. Harris, P. C. Wood, S. S. Wong, "UV-ozone precleaning

[8] Mark Schürmann, Stefan Dreiner, Ulf Berges, and Carsten Westphal, "Investigation of

[9] X. D. Chen, S. Dhar, T. Isaacs-Smith, J. R. Williams, L. C. Feldman,, and P. M. Mooney,

and NO-annealed SiO2 /4H-SiC", J. Appl. Phys., Vol. 103,p. 033701, 2008. [10] V. R. Vathulya. D. N. Wang and M. H. White, "On the correlation between the carbon

[11] I.C.Vickridge, J. J. Ganem, G. Battisig, and E. Szilagyi, "Oxygen isotropic tracing study

[12] Y. Song, S. Dhar, L.C. Feldman, G. Chung, and J.R. Williams, "Modified deal and grove

[13] J. M. Knaup, P. Deak, T. Frauenheim, A. Gali, Z. Hajnal, and W.J. Choyke, "Theoretical

[14] M. Schuermann, S. Dreiner, U. Berges and C. Westphal, "Structure of the interface

[15] P. Fiorenza and V. Raineri, "Reliability of thermally oxidized SiO2/4H-SiC by

[16] B.E. Deal and A.S. Grove, "General relationship of the thermal oxidation of silicon", J.

[17] Eckhard Pippel and Woltersfordf, "Interface between 4H-SiC and SiO2; microstructure, nanochemistry and interface traps", J. Appl. Phys., Vol.97, p. 034302, 2005. [18] D. Schmeiber, D. R. Batchelor, R. P. Mikolo, O. Halfmann and A. L-Spez, "Oxide

[19] M. T. Htun Aung, J. Szmidt and M. Bakowski, "The study of thermal oxidation on SiC

surface", J Wide Bandgap Material, Vol. 9. No. 4, pp. 313-318, 2002.

carbide", Mater. Sci. Semicond. Process., Vol. 2, Issue 1, pp. 23-27, 1998. [7] Eckhard Pippel and Jörg Woltersdorf, Halldor O. Oafsson and Einar O. Sveinbjornsson,

Issue 4, pp. 577-580, 2004.

113510, 2006.

Vol.161B, pp. 462- 466, 2000.

4953-4957, 2004.

pp.235321-235328, 2005.

035309-035313, 2006.

Appl. Phys.,Vol. 36, p. 3770, 1965.

2006.

2001.

Surf. Sci. Vol. 244, Issue 1-4, pp. 322-325, 2005.

interface traps", J. Appl. Phys., Vol. 97, p. 034302, 2005.

Carbide", Appl. Phys. Lett., Vol. 73, pp. 2161-2163, 1998.

grown on 6H-SiC in dry O2 plus trichloroethylene", Microelectron. Reliab. Vol. 44,

"Structural defect in SiO2/SiC interface probed by a slow positron beam", Appl.

and forming gas annealing applied to wet thermal oxidation of p-type silicon

"Interfaces between 4H-SiC and SiO2: Microstructure, nanochemistry, and near-

carbon contaminations in SiO2 films on 4H-SiC (0001)", J. Appl. Phys., Vol. 100, p.

"Electron capture and emission properties of interface states in thermally oxidized

content and the electrical quality of thermally grown oxide on p-type 6H-Silicon

of the dry thermal oxidation of 6H-SiC", Nucl. Instrum. Methods Phys. Res.,

model for the thermal oxidation of silicon carbide", J. Appl. Phys., Vol. 95, pp.

study of the mechanism of dry oxidation of 4H-SiC", Physical Review B Vol.71,

between ultra thin SiO2 film and 4H-SiC (0001)", Physical Review B Vol. 74, pp.

conductive atomic force microscopy*",* J. Appl. Phys., Vol 88. pp. 212112-212115,

growth on SiC (0001) surfaces", Appl. Surf. Sci. Vol 184, Issue 1-4, pp. 340-345,

#### **8. Conclusions**

This chapter presents a systematically experimental study of the thermal oxide mechanism on 4H-SiC. On the basis of experimental results obtained, the following conclusions have been drawn.


#### **9. References**


This chapter presents a systematically experimental study of the thermal oxide mechanism on 4H-SiC. On the basis of experimental results obtained, the following conclusions have

• Thermal oxidation is a process that incorporates the interaction of molecular oxygen with oxidizing species, which are present on the substrate surface. The different mechanisms, through which oxygen is incorporated in the bulk and interface oxide regions during thermal oxidation of 4H-SiC, is namely the reaction with the SiC

• A face terminated oxidation behavior has been observed which indicates that the

• In the thermal oxidation process of 4H-SiC, Si-face remains silicon rich face and C-face remains carbon rich face. This known observation indicates towards discrete nature of

• The growth rate multiplication factor (GRMF) has been calculated for both oxidizing ambient (dry and wet). It has been concluded that in case of dry oxidation GRMF is found in the range of 4-6, means in case of dry oxidation C-face oxidize 4 to 6 times faster than that of Si-face. Similarly, for wet oxidation this GRMF is found in the range of 8-12, means in case of wet oxidation C-face oxidize 8 to 12 times faster than that of Si-

• It has been observed that the nature of growth rate is parabolic for all cases and initial average growth rate for wet oxidation is always faster than that of dry oxidation. • It has been observed that the absolute value of rate constant (A) increases with decreasing oxidation temperature. At the same condition, the slope of the plots increases with increasing temperature means the value of rate constant B, increases

• The activation energy at both faces of 4H-SiC has been calculated using Arrhenius plots. It has been found that the activation energy of C-face for both oxidations ambient is always less than that of Si-face, which clearly indicates a face terminated mechanism.

[1] I. Vickridge, J. Ganem, Y. Hoshino and I. Trimaille, "Growth of SiO2 on SiC by dry

[2] Hiroshi Yano, Fumito Katafuchi, Tsunenobu Kimoto, and Hiroyuki Matsunami, "Effects

[3] K. Kamimura, D. Kobayashi, S. Okada, T. Mizuguchi, E. Ryu, R. Hayashibe, F. Nagaume

thermal oxidation: mechanisms", J. Phys. D: Appl. Phys. Vol. 40, pp. 6254-6263,

of Wet Oxidation/Anneal on Interface Properties of Thermally Oxidized SiO2 /SiC MOS System and MOSFET's", IEEE Trans. Electron Devices, Vol. 46, No. 3, pp. 504-

and Y. Onuma, " Preparation and characterization of SiO2/6H-SiC metal-insulatorsemiconductor structure using TEOS as source materials", Appl. Surf. Sci., Vol. 184,

substrate and consumption of carbon clusters at both terminating faces.

oxidation growth rate on C-face is faster than that of Si-face.

**8. Conclusions** 

oxidation mechanism.

with increasing temperature.

been drawn.

face.

**9. References** 

2007.

510, 1999.

Issue 1-4, pp. 346-349, 2001.


**0**

**10**

*USA*

**Creation of Ordered Layers on Semiconductor**

Yanli Zhang and Mark E. Tuckerman *Department of Chemistry, New York University*

**Surfaces: An ab Initio Molecular Dynamics Study**

**of the SiC(001)-3**×**2 and SiC(100)-c(2**×**2) Surfaces**

The chemistry of hybrid structures composed of organic molecules and semiconductor surfaces is opening up exciting new areas of development in molecular electronics, nanoscale sensing devices, and surface lithography (Filler & Bent, 2002; Kachian et al., 2010; Kruse & Wolkow, 2002). Covalent attachment of organic molecules to a semiconducting surface can yield active devices, such as molecular switches (Filler & Bent, 2003; Flatt et al., 2005; Guisinger, Basu, Greene, Baluch & Hersam, 2004; Guisinger, Greene, Basu, Baluch & Hersam, 2004; He et al., 2006; Rakshit et al., 2004) and sensors (Cattaruzza et al., 2006) or passivating insulating layers. Moreover, it is assumed that the reactions can be controlled by "engineering" specific modifications to organic

One of the goals of controlling the surface chemistry is the creation of ordered nanostructures on semiconducting surfaces. Indeed, there has been some success in obtaining locally ordered structures on the hydrogen terminated Si(100) surface (Basu et al., 2006; Hossain et al., 2005b; Kirczenow et al., 2005; Lopinski et al., 2000; Pitters et al., 2006). These methods require a dangling Si bond without a hydrogen to initialize the self-replicating reaction. Another popular approach eliminates the initialization step by exploiting the reactivity between surface dimers on certain reconstructed surfaces with the *π* bonds in many organic molecules. The challenge with this approach lies in designing the surface and/or the molecule so as to eliminate all but one desired reaction channel. Charge asymmetries, such as occur on the Si(100)-2×1 surface, lead to a violation of the usual Woodward-Hoffman selection rules, which govern many purely organic reactions, allowing a variety of possible [4+2] and [2+2] surface

Silicon-carbide (SiC) is often the material of choice for electronic and sensor applications under extreme conditions (Capano & Trew, 1997; Mélinon et al., 2007; Starke, 2004) or subject to biocompatibility constraints (Stutzmann et al., 2006). SiC has a variety of reconstructions that could possibly serve as candidates for creating ordered organic/semiconductor interfaces. However, the choice of the reconstruction is crucial. Multiple reactive sites, such as occur on

The exploration of hybrid organic-semiconductor materials and the reactions associated with them is an area in which theoretical and computational tools can play an important role. Indeed, modern theoretical methods combined with high-performance computing,

molecules, suggesting possible new lithographic techniques.

some of the SiC surfaces, will lead to a broad distribution of adducts.

**1. Introduction**

adducts.


## **Creation of Ordered Layers on Semiconductor Surfaces: An ab Initio Molecular Dynamics Study of the SiC(001)-3**×**2 and SiC(100)-c(2**×**2) Surfaces**

Yanli Zhang and Mark E. Tuckerman *Department of Chemistry, New York University USA*

#### **1. Introduction**

230 Silicon Carbide – Materials, Processing and Applications in Electronic Devices

[20] R. Kosugi, K. Fukuda and K Arai, "Thermal oxidation of (0001) 4H-SiC at high

[21] E. H. Nicollian and J. R. Brews, MOS (Metal Oxide Semiconductor) Physics

andTechnology*,* John Wiley and sons, New York, p. 673, 1981.

884, 2003.

temperature in ozone-admixed oxygen gas ambient", Appl. Phys. Lett. Vol. 83, p.

The chemistry of hybrid structures composed of organic molecules and semiconductor surfaces is opening up exciting new areas of development in molecular electronics, nanoscale sensing devices, and surface lithography (Filler & Bent, 2002; Kachian et al., 2010; Kruse & Wolkow, 2002). Covalent attachment of organic molecules to a semiconducting surface can yield active devices, such as molecular switches (Filler & Bent, 2003; Flatt et al., 2005; Guisinger, Basu, Greene, Baluch & Hersam, 2004; Guisinger, Greene, Basu, Baluch & Hersam, 2004; He et al., 2006; Rakshit et al., 2004) and sensors (Cattaruzza et al., 2006) or passivating insulating layers. Moreover, it is assumed that the reactions can be controlled by "engineering" specific modifications to organic molecules, suggesting possible new lithographic techniques.

One of the goals of controlling the surface chemistry is the creation of ordered nanostructures on semiconducting surfaces. Indeed, there has been some success in obtaining locally ordered structures on the hydrogen terminated Si(100) surface (Basu et al., 2006; Hossain et al., 2005b; Kirczenow et al., 2005; Lopinski et al., 2000; Pitters et al., 2006). These methods require a dangling Si bond without a hydrogen to initialize the self-replicating reaction. Another popular approach eliminates the initialization step by exploiting the reactivity between surface dimers on certain reconstructed surfaces with the *π* bonds in many organic molecules. The challenge with this approach lies in designing the surface and/or the molecule so as to eliminate all but one desired reaction channel. Charge asymmetries, such as occur on the Si(100)-2×1 surface, lead to a violation of the usual Woodward-Hoffman selection rules, which govern many purely organic reactions, allowing a variety of possible [4+2] and [2+2] surface adducts.

Silicon-carbide (SiC) is often the material of choice for electronic and sensor applications under extreme conditions (Capano & Trew, 1997; Mélinon et al., 2007; Starke, 2004) or subject to biocompatibility constraints (Stutzmann et al., 2006). SiC has a variety of reconstructions that could possibly serve as candidates for creating ordered organic/semiconductor interfaces. However, the choice of the reconstruction is crucial. Multiple reactive sites, such as occur on some of the SiC surfaces, will lead to a broad distribution of adducts.

The exploration of hybrid organic-semiconductor materials and the reactions associated with them is an area in which theoretical and computational tools can play an important role. Indeed, modern theoretical methods combined with high-performance computing,

allow us to define the electronic Hamiltonian (in atomic units) as

2

*M* ∑ *i*=1 ∇2 *<sup>i</sup>* + ∑ *i*>*j*

An ab Initio Molecular Dynamics Study of the SiC(001)-3x2 and SiC(100)-c(2x2) Surfaces

*M* ∑ *i*=1

1 |**r***<sup>i</sup>* − **r***j*|

where *ZI* is the charge on the *I*th nucleus. The time-independent electronic Schrödinger

<sup>233</sup> Creation of Ordered Layers on Semiconductor Surfaces:

⎤

which assumes the validity of the Born-Oppenheimer approximation, could, in principle, yield all of the electronic energy levels and eigenfunctions at the given nuclear configuration **R**. Here **x***<sup>i</sup>* = **r***i*,*si* is a combination of coordinate and spin variables. Unfortunately, for large condensed-phase problems of the type to be considered here, an exact solution of the

The Kohn-Sham (KS) (Kohn & Sham, 1965) formulation of density functional theory (DFT) (Hohenberg & Kohn, 1964) replaces the fully interacting electronic system described by Eq. (2) by an equivalent non-interacting system that is required to yield the same *ground-state* energy and wave function as the original interacting system. As the name implies, the central quantity in DFT is the ground-state density *n*0(**r**) generated from the ground-state wave

*ZI* |**R***<sup>I</sup>* − **r***i*| − *N* ∑ *I*=1

*M* ∑ *i*=1

*d***r**<sup>2</sup> · *d***r***M*|Ψ0(**r**,*s*1, ..., **x***M*)|

*ZI*

⎦ Ψ(**x**1, ..., **x***M*, **R**) = *E*(**R**)Ψ(**x**1, ..., **x***M*, **R**) (2)

<sup>|</sup>**R***<sup>I</sup>* <sup>−</sup> **<sup>r</sup>***i*<sup>|</sup> (1)

<sup>2</sup> (3)

<sup>2</sup> (4)

*d***r** *n*(**r**)*V*ext(**r**, **R**) (5)

*<sup>H</sup>*<sup>ˆ</sup> elec(**R**) = <sup>−</sup><sup>1</sup>

equation or electronic eigenvalue problem

1 |**r***<sup>i</sup>* − **r***j*|

*n*0(**r**) = *M*

In KS theory, the energy functional is taken to be

*fi*�*ψi*|∇2|*ψi*� <sup>+</sup>

− *N* ∑ *I*=1

electronic eigenvalue problem is computationally intractable.

1/2 ∑*s*1=−1/2

···

*n*(**r**) =

1 2 � *d***r** *d***r**

1/2 ∑*sM*=−1/2

�

where, for notational convenience, the dependence on **R** is left off. The central theorem of DFT is the Hohenberg-Kohn theorem, which states that there exists an exact energy *E*[*n*] that is a functional of electronic densities *n*(**r**) such that when *E*[*n*] is minimized with respect to *n*(**r**) subject to the constraint that � *d***r** *n*(**r**) = *M* (each *n*(**r**) must yield the correct number of electrons), the true ground-state density *n*0(**r**) is obtained. The true ground-state energy is then given by *E*<sup>0</sup> = *E*[*n*0]. The KS noninteracting system is constructed in terms of a set of mutually orthogonal single-particle orbitals *ψi*(**r**) in terms of which the density *n*(**r**) is given

> *N*s ∑ *i*=1

where *fi* are the occupation numbers of a set of *N*<sup>s</sup> such orbitals, where ∑*<sup>i</sup> fi* = *M*. In closed-shell systems, the orbitals are all doubly occupied so that *N*<sup>s</sup> = *M*/2, and *fi* = 2. In open-shell systems, we treat all of the electrons in double and singly occupied orbitals explicitly and take *N*<sup>s</sup> = *M*. When virtual or unoccupied orbitals are needed, we can take *N*<sup>s</sup> > *M*/2 or *N*<sup>s</sup> > *M* for closed and open-shell systems, respectively, and take *fi* = 0 for the

*fi*|*ψi*(**r**)|

� *<sup>n</sup>*(**r**)*n*(**r**�

) <sup>|</sup>**<sup>r</sup>** <sup>−</sup> **<sup>r</sup>**�| <sup>+</sup> *<sup>E</sup>*xc[*n*] + �

⎡ ⎣−<sup>1</sup> 2

*M* ∑ *i*=1 ∇2 *<sup>i</sup>* + ∑ *i*>*j*

function Ψ<sup>0</sup> via

by

virtual orbitals.

<sup>E</sup>[{*ψ*}] = <sup>−</sup><sup>1</sup>

2

*N*s ∑ *i*=1

have advanced to a level such that the thermodynamics and reaction mechanisms can be routinely studied. These studies can aid in the interpretation of experimental results and can leverage theoretical mechanisms to predict the outcomes of new experiments. This chapter will focus on a description of one set of such techniques, namely, those based on density functional theory and first-principles or *ab initio* molecular dynamics (Car & Parrinello, 1985; Marx & Hutter, 2000; 2009; Tuckerman, 2002). As these methods employ an explicit representation of the electronic structure, electron localization techniques can be used to follow local electronic rearrangements during a reaction and, therefore, generate a clear picture of the reaction mechanism. In addition, statistical mechanical tools can be employed to obtain thermodynamic properties of the reaction products, including relative free energies and populations of the various products. Following a detailed description of the computational approaches, we will present two applications of conjugated dienes reacting with different choices of SiC surfaces (Hayes & Tuckerman, 2008). We will investigate how the surface structure influences the thermodynamics of the reaction products and how these thermodynamic properties can be used to guide the choice of the surface in order to control the product distribution and associated free energies.

#### **2. Computational methods**

Because the problem of covalently attaching an organic molecule to a semiconductor surface requires the formation of chemical bonds, a theoretical treatment of this problem must be able to describe this bond formation process, which generally requires an *ab initio* approach in which the electronic structure is accounted for explicitly. Assuming the validity of the Born-Oppenheimer approximation, the goal of any *ab initio* approach is to approximate the ground-state solution of the electronic Schrödinger equation *<sup>H</sup>*<sup>ˆ</sup> elec(**R**)|Ψ0(**R**)� <sup>=</sup> *<sup>E</sup>*0(**R**)|Ψ0(**R**)�, where *<sup>H</sup>*<sup>ˆ</sup> elec is the electronic Hamiltonian, and **<sup>R</sup>** denotes a classical configuration of the chemical nuclei in the system. Ultimately, in order to predict reaction mechanisms and thermodynamics, one needs to use the approximate solution of the Schrödinger equation to propagate the nuclei dynamically using Newton's laws of motion. This is the essence of the method known as *ab initio* molecular dynamics (AIMD) (Car & Parrinello, 1985; Marx & Hutter, 2000; 2009; Tuckerman, 2002). Unless otherwise stated, all of the calculations to be presented in this chapter were carried out using the implementation of plane-wave based AIMD implemented in the PINY\_MD package (Tuckerman et al., 2000).

In this section, we will briefly review density functional theory (DFT) as the electronic structure method of choice for the studies to be described in this chapter. DFT represents an optimal compromise between accuracy and computational efficiency. This is an important consideration, as a typical AIMD calculation requires that the electronic structure problem be solved tens to hundreds of thousands of time in order to generate one or more trajectories of sufficient length to extract dynamic and thermodynamic properties. We will then describe the AIMD approach, including several technical considerations such as basis sets, boundary conditions, and electron localization schemes.

#### **2.1 Density functional theory**

As noted above, we seek approximate solutions to the electronic Schrödinger equation. To this end, we begin by considering a system of *N* nuclei at positions **R**1, ..., **R***<sup>N</sup>* ≡ **R** and *M* electrons with coordinate labels **r**1, ...,**r***<sup>M</sup>* and spin states *s*1, ...,*sM*. The fixed nuclear positions allow us to define the electronic Hamiltonian (in atomic units) as

2 Will-be-set-by-IN-TECH

have advanced to a level such that the thermodynamics and reaction mechanisms can be routinely studied. These studies can aid in the interpretation of experimental results and can leverage theoretical mechanisms to predict the outcomes of new experiments. This chapter will focus on a description of one set of such techniques, namely, those based on density functional theory and first-principles or *ab initio* molecular dynamics (Car & Parrinello, 1985; Marx & Hutter, 2000; 2009; Tuckerman, 2002). As these methods employ an explicit representation of the electronic structure, electron localization techniques can be used to follow local electronic rearrangements during a reaction and, therefore, generate a clear picture of the reaction mechanism. In addition, statistical mechanical tools can be employed to obtain thermodynamic properties of the reaction products, including relative free energies and populations of the various products. Following a detailed description of the computational approaches, we will present two applications of conjugated dienes reacting with different choices of SiC surfaces (Hayes & Tuckerman, 2008). We will investigate how the surface structure influences the thermodynamics of the reaction products and how these thermodynamic properties can be used to guide the choice of the surface in order to control

Because the problem of covalently attaching an organic molecule to a semiconductor surface requires the formation of chemical bonds, a theoretical treatment of this problem must be able to describe this bond formation process, which generally requires an *ab initio* approach in which the electronic structure is accounted for explicitly. Assuming the validity of the Born-Oppenheimer approximation, the goal of any *ab initio* approach is to approximate the ground-state solution of the electronic Schrödinger equation *<sup>H</sup>*<sup>ˆ</sup> elec(**R**)|Ψ0(**R**)� <sup>=</sup> *<sup>E</sup>*0(**R**)|Ψ0(**R**)�, where *<sup>H</sup>*<sup>ˆ</sup> elec is the electronic Hamiltonian, and **<sup>R</sup>** denotes a classical configuration of the chemical nuclei in the system. Ultimately, in order to predict reaction mechanisms and thermodynamics, one needs to use the approximate solution of the Schrödinger equation to propagate the nuclei dynamically using Newton's laws of motion. This is the essence of the method known as *ab initio* molecular dynamics (AIMD) (Car & Parrinello, 1985; Marx & Hutter, 2000; 2009; Tuckerman, 2002). Unless otherwise stated, all of the calculations to be presented in this chapter were carried out using the implementation of plane-wave based AIMD implemented in the PINY\_MD

In this section, we will briefly review density functional theory (DFT) as the electronic structure method of choice for the studies to be described in this chapter. DFT represents an optimal compromise between accuracy and computational efficiency. This is an important consideration, as a typical AIMD calculation requires that the electronic structure problem be solved tens to hundreds of thousands of time in order to generate one or more trajectories of sufficient length to extract dynamic and thermodynamic properties. We will then describe the AIMD approach, including several technical considerations such as basis sets, boundary

As noted above, we seek approximate solutions to the electronic Schrödinger equation. To this end, we begin by considering a system of *N* nuclei at positions **R**1, ..., **R***<sup>N</sup>* ≡ **R** and *M* electrons with coordinate labels **r**1, ...,**r***<sup>M</sup>* and spin states *s*1, ...,*sM*. The fixed nuclear positions

the product distribution and associated free energies.

**2. Computational methods**

package (Tuckerman et al., 2000).

**2.1 Density functional theory**

conditions, and electron localization schemes.

$$\hat{H}\_{\text{elec}}(\mathbf{R}) = -\frac{1}{2} \sum\_{i=1}^{M} \nabla\_i^2 + \sum\_{i>j} \frac{1}{|\mathbf{r}\_i - \mathbf{r}\_j|} - \sum\_{I=1}^{N} \sum\_{i=1}^{M} \frac{Z\_I}{|\mathbf{R}\_I - \mathbf{r}\_i|} \tag{1}$$

where *ZI* is the charge on the *I*th nucleus. The time-independent electronic Schrödinger equation or electronic eigenvalue problem

$$\mathbb{E}\left[-\frac{1}{2}\sum\_{i=1}^{M}\nabla\_{i}^{2} + \sum\_{i>j} \frac{1}{|\mathbf{r}\_{i} - \mathbf{r}\_{j}|} - \sum\_{I=1}^{N}\sum\_{i=1}^{M}\frac{Z\_{I}}{|\mathbf{R}\_{I} - \mathbf{r}\_{i}|}\right] \Psi(\mathbf{x}\_{1}, \dots, \mathbf{x}\_{M}, \mathbf{R}) = E(\mathbf{R})\Psi(\mathbf{x}\_{1}, \dots, \mathbf{x}\_{M}, \mathbf{R}) \tag{2}$$

which assumes the validity of the Born-Oppenheimer approximation, could, in principle, yield all of the electronic energy levels and eigenfunctions at the given nuclear configuration **R**. Here **x***<sup>i</sup>* = **r***i*,*si* is a combination of coordinate and spin variables. Unfortunately, for large condensed-phase problems of the type to be considered here, an exact solution of the electronic eigenvalue problem is computationally intractable.

The Kohn-Sham (KS) (Kohn & Sham, 1965) formulation of density functional theory (DFT) (Hohenberg & Kohn, 1964) replaces the fully interacting electronic system described by Eq. (2) by an equivalent non-interacting system that is required to yield the same *ground-state* energy and wave function as the original interacting system. As the name implies, the central quantity in DFT is the ground-state density *n*0(**r**) generated from the ground-state wave function Ψ<sup>0</sup> via

$$m\_0(\mathbf{r}) = M \sum\_{s\_1=-1/2}^{1/2} \cdots \sum\_{s\_M=-1/2}^{1/2} \int d\mathbf{r}\_2 \cdot d\mathbf{r}\_M |\Psi\_0(\mathbf{r}, \mathbf{s}\_1, \dots, \mathbf{r}\_M)|^2 \tag{3}$$

where, for notational convenience, the dependence on **R** is left off. The central theorem of DFT is the Hohenberg-Kohn theorem, which states that there exists an exact energy *E*[*n*] that is a functional of electronic densities *n*(**r**) such that when *E*[*n*] is minimized with respect to *n*(**r**) subject to the constraint that � *d***r** *n*(**r**) = *M* (each *n*(**r**) must yield the correct number of electrons), the true ground-state density *n*0(**r**) is obtained. The true ground-state energy is then given by *E*<sup>0</sup> = *E*[*n*0]. The KS noninteracting system is constructed in terms of a set of mutually orthogonal single-particle orbitals *ψi*(**r**) in terms of which the density *n*(**r**) is given by

$$m(\mathbf{r}) = \sum\_{i=1}^{N\_s} f\_i |\psi\_i(\mathbf{r})|^2 \tag{4}$$

where *fi* are the occupation numbers of a set of *N*<sup>s</sup> such orbitals, where ∑*<sup>i</sup> fi* = *M*. In closed-shell systems, the orbitals are all doubly occupied so that *N*<sup>s</sup> = *M*/2, and *fi* = 2. In open-shell systems, we treat all of the electrons in double and singly occupied orbitals explicitly and take *N*<sup>s</sup> = *M*. When virtual or unoccupied orbitals are needed, we can take *N*<sup>s</sup> > *M*/2 or *N*<sup>s</sup> > *M* for closed and open-shell systems, respectively, and take *fi* = 0 for the virtual orbitals.

In KS theory, the energy functional is taken to be

$$\mathcal{E}\left[\{\psi\}\right] = -\frac{1}{2}\sum\_{i=1}^{N\_\star} f\_i \langle \psi\_i | \nabla^2 | \psi\_i \rangle + \frac{1}{2} \int d\mathbf{r} \, d\mathbf{r}' \, \frac{n(\mathbf{r})n(\mathbf{r}')}{|\mathbf{r} - \mathbf{r}'|} + E\_{\text{xc}}[n] + \int d\mathbf{r} \, n(\mathbf{r}) V\_{\text{ext}}(\mathbf{r}, \mathbf{R}) \tag{5}$$

where we have introduced the nuclear-nuclear Coulomb repulsion

Within the framework of KS DFT, the force expression becomes

**R**˙ <sup>1</sup>(0), ..., **R**˙ *<sup>N</sup>*(0) using a solver such as the velocity Verlet algorithm:

**<sup>R</sup>**˙ *<sup>I</sup>*(Δ*t*) = **<sup>R</sup>**˙ *<sup>I</sup>*(0) + <sup>Δ</sup>*<sup>t</sup>*

**F***<sup>I</sup>* = −

to the ground-state Born-Oppenheimer surface.

equations of motion of the CP method are

*U*NN(**R**) = ∑

An ab Initio Molecular Dynamics Study of the SiC(001)-3x2 and SiC(100)-c(2x2) Surfaces

*I*>*J*

<sup>235</sup> Creation of Ordered Layers on Semiconductor Surfaces:

The equations of motion, Eq. (10), are integrated numerically for a set of discrete times *t* = 0, Δ*t*, 2Δ*t*, ..., N Δ*t* subject to a set of initial coordinates **R**1(0), ..., **R***N*(0) and velocities

2*MI*

where **F***I*(0) and **F***I*(Δ*t*) are the forces at *t* = 0 and *t* = Δ*t*, respectively. Iteration of Eq. (14) yields a full trajectory of N steps. Eqs. (13) and (14) suggest an algorithm for generating the finite-temperature dynamics of a system using forces generated from electronic structure calculations performed "on the fly" as the simulation proceeds: Starting with the initial nuclear configuration, one minimizes the KS energy functional to obtain the ground-state density, and Eq. (13) is used to obtain the initial forces. These forces are then used to propagate the nuclear positions to the next time step using the first of Eqs. (14). At this new nuclear configuration, the KS functional is minimized again to obtain the new ground-state density and forces using Eq. (13), and these forces are used to propagate the velocities to time *t* = Δ*t*. These forces can also be used again to propagate the positions to time *t* = 2Δ*t*. The procedure is iterated until a full trajectory is generated. This approach is known as "Born-Oppenheimer" dynamics because it employs, at each step, an electronic configuration that is fully quenched

An alternative to Born-Oppenheimer dynamics is the Car-Parrinello (CP) method (Car & Parrinello, 1985; Marx & Hutter, 2000; Tuckerman, 2002). In this approach, an initially minimized electronic configuration is subsequently "propagated" from one nuclear configuration to the next using a fictitious Newtonian dynamics for the orbitals. In this "dynamics", the orbitals are given a small amount of thermal kinetic energy and are made "light" compared to the nuclei. Under these conditions, the orbitals actually generate a potential of mean force surface that is very close to the true Born-Oppenheimer surface. The

*MI***R**¨ *<sup>I</sup>* <sup>=</sup> −∇*<sup>I</sup>* [E[{*ψ*}, **<sup>R</sup>**] + *<sup>U</sup>*NN(**R**)]

*<sup>∂</sup>*�*ψi*�| <sup>E</sup>[{*ψ*}, **<sup>R</sup>**] + <sup>∑</sup>

where *<sup>μ</sup>* is a mass-like parameter for the orbitals (which actually has units of energy<sup>×</sup> time2), and *λij* is the Lagrange multiplier matrix that enforces the orthogonality of the orbitals as a holonomic constraint on the fictitious orbital dynamics. Choosing *μ* small ensures that the

*j*

*λij*|*ψj*� (15)

*<sup>μ</sup>*|*ψ*¨*i*� <sup>=</sup> <sup>−</sup> *<sup>∂</sup>*

**<sup>R</sup>***I*(Δ*t*) = **<sup>R</sup>***I*(0) + <sup>Δ</sup>*t***R**˙ *<sup>I</sup>*(0) + <sup>Δ</sup>*<sup>t</sup>*

*ZIZJ*

<sup>|</sup>**R***<sup>I</sup>* <sup>−</sup> **<sup>R</sup>***J*<sup>|</sup> (12)

[**F***I*(0) + **F***I*(Δ*t*)] (14)

*d***r** *n*0(**r**)∇*IV*ext(**r**, **R**) − ∇*IU*NN(**R**) (13)

**F***I*(0)

2 2*MI*

The first term in the functional represents the noninteracting quantum kinetic energy of the electrons, the second term is the direct Coulomb interaction between two charge distributions, the third therm is the exchange-correlation energy, whose exact form is unknown, and the fourth represents the "external" Coulomb potential on the electrons due to the fixed nuclei, *V*ext(**r**, **R**) = − ∑*<sup>I</sup> ZI*/|**r** − **R***I*|. Minimization of Eq. (5) with respect to the orbitals subject to the orthogonality constraint leads to a set of coupled self-consistent field equations of the form

$$\left[-\frac{1}{2}\nabla^2 + V\_{\mathbf{KS}}(\mathbf{r})\right]\psi\_i(\mathbf{r}) = \sum\_j \lambda\_{ij}\psi\_j(\mathbf{r})\tag{6}$$

where the KS potential *V*KS(**r**) is given by

$$V\_{\rm KS}(\mathbf{r}) = \int d\mathbf{r}' \, \frac{n(\mathbf{r}')}{|\mathbf{r} - \mathbf{r}'|} + \frac{\delta E\_{\rm xc}}{\delta n(\mathbf{r})} + V\_{\rm ext}(\mathbf{r}, \mathbf{R}) \tag{7}$$

and *λij* is a set of Lagrange multipliers used to enforce the orthogonality constraint �*ψi*|*ψj*� = *δij*. If we introduce a unitary transformation *U* that diagonalizes the matrix *λij* into Eq. (6), then we obtain the Kohn-Sham equations in the form

$$\left[-\frac{1}{2}\nabla^2 + V\_{\text{KS}}(\mathbf{r})\right]\phi\_l(\mathbf{r}) = \varepsilon\_l \phi\_l(\mathbf{r})\tag{8}$$

where *φi*(**r**) = ∑*<sup>j</sup> Uijψj*(**r**) are the KS orbitals and *ε<sup>i</sup>* are the KS energy levels, i.e., the eigenvalues of the matrix *λij*. If the exact exchange-correlation functional were known, the KS theory would be exact. However, because *E*xc[*n*] is unknown, approximations must be introduced for this term in practice. The accuracy of DFT results depends critically on the quality of the approximation. One of the most widely used forms for *E*xc[*n*] is known as the generalized-gradient approximation (GGA), where in *E*xc[*n*] is approximated as a local functional of the form

$$E\_{\rm xC}[n] \approx \int d\mathbf{r} \, f\_{\rm GGA}(n(\mathbf{r})\_\prime | \nabla n(\mathbf{r}) |)\tag{9}$$

where the form of the function *f*GGA determines the specific GGA approximation. Commonly used GGA functionals are the Becke-Lee-Yang-Parr (BLYP) (1988; 1988) and Perdew-Burke-Ernzerhof (PBE) (1996) functionals.

#### **2.2 Ab initio molecular dynamics**

Solution of the KS equations yields the electronic structure at a set of fixed nuclear positions **R**1, ..., **R***<sup>N</sup>* ≡ **R**. Thus, in order to follow the progress of a chemical reaction, we need an approach that allows us to propagate the nuclei in time. If we assume the nuclei can be treated as classical point particles, then we seek the nuclear positions **R**1(*t*), ..., **R***N*(*t*) as functions of time, which are given by Newton's second law

$$M\_I \ddot{\mathbf{R}}\_I = \mathbf{F}\_I \tag{10}$$

where *MI* and **F***<sup>I</sup>* are the mass and total force on the *I*th nucleus. If the exact ground-state wave function Ψ0(**R**) were known, then the forces would be given by the Hellman-Feynman theorem

$$\mathbf{F}\_{I} = -\langle \Psi\_{0}(\mathbf{R}) | \nabla\_{I} \hat{H}\_{\text{elec}}(\mathbf{R}) | \Psi\_{0}(\mathbf{R}) \rangle - \nabla\_{I} \mathcal{U}\_{\text{NN}}(\mathbf{R}) \tag{11}$$

where we have introduced the nuclear-nuclear Coulomb repulsion

4 Will-be-set-by-IN-TECH

The first term in the functional represents the noninteracting quantum kinetic energy of the electrons, the second term is the direct Coulomb interaction between two charge distributions, the third therm is the exchange-correlation energy, whose exact form is unknown, and the fourth represents the "external" Coulomb potential on the electrons due to the fixed nuclei, *V*ext(**r**, **R**) = − ∑*<sup>I</sup> ZI*/|**r** − **R***I*|. Minimization of Eq. (5) with respect to the orbitals subject to the orthogonality constraint leads to a set of coupled self-consistent field equations of the form

*ψi*(**r**) = ∑

+ *δE*xc

and *λij* is a set of Lagrange multipliers used to enforce the orthogonality constraint �*ψi*|*ψj*� = *δij*. If we introduce a unitary transformation *U* that diagonalizes the matrix *λij* into Eq. (6),

where *φi*(**r**) = ∑*<sup>j</sup> Uijψj*(**r**) are the KS orbitals and *ε<sup>i</sup>* are the KS energy levels, i.e., the eigenvalues of the matrix *λij*. If the exact exchange-correlation functional were known, the KS theory would be exact. However, because *E*xc[*n*] is unknown, approximations must be introduced for this term in practice. The accuracy of DFT results depends critically on the quality of the approximation. One of the most widely used forms for *E*xc[*n*] is known as the generalized-gradient approximation (GGA), where in *E*xc[*n*] is approximated as a local

where the form of the function *f*GGA determines the specific GGA approximation. Commonly used GGA functionals are the Becke-Lee-Yang-Parr (BLYP) (1988; 1988) and

Solution of the KS equations yields the electronic structure at a set of fixed nuclear positions **R**1, ..., **R***<sup>N</sup>* ≡ **R**. Thus, in order to follow the progress of a chemical reaction, we need an approach that allows us to propagate the nuclei in time. If we assume the nuclei can be treated as classical point particles, then we seek the nuclear positions **R**1(*t*), ..., **R***N*(*t*) as functions of

where *MI* and **F***<sup>I</sup>* are the mass and total force on the *I*th nucleus. If the exact ground-state wave function Ψ0(**R**) were known, then the forces would be given by the Hellman-Feynman

<sup>∇</sup><sup>2</sup> <sup>+</sup> *<sup>V</sup>*KS(**r**)

*j*

*λijψj*(**r**) (6)

*<sup>δ</sup>n*(**r**) <sup>+</sup> *<sup>V</sup>*ext(**r**, **<sup>R</sup>**) (7)

*φi*(**r**) = *εiφi*(**r**) (8)

*d***r** *f*GGA(*n*(**r**), |∇*n*(**r**)|) (9)

*MI***R**¨ *<sup>I</sup>* = **F***<sup>I</sup>* (10)

**<sup>F</sup>***<sup>I</sup>* <sup>=</sup> −�Ψ0(**R**)|∇*IH*<sup>ˆ</sup> elec(**R**)|Ψ0(**R**)�−∇*IU*NN(**R**) (11)

 −1 2

*V*KS(**r**) =

 −1 2

*E*xc[*n*] ≈

then we obtain the Kohn-Sham equations in the form

Perdew-Burke-Ernzerhof (PBE) (1996) functionals.

time, which are given by Newton's second law

 *d***r** � *<sup>n</sup>*(**r**� ) |**r** − **r**�|

where the KS potential *V*KS(**r**) is given by

functional of the form

theorem

**2.2 Ab initio molecular dynamics**

<sup>∇</sup><sup>2</sup> <sup>+</sup> *<sup>V</sup>*KS(**r**)

$$\mathcal{U}\_{\text{NN}}(\mathbf{R}) = \sum\_{I \ge I} \frac{Z\_I Z\_I}{|\mathbf{R}\_I - \mathbf{R}\_I|} \tag{12}$$

Within the framework of KS DFT, the force expression becomes

$$\mathbf{F}\_{I} = -\int d\mathbf{r} \, n\_{0}(\mathbf{r}) \nabla\_{I} V\_{\text{ext}}(\mathbf{r}, \mathbf{R}) - \nabla\_{I} \mathcal{U}\_{\text{NN}}(\mathbf{R}) \tag{13}$$

The equations of motion, Eq. (10), are integrated numerically for a set of discrete times *t* = 0, Δ*t*, 2Δ*t*, ..., N Δ*t* subject to a set of initial coordinates **R**1(0), ..., **R***N*(0) and velocities **R**˙ <sup>1</sup>(0), ..., **R**˙ *<sup>N</sup>*(0) using a solver such as the velocity Verlet algorithm:

$$\mathbf{R}\_{I}(\Delta t) = \mathbf{R}\_{I}(0) + \Delta t \dot{\mathbf{R}}\_{I}(0) + \frac{\Delta t^{2}}{2M\_{I}} \mathbf{F}\_{I}(0)$$

$$\dot{\mathbf{R}}\_{I}(\Delta t) = \dot{\mathbf{R}}\_{I}(0) + \frac{\Delta t}{2M\_{I}} \left[ \mathbf{F}\_{I}(0) + \mathbf{F}\_{I}(\Delta t) \right] \tag{14}$$

where **F***I*(0) and **F***I*(Δ*t*) are the forces at *t* = 0 and *t* = Δ*t*, respectively. Iteration of Eq. (14) yields a full trajectory of N steps. Eqs. (13) and (14) suggest an algorithm for generating the finite-temperature dynamics of a system using forces generated from electronic structure calculations performed "on the fly" as the simulation proceeds: Starting with the initial nuclear configuration, one minimizes the KS energy functional to obtain the ground-state density, and Eq. (13) is used to obtain the initial forces. These forces are then used to propagate the nuclear positions to the next time step using the first of Eqs. (14). At this new nuclear configuration, the KS functional is minimized again to obtain the new ground-state density and forces using Eq. (13), and these forces are used to propagate the velocities to time *t* = Δ*t*. These forces can also be used again to propagate the positions to time *t* = 2Δ*t*. The procedure is iterated until a full trajectory is generated. This approach is known as "Born-Oppenheimer" dynamics because it employs, at each step, an electronic configuration that is fully quenched to the ground-state Born-Oppenheimer surface.

An alternative to Born-Oppenheimer dynamics is the Car-Parrinello (CP) method (Car & Parrinello, 1985; Marx & Hutter, 2000; Tuckerman, 2002). In this approach, an initially minimized electronic configuration is subsequently "propagated" from one nuclear configuration to the next using a fictitious Newtonian dynamics for the orbitals. In this "dynamics", the orbitals are given a small amount of thermal kinetic energy and are made "light" compared to the nuclei. Under these conditions, the orbitals actually generate a potential of mean force surface that is very close to the true Born-Oppenheimer surface. The equations of motion of the CP method are

$$M\_I \ddot{\mathbf{R}}\_I = -\nabla\_I \left[ \mathcal{E} \left[ \{ \psi \} , \mathbf{R} \right] + \mathcal{U}\_{\text{NN}} (\mathbf{R}) \right]$$

$$\mu | \ddot{\boldsymbol{\psi}}\_i \rangle = -\frac{\partial}{\partial \langle \boldsymbol{\psi}\_i \rangle |} \mathcal{E} [\{ \boldsymbol{\psi} \} , \mathbf{R} ] + \sum\_j \lambda\_{ij} | \psi\_j \rangle \tag{15}$$

where *<sup>μ</sup>* is a mass-like parameter for the orbitals (which actually has units of energy<sup>×</sup> time2), and *λij* is the Lagrange multiplier matrix that enforces the orthogonality of the orbitals as a holonomic constraint on the fictitious orbital dynamics. Choosing *μ* small ensures that the

Tuckerman & Martyna, 1999), Martyna, Tuckerman, and coworkers showed that clusters (systems with no periodicity), wires (systems with one periodic dimension), and surfaces (systems with two periodic dimensions) could all be treated using a plane-wave basis within a single unified formalism. Let *n*(**r**) be a particle density with a Fourier expansion given by Eq.

<sup>237</sup> Creation of Ordered Layers on Semiconductor Surfaces:

) is given by

where *φ*˜**<sup>g</sup>** is the Fourier transform of the potential. For systems with fewer than three periodic

<sup>2</sup>*<sup>V</sup>* ∑ **g** |*n***g**|

where *φ*¯**<sup>g</sup>** denotes a Fourier expansion coefficient of the potential in the non-periodic dimensions and a Fourier transform along the periodic dimensions. For clusters, *φ*¯**<sup>g</sup>** is given

> *dy Lx*/2 −*Lx*/2

> > *dy* <sup>∞</sup> −∞

*dy* <sup>∞</sup> −∞

The error in the first-image approximation drops off as a function of the volume, area, or length in the non-periodic directions, as analyzed in Minary et al. (2004; 2002);

In order to have an expression that is easily computed within the plane wave description, consider two functions *φ*long(**r**) and *φ*short(**r**), which are assumed to be the long and short

*φ*(**r**) = *φ*long(**r**) + *φ*short(**r**)

We require that *φ*short(**r**) vanish exponentially quickly at large distances from the center of the parallelepiped and that *φ*long(**r**) contain the long range dependence of the full potential, *φ*(**r**).

)*n*(**r**�

*d***r** *d***r**� *n*(**r**)*φ*(**r** − **r**�

An ab Initio Molecular Dynamics Study of the SiC(001)-3x2 and SiC(100)-c(2x2) Surfaces

dimensions, the idea is to replace Eq. (20) with its first-image approximation

*<sup>E</sup>* <sup>≈</sup> *<sup>E</sup>*(1) <sup>≡</sup> <sup>1</sup>

*dz Ly*/2 −*Ly*/2

> *dz Ly*/2 −*Ly*/2

> > *dz* <sup>∞</sup> −∞

) denote an interaction potential. In a fully periodic system, the energy of

) = <sup>1</sup> <sup>2</sup>*<sup>V</sup>* ∑ **g** |*n***g**|

<sup>2</sup>*φ*˜−**<sup>g</sup>** (20)

<sup>2</sup>*φ*¯−**<sup>g</sup>** (21)

*dx φ*(**r**)*e*−*i***g**·**<sup>r</sup>** (22)

*dx φ*(**r**)*e*−*i***g**·**<sup>r</sup>** (23)

*dx φ*(**r**)*e*−*i***g**·**<sup>r</sup>** (24)

*φ*¯(**g**) = *φ*¯long(**g**) + *φ*¯short(**g**). (25)

(19), and let *φ*(**r** − **r**�

for wires, it becomes

and for surfaces, we obtain

Tuckerman & Martyna (1999).

range contributions to the total potential, i.e.

by

a system described by *n*(**r**) and *φ*(**r** − **r**�

*<sup>E</sup>* <sup>=</sup> <sup>1</sup> 2 

*φ*¯**<sup>g</sup>** =

*φ*¯**<sup>g</sup>** =

*φ*¯**<sup>g</sup>** =

 *Lz*/2 −*Lz*/2

> *Lz*/2 −*Lz*/2

> > *Lz*/2 −*Lz*/2

orbital dynamics is adiabatically decoupled from the true nuclear dynamics, thereby allowing the orbitals to generate the aforementioned potential of mean force surface. For a detailed analysis of the CP dynamics, see Marx et al. (1999); Tuckerman (2002). As an illustration of the CP dynamics, Fig. 1 of Tuckerman & Parrinello (1994) shows the temperature profile for a short CPAIMD simulation of bulk silicon together with the kinetic energy profile from the fictitious orbital dynamics. The figure demonstrates that the orbital dynamics is essentially a "slave" to the nuclear dynamics, which shows that the electronic configuration closely follows that dynamics of the nuclei in the spirit of the Born-Oppenheimer approximation.

#### **2.3 Plane wave basis sets and surface boundary conditions**

In AIMD calculations, the most commonly employed boundary conditions are periodic boundary conditions, in which the system is replicated infinitely in all three spatial directions. This is clearly a natural choice for solids and is particularly convenient for liquids. In an infinite periodic system, the KS orbitals become Bloch functions of the form

$$
\psi\_{i\mathbf{k}}(\mathbf{r}) = e^{i\mathbf{k}\cdot\mathbf{r}} u\_{i\mathbf{k}}(\mathbf{r}) \tag{16}
$$

where **k** is a vector in the first Brioullin zone and *ui***k**(**r**) is a periodic function. A natural basis set for expanding a periodic function is the Fourier or plane wave basis set, in which *ui***k**(**r**) is expanded according to

$$u\_{i\mathbf{k}}(\mathbf{r}) = \frac{1}{\sqrt{V}} \sum\_{\mathbf{g}} c\_{i,\mathbf{g}}^{\mathbf{k}} e^{i\mathbf{g} \cdot \mathbf{r}} \tag{17}$$

where *V* is the volume of the cell, **g** = 2*π***h**−1**g**ˆ is a reciprocal lattice vector, **h** is the cell matrix, whose columns are the cell vectors (*<sup>V</sup>* <sup>=</sup> det(**h**)), ˆ**<sup>g</sup>** is a vector of integers, and {*c***<sup>k</sup>** *<sup>i</sup>*,**g**} are the expansion coefficients. An advantage of plane waves is that the sums needed to go back and forth between reciprocal space and real space can be performed efficiently using fast Fourier transforms (FFTs). In general, the properties of a periodic system are only correctly described if a sufficient number of **k**-vectors are sampled from the Brioullin zone. However, for the applications we will consider, we are able to choose sufficiently large system sizes that we can restrict our **k**-point sampling to the single point, **k** = (0, 0, 0), known as the Γ-point. At the Γ-point, the plane wave expansion reduces to

$$\psi\_i(\mathbf{r}) = \frac{1}{\sqrt{V}} \sum\_{\mathbf{g}} c\_{i,\mathbf{g}} e^{i\mathbf{g} \cdot \mathbf{r}} \tag{18}$$

At the Γ-point, the orbitals can always be chosen to be real functions. Therefore, the plane-wave expansion coefficients satisfy the property that *c*∗ *<sup>i</sup>*,**<sup>g</sup>** = *ci*,−**g**, which requires keeping only half of the full set of plane-wave expansion coefficients. In actual applications, plane waves up to a given cutoff |**g**| 2/2 < *E*cut are retained. Similarly, the density *n*(**r**) given by Eq. (4) can also be expanded in a plane wave basis:

$$m(\mathbf{r}) = \frac{1}{V} \sum\_{\mathbf{g}} n\_{\mathbf{g}} e^{i \mathbf{g} \cdot \mathbf{r}} \tag{19}$$

However, since *n*(**r**) is obtained as a square of the KS orbitals, the cutoff needed for this expansion is 4*E*cut for consistency with the orbital expansion.

At first glance, it might seem that plane waves are ill-suited to treat surfaces because of their two-dimensional periodicity. However, in a series of papers (Minary et al., 2004; 2002; Tuckerman & Martyna, 1999), Martyna, Tuckerman, and coworkers showed that clusters (systems with no periodicity), wires (systems with one periodic dimension), and surfaces (systems with two periodic dimensions) could all be treated using a plane-wave basis within a single unified formalism. Let *n*(**r**) be a particle density with a Fourier expansion given by Eq. (19), and let *φ*(**r** − **r**� ) denote an interaction potential. In a fully periodic system, the energy of a system described by *n*(**r**) and *φ*(**r** − **r**� ) is given by

$$E = \frac{1}{2} \int d\mathbf{r} \, d\mathbf{r}' \, n(\mathbf{r}) \phi(\mathbf{r} - \mathbf{r}') n(\mathbf{r}') = \frac{1}{2V} \sum\_{\mathbf{g}} |n\_{\mathbf{g}}|^2 \tilde{\phi}\_{-\mathbf{g}} \tag{20}$$

where *φ*˜**<sup>g</sup>** is the Fourier transform of the potential. For systems with fewer than three periodic dimensions, the idea is to replace Eq. (20) with its first-image approximation

$$E \approx E^{(1)} \equiv \frac{1}{2V} \sum\_{\mathbf{g}} |n\_{\mathbf{g}}|^2 \bar{\phi}\_{-\mathbf{g}} \tag{21}$$

where *φ*¯**<sup>g</sup>** denotes a Fourier expansion coefficient of the potential in the non-periodic dimensions and a Fourier transform along the periodic dimensions. For clusters, *φ*¯**<sup>g</sup>** is given by

$$\Phi\_{\mathbf{g}} = \int\_{-L\_{\mathbf{z}}/2}^{L\_{\mathbf{z}}/2} dz \int\_{-L\_{\mathbf{y}}/2}^{L\_{\mathbf{y}}/2} dy \int\_{-L\_{\mathbf{x}}/2}^{L\_{\mathbf{x}}/2} dx \, \phi(\mathbf{r}) e^{-i\mathbf{g}\cdot\mathbf{r}} \tag{22}$$

for wires, it becomes

6 Will-be-set-by-IN-TECH

orbital dynamics is adiabatically decoupled from the true nuclear dynamics, thereby allowing the orbitals to generate the aforementioned potential of mean force surface. For a detailed analysis of the CP dynamics, see Marx et al. (1999); Tuckerman (2002). As an illustration of the CP dynamics, Fig. 1 of Tuckerman & Parrinello (1994) shows the temperature profile for a short CPAIMD simulation of bulk silicon together with the kinetic energy profile from the fictitious orbital dynamics. The figure demonstrates that the orbital dynamics is essentially a "slave" to the nuclear dynamics, which shows that the electronic configuration closely follows

In AIMD calculations, the most commonly employed boundary conditions are periodic boundary conditions, in which the system is replicated infinitely in all three spatial directions. This is clearly a natural choice for solids and is particularly convenient for liquids. In an

where **k** is a vector in the first Brioullin zone and *ui***k**(**r**) is a periodic function. A natural basis set for expanding a periodic function is the Fourier or plane wave basis set, in which *ui***k**(**r**) is

> <sup>√</sup>*<sup>V</sup>* ∑ **g** *c***k** *<sup>i</sup>*,**g***e*

where *V* is the volume of the cell, **g** = 2*π***h**−1**g**ˆ is a reciprocal lattice vector, **h** is the cell matrix,

expansion coefficients. An advantage of plane waves is that the sums needed to go back and forth between reciprocal space and real space can be performed efficiently using fast Fourier transforms (FFTs). In general, the properties of a periodic system are only correctly described if a sufficient number of **k**-vectors are sampled from the Brioullin zone. However, for the applications we will consider, we are able to choose sufficiently large system sizes that we can restrict our **k**-point sampling to the single point, **k** = (0, 0, 0), known as the Γ-point. At the

> <sup>√</sup>*<sup>V</sup>* ∑ **g**

At the Γ-point, the orbitals can always be chosen to be real functions. Therefore, the

keeping only half of the full set of plane-wave expansion coefficients. In actual applications,

*<sup>V</sup>* ∑ **g**

However, since *n*(**r**) is obtained as a square of the KS orbitals, the cutoff needed for this

At first glance, it might seem that plane waves are ill-suited to treat surfaces because of their two-dimensional periodicity. However, in a series of papers (Minary et al., 2004; 2002;

*ui***k**(**r**) (16)

*<sup>i</sup>***g**·**<sup>r</sup>** (17)

*ci*,**g***ei***g**·**<sup>r</sup>** (18)

*n***g***ei***g**·**<sup>r</sup>** (19)

2/2 < *E*cut are retained. Similarly, the density *n*(**r**) given

*<sup>i</sup>*,**<sup>g</sup>** = *ci*,−**g**, which requires

*<sup>i</sup>*,**g**} are the

*ψi***k**(**r**) = *ei***k**·**<sup>r</sup>**

*ui***k**(**r**) = <sup>1</sup>

whose columns are the cell vectors (*<sup>V</sup>* <sup>=</sup> det(**h**)), ˆ**<sup>g</sup>** is a vector of integers, and {*c***<sup>k</sup>**

*<sup>ψ</sup>i*(**r**) = <sup>1</sup>

*<sup>n</sup>*(**r**) = <sup>1</sup>

plane-wave expansion coefficients satisfy the property that *c*∗

by Eq. (4) can also be expanded in a plane wave basis:

expansion is 4*E*cut for consistency with the orbital expansion.

that dynamics of the nuclei in the spirit of the Born-Oppenheimer approximation.

infinite periodic system, the KS orbitals become Bloch functions of the form

**2.3 Plane wave basis sets and surface boundary conditions**

expanded according to

Γ-point, the plane wave expansion reduces to

plane waves up to a given cutoff |**g**|

$$\Phi\_{\mathbf{g}} = \int\_{-L\_{2}/2}^{L\_{2}/2} dz \int\_{-L\_{y}/2}^{L\_{y}/2} dy \int\_{-\infty}^{\infty} d\mathbf{x} \,\phi(\mathbf{r}) e^{-i\mathbf{g}\cdot\mathbf{r}} \tag{23}$$

and for surfaces, we obtain

$$\bar{\boldsymbol{\phi}}\_{\mathbf{g}} = \int\_{-L\_{z}/2}^{L\_{z}/2} dz \int\_{-\infty}^{\infty} dy \int\_{-\infty}^{\infty} d\mathbf{x} \,\boldsymbol{\phi}(\mathbf{r}) e^{-i\mathbf{g}\cdot\mathbf{r}} \tag{24}$$

The error in the first-image approximation drops off as a function of the volume, area, or length in the non-periodic directions, as analyzed in Minary et al. (2004; 2002); Tuckerman & Martyna (1999).

In order to have an expression that is easily computed within the plane wave description, consider two functions *φ*long(**r**) and *φ*short(**r**), which are assumed to be the long and short range contributions to the total potential, i.e.

$$
\boldsymbol{\phi}(\mathbf{r}) = \boldsymbol{\phi}^{\text{long}}(\mathbf{r}) + \boldsymbol{\phi}^{\text{short}}(\mathbf{r})
$$

$$
\boldsymbol{\bar{\phi}}(\mathbf{g}) = \boldsymbol{\bar{\phi}}^{\text{long}}(\mathbf{g}) + \boldsymbol{\bar{\phi}}^{\text{short}}(\mathbf{g}).\tag{25}
$$

We require that *φ*short(**r**) vanish exponentially quickly at large distances from the center of the parallelepiped and that *φ*long(**r**) contain the long range dependence of the full potential, *φ*(**r**).

worked out. In particular, for surfaces, the screening function is

cos *gcLc* 2

An ab Initio Molecular Dynamics Study of the SiC(001)-3x2 and SiC(100)-c(2x2) Surfaces

 − 1 <sup>2</sup> exp

−1

− *g*2 4*α*<sup>2</sup> Re

> ∞ ∑ *l*=0

*l* ∑ *m*=−*l*

where *r* is the distance from the ion, and |*lm*��*lm*| is a projection operator onto each angular momentum component. In order to truncate the infinite sum over *l* in Eq. (32), we assume

(*vl*(*r*) − *v*¯*l*(*r*))|*lm*��*lm*| + *v*¯*l*(*r*)

where the second line follows from the fact that the sum of the projection operators is unity,

*v*loc(|**r** − **R***I*|) +

*<sup>l</sup>*(*r*) and add and subtract the function *v*¯

*<sup>l</sup>*(*r*))|*lm*��*lm*| + *v*¯

*l*

<sup>2</sup> exp *gsLc* 2

When a plane wave basis set is employed, the external energy is made somewhat complicated by the fact that very large basis sets are needed to treat the rapid spatial fluctuations of core electrons. Therefore, core electrons are often replaced by atomic pseudopotentials or augmented plane wave techniques. Here, we shall discuss the former. In the atomic pseudopotential scheme, the nucleus plus the core electrons are treated in a frozen core type approximation as an "ion" carrying only the valence charge. In order to make this approximation, the valence orbitals, which, in principle must be orthogonal to the core orbitals, must see a different pseudopotential for each angular momentum component in the core, which means that the pseudopotential must generally be nonlocal. In order to see this,

<sup>−</sup> *gsLc* 2

<sup>+</sup> exp

*V*ˆ pseud = <sup>239</sup> Creation of Ordered Layers on Semiconductor Surfaces:

<sup>−</sup> *gsLc* 2

erfc *<sup>α</sup>*2*Lc* <sup>+</sup> *igc* 2*α*

erfc *<sup>α</sup>*2*Lc* <sup>+</sup> *gs* 2*α*

erfc *<sup>α</sup>*2*Lc* <sup>−</sup> *gs* 2*α*

*vl*(*r*)|*lm*��*lm*| (32)

∞ ∑ *l*=0

*<sup>l</sup>*(*r*)

(*r*), and the sum in the third line is truncated before Δ*vl*(*r*) = 0. The

¯ *l*−1 ∑ *l*=0

*l* ∑ *m*=−*l*

*<sup>l</sup>*(*r*) in Eq. (32):


(*r*) (33)

Δ*vl*(|**r** − **R***I*|)|*lm*��*lm*|

(34)

(31)

*g*2 

*<sup>φ</sup>*¯screen(**g**) = <sup>−</sup>4*<sup>π</sup>*

we consider a potential operator of the form

*l*, *vl*(*r*) = *v*¯

= ∞ ∑ *l*=0

≈ ¯ *l*−1 ∑ *l*=0

*l*

pseud(*r*; **R**1, ..., **R***N*) =

complete pseudopotential operator is

∞ ∑ *l*=0

*l* ∑ *m*=−*l*

*l* ∑ *m*=−*l*

*l* ∑ *m*=−*l*

(*vl*(*r*) − *v*¯

*N* ∑ *I*=1 Δ*vl*(*r*)|*lm*��*lm*| + *v*¯

that for some *<sup>l</sup>* <sup>≥</sup> ¯

Δ*vl*(*r*) = *vl*(*r*) − *v*¯

*V*ˆ

*V*ˆ pseud = × exp

With these two requirements, it is possible to write

$$\boldsymbol{\tilde{\phi}}^{\text{short}}(\mathbf{g}) = \int\_{D(V)} d\mathbf{r} \, e^{-i\mathbf{g}\cdot\mathbf{r}} \boldsymbol{\phi}^{\text{short}}(\mathbf{r})$$

$$= \int\_{\text{all space}} d\mathbf{r} e^{-i\mathbf{g}\cdot\mathbf{r}} \boldsymbol{\phi}^{\text{short}}(\mathbf{r}) + \boldsymbol{\varepsilon}(\mathbf{g})$$

$$= \boldsymbol{\tilde{\phi}}^{\text{short}}(\mathbf{g}) + \boldsymbol{\varepsilon}(\mathbf{g}) \tag{26}$$

with exponentially small error, *�*(**g**), provided the range of *φ*short(**r**) is small compared size of the parallelepiped. In order to ensure that Eq. (26) is satisfied, a convergence parameter, *α*, is introduced which can be used to adjust the range of *<sup>φ</sup>*short(**r**) such that *�*(**g**) <sup>∼</sup> 0 and the error, *�*(**g**), will be neglected in the following.

The function, *φ*˜short(**g**), is the Fourier transform of *φ*short(**r**). Therefore,

$$
\boldsymbol{\dot{\phi}}(\mathbf{g}) = \boldsymbol{\dot{\phi}}^{\text{long}}(\mathbf{g}) + \boldsymbol{\dot{\phi}}^{\text{short}}(\mathbf{g}) \tag{27}
$$

$$
= \boldsymbol{\ddot{\phi}}^{\text{long}}(\mathbf{g}) - \boldsymbol{\ddot{\phi}}^{\text{long}}(\mathbf{g}) + \boldsymbol{\ddot{\phi}}^{\text{short}}(\mathbf{g}) + \boldsymbol{\ddot{\phi}}^{\text{long}}(\mathbf{g})
$$

$$
= \boldsymbol{\dot{\phi}}^{\text{screen}}(\mathbf{g}) + \boldsymbol{\ddot{\phi}}(\mathbf{g})
$$

where *φ*˜(**g**) = *φ*˜short(**g**) + *φ*˜long(**g**) is the Fourier transform of the full potential, *φ*(**r**) = *φ*short(**r**) + *φ*long(**r**) and

$$
\hat{\phi}^{\text{screen}}(\mathbf{g}) = \tilde{\phi}^{\text{long}}(\mathbf{g}) - \tilde{\phi}^{\text{long}}(\mathbf{g}).\tag{28}
$$

Thus, Eq. (28) becomes leads to

$$\langle \phi \rangle = \frac{1}{2V} \sum\_{\mathbf{g}} |\bar{n}(\mathbf{g})|^2 \left[ \tilde{\phi}(-\mathbf{g}) + \hat{\phi}^{\text{screen}}(-\mathbf{g}) \right] \tag{29}$$

The new function appearing in the average potential energy, Eq. (29), is the difference between the Fourier series and Fourier transform form of the long range part of the potential energy and will be referred to as the screening function because it is constructed to "screen" the interaction of the system with an infinite array of periodic images. The specific case of the Coulomb potential, *φ*(**r**) = 1/*r*, can be separated into short and long range components via

$$\frac{1}{r} = \frac{\text{erf}(\alpha r)}{r} + \frac{\text{erfc}(\alpha r)}{r} \tag{30}$$

where the first term is long range. The parameter *α* determines the specific ranges of these terms. The screening function for the cluster case is easily computed by introducing an FFT grid and performing the integration numerically (Tuckerman & Martyna, 1999). For the wire (Minary et al., 2002) and surface (Minary et al., 2004) cases, analytical expressions can be worked out. In particular, for surfaces, the screening function is

8 Will-be-set-by-IN-TECH

*d***r** *e* −*i***g**·**r**

with exponentially small error, *�*(**g**), provided the range of *φ*short(**r**) is small compared size of the parallelepiped. In order to ensure that Eq. (26) is satisfied, a convergence parameter, *α*, is introduced which can be used to adjust the range of *<sup>φ</sup>*short(**r**) such that *�*(**g**) <sup>∼</sup> 0 and the error,

<sup>=</sup> *<sup>φ</sup>*¯long(**g**) <sup>−</sup> *<sup>φ</sup>*˜long(**g**) + *<sup>φ</sup>*˜short(**g**) + *<sup>φ</sup>*˜long(**g**)

where *φ*˜(**g**) = *φ*˜short(**g**) + *φ*˜long(**g**) is the Fourier transform of the full potential, *φ*(**r**) =

The new function appearing in the average potential energy, Eq. (29), is the difference between the Fourier series and Fourier transform form of the long range part of the potential energy and will be referred to as the screening function because it is constructed to "screen" the interaction of the system with an infinite array of periodic images. The specific case of the Coulomb potential, *φ*(**r**) = 1/*r*, can be separated into short and long range components via

+

where the first term is long range. The parameter *α* determines the specific ranges of these terms. The screening function for the cluster case is easily computed by introducing an FFT grid and performing the integration numerically (Tuckerman & Martyna, 1999). For the wire (Minary et al., 2002) and surface (Minary et al., 2004) cases, analytical expressions can be

erfc(*αr*) *r*

all space *d***r***e*−*i***g**·**<sup>r</sup>** *φ*short(**r**)

*φ*short(**r**) + *�*(**g**)

*φ*¯(**g**) = *φ*¯long(**g**) + *φ*˜short(**g**) (27)

*<sup>φ</sup>*ˆscreen(**g**) = *<sup>φ</sup>*¯long(**g**) <sup>−</sup> *<sup>φ</sup>*˜long(**g**). (28)

(29)

(30)

*<sup>φ</sup>*˜(−**g**) + *<sup>φ</sup>*ˆscreen(−**g**)

= *φ*˜short(**g**) + *�*(**g**) (26)

With these two requirements, it is possible to write

*�*(**g**), will be neglected in the following.

*φ*short(**r**) + *φ*long(**r**) and

Thus, Eq. (28) becomes leads to

*φ*¯short(**g**) =

 *D*(*V*)

= 

The function, *φ*˜short(**g**), is the Fourier transform of *φ*short(**r**). Therefore,

= *φ*ˆscreen(**g**) + *φ*˜(**g**)

�*φ*� <sup>=</sup> <sup>1</sup>

<sup>2</sup>*<sup>V</sup>* ∑ **g**ˆ

1


*<sup>r</sup>* <sup>=</sup> erf(*αr*) *r*

$$\bar{\Phi}^{\text{sreen}}(\mathbf{g}) = -\frac{4\pi}{g^2} \left\{ \cos\left(\frac{g\_c L\_c}{2}\right) \right. \tag{31}$$

$$\times \left[ \exp\left(-\frac{\mathcal{G}\_5 L\_c}{2}\right) - \frac{1}{2} \exp\left(-\frac{\mathcal{G}\_5 L\_c}{2}\right) \text{erfc}\left(\frac{a^2 L\_c - \mathcal{G}\_s}{2a}\right) \right.$$

$$-\frac{1}{2} \exp\left(\frac{\mathcal{G}\_5 L\_c}{2}\right) \text{erfc}\left(\frac{a^2 L\_c + \mathcal{G}\_s}{2a}\right) \right]$$

$$+ \exp\left(-\frac{\mathcal{G}^2}{4a^2}\right) \text{Re}\left[\text{erfc}\left(\frac{a^2 L\_c + i g\_c}{2a}\right)\right] \right\}$$

When a plane wave basis set is employed, the external energy is made somewhat complicated by the fact that very large basis sets are needed to treat the rapid spatial fluctuations of core electrons. Therefore, core electrons are often replaced by atomic pseudopotentials or augmented plane wave techniques. Here, we shall discuss the former. In the atomic pseudopotential scheme, the nucleus plus the core electrons are treated in a frozen core type approximation as an "ion" carrying only the valence charge. In order to make this approximation, the valence orbitals, which, in principle must be orthogonal to the core orbitals, must see a different pseudopotential for each angular momentum component in the core, which means that the pseudopotential must generally be nonlocal. In order to see this, we consider a potential operator of the form

$$\hat{\mathcal{V}}\_{\text{pseudo}} = \sum\_{l=0}^{\infty} \sum\_{m=-l}^{l} v\_l(r) |lm\rangle\langle lm| \tag{32}$$

where *r* is the distance from the ion, and |*lm*��*lm*| is a projection operator onto each angular momentum component. In order to truncate the infinite sum over *l* in Eq. (32), we assume that for some *<sup>l</sup>* <sup>≥</sup> ¯ *l*, *vl*(*r*) = *v*¯ *<sup>l</sup>*(*r*) and add and subtract the function *v*¯ *<sup>l</sup>*(*r*) in Eq. (32):

$$\hat{\mathcal{V}}\_{\text{pseudo}} = \sum\_{l=0}^{\infty} \sum\_{m=-l}^{l} \left( v\_{l}(r) - v\_{l}(r) \right) |lm\rangle\langle lm| + v\_{l}(r) \sum\_{l=0}^{\infty} \sum\_{m=-l}^{l} |lm\rangle\langle lm|$$

$$= \sum\_{l=0}^{\infty} \sum\_{m=-l}^{l} \left( v\_{l}(r) - v\_{l}(r) \right) |lm\rangle\langle lm| + v\_{l}(r)$$

$$\approx \sum\_{l=0}^{\overline{l}-1} \sum\_{m=-l}^{l} \Delta v\_{l}(r) |lm\rangle\langle lm| + v\_{\overline{l}}(r) \tag{33}$$

where the second line follows from the fact that the sum of the projection operators is unity, Δ*vl*(*r*) = *vl*(*r*) − *v*¯ *l* (*r*), and the sum in the third line is truncated before Δ*vl*(*r*) = 0. The complete pseudopotential operator is

$$\hat{\mathcal{V}}\_{\text{pseudo}}(r; \mathbf{R}\_1, \dots, \mathbf{R}\_N) = \sum\_{I=1}^N \left[ v\_{\text{loc}}(|\mathbf{r} - \mathbf{R}\_I|) + \sum\_{l=0}^{I-1} \Delta v\_l(|\mathbf{r} - \mathbf{R}\_I|) |lm\rangle\langle lm| \right] \tag{34}$$

where *v*loc(*r*) ≡ *v*¯*l*(*r*) is known as the local part of the pseudopotential (having no projection operator attached to it). Now, the external energy, being derived from the ground-state expectation value of a one-body operator, is given by

$$\varepsilon\_{\rm ext} = \sum\_{i} f\_i \langle \psi\_i | \hat{\mathcal{V}}\_{\rm pseudo} | \psi\_i \rangle \tag{35}$$

In order to obtain the unitary transformation *Uij* that generates maximally localized orbitals, we seek a functional that measures the total spatial spread of the orbitals. One possibility for this functional is simply to use the variance of the position operator ˆ**r** with respect to each

<sup>241</sup> Creation of Ordered Layers on Semiconductor Surfaces:

The procedure for obtaining the maximally localized orbitals is to introduce the transformation in Eq. (38) into Eq. (39) and then to minimize the spread functional with respect

Ω[{*ψ*�

The minimization must be carried out subject to the constraint the *Uij* be an element of SU(*N*s). This constraint condition can be eliminated if we choose U to have the form U = exp(*i*A), where A is an *N*<sup>s</sup> × *N*<sup>s</sup> Hermitian matrix, and performing the minimization of Ω with respect

A little reflection reveals that the spread functional in Eq. (39) is actually not suitable for periodic systems. The reason for this is that the position operator ˆ**r** lacks the translational invariance of the underlying periodic supercell. A generalization of the spread functional that

where *σ* and *L* denote the typical spatial extent of a localized orbital and box length,

Here *GI* = 2*π*(**h**−1)*T***g**ˆ *<sup>I</sup>*, where ˆ**g***<sup>I</sup>* = (*lI*, *mI*, *nI*) is the *I*th Miller index and *ω<sup>I</sup>* is a weight

several choices are possible. The orbitals that result from minimizing Eq. (41) are known as *Wannier orbitals* |*wi*�. If *zI*,*ii* is evaluated with respect to these orbitals, then the orbital centers,

> *hαβ* 2*π*

Wannier orbitals and their centers are useful in analyzing chemically reactive systems and will

Like the KS energy, the fictitious CP dynamics is invariant with respect to gauge transformations of the form given in Eq. (38). They are not, however, invariant under

> *N*s ∑ *j*=1

*<sup>i</sup>* (**r**)*ei***G***I*·**<sup>r</sup>**

*ω<sup>I</sup> f*(|*zI*,*ii*|

*<sup>ψ</sup>j*(**r**) ≡ �*ψi*|*O*<sup>ˆ</sup> *<sup>I</sup>*

<sup>2</sup>|*ψi*�−�*ψi*|**r**ˆ|*ψi*�

2 

<sup>2</sup>) + <sup>O</sup>((*σ*/*L*)

<sup>2</sup>) is often taken to be 1 − |*z*<sup>|</sup>

Im ln *zβ*,*ii* (43)

*Uij*(*t*)*ψj*(**r**, *t*) (44)

}] = 0 (40)

<sup>2</sup>) (41)

2, although


(39)

Ω[{*ψ*}] =

*N*s ∑ *i*=1 �*ψi*|*r*ˆ

An ab Initio Molecular Dynamics Study of the SiC(001)-3x2 and SiC(100)-c(2x2) Surfaces

*∂ ∂Uij*

does not suffer from this deficiency is (Berghold et al., 2000; Resta & Sorella, 1999)

*N*s ∑ *i*=1 ∑ *I*

(2*π*)<sup>2</sup>

*d***r** *ψ*∗

*<sup>w</sup><sup>α</sup>* = − ∑

*β*

<sup>Ω</sup>[{*ψ*}] = <sup>1</sup>

*zI*,*ii* = 

having dimensions of (length)2. The function *<sup>f</sup>*(|*z*<sup>|</sup>

known as *Wannier centers*, can be computed according to

be employed in the present surface chemistry studies.

time-dependent unitary transformations of the form

*ψ*� *<sup>i</sup>*(**r**, *t*) =

orbital and sum these variances:

to *Uij*:

to A.

respectively, and

The first (local) term gives simply a local energy of the form

$$\varepsilon\_{\rm loc} = \sum\_{I=1}^{N} \int d\mathbf{r} \, n(\mathbf{r}) v\_{\rm loc}(|\mathbf{r} - \mathbf{R}\_I|) \tag{36}$$

which can be evaluated in reciprocal space as

$$\varepsilon\_{\rm loc} = \frac{1}{\Omega} \sum\_{I=1}^{N} \sum\_{\mathbf{g}} n\_{\mathbf{g}}^{\*} \tilde{v}\_{\rm loc}(\mathbf{g}) e^{-i \mathbf{g} \cdot \mathbf{R}\_{I}} \tag{37}$$

where *V*˜ loc(**g**) is the Fourier transform of the local potential. Note that at **g** = (0, 0, 0), only the nonsingular part of *v*˜loc(**g**) contributes. In the evaluation of the local term, it is often convenient to add and subtract a long-range term of the form *ZI*erf(*αIr*)/*r*, where erf(*x*) is the error function, each ion in order to obtain the nonsingular part explicitly and a residual short-range function *v*¯loc(|**r** − **R***I*|) = *v*loc(|**r** − **R***I*|) − *ZI*erf(*αI*|**r** − **R***I*|)/|**r** − **R***I*| for each ionic core.

#### **2.4 Electron localization methods**

An important feature of the KS energy functional is the fact that the total energy *E*[{*ψ*}, **R**] is invariant with respect to a unitary transformation within space of occupied orbitals. That is, if we introduce a new set of orbitals *ψ*� *i* (**r**) related to the *ψi*(**r**) by

$$\psi\_i'(\mathbf{r}) = \sum\_{j=1}^{N\_\mathbf{s}} l I\_{ij} \psi\_j(\mathbf{r}) \tag{38}$$

where *Uij* is a *N*<sup>s</sup> × *N*<sup>s</sup> unitary matrix, the energy *E*[{*ψ*� }, **R**] = *E*[{*ψ*}, **R**]. We say that the energy is invariant with respect to the group SU(*N*s), i.e., the group of all *N*<sup>s</sup> × *N*<sup>s</sup> unitary matrices with unit determinant. This invariance is a type of gauge invariance, specifically that in the occupied orbital subspace. The fictitious orbital dynamics of the AIMD scheme as written in Eqs. (15) does not preserve any particular unitary representation or gauge of the orbitals but allows the orbitals to mix arbitrarily according to Eq. (38). This mixing happens intrinsically as part of the dynamics rather than by explicit application of the unitary transformation.

Although this arbitrariness has no effect on the nuclear dynamics, it is often desirable for the orbitals to be in a particular unitary representation. For example, we might wish to have the true Kohn-Sham orbitals at each step in an AIMD simulation in order to calculate the Kohn-Sham eigenvalues and generate the corresponding density of states from a histogram of these eigenvalues. This would require choosing *Uij* to be the unitary transformation that diagonalizes the matrix of Lagrange multipliers in Eq. (6). Another important representation is that in which the orbitals are maximally localized in real space. In this representation, the orbitals are closest to the classic "textbook" molecular orbital picture.

10 Will-be-set-by-IN-TECH

where *v*loc(*r*) ≡ *v*¯*l*(*r*) is known as the local part of the pseudopotential (having no projection operator attached to it). Now, the external energy, being derived from the ground-state

*fi*�*ψi*|*V*<sup>ˆ</sup>

loc(**g**) is the Fourier transform of the local potential. Note that at **g** = (0, 0, 0), only

the nonsingular part of *v*˜loc(**g**) contributes. In the evaluation of the local term, it is often convenient to add and subtract a long-range term of the form *ZI*erf(*αIr*)/*r*, where erf(*x*) is the error function, each ion in order to obtain the nonsingular part explicitly and a residual short-range function *v*¯loc(|**r** − **R***I*|) = *v*loc(|**r** − **R***I*|) − *ZI*erf(*αI*|**r** − **R***I*|)/|**r** − **R***I*| for each ionic

An important feature of the KS energy functional is the fact that the total energy *E*[{*ψ*}, **R**] is invariant with respect to a unitary transformation within space of occupied orbitals. That is,

> *N*s ∑ *j*=1

energy is invariant with respect to the group SU(*N*s), i.e., the group of all *N*<sup>s</sup> × *N*<sup>s</sup> unitary matrices with unit determinant. This invariance is a type of gauge invariance, specifically that in the occupied orbital subspace. The fictitious orbital dynamics of the AIMD scheme as written in Eqs. (15) does not preserve any particular unitary representation or gauge of the orbitals but allows the orbitals to mix arbitrarily according to Eq. (38). This mixing happens intrinsically as part of the dynamics rather than by explicit application of the unitary

Although this arbitrariness has no effect on the nuclear dynamics, it is often desirable for the orbitals to be in a particular unitary representation. For example, we might wish to have the true Kohn-Sham orbitals at each step in an AIMD simulation in order to calculate the Kohn-Sham eigenvalues and generate the corresponding density of states from a histogram of these eigenvalues. This would require choosing *Uij* to be the unitary transformation that diagonalizes the matrix of Lagrange multipliers in Eq. (6). Another important representation is that in which the orbitals are maximally localized in real space. In this representation, the

(**r**) related to the *ψi*(**r**) by

*i*

*ψ*� *<sup>i</sup>*(**r**) =

orbitals are closest to the classic "textbook" molecular orbital picture.

where *Uij* is a *N*<sup>s</sup> × *N*<sup>s</sup> unitary matrix, the energy *E*[{*ψ*�

pseud|*ψi*� (35)

*d***r** *n*(**r**)*v*loc(|**r** − **R***I*|) (36)

**<sup>g</sup>***v*˜loc(**g**)*e*−*i***g**·**R***<sup>I</sup>* (37)

*Uijψj*(**r**) (38)

}, **R**] = *E*[{*ψ*}, **R**]. We say that the

*ε*ext = ∑ *i*

> *N* ∑ *I*=1

*N* ∑ *I*=1 ∑ **g** *n*∗

expectation value of a one-body operator, is given by

which can be evaluated in reciprocal space as

**2.4 Electron localization methods**

if we introduce a new set of orbitals *ψ*�

where *V*˜

core.

transformation.

The first (local) term gives simply a local energy of the form

*ε*loc =

*<sup>ε</sup>*loc <sup>=</sup> <sup>1</sup> Ω In order to obtain the unitary transformation *Uij* that generates maximally localized orbitals, we seek a functional that measures the total spatial spread of the orbitals. One possibility for this functional is simply to use the variance of the position operator ˆ**r** with respect to each orbital and sum these variances:

$$\Omega[\{\psi\}] = \sum\_{i=1}^{N\_\ast} \left[ \langle \psi\_i | \mathfrak{f}^2 | \psi\_i \rangle - \langle \psi\_i | \mathfrak{f} | \psi\_i \rangle^2 \right] \tag{39}$$

The procedure for obtaining the maximally localized orbitals is to introduce the transformation in Eq. (38) into Eq. (39) and then to minimize the spread functional with respect to *Uij*:

$$\frac{\partial}{\partial \mathcal{U}\_{ij}} \Omega[\{\psi'\}] = 0 \tag{40}$$

The minimization must be carried out subject to the constraint the *Uij* be an element of SU(*N*s). This constraint condition can be eliminated if we choose U to have the form U = exp(*i*A), where A is an *N*<sup>s</sup> × *N*<sup>s</sup> Hermitian matrix, and performing the minimization of Ω with respect to A.

A little reflection reveals that the spread functional in Eq. (39) is actually not suitable for periodic systems. The reason for this is that the position operator ˆ**r** lacks the translational invariance of the underlying periodic supercell. A generalization of the spread functional that does not suffer from this deficiency is (Berghold et al., 2000; Resta & Sorella, 1999)

$$\Omega[\{\psi\}] = \frac{1}{(2\pi)^2} \sum\_{i=1}^{N\_s} \sum\_{I} \omega\_I f(|z\_{I,\bar{\text{ii}}}|^2) + \mathcal{O}((\sigma/L)^2) \tag{41}$$

where *σ* and *L* denote the typical spatial extent of a localized orbital and box length, respectively, and

$$z\_{I, \mathrm{i}i} = \int d\mathbf{r} \,\psi\_{\mathrm{i}}^{\*}(\mathbf{r})e^{i\mathbf{G}\_{I} \cdot \mathbf{r}} \psi\_{\mathrm{j}}(\mathbf{r}) \equiv \langle \psi\_{\mathrm{i}}|\hat{\mathcal{O}}^{I}|\psi\_{\mathrm{j}}\rangle \tag{42}$$

Here *GI* = 2*π*(**h**−1)*T***g**ˆ *<sup>I</sup>*, where ˆ**g***<sup>I</sup>* = (*lI*, *mI*, *nI*) is the *I*th Miller index and *ω<sup>I</sup>* is a weight having dimensions of (length)2. The function *<sup>f</sup>*(|*z*<sup>|</sup> <sup>2</sup>) is often taken to be 1 − |*z*<sup>|</sup> 2, although several choices are possible. The orbitals that result from minimizing Eq. (41) are known as *Wannier orbitals* |*wi*�. If *zI*,*ii* is evaluated with respect to these orbitals, then the orbital centers, known as *Wannier centers*, can be computed according to

$$w\_{\mathfrak{a}} = -\sum\_{\mathfrak{f}} \frac{h\_{\mathfrak{a}\mathfrak{f}}}{2\pi} \mathrm{Im} \ln z\_{\mathfrak{f}, \bar{\mathfrak{i}}} \tag{43}$$

Wannier orbitals and their centers are useful in analyzing chemically reactive systems and will be employed in the present surface chemistry studies.

Like the KS energy, the fictitious CP dynamics is invariant with respect to gauge transformations of the form given in Eq. (38). They are not, however, invariant under time-dependent unitary transformations of the form

$$\Psi\_i'(\mathbf{r}, t) = \sum\_{j=1}^{N\_\mathbf{s}} \mathcal{U}\_{ij}(t) \psi\_j(\mathbf{r}, t) \tag{44}$$

(b)

dd2 du3

Δz

<sup>243</sup> Creation of Ordered Layers on Semiconductor Surfaces:

An ab Initio Molecular Dynamics Study of the SiC(001)-3x2 and SiC(100)-c(2x2) Surfaces

Fig. 1. View of 1,3-CHD + 3C-SiC(001)-3×2 system (a) along dimer rows and (b) between dimers in a row. Si, C, H, and the top Si surface dimers are represented by yellow, blue, white, and red, respectively. The dimers are spaced farther apart by ∼60% along a dimer row

Silicon-carbide (SiC) and its associated reactions with a conjugated diene is an interesting surface to study and to compare to the pure silicon surface. In previous work (Hayes & Tuckerman, 2007; Minary & Tuckerman, 2004; 2005), we have shown that when a conjugated diene reacts with the Si(100)-2×1 surface, a relatively broad distribution of products results, in agreement with experiment (Teague & Boland, 2003; 2004), because the surface dimers are relatively closely spaced. Because of this, creating ordered organic layers on this surface using conjugated dienes seems unlikely unless some method can be found to enhance the population of one of the adducts, rendering the remaining adducts negligible. SiC exhibits a number of complicated surface reconstructions depending on the surface orientation and growth conditions. Some of these reconstructions offer the intriguing possibility of restricting the product distribution due to the fact that carbon-carbon

SiC is often the material of choice for electronic and sensor applications under extreme conditions (Capano & Trew, 1997; Mélinon et al., 2007; Starke, 2004) or subject to biocompatibility constraints (Stutzmann et al., 2006). Although most reconstructions are still being debated both experimentally and theoretically (Pollmann & Krüger, 2004; Soukiassian & Enriquez, 2004), there is widespread agreement on the structure of the 3C-SiC(001)-3×2 surface (D'angelo et al., 2003; Tejeda et al., 2004)(see Fig. 1), which will be studied in this section. SiC(001) shares the same zinc blend structure as pure Si(001), but with alternating layers of Si and C. The top three layers are Si, the bottom in bulk-like positions and the top decomposed into an open 2/3 + 1/3 adlayer structure. Si atoms in the bottom two-thirds layers are 4-fold coordinated dimers while those Si atoms in the top one-third are asymmetric tilted dimers with dangling bonds. Given the Si-rich surface environment and presence of asymmetric surface dimers, one might expect much of the same Si-based chemistry to occur with two significant differences: (1) altered reactivity due to the surface strain (the SiC lattice constant is ∼ 20% smaller than Si) and (2) suppression of interdimer adducts due to the larger dimer spacing compared to Si (∼60% along a dimer row, ∼20% across dimer rows). Previous theoretical studies used either static (0 K) DFT calculations of hydrogen (Chang et al., 2005; Di Felice et al., 2005; Peng et al., 2007a; 2005; 2007b), a carbon

(a)

d23

7.1 Å

d1

d4 d12

and ∼20% across dimer rows relative to Si(100)-2×1.

or silicon-silicon dimer spacings are considerably larger.

**3. Reactions on the 3C-SiC(001)-3**×**2 surface**

6.2 Å

d3

d2

and consequently, the orbital gauge changes at each step of an AIMD simulation. If, however, we impose the requirement of invariance under Eq. (44) on the CP dynamics, then not only would we obtain a gauge-invariant version of the AIMD algorithm, but we could also then fix a particular orbital gauge and have this gauge be preserved under the CP evolution. Using techniques for gauge field theory, it is possible to devise such a AIMD algorithm (Thomas et al., 2004). Introducing orbital momenta |*πi*� conjugate to the orbital degrees of freedom, the gauge-invariant AIMD equations of motion have the basic structure

$$M\_I \ddot{\mathbf{R}}\_I = -\nabla\_I \left[ \mathcal{E} \left[ \{ \psi \} , \mathbf{R} \right] + \mathcal{U}\_{\text{NN}} (\mathbf{R}) \right],$$

$$\begin{aligned} \vert \psi\_{i} \rangle &= \vert \pi\_{i} \rangle + \sum\_{j} B\_{ij}(t) \vert \psi\_{j} \rangle \\\\ \vert \dot{\pi}\_{i} \rangle &= -\frac{1}{\mu} \frac{\partial}{\partial \langle \psi\_{i} \rangle} \mathcal{E} [\![\{\psi\} \!] , \mathbf{R}] + \sum\_{j} \lambda\_{ij} \vert \psi\_{j} \rangle + \sum\_{j} B\_{ij}(t) \vert \pi\_{j} \rangle \end{aligned} \tag{45}$$

where

$$B\_{\bar{l}\bar{j}}(t) = \sum\_{k} \mathcal{U}\_{\bar{k}\bar{l}} \frac{d}{dt} \mathcal{U}\_{\bar{k}\bar{j}} \tag{46}$$

Here, the terms involving the matrix *Bij*(*t*) are gauge-fixing terms that preserve a desired orbital gauge. If we choose the unitary transformation *Uij*(*t*) to be the matrix that satisfies Eq. (40), then Eqs. (45) will propagate maximally localized orbitals (Iftimie et al., 2004). As was shown in Iftimie et al. (2004); Thomas et al. (2004), it is possible to evaluate the gauge-fixing terms in a way that does not require explicit minimization of the spread functional (Sharma et al., 2003). In this way, if the orbitals are initially localized, they remain localized throughout the trajectory.

While the Wannier orbitals and Wannier centers are useful concepts, it is also useful to have a measure of electron localization that does not depend on a specific orbital representation, as the latter does have some arbitrariness associated with it. An alternative measure of electron localization that involves only the electron density *n*(**r**) and the so-called kinetic energy density

$$\tau(\mathbf{r}) = \sum\_{i=1}^{N\_s} |f\_i \nabla \psi\_i(\mathbf{r})|^2 \tag{47}$$

was introduced by Becke and Edgecombe (1990). Defining the ratio *χ*(**r**) = *D*(**r**)/*D*0(**r**), where

$$D(\mathbf{r}) = \tau(\mathbf{r}) - \frac{1}{4} \frac{|\nabla n(\mathbf{r})|^2}{n(\mathbf{r})}$$

$$D\_0(\mathbf{r}) = \frac{3}{4} \left(6\pi^2\right)^{2/3} n^{5/3}(\mathbf{r})\tag{48}$$

the function *<sup>f</sup>*(**r**) = 1/(1<sup>+</sup> *<sup>χ</sup>*2(**r**)) can be shown to lie in the interval *<sup>f</sup>*(**r**) <sup>∈</sup> [0, 1], where *<sup>f</sup>*(**r**) = 1 corresponds to perfect localization, and *f*(**r**) = 1/2 corresponds to a gas-like localization. The function *f*(**r**) is known as the *electron localization function* or ELF. In the studies to be presented below, we will make use both of the ELF and the Wannier orbitals and centers to quantify electron localization.

Fig. 1. View of 1,3-CHD + 3C-SiC(001)-3×2 system (a) along dimer rows and (b) between dimers in a row. Si, C, H, and the top Si surface dimers are represented by yellow, blue, white, and red, respectively. The dimers are spaced farther apart by ∼60% along a dimer row and ∼20% across dimer rows relative to Si(100)-2×1.

### **3. Reactions on the 3C-SiC(001)-3**×**2 surface**

12 Will-be-set-by-IN-TECH

and consequently, the orbital gauge changes at each step of an AIMD simulation. If, however, we impose the requirement of invariance under Eq. (44) on the CP dynamics, then not only would we obtain a gauge-invariant version of the AIMD algorithm, but we could also then fix a particular orbital gauge and have this gauge be preserved under the CP evolution. Using techniques for gauge field theory, it is possible to devise such a AIMD algorithm (Thomas et al., 2004). Introducing orbital momenta |*πi*� conjugate to the orbital degrees of freedom, the gauge-invariant AIMD equations of motion have the basic structure

*MI***R**¨ *<sup>I</sup>* <sup>=</sup> −∇*<sup>I</sup>* [E[{*ψ*}, **<sup>R</sup>**] + *<sup>U</sup>*NN(**R**)]

*Bij*(*t*)|*ψj*�

*<sup>∂</sup>*�*ψi*�| <sup>E</sup>[{*ψ*}, **<sup>R</sup>**] + <sup>∑</sup>

*Bij*(*t*) = ∑

*k Uki d*

Here, the terms involving the matrix *Bij*(*t*) are gauge-fixing terms that preserve a desired orbital gauge. If we choose the unitary transformation *Uij*(*t*) to be the matrix that satisfies Eq. (40), then Eqs. (45) will propagate maximally localized orbitals (Iftimie et al., 2004). As was shown in Iftimie et al. (2004); Thomas et al. (2004), it is possible to evaluate the gauge-fixing terms in a way that does not require explicit minimization of the spread functional (Sharma et al., 2003). In this way, if the orbitals are initially localized, they remain

While the Wannier orbitals and Wannier centers are useful concepts, it is also useful to have a measure of electron localization that does not depend on a specific orbital representation, as the latter does have some arbitrariness associated with it. An alternative measure of electron localization that involves only the electron density *n*(**r**) and the so-called kinetic

> *N*s ∑ *i*=1

was introduced by Becke and Edgecombe (1990). Defining the ratio *χ*(**r**) = *D*(**r**)/*D*0(**r**),

the function *<sup>f</sup>*(**r**) = 1/(1<sup>+</sup> *<sup>χ</sup>*2(**r**)) can be shown to lie in the interval *<sup>f</sup>*(**r**) <sup>∈</sup> [0, 1], where *<sup>f</sup>*(**r**) = 1 corresponds to perfect localization, and *f*(**r**) = 1/2 corresponds to a gas-like localization. The function *f*(**r**) is known as the *electron localization function* or ELF. In the studies to be presented below, we will make use both of the ELF and the Wannier orbitals and centers to

4


*n*(**r**)


*τ*(**r**) =

*<sup>D</sup>*(**r**) = *<sup>τ</sup>*(**r**) <sup>−</sup> <sup>1</sup>

4 6*π*<sup>2</sup> 2/3

*<sup>D</sup>*0(**r**) = <sup>3</sup>

*j*

*<sup>λ</sup>ij*|*ψj*� + ∑

*j*

*Bij*(*t*)|*πj*� (45)

*dtUkj* (46)

<sup>2</sup> (47)

*n*5/3(**r**) (48)

*j*

*∂*


localized throughout the trajectory.

quantify electron localization.

where

energy density

where

*<sup>i</sup>*� = |*πi*� + ∑

*μ*

<sup>|</sup>*π*˙ *<sup>i</sup>*� <sup>=</sup> <sup>−</sup> <sup>1</sup>

Silicon-carbide (SiC) and its associated reactions with a conjugated diene is an interesting surface to study and to compare to the pure silicon surface. In previous work (Hayes & Tuckerman, 2007; Minary & Tuckerman, 2004; 2005), we have shown that when a conjugated diene reacts with the Si(100)-2×1 surface, a relatively broad distribution of products results, in agreement with experiment (Teague & Boland, 2003; 2004), because the surface dimers are relatively closely spaced. Because of this, creating ordered organic layers on this surface using conjugated dienes seems unlikely unless some method can be found to enhance the population of one of the adducts, rendering the remaining adducts negligible. SiC exhibits a number of complicated surface reconstructions depending on the surface orientation and growth conditions. Some of these reconstructions offer the intriguing possibility of restricting the product distribution due to the fact that carbon-carbon or silicon-silicon dimer spacings are considerably larger.

SiC is often the material of choice for electronic and sensor applications under extreme conditions (Capano & Trew, 1997; Mélinon et al., 2007; Starke, 2004) or subject to biocompatibility constraints (Stutzmann et al., 2006). Although most reconstructions are still being debated both experimentally and theoretically (Pollmann & Krüger, 2004; Soukiassian & Enriquez, 2004), there is widespread agreement on the structure of the 3C-SiC(001)-3×2 surface (D'angelo et al., 2003; Tejeda et al., 2004)(see Fig. 1), which will be studied in this section. SiC(001) shares the same zinc blend structure as pure Si(001), but with alternating layers of Si and C. The top three layers are Si, the bottom in bulk-like positions and the top decomposed into an open 2/3 + 1/3 adlayer structure. Si atoms in the bottom two-thirds layers are 4-fold coordinated dimers while those Si atoms in the top one-third are asymmetric tilted dimers with dangling bonds. Given the Si-rich surface environment and presence of asymmetric surface dimers, one might expect much of the same Si-based chemistry to occur with two significant differences: (1) altered reactivity due to the surface strain (the SiC lattice constant is ∼ 20% smaller than Si) and (2) suppression of interdimer adducts due to the larger dimer spacing compared to Si (∼60% along a dimer row, ∼20% across dimer rows). Previous theoretical studies used either static (0 K) DFT calculations of hydrogen (Chang et al., 2005; Di Felice et al., 2005; Peng et al., 2007a; 2005; 2007b), a carbon

A D

An ab Initio Molecular Dynamics Study of the SiC(001)-3x2 and SiC(100)-c(2x2) Surfaces

<sup>245</sup> Creation of Ordered Layers on Semiconductor Surfaces:

H G

interfaces.

[4+2] subdimer adducts are stable.

Fig. 2. Snapshots of the four adducts which formed on the SiC surface: (A) [4+2] intradimer adduct, (D) [2+2] intradimer adduct, (H) hydrogen abstraction, and (G) [4+2] subsurface dimer adduct. Si, C, and H are represented by yellow, blue, and silver, respectively. The remaining C=C bond(s) is highlighted in green. The larger spacing between dimers suppresses interdimer adducts. However, adduct (G) destroys the surface, rendering this system inappropriate for applications requiring well-defined organic-semiconducting

organic-semiconducting interfaces is the presence of the subdimer adduct G. All the surface bonds directly connected to the adduct slightly expand to 2.42-2.47 Å, with the exception of one bond to a Si in the third layer, (highlighted in red in Fig. 2G) which disappears entirely. The energetic gain of the additional strong C-Si bond outweighs the loss of a strained Si-Si bond. The end effect is the destruction of the perfect surface and the creation of an unsaturated Si in the bulk. One adduct is noticeably missing: the [2+2] subdimer adduct. At several points during the simulation this adduct was poised to form but quickly left the vicinity. Most likely, the strain caused by the four-member ring combined with the two energetically less stable unsaturated Si prevented this adduct from forming, even though the [2+2] intradimer and

In Fig. 3, we show the carbon-carbon and CHD-Si distances as functions of time for the different adducts observed. This figure reveals that the mechanism of the reactions proceeds in a manner very similar to that of CHD and 1,3-butadiene on the Si(100)-2×1 surface: It is an asymmetric, nonconcerted mechanism that involves a carbocation intermediate. What differs from Si(100) is the time elapsed before the first bond forms and the intermediate lifetime. On the Si(100)-2×1 surface the CHD always found an available "down" Si to form the first bond within less than 10 ps or 40 Å of wandering over the surface. On the SiC(001)-3×2 surface the exploration process sometimes required up to 20 ps and over 100 Å. While the exact numbers are only qualitative, the trend is significant. The Si(100) dimers are more tilted on average, and hence expected to be slightly more reactive. However, the dominant contribution is

nanotube (de Brito Mota & de Castilho, 2006), or ethylene/acetylene (Wieferink et al., 2006; 2007) adsorbed on SiC(001)-3×2 or employed molecular dynamics of water (Cicero et al., 2004) or small molecules of the CH3-X family (Cicero & Catellani, 2005) on the less thermodynamically stable SiC(001)-2×1 surface. Here, we consider cycloaddition reactions on the SiC-3×2 surface that include dynamic and thermal effects. A primary goal for considering this surface is to determine whether 3C-SiC(001)-3×2 is a promising candidate for creating ordered semiconducting-organic interfaces via cycloaddition reactions.

In the study Hayes and Tuckerman (2008), the KS orbitals were expanded in a plane-wave basis set up to a kinetic energy cut-off of 40 Ry. As in the 1,3-CHD studies described above, exchange and correlation are treated with the spin restricted form of the PBE functional (Perdew et al., 1996), and core electrons were replaced by Troullier-Martins pseudopotentials (Troullier & Martins, 1991) with S, P, and D treated as local for H, C, and Si, respectively. The resulting SiC theoretical lattice constant, 4.39 Å, agrees well with the experimental value of 4.36 Å (Tejeda et al., 2004). The full system is shown in Fig. 1. The 3×2 unit cell is doubled in both directions to include four surface dimers to allow the possibility of all interdimer adducts. Again, the resulting large surface area, (18.6 Å x 12.4 Å), allows the Γ-point approximation to be used in lieu of explicit k-point sampling. Two bulk layers of Si and C, terminated by H on the bottom surface, provide a reconstructed (1/3 + 2/3) Si surface in reasonable agreement with experiment (see below). The final system has 182 atoms [24 atoms/layer \* (1 Si adlayer + 4 atomic layers) + 2\*24 terminating H]. The simulation cell employed lengths of 18.6 Å and 12.4 Å along the periodic directions and 31.2 Å along the nonperiodic *z* direction.

Both the CHD and SiC(001) surface were equilibrated separately under NVT conditions using Nosé-Hoover chain thermostats (Martyna et al., 1992) at 300 K with a timestep of 0.1 fs for 1 ps and 3 ps, respectively. When the equilibrated CHD was allowed to react with the equilibrated surface, the time step was reduced to 0.05 fs in order to ensure adiabaticity. The CHD was placed 3 Å above the surface, as defined by the lowest point on the CHD and the highest point on the surface. Each of twelve trajectories was initiated from the same CHD and SiC structures but with the CHD placed at a different orientations and/or locations over the surface. The subsequent initialization procedure was identical to the CHD-Si(100) system: First the system was annealed from 0 K to 300 K in the NVE ensemble. Following this, it was equilibrated with Nosé-Hoover chain thermostats for 1 ps at 300K under NVT conditions, keeping the center of mass of the CHD fixed. Finally, the CHD center of mass constraint was removed and the system was allowed to evolve under the NVE ensemble until an adduct formed or 20 ps elapsed.

The reactions that occur on this surface all take place on or in the vicinity of a single surface Si-Si dimer. However, as Fig. 2 shows, there is not one but rather four adducts that are observed to form. Adduct labels from the Si + CHD study are used for consistency. As postulated, the widely spaced dimers successfully suppressed the interdimer adducts that formed on the Si(100)-2×1 surface (Hayes & Tuckerman, 2007). From the twelve trajectories, three formed the [4+2] Diels-Alder type intradimer adduct (A), one produced the [2+2] intradimer adduct (D), five exhibited hydrogen abstraction (H), and one resulted in a novel [4+2] subdimer adduct between Si in d1 and d2 (G) (see Fig. 1). The remaining trajectories only formed 1 C-Si bond within 20 ps. Although the statistics are limited, these results suggest that H abstraction is favorable, consistent with the high reactivity of atomic H observed in experimental studies on this system (Amy & Chabal, 2003; Derycke et al., 2003). What is somewhat more troublesome, from the point of view of creating well-ordered 14 Will-be-set-by-IN-TECH

nanotube (de Brito Mota & de Castilho, 2006), or ethylene/acetylene (Wieferink et al., 2006; 2007) adsorbed on SiC(001)-3×2 or employed molecular dynamics of water (Cicero et al., 2004) or small molecules of the CH3-X family (Cicero & Catellani, 2005) on the less thermodynamically stable SiC(001)-2×1 surface. Here, we consider cycloaddition reactions on the SiC-3×2 surface that include dynamic and thermal effects. A primary goal for considering this surface is to determine whether 3C-SiC(001)-3×2 is a promising candidate for creating

In the study Hayes and Tuckerman (2008), the KS orbitals were expanded in a plane-wave basis set up to a kinetic energy cut-off of 40 Ry. As in the 1,3-CHD studies described above, exchange and correlation are treated with the spin restricted form of the PBE functional (Perdew et al., 1996), and core electrons were replaced by Troullier-Martins pseudopotentials (Troullier & Martins, 1991) with S, P, and D treated as local for H, C, and Si, respectively. The resulting SiC theoretical lattice constant, 4.39 Å, agrees well with the experimental value of 4.36 Å (Tejeda et al., 2004). The full system is shown in Fig. 1. The 3×2 unit cell is doubled in both directions to include four surface dimers to allow the possibility of all interdimer adducts. Again, the resulting large surface area, (18.6 Å x 12.4 Å), allows the Γ-point approximation to be used in lieu of explicit k-point sampling. Two bulk layers of Si and C, terminated by H on the bottom surface, provide a reconstructed (1/3 + 2/3) Si surface in reasonable agreement with experiment (see below). The final system has 182 atoms [24 atoms/layer \* (1 Si adlayer + 4 atomic layers) + 2\*24 terminating H]. The simulation cell employed lengths of 18.6 Å and 12.4 Å along the periodic directions and 31.2 Å along the

Both the CHD and SiC(001) surface were equilibrated separately under NVT conditions using Nosé-Hoover chain thermostats (Martyna et al., 1992) at 300 K with a timestep of 0.1 fs for 1 ps and 3 ps, respectively. When the equilibrated CHD was allowed to react with the equilibrated surface, the time step was reduced to 0.05 fs in order to ensure adiabaticity. The CHD was placed 3 Å above the surface, as defined by the lowest point on the CHD and the highest point on the surface. Each of twelve trajectories was initiated from the same CHD and SiC structures but with the CHD placed at a different orientations and/or locations over the surface. The subsequent initialization procedure was identical to the CHD-Si(100) system: First the system was annealed from 0 K to 300 K in the NVE ensemble. Following this, it was equilibrated with Nosé-Hoover chain thermostats for 1 ps at 300K under NVT conditions, keeping the center of mass of the CHD fixed. Finally, the CHD center of mass constraint was removed and the system was allowed to evolve under the NVE ensemble until an adduct formed or 20 ps

The reactions that occur on this surface all take place on or in the vicinity of a single surface Si-Si dimer. However, as Fig. 2 shows, there is not one but rather four adducts that are observed to form. Adduct labels from the Si + CHD study are used for consistency. As postulated, the widely spaced dimers successfully suppressed the interdimer adducts that formed on the Si(100)-2×1 surface (Hayes & Tuckerman, 2007). From the twelve trajectories, three formed the [4+2] Diels-Alder type intradimer adduct (A), one produced the [2+2] intradimer adduct (D), five exhibited hydrogen abstraction (H), and one resulted in a novel [4+2] subdimer adduct between Si in d1 and d2 (G) (see Fig. 1). The remaining trajectories only formed 1 C-Si bond within 20 ps. Although the statistics are limited, these results suggest that H abstraction is favorable, consistent with the high reactivity of atomic H observed in experimental studies on this system (Amy & Chabal, 2003; Derycke et al., 2003). What is somewhat more troublesome, from the point of view of creating well-ordered

ordered semiconducting-organic interfaces via cycloaddition reactions.

nonperiodic *z* direction.

elapsed.

Fig. 2. Snapshots of the four adducts which formed on the SiC surface: (A) [4+2] intradimer adduct, (D) [2+2] intradimer adduct, (H) hydrogen abstraction, and (G) [4+2] subsurface dimer adduct. Si, C, and H are represented by yellow, blue, and silver, respectively. The remaining C=C bond(s) is highlighted in green. The larger spacing between dimers suppresses interdimer adducts. However, adduct (G) destroys the surface, rendering this system inappropriate for applications requiring well-defined organic-semiconducting interfaces.

organic-semiconducting interfaces is the presence of the subdimer adduct G. All the surface bonds directly connected to the adduct slightly expand to 2.42-2.47 Å, with the exception of one bond to a Si in the third layer, (highlighted in red in Fig. 2G) which disappears entirely. The energetic gain of the additional strong C-Si bond outweighs the loss of a strained Si-Si bond. The end effect is the destruction of the perfect surface and the creation of an unsaturated Si in the bulk. One adduct is noticeably missing: the [2+2] subdimer adduct. At several points during the simulation this adduct was poised to form but quickly left the vicinity. Most likely, the strain caused by the four-member ring combined with the two energetically less stable unsaturated Si prevented this adduct from forming, even though the [2+2] intradimer and [4+2] subdimer adducts are stable.

In Fig. 3, we show the carbon-carbon and CHD-Si distances as functions of time for the different adducts observed. This figure reveals that the mechanism of the reactions proceeds in a manner very similar to that of CHD and 1,3-butadiene on the Si(100)-2×1 surface: It is an asymmetric, nonconcerted mechanism that involves a carbocation intermediate. What differs from Si(100) is the time elapsed before the first bond forms and the intermediate lifetime. On the Si(100)-2×1 surface the CHD always found an available "down" Si to form the first bond within less than 10 ps or 40 Å of wandering over the surface. On the SiC(001)-3×2 surface the exploration process sometimes required up to 20 ps and over 100 Å. While the exact numbers are only qualitative, the trend is significant. The Si(100) dimers are more tilted on average, and hence expected to be slightly more reactive. However, the dominant contribution is

0 1000 2000 3000


(a) (b)

0 1000 2000 3000

An ab Initio Molecular Dynamics Study of the SiC(001)-3x2 and SiC(100)-c(2x2) Surfaces

0 1000 2000 3000 4000

silicon-carbide family is the SiC(100)-2×2 surface.

at 300 K for the reaction of this surface with 1,3-cyclohexadiene.

0 1000 2000 3000 4000

1000 2000 3000 4000 5000 6000

2000 4000 6000 8000

0 1000 2000 3000 4000 5000 6000

0 2000 4000 6000 8000

(c) (d)



<sup>247</sup> Creation of Ordered Layers on Semiconductor Surfaces:

time (fs) time (fs)

Fig. 4. Spin restricted (black down triangles), singlet spin-unrestricted (red up triangles), and triplet unrestricted (green squares) energies at regular intervals during a representative (a) [4+2] intradimer adduct [A], (b) [2+2] intradimer adduct [D], (c) H-abstraction, and (d) [4+2] subdimer trajectory. Energies are relative to the value at t=0 in (a). The insets show the difference between the spin restricted and unrestricted singlet energies (blue line) and spin restricted and triplet unrestricted energies (purple). The triplet configuration is always highest in energy. In (a) at 3000 fs and (d) at 8500 fs the singlet transition state configuration is favorable by 2.3 and 0.5 kcal/mol, respectively. Thus, a radical mechanism may also occur

semiconductors such as H-terminated Si(111) and Si(100) or Si(100)-2×1 as the preferred substrates. Various molecules can be grown into lines on the H-terminated surfaces (McNab & Polanyi, 2006), and on the Si(100)-2×1 surface, styrene and derivatives such as 2,4-dimethylstyrene or longer chain alkenes can be used to grow wires along the dimer rows (DiLabio et al., 2007; 2004; Hossain et al., 2005a;c; 2007a;b; 2008; Zikovsky et al., 2007). More recently, allylic mercaptan and acetophenone have been shown to grow across dimer rows on the H:Si(100)-2×1 surface (Ferguson et al., 2009; 2010; Hossain et al., 2005c; 2008; 2009). Other semiconductor surface can be considered for such applications, however, these have not received as much attention. An intriguing possible alternate in the

The SiC(100)-2×2 surface exhibits the crucial difference from the SiC(100)-3×2 in that it is characterized by C≡C triple bonds, which bridge Si-Si single bonds. These triple bonds are well separated and reactive, suggesting the possibility of restricting the product distribution for the addition of conjugated dienes on this surface. Fig. 5 shows a snapshot of this surface. Previous *ab initio* calculations suggest that these dimers react favorably with 1,4-cyclohexadiene (Bermudez, 2003). Here, we present new results on the free energy profile

In general, reaction mechanisms and thermodynamic barriers for the cycloaddition reactions studied here can be analyzed by computing a free energy profile for one of the product states,

in this system.


Energy (kcal/mol)

Energy (kcal/mol)

Fig. 3. Relevant bond lengths () vs time (fs) during product formation for four representative adducts. The top row displays the C-C bonds lengths (moving average over 25 fs) while the bottom row plots the first and second CHD - SiC surface bond. The color-coded inset identifies the bond being plotted for each adduct type. Change in the C-C bond length closely correlates with surface-adduct bond formation. Intermediate lifetimes over all trajectories range from 0.05 - 18<sup>+</sup> ps.

likely the density of tilted dimers: Si has 0.033 dimers/Å2, but SiC only has 0.017 dimers/Å2. Regardless of whether dimer flipping occurs, it is simply more difficult to find a dimer on the SiC surface.

An important consideration in cycloaddition reactions such as those studied here is the possibility of their occurring through a radical mechanism. Multi-reference self consistent field cluster calculations of the SiC(001)-2x1 surface suggest that the topmost dimer exhibits significant diradical character (Tamura & Gordon, 2003), and since DFT is a single-reference method, multi-reference contributions are generally not included. However, cluster methods may bias the results by unphysically truncating the system instead of treating the full periodicity. For instance, cluster methods predict that Si(100)-2×1 dimers are symmetric (Olson & Gordon, 2006), contrary to experimental evidence (Mizuno et al., 2004; Over et al., 1997), while periodic DFT correctly captures the dimer tilt (Hayes & Tuckerman, 2007). In order to estimate the importance of diradical mechanisms and surface crossing, a series of single point energy calculations at regular intervals during four representative trajectories are plotted in Fig. 4. Three electronic configurations are considered: singlet spin restricted (SR) where the up and down spin are identical (black down triangles), singlet spin unrestricted (SU) where the up and down spin can vary spatially (red up triangles), and triplet SU (green squares). In all cases, the triplet configuration is unfavorable. However, at two places in the transition state (Adduct A in Fig. 4a at 3000 fs and Adduct G in Fig. 4d at 8500 fs) the single SU is slightly favored. Thus, multi-reference methods, which can account for surface crossing, may yield alternative reaction mechanisms.

### **4. Reactions on the SiC(100)-2**×**2 surface**

There is considerable interest in the growth of molecular lines or wires on semiconductor surfaces. Such structures allow molecular scale devices to be constructed using 16 Will-be-set-by-IN-TECH

D

Si Si H

H G

Si Si Sisub Sisub

7000 8000 9000

4800 5200 5600 12000 16000

Fig. 3. Relevant bond lengths () vs time (fs) during product formation for four representative adducts. The top row displays the C-C bonds lengths (moving average over 25 fs) while the bottom row plots the first and second CHD - SiC surface bond. The color-coded inset identifies the bond being plotted for each adduct type. Change in the C-C bond length closely correlates with surface-adduct bond formation. Intermediate lifetimes over all

likely the density of tilted dimers: Si has 0.033 dimers/Å2, but SiC only has 0.017 dimers/Å2. Regardless of whether dimer flipping occurs, it is simply more difficult to find a dimer on the

An important consideration in cycloaddition reactions such as those studied here is the possibility of their occurring through a radical mechanism. Multi-reference self consistent field cluster calculations of the SiC(001)-2x1 surface suggest that the topmost dimer exhibits significant diradical character (Tamura & Gordon, 2003), and since DFT is a single-reference method, multi-reference contributions are generally not included. However, cluster methods may bias the results by unphysically truncating the system instead of treating the full periodicity. For instance, cluster methods predict that Si(100)-2×1 dimers are symmetric (Olson & Gordon, 2006), contrary to experimental evidence (Mizuno et al., 2004; Over et al., 1997), while periodic DFT correctly captures the dimer tilt (Hayes & Tuckerman, 2007). In order to estimate the importance of diradical mechanisms and surface crossing, a series of single point energy calculations at regular intervals during four representative trajectories are plotted in Fig. 4. Three electronic configurations are considered: singlet spin restricted (SR) where the up and down spin are identical (black down triangles), singlet spin unrestricted (SU) where the up and down spin can vary spatially (red up triangles), and triplet SU (green squares). In all cases, the triplet configuration is unfavorable. However, at two places in the transition state (Adduct A in Fig. 4a at 3000 fs and Adduct G in Fig. 4d at 8500 fs) the single SU is slightly favored. Thus, multi-reference methods, which can account for

There is considerable interest in the growth of molecular lines or wires on semiconductor surfaces. Such structures allow molecular scale devices to be constructed using

time (fs) time (fs) time (fs) time (fs)

A 1.7

1 2

Si Si Si Si

6800 7200 7600

surface crossing, may yield alternative reaction mechanisms.

**4. Reactions on the SiC(100)-2**×**2 surface**

1.6 1.5 1.4 1.3 4.5

C-C bond (

Å)

3.5

CHD-SiC bonds (Å)

SiC surface.

2.5

1.5

trajectories range from 0.05 - 18<sup>+</sup> ps.

Fig. 4. Spin restricted (black down triangles), singlet spin-unrestricted (red up triangles), and triplet unrestricted (green squares) energies at regular intervals during a representative (a) [4+2] intradimer adduct [A], (b) [2+2] intradimer adduct [D], (c) H-abstraction, and (d) [4+2] subdimer trajectory. Energies are relative to the value at t=0 in (a). The insets show the difference between the spin restricted and unrestricted singlet energies (blue line) and spin restricted and triplet unrestricted energies (purple). The triplet configuration is always highest in energy. In (a) at 3000 fs and (d) at 8500 fs the singlet transition state configuration is favorable by 2.3 and 0.5 kcal/mol, respectively. Thus, a radical mechanism may also occur in this system.

semiconductors such as H-terminated Si(111) and Si(100) or Si(100)-2×1 as the preferred substrates. Various molecules can be grown into lines on the H-terminated surfaces (McNab & Polanyi, 2006), and on the Si(100)-2×1 surface, styrene and derivatives such as 2,4-dimethylstyrene or longer chain alkenes can be used to grow wires along the dimer rows (DiLabio et al., 2007; 2004; Hossain et al., 2005a;c; 2007a;b; 2008; Zikovsky et al., 2007). More recently, allylic mercaptan and acetophenone have been shown to grow across dimer rows on the H:Si(100)-2×1 surface (Ferguson et al., 2009; 2010; Hossain et al., 2005c; 2008; 2009). Other semiconductor surface can be considered for such applications, however, these have not received as much attention. An intriguing possible alternate in the silicon-carbide family is the SiC(100)-2×2 surface.

The SiC(100)-2×2 surface exhibits the crucial difference from the SiC(100)-3×2 in that it is characterized by C≡C triple bonds, which bridge Si-Si single bonds. These triple bonds are well separated and reactive, suggesting the possibility of restricting the product distribution for the addition of conjugated dienes on this surface. Fig. 5 shows a snapshot of this surface. Previous *ab initio* calculations suggest that these dimers react favorably with 1,4-cyclohexadiene (Bermudez, 2003). Here, we present new results on the free energy profile at 300 K for the reaction of this surface with 1,3-cyclohexadiene.

In general, reaction mechanisms and thermodynamic barriers for the cycloaddition reactions studied here can be analyzed by computing a free energy profile for one of the product states,

Fig. 5. Snapshot of the SiC-2×2 surface. Pink and grey spheres represent carbon and silicon atoms, respectively.

which we take to be the Diels-Alder-type [4+2] intradimer product. In the present case, the expect some of the barriers to product formation to be sufficiently high that specialized free energy sampling techniques are needed. Here, we employ the so-called blue moon ensemble approach (Carter et al., 1989; Sprik & Ciccotti, 1998) combined with thermodynamic integration. In order to define such a free energy profile, we first need to specify a reaction coordinate capable of following the progress of the reaction. For this purpose, we choose a coordinate *ξ* of the form

$$\zeta = \frac{1}{2} \left| \left( \mathbf{r}\_{\mathbf{C}\_4^s} + \mathbf{r}\_{\mathbf{C}\_b^s} \right) - \left( \mathbf{r}\_{\mathbf{C}\_1^w} + \mathbf{r}\_{\mathbf{C}\_4^w} \right) \right| \tag{49}$$

Fig. 6. Free energy along the reaction pathway leading to a Diels–Alder [4+2] adduct. Blue and red triangles indicate the product (EQ) and intermediate states (IS), respectively. Inset shows the buckling angle (*α*) distribution of the Si dimer for both the IS (red) and the EQ configurations (blue). The snapshots include configurations representing the IS and EQ geometries. Blue, green, and white spheres denote Si, C, and H atoms, respectively, and gray spheres indicate the location of Wannier centers. Red spheres locate positively charged atoms. The purple surface is a 0.95 electron localization function (ELF) isosurface.

<sup>249</sup> Creation of Ordered Layers on Semiconductor Surfaces:

An ab Initio Molecular Dynamics Study of the SiC(001)-3x2 and SiC(100)-c(2x2) Surfaces

In the present study of 1,3-cyclohexadiene with the SiC(100)-2×2 surface, the KS orbitals were expanded in a plane-wave basis set up to a kinetic energy cut-off of 60 Ry. As in the 1,3-CHD studies described above, exchange and correlation are treated with the spin restricted form of the PBE functional (Perdew et al., 1996), and core electrons were replaced by Troullier-Martins pseudopotentials (Troullier & Martins, 1991) with S, P, and D treated as local for H, C, and Si, respectively. The periodic slab contains 128 atoms arranged in 6 layers (including a bottom passivating hydrogen layer). Proper treatment of surface boundary conditions allowed for a simulation cell with dimensions *Lx* = 17.56Å, *Ly* =8.78 Å, and *Lz* =31 Å along the nonperiodic dimension. The surface contains 8 C≡C dimers. This setup is capable of reproducing the experimentally observed dimer buckling (Derycke et al., 2000) that static *ab initio* calculations using cluster models are unable to describe (Bermudez, 2003). In Fig. 7, we show the free energy profile for the [4+2] cycloaddition reaction of 1,3-cyclohexadiene with one of the C≡C surface dimers. The free energy profile is calculated by dividing the *ξ* interval *ξ* ∈ [1.59, 3.69] into 15 equally spaced intervals, and each constrained simulation was equilibrated for 1.0 ps followed by 3.0 ps of averaging using a time step of 0.025 fs. All calculations are carried out in the NVT ensemble at 300 K using Nosé-Hoover chain thermostats (Martyna et al., 1992) In contrast to the free energy profile of Fig. 6, the profile in Fig. 7 shows no evidence of a stable intermediate. Rather, apart from an initial barrier of approximately 8 kcal/mol, the free energy is strictly downhill. The reaction is thermodynamically favored by approximately 48 kcal/mol. The suggestion from Fig. 7 is that the reaction is symmetric and concerted in contrast to the reactions on the other surfaces we have considered thus far. Fig. 7 shows snapshots of the molecule and the surface atoms

where C*<sup>m</sup>* <sup>1</sup> and C*<sup>m</sup>* <sup>4</sup> are the carbons in the 1 and 4 positions in the organic molecule, and C*<sup>s</sup> a* and C*<sup>s</sup> <sup>b</sup>* are the two surface carbon atoms with which covalent bonds will form with C*<sup>m</sup>* <sup>1</sup> and C*<sup>m</sup>* <sup>4</sup> . Over the course of the reactions considered, *ξ* decreases from approximately 4 Å to a value less than 1.5 Å. In the aforementioned blue moon ensemble approach (Carter et al., 1989; Sprik & Ciccotti, 1998), the coordinate *ξ* is constrained at a set of equally spaced points between the two endpoints. At each constrained value, an AIMD simulation is performed over which we compute a conditional average �*∂H*/*∂ξ*�cond, where *H* is the nuclear Hamiltonian. Finally, the full free energy profile is reconstructed via thermodynamic integration:

$$
\Delta G(\xi) = \int\_{\overline{\xi}\_0}^{\overline{\xi}} d\xi' \left< \frac{\partial H}{\partial \overline{\xi}'} \right>\_{\text{cond}} \tag{50}
$$

An example of such a free energy profile for the [4+2] cycloaddition reaction of 1,3-butadiene with a single silicon surface dimer on the Si(100)-2×1 surface is shown in Fig. 6 (Minary & Tuckerman, 2004). We show this profile as an example in order that direct comparison can be made between reactions on this surface and those on the SiC(100)2×2 surface. The profile in Fig. 6 shows an initial barrier at *ξ* =3.2 Åof approximately 23 kcal/mol. As *ξ* decreases, a shallow minimum/plateau is seen at *ξ* =2.75 Å, and such a minimum indicates a stable intermediate. This intermediate was identified as a carbocation in which one of the C-Si bonds had formed prior to the second bond formation (Hayes & Tuckerman, 2007; Minary & Tuckerman, 2004; 2005). This stable intermediate was interpreted as clear evidence that the reaction proceeds via an asymmetric, non-concerted mechanism.

18 Will-be-set-by-IN-TECH

Fig. 5. Snapshot of the SiC-2×2 surface. Pink and grey spheres represent carbon and silicon

which we take to be the Diels-Alder-type [4+2] intradimer product. In the present case, the expect some of the barriers to product formation to be sufficiently high that specialized free energy sampling techniques are needed. Here, we employ the so-called blue moon ensemble approach (Carter et al., 1989; Sprik & Ciccotti, 1998) combined with thermodynamic integration. In order to define such a free energy profile, we first need to specify a reaction coordinate capable of following the progress of the reaction. For this purpose, we choose a

*<sup>b</sup>* are the two surface carbon atoms with which covalent bonds will form with C*<sup>m</sup>*

<sup>4</sup> . Over the course of the reactions considered, *ξ* decreases from approximately 4 Å to a value less than 1.5 Å. In the aforementioned blue moon ensemble approach (Carter et al., 1989; Sprik & Ciccotti, 1998), the coordinate *ξ* is constrained at a set of equally spaced points between the two endpoints. At each constrained value, an AIMD simulation is performed over which we compute a conditional average �*∂H*/*∂ξ*�cond, where *H* is the nuclear Hamiltonian. Finally, the full free energy profile is reconstructed via thermodynamic

<sup>4</sup> are the carbons in the 1 and 4 positions in the organic molecule, and C*<sup>s</sup>*

 *∂H ∂ξ*� 

cond

(49)

*a*

<sup>1</sup> and

(50)

*<sup>ξ</sup>* <sup>=</sup> <sup>1</sup> 2 **r**C*<sup>s</sup> <sup>a</sup>* + **r**C*<sup>s</sup> b* − **r**C*<sup>m</sup>* <sup>1</sup> + **r**C*<sup>m</sup>* 4 

Δ*G*(*ξ*) =

that the reaction proceeds via an asymmetric, non-concerted mechanism.

 *ξ ξ*0 *dξ*�

An example of such a free energy profile for the [4+2] cycloaddition reaction of 1,3-butadiene with a single silicon surface dimer on the Si(100)-2×1 surface is shown in Fig. 6 (Minary & Tuckerman, 2004). We show this profile as an example in order that direct comparison can be made between reactions on this surface and those on the SiC(100)2×2 surface. The profile in Fig. 6 shows an initial barrier at *ξ* =3.2 Åof approximately 23 kcal/mol. As *ξ* decreases, a shallow minimum/plateau is seen at *ξ* =2.75 Å, and such a minimum indicates a stable intermediate. This intermediate was identified as a carbocation in which one of the C-Si bonds had formed prior to the second bond formation (Hayes & Tuckerman, 2007; Minary & Tuckerman, 2004; 2005). This stable intermediate was interpreted as clear evidence

atoms, respectively.

coordinate *ξ* of the form

<sup>1</sup> and C*<sup>m</sup>*

where C*<sup>m</sup>*

integration:

and C*<sup>s</sup>*

C*<sup>m</sup>*

Fig. 6. Free energy along the reaction pathway leading to a Diels–Alder [4+2] adduct. Blue and red triangles indicate the product (EQ) and intermediate states (IS), respectively. Inset shows the buckling angle (*α*) distribution of the Si dimer for both the IS (red) and the EQ configurations (blue). The snapshots include configurations representing the IS and EQ geometries. Blue, green, and white spheres denote Si, C, and H atoms, respectively, and gray spheres indicate the location of Wannier centers. Red spheres locate positively charged atoms. The purple surface is a 0.95 electron localization function (ELF) isosurface.

In the present study of 1,3-cyclohexadiene with the SiC(100)-2×2 surface, the KS orbitals were expanded in a plane-wave basis set up to a kinetic energy cut-off of 60 Ry. As in the 1,3-CHD studies described above, exchange and correlation are treated with the spin restricted form of the PBE functional (Perdew et al., 1996), and core electrons were replaced by Troullier-Martins pseudopotentials (Troullier & Martins, 1991) with S, P, and D treated as local for H, C, and Si, respectively. The periodic slab contains 128 atoms arranged in 6 layers (including a bottom passivating hydrogen layer). Proper treatment of surface boundary conditions allowed for a simulation cell with dimensions *Lx* = 17.56Å, *Ly* =8.78 Å, and *Lz* =31 Å along the nonperiodic dimension. The surface contains 8 C≡C dimers. This setup is capable of reproducing the experimentally observed dimer buckling (Derycke et al., 2000) that static *ab initio* calculations using cluster models are unable to describe (Bermudez, 2003). In Fig. 7, we show the free energy profile for the [4+2] cycloaddition reaction of 1,3-cyclohexadiene with one of the C≡C surface dimers. The free energy profile is calculated by dividing the *ξ* interval *ξ* ∈ [1.59, 3.69] into 15 equally spaced intervals, and each constrained simulation was equilibrated for 1.0 ps followed by 3.0 ps of averaging using a time step of 0.025 fs. All calculations are carried out in the NVT ensemble at 300 K using Nosé-Hoover chain thermostats (Martyna et al., 1992) In contrast to the free energy profile of Fig. 6, the profile in Fig. 7 shows no evidence of a stable intermediate. Rather, apart from an initial barrier of approximately 8 kcal/mol, the free energy is strictly downhill. The reaction is thermodynamically favored by approximately 48 kcal/mol. The suggestion from Fig. 7 is that the reaction is symmetric and concerted in contrast to the reactions on the other surfaces we have considered thus far. Fig. 7 shows snapshots of the molecule and the surface atoms

Fig. 8. Average carbon-carbon bond lengths obtained from each constrained simulation.

<sup>251</sup> Creation of Ordered Layers on Semiconductor Surfaces:

An ab Initio Molecular Dynamics Study of the SiC(001)-3x2 and SiC(100)-c(2x2) Surfaces

Fig. 9. Free energy profile for the formation of the [2+2] adduct between 1,3-cyclohexadiene a C≡C dimer on the SiC-2×2 surface. Blue, white and yellow spheres represent C, H, and Si, respectively. Red spheres are the centers of maximally localized Wannier functions.

Fig. 7. Free energy profile for the formation of the [4+2] Diels-Alder-like adduct between 1,3-cyclohexadiene a C≡C dimer on the SiC-2×2 surface. Blue, white and yellow spheres represent C, H, and Si, respectively. Red spheres are the centers of maximally localized Wannier functions.

with which it interacts at various points along the free energy profile. In these snapshots, red spheres represent the centers of maximally localized Wannier functions. These provide a visual picture of where new covalent bonds are forming as the reaction coordinate *ξ* is decreased. By following these, we clearly see that one CC bond forms before the other, demonstrating the asymmetry of the reaction, which is a result of the buckling of the surface dimers. The buckling gives rise to a charge asymmetry in the C≡C surface dimer, and as a result, the first step in the reaction is a nucleophilic attack of one of the C=C bonds in the cyclohexadiene on the positively charged carbon in the surface dimer, this carbon being the lower of the two. Once this first CC bond forms, the second CC bond follows after a change of approximately 0.3 Å in the reaction coordinate with no stable intermediate along the way toward the final [4+2] cycloaddition product. In addition, the Wannier centers show the conversion of the triple bond on the surface to a double bond in the final product state.

Further evidence for the concerted asymmetric nature of the reaction is provided in Fig. 8, which shows the average carbon-carbon lengths computed over the constrained trajectories at each point of the free energy profile. It can be seen by the fact that one CC bond forms before the other that there is a slight tendency for an asymmetric reaction, despite its being concerted.

In order to demonstrate that the [4+2] Diels-Alder type cycloaddition product is highly favored over other reaction products on this surface, we show one additional example of a free energy profile, specifically, that for the formation of a [2+2] cycloaddition reaction with a single surface C≡C dimer. This profile is shown in Fig. 9. In contrast to the [4+2] Diels-Alder type adduct, the barrier to formation of this adduct is roughly 27 kcal/mol (compared to 8 kcal/mol for the Diels-Alder product). Thus, although the [2+2] reaction 20 Will-be-set-by-IN-TECH

Fig. 7. Free energy profile for the formation of the [4+2] Diels-Alder-like adduct between 1,3-cyclohexadiene a C≡C dimer on the SiC-2×2 surface. Blue, white and yellow spheres represent C, H, and Si, respectively. Red spheres are the centers of maximally localized

with which it interacts at various points along the free energy profile. In these snapshots, red spheres represent the centers of maximally localized Wannier functions. These provide a visual picture of where new covalent bonds are forming as the reaction coordinate *ξ* is decreased. By following these, we clearly see that one CC bond forms before the other, demonstrating the asymmetry of the reaction, which is a result of the buckling of the surface dimers. The buckling gives rise to a charge asymmetry in the C≡C surface dimer, and as a result, the first step in the reaction is a nucleophilic attack of one of the C=C bonds in the cyclohexadiene on the positively charged carbon in the surface dimer, this carbon being the lower of the two. Once this first CC bond forms, the second CC bond follows after a change of approximately 0.3 Å in the reaction coordinate with no stable intermediate along the way toward the final [4+2] cycloaddition product. In addition, the Wannier centers show the conversion of the triple bond on the surface to a double bond in the final product state. Further evidence for the concerted asymmetric nature of the reaction is provided in Fig. 8, which shows the average carbon-carbon lengths computed over the constrained trajectories at each point of the free energy profile. It can be seen by the fact that one CC bond forms before the other that there is a slight tendency for an asymmetric reaction, despite its being

In order to demonstrate that the [4+2] Diels-Alder type cycloaddition product is highly favored over other reaction products on this surface, we show one additional example of a free energy profile, specifically, that for the formation of a [2+2] cycloaddition reaction with a single surface C≡C dimer. This profile is shown in Fig. 9. In contrast to the [4+2] Diels-Alder type adduct, the barrier to formation of this adduct is roughly 27 kcal/mol (compared to 8 kcal/mol for the Diels-Alder product). Thus, although the [2+2] reaction

Wannier functions.

concerted.

Fig. 8. Average carbon-carbon bond lengths obtained from each constrained simulation.

Fig. 9. Free energy profile for the formation of the [2+2] adduct between 1,3-cyclohexadiene a C≡C dimer on the SiC-2×2 surface. Blue, white and yellow spheres represent C, H, and Si, respectively. Red spheres are the centers of maximally localized Wannier functions.

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Although we have not shown them here, we have computed free energy profiles for a variety of other adducts, including interdimer and sublayer adducts, and in all cases, free energy barriers exceeding 20 kcal/mol (or 40 kcal/mol in the case of the sublayer adduct) were obtained. These results strongly suggest that the product distribution this surface would, for all intents and purposes, restricted to the single [4+2] Diels-Alder type product, implying that this surface might be a candidate for creating an ordered organic/semiconductor interface.

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22 Will-be-set-by-IN-TECH

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**11** 

*USA* 

**Optical Properties and Applications of** 

**Silicon Carbide in Astrophysics** 

Anne M. Hofmeister3 and Adrian B. Corman3

*2Dept. of Physics & Astronomy, University of Missouri-Columbia* 

*3Dept. of Earth & Planetary Sciences, Washington University in St. Louis* 

Optical properties, namely, spectra and optical functions, of silicon carbide (SiC) have been of great interest to astrophysicists since SiC was first theoretically posited to exist as dust, i.e., submicron-sized solid state particles, in carbon-rich circumstellar regions (Gilman, 1969; Friedemann, 1969). The prediction that SiC in space should re-emit absorbed radiation as a spectral feature in the λ = 10-13 μm wavelength region (Gilra, 1971, 1972) was confirmed by a broad emission feature at λ ~ 11.4 μm in the spectra of several carbon-rich stars (Hackwell, 1972; Treffers & Cohen, 1974). Many carbon-rich, evolved stars exhibit the λ ~ 11 μm feature in emission, and SiC is now believed to be a significant constituent around them (Speck,

Detection of SiC in space provides much information on circumstellar environments because the chemical composition and structure of dust in space is correlated with, e.g., the pressure, temperature, and ratios of available elements in gas around stars. The mere presence of SiC implies that the carbon-to-oxygen (C/O) must be high. Different polytypes of SiC identify the temperature and gas pressure within the dust forming region around a star. The significance of SiC in stars is tied intimately to stellar evolution, as dust grains participate in feedback relationships between stars and their circumstellar envelopes that affect mass-loss rates, i.e., stellar lifetimes. Meteoritic SiC grains exhibit signatures of s-process enrichment,

Elements more massive than helium have been formed in stars. All elements > 56Fe are generated by neutron capture because there is no Coulomb barrier for adding a neutral particle. In the s-process (slow neutron capture), neutrons are added to atomic nuclei slowly as compared to the rate of beta decay (cf. Burbidge, et al. 1957, a.k.a., B2FH; Cameron 1957). The precise isotopes of heavy elements depend on the rate of neutron capture, which, in turn, is strongly dependent on the properties of the stellar sources. Thus, it is possible to

one of the main attributes of the evolutionary track of carbon-rich stars.

**1. Introduction** 

1998; Speck et al., 2009 and references therein).

**1.1 Role of SiC in stellar environments** 

**1.1.1 S-process isotopic signatures in SiC** 

Karly M. Pitman1, Angela K. Speck2,

*1Planetary Science Institute* 


### **Optical Properties and Applications of Silicon Carbide in Astrophysics**

Karly M. Pitman1, Angela K. Speck2, Anne M. Hofmeister3 and Adrian B. Corman3 *1Planetary Science Institute 2Dept. of Physics & Astronomy, University of Missouri-Columbia 3Dept. of Earth & Planetary Sciences, Washington University in St. Louis USA* 

#### **1. Introduction**

26 Will-be-set-by-IN-TECH

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Optical properties, namely, spectra and optical functions, of silicon carbide (SiC) have been of great interest to astrophysicists since SiC was first theoretically posited to exist as dust, i.e., submicron-sized solid state particles, in carbon-rich circumstellar regions (Gilman, 1969; Friedemann, 1969). The prediction that SiC in space should re-emit absorbed radiation as a spectral feature in the λ = 10-13 μm wavelength region (Gilra, 1971, 1972) was confirmed by a broad emission feature at λ ~ 11.4 μm in the spectra of several carbon-rich stars (Hackwell, 1972; Treffers & Cohen, 1974). Many carbon-rich, evolved stars exhibit the λ ~ 11 μm feature in emission, and SiC is now believed to be a significant constituent around them (Speck, 1998; Speck et al., 2009 and references therein).

#### **1.1 Role of SiC in stellar environments**

Detection of SiC in space provides much information on circumstellar environments because the chemical composition and structure of dust in space is correlated with, e.g., the pressure, temperature, and ratios of available elements in gas around stars. The mere presence of SiC implies that the carbon-to-oxygen (C/O) must be high. Different polytypes of SiC identify the temperature and gas pressure within the dust forming region around a star. The significance of SiC in stars is tied intimately to stellar evolution, as dust grains participate in feedback relationships between stars and their circumstellar envelopes that affect mass-loss rates, i.e., stellar lifetimes. Meteoritic SiC grains exhibit signatures of s-process enrichment, one of the main attributes of the evolutionary track of carbon-rich stars.

#### **1.1.1 S-process isotopic signatures in SiC**

Elements more massive than helium have been formed in stars. All elements > 56Fe are generated by neutron capture because there is no Coulomb barrier for adding a neutral particle. In the s-process (slow neutron capture), neutrons are added to atomic nuclei slowly as compared to the rate of beta decay (cf. Burbidge, et al. 1957, a.k.a., B2FH; Cameron 1957). The precise isotopes of heavy elements depend on the rate of neutron capture, which, in turn, is strongly dependent on the properties of the stellar sources. Thus, it is possible to

Optical Properties and Applications of Silicon Carbide in Astrophysics 259

allowing the central star to be seen and making such objects optically bright. The effect of decreasing optical depth and cooling dust temperatures changes the appearance of the

Fig. 1. Astronomical objects in which SiC has been detected. Left to right: (a) Hubble Space Telescope image of the extreme carbon star AFGL 3068. Source: Mauron & Huggins (2006); http://www.planetastronomy.com (b) The Egg Nebula, illustrating polarization through a thick vertical dust belt in the center of a pre- or proto-planetary nebula. Source: NASA and

http://heritage.stsci.edu (c) IC 418, the Spirograph Nebula, is one of only a handful of galactic planetary nebulae that actually show SiC emission. Source: NASA and The Hubble Heritage Team (STScI/AURA); R. Sahai (JPL), A. Hajian (USNO); http://hubblesite.org

Fig. 2. Schematic diagram of the evolution of low-to-intermediate-mass stars. Bottom: A 1Mstar begins its life on the main sequence, converting H into He in its core; when H is depleted, it exits to the Red Giant Branch (RGB), then the Asymptotic Giant Branch (AGB), where SiC formation occurs. Top: During the AGB phase, the dust shell get thicker and stars become very bright in the IR. Intense mass loss depletes the remaining H in the star's outer envelope in a few x 104 years (Volk et al., 2000) and terminates the AGB phase. Stars may

then become proto-planetary nebulae (PPN), or later planetary nebulae (PN).

The Hubble Heritage Team (STScI/AURA); W. Sparks (STScI), R. Sahai (JPL);

circumstellar envelope, revealing features that were hidden during the AGB phase.

uniquely identify different masses or types of stars as the sources of isotopically non-solar dust grains. SiC was the first meteoritic dust grain to be discovered that, on the basis of its isotopic composition, obviously formed before and survived the formation of the solar system (Bernatowicz et al., 1987). Further studies of the precise isotopic compositions of these meteoritic "presolar" grains have identified their stellar sources. For SiC, 99% of the presolar grains are characterized by high abundances of s-process elements, indicative of formation around certain classes of evolved, intermediate mass stars (described below).

#### **1.1.2 Space environments containing SiC**

Figure 1 illustrates the varied space environments in which SiC has been detected. To understand the nature of SiC in these environments and how SiC originally formed in the universe, Figure 2 and the following text describe how these categories of stars evolve.

#### **1.1.2.1 Asymptotic Giant Branch (AGB) stars**

Figure 2 illustrates the evolution of low-to-intermediate-mass stars (LIMS; 0.8-8 times the mass of the Sun, M = 1.98892 x 1030 kg). In the late stages of evolution, LIMS follow a path up the Asymptotic Giant Branch (AGB; Iben & Renzini, 1983). During the AGB phase, stars are very luminous (~103-104 L, where L = 3.839×1033 erg/s) and large (~ 300 R, where R = 6.995×108 m) but have relatively low surface temperature (~ 3000 K). AGB stars pulsate due to dynamical instabilities, leading to intensive mass loss and the formation of circumstellar shells of gas and dust. The carbon-to-oxygen ratio (C/O) controls the chemistry around the star: whichever element is less abundant will be entirely locked into CO molecules, leaving the more abundant element to control dust formation. Therefore, AGB stars can be either oxygenrich or carbon-rich. Approximately 1/3 of AGB stars are C-rich (i.e., C/O > 1). Whereas Cstars are expected to have circumstellar shells dominated by amorphous or graphitic carbon, SiC is also expected to form; its IR spectrum provides a diagnostic tool not available from the carbonaceous grains. Therefore, SiC has been of greatest interest to astrophysicists seeking to understand the evolution of dust shells and infrared features of C-stars (Baron et al., 1987; Chan & Kwok, 1990; Goebel et al., 1995; Speck et al., 1997; Sloan et al., 1998; Speck et al., 2005, 2006; Thompson et al., 2006). For Galactic sources, the majority of C-stars should first condense TiC, then C, then SiC, as supported by meteoritic evidence (e.g., Bernatowicz et al., 2005). As C-stars evolve, mass loss is expected to increase. Consequently, their circumstellar shells become progressively more optically thick, and eventually the central star is obscured. Volk et al. (1992, 2000) christened such stars "extreme carbon stars" (e.g., Fig. 1a). Extreme carbon stars are expected to represent that small subset of C-rich AGB stars just prior to leaving the AGB. Because that phase is short-lived, the number of extreme C-stars is intrinsically small and few of these objects have been found in space (~30 known in the Galaxy: Volk et al., 1992, versus ~30,000 known visible C-stars: Skrutskie et al., 2001).

#### **1.1.2.2 Post-AGB stars**

Once the AGB phase ends, mass loss virtually stops, and the circumstellar shell begins to drift away from the star. At the same time, the central star begins to shrink and heat up from T = 3000 K until it is hot enough to ionize the surrounding gas, at which point the object becomes a planetary nebula (PN; e.g., Fig. 1c). The short-lived post-AGB phase, as the star evolves toward the PN phase, is also known as the proto- or pre-planetary nebula (PPN) phase (e.g., Fig. 1b). As the detached dust shell drifts away from the central star, the dust cools, causing a PPN to have cool infrared colors. Meanwhile, the optical depth of the dust shell decreases,

uniquely identify different masses or types of stars as the sources of isotopically non-solar dust grains. SiC was the first meteoritic dust grain to be discovered that, on the basis of its isotopic composition, obviously formed before and survived the formation of the solar system (Bernatowicz et al., 1987). Further studies of the precise isotopic compositions of these meteoritic "presolar" grains have identified their stellar sources. For SiC, 99% of the presolar grains are characterized by high abundances of s-process elements, indicative of formation around certain classes of evolved, intermediate mass stars (described below).

Figure 1 illustrates the varied space environments in which SiC has been detected. To understand the nature of SiC in these environments and how SiC originally formed in the universe, Figure 2 and the following text describe how these categories of stars evolve.

Figure 2 illustrates the evolution of low-to-intermediate-mass stars (LIMS; 0.8-8 times the mass of the Sun, M = 1.98892 x 1030 kg). In the late stages of evolution, LIMS follow a path up the Asymptotic Giant Branch (AGB; Iben & Renzini, 1983). During the AGB phase, stars are very luminous (~103-104 L, where L = 3.839×1033 erg/s) and large (~ 300 R, where R = 6.995×108 m) but have relatively low surface temperature (~ 3000 K). AGB stars pulsate due to dynamical instabilities, leading to intensive mass loss and the formation of circumstellar shells of gas and dust. The carbon-to-oxygen ratio (C/O) controls the chemistry around the star: whichever element is less abundant will be entirely locked into CO molecules, leaving the more abundant element to control dust formation. Therefore, AGB stars can be either oxygenrich or carbon-rich. Approximately 1/3 of AGB stars are C-rich (i.e., C/O > 1). Whereas Cstars are expected to have circumstellar shells dominated by amorphous or graphitic carbon, SiC is also expected to form; its IR spectrum provides a diagnostic tool not available from the carbonaceous grains. Therefore, SiC has been of greatest interest to astrophysicists seeking to understand the evolution of dust shells and infrared features of C-stars (Baron et al., 1987; Chan & Kwok, 1990; Goebel et al., 1995; Speck et al., 1997; Sloan et al., 1998; Speck et al., 2005, 2006; Thompson et al., 2006). For Galactic sources, the majority of C-stars should first condense TiC, then C, then SiC, as supported by meteoritic evidence (e.g., Bernatowicz et al., 2005). As C-stars evolve, mass loss is expected to increase. Consequently, their circumstellar shells become progressively more optically thick, and eventually the central star is obscured. Volk et al. (1992, 2000) christened such stars "extreme carbon stars" (e.g., Fig. 1a). Extreme carbon stars are expected to represent that small subset of C-rich AGB stars just prior to leaving the AGB. Because that phase is short-lived, the number of extreme C-stars is intrinsically small and few of these objects have been found in space (~30 known in the Galaxy: Volk et al., 1992,

Once the AGB phase ends, mass loss virtually stops, and the circumstellar shell begins to drift away from the star. At the same time, the central star begins to shrink and heat up from T = 3000 K until it is hot enough to ionize the surrounding gas, at which point the object becomes a planetary nebula (PN; e.g., Fig. 1c). The short-lived post-AGB phase, as the star evolves toward the PN phase, is also known as the proto- or pre-planetary nebula (PPN) phase (e.g., Fig. 1b). As the detached dust shell drifts away from the central star, the dust cools, causing a PPN to have cool infrared colors. Meanwhile, the optical depth of the dust shell decreases,

**1.1.2 Space environments containing SiC** 

**1.1.2.1 Asymptotic Giant Branch (AGB) stars** 

versus ~30,000 known visible C-stars: Skrutskie et al., 2001).

**1.1.2.2 Post-AGB stars** 

allowing the central star to be seen and making such objects optically bright. The effect of decreasing optical depth and cooling dust temperatures changes the appearance of the circumstellar envelope, revealing features that were hidden during the AGB phase.

Fig. 1. Astronomical objects in which SiC has been detected. Left to right: (a) Hubble Space Telescope image of the extreme carbon star AFGL 3068. Source: Mauron & Huggins (2006); http://www.planetastronomy.com (b) The Egg Nebula, illustrating polarization through a thick vertical dust belt in the center of a pre- or proto-planetary nebula. Source: NASA and The Hubble Heritage Team (STScI/AURA); W. Sparks (STScI), R. Sahai (JPL); http://heritage.stsci.edu (c) IC 418, the Spirograph Nebula, is one of only a handful of galactic planetary nebulae that actually show SiC emission. Source: NASA and The Hubble Heritage Team (STScI/AURA); R. Sahai (JPL), A. Hajian (USNO); http://hubblesite.org

Fig. 2. Schematic diagram of the evolution of low-to-intermediate-mass stars. Bottom: A 1Mstar begins its life on the main sequence, converting H into He in its core; when H is depleted, it exits to the Red Giant Branch (RGB), then the Asymptotic Giant Branch (AGB), where SiC formation occurs. Top: During the AGB phase, the dust shell get thicker and stars become very bright in the IR. Intense mass loss depletes the remaining H in the star's outer envelope in a few x 104 years (Volk et al., 2000) and terminates the AGB phase. Stars may then become proto-planetary nebulae (PPN), or later planetary nebulae (PN).

Optical Properties and Applications of Silicon Carbide in Astrophysics 261

types A, B, X, Y, and Z. The "mainstream" SiC population, constituting ~ 87-94% of known presolar SiC grains, is believed to have originated around C-rich AGB stars. Compared to "mainstream" SiC, A and B SiC grains have low 12C/13C but a similar Si profile; they are thought to derive from a particular class of C-star. Y and Z SiC grains are typically small as compared to other presolar SiC grains, are easily distinguished from the "mainstream" class by their Si content, and come from either low mass, low metallicity AGB stars that undergo different types of processing or possibly novae. Type X SiC grains are the most rare (~1% of presolar SiC), are generally collections of many < 100 nm-sized rather than individual grains, and have been posited to derive from ejecta of core-collapse (Type II) supernovae. Laboratory studies of presolar meteoritic SiC grains have utilized and developed many innovative techniques (see review by Hoppe, 2009). Initial works relied on ion microprobe and secondary ion mass spectrometry (SIMS) techniques to determine isotopic compositions for light and intermediate mass elements in individual presolar SiC grains, including C, N, Si, Ca, Ti, Mg, Al, O, V, Fe, Sr, Y, Zr, Nb, Ba, Ce, Nd, B (Amari et al., 1992, 1995, 1996, 1997a, 1997b; Hoppe et al. 1994a, 1994b, 1996, 2000, 2001). Post 2001, efforts to drive down the diameter of the primary ion beam and thus be able to probe presolar grains smaller than 0.5 μm resulted in a series of studies using the Cameca NanoSIMS 50 ion microprobe (Besmehn & Hoppe, 2002; Hoppe & Besmehn, 2002; Gyngard, 2009). Time-of-flight secondary ion mass spectrometry (TOF-SIMS) has been applied to submicron presolar SiC grains in an effort to sputter less sample (Henkel et al., 2007), and atomic probe tomography (field ion microscope + TOF mass spectrometer) has also been tested on presolar and synthetic SiC grains to significantly improve upon the spatial resolution of NanoSIMS (Heck et al., 2010). Resonance ion mass spectrometry (RIMS) studies have further quantified the isotopic compositions of heavy elements such as Zr, Mo, and Ba in presolar SiC grains (e.g., Nicolussi et al., 1997, 1998; Savina et al., 2003; Barzyk, 2007). Laser heating experiments by Nichols et al. (1992) and later work by Heck (2005) have yielded the isotopic compositions of He and Ne in presolar SiC. Combinations of SIMS, RIMS, gas mass spectrometry, and other experimental methods (e.g., SEM, TEM, Auger spectroscopy) are currently being employed

A subset of studies on the isotopic compositions of presolar SiC grains investigates the effect of grain sizes on concentrations of s-process elements. Prombo et al. (1993) found a correlation between grain size and the concentration of s-process elements in the presolar SiC grains taken from the Murchison meteorites. Presolar SiC grains from the Indarch meteorite yielded similar results (Jennings et al., 2002). In both cases, the smaller grains have

In addition to the isotopic studies of presolar SiC, crystallographic studies have shown that nearly all are of the β-polytype (cubic crystal structure) and the 6H-α-polytype is never found. In the Murray C2 carbonaceous chondritic meteorite in which presolar SiC was first unequivocally detected, cubic and {111}-twinned cubic were the most common structural forms (Bernatowicz et al. 1987, 1988a, 1988b). Daulton et al. (2002, 2003) itemize the amount of 3C β-SiC (80%), 2H α-SiC (3%), and intergrowths of these two forms (17%) present in presolar SiC grains. This is significant in astrophysics because which polytype of SiC forms in space strongly depends on the temperature and gas pressure within the dust-forming region. 2H and 3C are the polytypes that form at the lowest temperature where SiC condenses; which of 2H or 3C SiC forms depends on many factors, such as Si/C ratio. For further reviews of SiC and cosmic dust in meteorites, see also Anders & Zinner (1993), Hoppe & Ott (1997), Hoppe & Zinner (2000), Hoppe (2009), Ott (2010), and Henning (2010).

in analyses of presolar SiC grains (cf. Stroud et al., 2004).

higher relative abundances of s-process elements.

Infrared (IR) spectroscopy is used to probe the nature of SiC dust grains in space because dust particles of a given size, shape, temperature, structure, and composition have their own signature IR spectrum. Dust grains absorb high energy photons from stars and re-emit in the IR, in accordance with the specific (low) temperatures of any given grain. Therefore, to account for the energy budget in astronomical environments, astrophysicists are also interested in how SiC dust grains absorb and scatter UV-vis photons, which requires knowledge of SiC optical functions. Lines of evidence or constraints that astrophysicists use to aid studies of SiC dust in space include evidence from meteoritic studies, comparisons between the positions and shapes of spectral features for astronomical objects and laboratory analogue materials, spatial distributions of materials, and theoretical models for dust formation.

#### **2. Silicon carbide in meteorites**

SiC particles were the first presolar dust grains found in meteorites (Bernatowicz et al., 1987) and remain the best studied (e.g. Clayton & Nittler, 2004; Bernatowicz et al., 2006; Hoppe, 2009). Presolar grains are ancient refractory dust with the isotopic makeup of stars that exist as individual particles or clusters found in the matrix, or fine-grained crystalline mass, of a meteorite. Ages of meteoritic SiC grains are discussed by Ott (2010). Figure 3 describes the family of meteorite classes that contain presolar SiC grains. The most studied meteorites that contain presolar SiC are carbonaceous chondrites (e.g., the class CM2 Murchison and Murray meteorites, classes CI1 = Orgueil, CV3 = Allende) which are considered to be the most primitive or least processed solid materials in the Solar System. Presolar SiC is also found in other stony meteorite types as well: enstatite chondrites (e.g., EH4 = Indarch, EH3 = Qingzhen) and ordinary chondrites (e.g., H/L 3.6 = Tieschitz, LL 3.1 = Bishunpur, Krymka, LL 3.5 = Chainpur, L/LL 3.4 = Inman; LL 3.0 = Semarkona). Investigations via scanning and transmission electron microscopy have revealed the physical morphology of presolar SiC grains (Figure 4). Whereas presolar grains are rare (Clayton & Nittler, 2004) and very small (typically less than 1 μm in size: Amari et al., 1994), presolar SiC grains are more abundant than other presolar compositions (up to 30 ppm in the Murchison meteorite: Ott & Merchel, 2000) and, at 1.5 nm to 26 μm in size, many are large enough to be probed for their isotopic composition (Yin et al., 2006; Speck et al. 2009, and references therein).

As discussed in the introduction, SiC presolar grains are identified by their anomalous isotopic compositions. In fact, their isotopic compositions have not only identified their likely cosmic sources, but also have provided key tests of hypotheses for nucleosynthesis (element creation) and generate the data needed to refine those hypotheses. Whereas ~1% of presolar SiC probably emanates from stellar environments such as novae and supernovae, the vast majority have isotopic compositions consistent with formation around AGB stars. Because the s-process is the dominant method of forming heavy elements in AGB stars, the SiC grains that form within AGB stellar envelopes are excellent tracers of unadulterated sprocess isotopes. Studies of these presolar grains are used to determine s-process timescales, stellar temperature and masses, and neutron exposure rates of stellar nuclei.

Compared to solar isotopes, presolar SiC grains exhibit anomalous isotopic compositions for their major components C and Si, as well as trace elements: N, Mg, Ca, Ti, Sr, Zr, Mo, Ba, Nd, Sm, Dy, and the noble gases (Hoppe & Ott, 1997). Based on such isotopic analyses, six types of presolar SiC have been established according to their Si, 12C/13C, 14N/15N, and 26Al/27Al ratios (e.g., table 2, Ott, 2010 and references therein): "mainstream" SiC, versus

Infrared (IR) spectroscopy is used to probe the nature of SiC dust grains in space because dust particles of a given size, shape, temperature, structure, and composition have their own signature IR spectrum. Dust grains absorb high energy photons from stars and re-emit in the IR, in accordance with the specific (low) temperatures of any given grain. Therefore, to account for the energy budget in astronomical environments, astrophysicists are also interested in how SiC dust grains absorb and scatter UV-vis photons, which requires knowledge of SiC optical functions. Lines of evidence or constraints that astrophysicists use to aid studies of SiC dust in space include evidence from meteoritic studies, comparisons between the positions and shapes of spectral features for astronomical objects and laboratory analogue materials, spatial distributions of materials, and theoretical models for

SiC particles were the first presolar dust grains found in meteorites (Bernatowicz et al., 1987) and remain the best studied (e.g. Clayton & Nittler, 2004; Bernatowicz et al., 2006; Hoppe, 2009). Presolar grains are ancient refractory dust with the isotopic makeup of stars that exist as individual particles or clusters found in the matrix, or fine-grained crystalline mass, of a meteorite. Ages of meteoritic SiC grains are discussed by Ott (2010). Figure 3 describes the family of meteorite classes that contain presolar SiC grains. The most studied meteorites that contain presolar SiC are carbonaceous chondrites (e.g., the class CM2 Murchison and Murray meteorites, classes CI1 = Orgueil, CV3 = Allende) which are considered to be the most primitive or least processed solid materials in the Solar System. Presolar SiC is also found in other stony meteorite types as well: enstatite chondrites (e.g., EH4 = Indarch, EH3 = Qingzhen) and ordinary chondrites (e.g., H/L 3.6 = Tieschitz, LL 3.1 = Bishunpur, Krymka, LL 3.5 = Chainpur, L/LL 3.4 = Inman; LL 3.0 = Semarkona). Investigations via scanning and transmission electron microscopy have revealed the physical morphology of presolar SiC grains (Figure 4). Whereas presolar grains are rare (Clayton & Nittler, 2004) and very small (typically less than 1 μm in size: Amari et al., 1994), presolar SiC grains are more abundant than other presolar compositions (up to 30 ppm in the Murchison meteorite: Ott & Merchel, 2000) and, at 1.5 nm to 26 μm in size, many are large enough to be probed for their

isotopic composition (Yin et al., 2006; Speck et al. 2009, and references therein).

As discussed in the introduction, SiC presolar grains are identified by their anomalous isotopic compositions. In fact, their isotopic compositions have not only identified their likely cosmic sources, but also have provided key tests of hypotheses for nucleosynthesis (element creation) and generate the data needed to refine those hypotheses. Whereas ~1% of presolar SiC probably emanates from stellar environments such as novae and supernovae, the vast majority have isotopic compositions consistent with formation around AGB stars. Because the s-process is the dominant method of forming heavy elements in AGB stars, the SiC grains that form within AGB stellar envelopes are excellent tracers of unadulterated sprocess isotopes. Studies of these presolar grains are used to determine s-process timescales, stellar temperature and masses, and neutron exposure rates of stellar nuclei. Compared to solar isotopes, presolar SiC grains exhibit anomalous isotopic compositions for their major components C and Si, as well as trace elements: N, Mg, Ca, Ti, Sr, Zr, Mo, Ba, Nd, Sm, Dy, and the noble gases (Hoppe & Ott, 1997). Based on such isotopic analyses, six types of presolar SiC have been established according to their Si, 12C/13C, 14N/15N, and 26Al/27Al ratios (e.g., table 2, Ott, 2010 and references therein): "mainstream" SiC, versus

dust formation.

**2. Silicon carbide in meteorites** 

types A, B, X, Y, and Z. The "mainstream" SiC population, constituting ~ 87-94% of known presolar SiC grains, is believed to have originated around C-rich AGB stars. Compared to "mainstream" SiC, A and B SiC grains have low 12C/13C but a similar Si profile; they are thought to derive from a particular class of C-star. Y and Z SiC grains are typically small as compared to other presolar SiC grains, are easily distinguished from the "mainstream" class by their Si content, and come from either low mass, low metallicity AGB stars that undergo different types of processing or possibly novae. Type X SiC grains are the most rare (~1% of presolar SiC), are generally collections of many < 100 nm-sized rather than individual grains, and have been posited to derive from ejecta of core-collapse (Type II) supernovae. Laboratory studies of presolar meteoritic SiC grains have utilized and developed many innovative techniques (see review by Hoppe, 2009). Initial works relied on ion microprobe and secondary ion mass spectrometry (SIMS) techniques to determine isotopic compositions for light and intermediate mass elements in individual presolar SiC grains, including C, N, Si, Ca, Ti, Mg, Al, O, V, Fe, Sr, Y, Zr, Nb, Ba, Ce, Nd, B (Amari et al., 1992, 1995, 1996, 1997a, 1997b; Hoppe et al. 1994a, 1994b, 1996, 2000, 2001). Post 2001, efforts to drive down the diameter of the primary ion beam and thus be able to probe presolar grains smaller than 0.5 μm resulted in a series of studies using the Cameca NanoSIMS 50 ion microprobe (Besmehn & Hoppe, 2002; Hoppe & Besmehn, 2002; Gyngard, 2009). Time-of-flight secondary ion mass spectrometry (TOF-SIMS) has been applied to submicron presolar SiC grains in an effort to sputter less sample (Henkel et al., 2007), and atomic probe tomography (field ion microscope + TOF mass spectrometer) has also been tested on presolar and synthetic SiC grains to significantly improve upon the spatial resolution of NanoSIMS (Heck et al., 2010). Resonance ion mass spectrometry (RIMS) studies have further quantified the isotopic compositions of heavy elements such as Zr, Mo, and Ba in presolar SiC grains (e.g., Nicolussi et al., 1997, 1998; Savina et al., 2003; Barzyk, 2007). Laser heating experiments by Nichols et al. (1992) and later work by Heck (2005) have yielded the isotopic compositions of He and Ne in presolar SiC. Combinations of SIMS, RIMS, gas mass spectrometry, and other experimental methods (e.g., SEM, TEM, Auger spectroscopy) are currently being employed in analyses of presolar SiC grains (cf. Stroud et al., 2004).

A subset of studies on the isotopic compositions of presolar SiC grains investigates the effect of grain sizes on concentrations of s-process elements. Prombo et al. (1993) found a correlation between grain size and the concentration of s-process elements in the presolar SiC grains taken from the Murchison meteorites. Presolar SiC grains from the Indarch meteorite yielded similar results (Jennings et al., 2002). In both cases, the smaller grains have higher relative abundances of s-process elements.

In addition to the isotopic studies of presolar SiC, crystallographic studies have shown that nearly all are of the β-polytype (cubic crystal structure) and the 6H-α-polytype is never found. In the Murray C2 carbonaceous chondritic meteorite in which presolar SiC was first unequivocally detected, cubic and {111}-twinned cubic were the most common structural forms (Bernatowicz et al. 1987, 1988a, 1988b). Daulton et al. (2002, 2003) itemize the amount of 3C β-SiC (80%), 2H α-SiC (3%), and intergrowths of these two forms (17%) present in presolar SiC grains. This is significant in astrophysics because which polytype of SiC forms in space strongly depends on the temperature and gas pressure within the dust-forming region. 2H and 3C are the polytypes that form at the lowest temperature where SiC condenses; which of 2H or 3C SiC forms depends on many factors, such as Si/C ratio.

For further reviews of SiC and cosmic dust in meteorites, see also Anders & Zinner (1993), Hoppe & Ott (1997), Hoppe & Zinner (2000), Hoppe (2009), Ott (2010), and Henning (2010).

Optical Properties and Applications of Silicon Carbide in Astrophysics 263

For SiC, the major spectral features result from cation-anion charge transfer and/or electronic band gap transitions in the visible-UV, as well as from lattice vibrations in the IR. Vibrational motions involving a change in the dipole moment are IR active. The nearest-neighbor interaction between Si and C produces a strong band in the IR, regardless of polytype. The stacking disorder that exists for SiC lowers crystal symmetry, resulting in vibrational transitions that increase in number with polytype complexity. For all polytypes of SiC, the transverse optic mode (TO) is present at ~ 12.5 μm and the longitudinal optic mode (LO) is seen at ~ 10.3 μm (Nakashima & Harima, 1997). Electronic transitions occur throughout the visible-UV and are strongest at ~ 0.111 μm (Philipp & Taft, 1960). Laboratory astrophysics studies focus on low energy or IR wavelength SiC spectral features (at λ ~ 11 μm, 21 μm) to identify cosmic SiC in space, and also quantify the optical depth of and chemical impurities or defects in cosmic SiC via

Past laboratory spectral studies utilized by astrophysicists are published across multiple disciplines. Although UV measurements for other sample types, e.g., extinction of light from SiC smoke particles (Stephens, 1980), have also been used in astrophysics, this paragraph reviews the state of single-crystal SiC spectroscopic studies in the UV and gives examples of UV SiC spectra in Figures 5 and 6. The polytypes that matter most to astrophysicists are 3C, 2H, and 4H, on the basis of the meteoritic record; data on other forms (e.g., 8H, 15R, 21R) have not been considered. Because the 6H form of α-SiC is available commercially with large faces perpendicular to c axis, for which unpolarized measurements provide data on E ⊥ c, there is a wealth of laboratory spectra on 6H in this orientation. The first α-SiC laboratory reflectance data (e.g., Philipp, 1958; Wheeler, 1966) were gathered at resolutions lower by at least a factor of two than can be attained with modern instrumentation. In the ultraviolet, modern commercial instruments exist and are inexpensive for wavelengths down to 0.192 μm (or, for a factor of x10 more in cost, down to 0.164 μm, the "vacuum UV"). However, spectral data for SiC used by astrophysicists does not extend much past 200 nm, as summarized in Figure 5. Early works on UV SiC spectroscopy studied in the astrophysics literature include Choyke & Patrick (1957), Philipp (1958), and Philipp & Taft (1960). Choyke & Patrick (1957) measured transmission (converted to absorption coefficient in cm-1) for one α-SiC plate, whereas Philipp (1958) measured absorption for yellow 3C and colorless 6H SiC single crystal samples of varying thicknesses. In both studies, samples were not well characterized in terms of SiC impurities, stacking faults, and defects, which are highly important in the UV-vis. Philipp & Taft (1960) presented reflectance spectra from ~ 0.11 to 0.62 μm for hexagonal SiC. Because reliable reflectivity standards were not available at that time, uncertainties in absolute R were large (i.e., > 5%). Hofmeister et al. (2009) published new data on the visible to soft UV range (1.11-0.303 μm) for α- and β-SiC single crystals with emphasis on impurities. In that study, absorbance spectra were provided for 6H and 3C SiC (E || c and E ⊥ c) as electronic tables for λ = 2.5-16.36 μm; figure 7 of that work provides absorbance spectra shortward of 2.5 μm. Additional laboratory UV absorption spectra (e.g., Choyke & Patrick 1968, 1969) and reflectivity spectra, including experimentally measured and calculated data (Wheeler, 1966; Belle et al., 1967; Lubinsky et al., 1975; Rehn et al., 1976; Gavrilenko, 1995; Logothetidis & Petalas, 1996; Adolph et al., 1997; Gavrilenko & Bechstedt,

**3. Laboratory astrophysics of silicon carbide** 

the general spectral behavior of the UV.

**3.1 Spectroscopic studies: Ultraviolet and infrared** 

Fig. 3. Meteorite classification formalism, adapted from The Natural History Museum, London (http://www.nhm.ac.uk). Presolar SiC grains are dominantly found in the carbonaceous chondrite classes CM, CI, and CV, but occur over a range of subclasses. The numbers (e.g., the "2" in "CM2") represent the petrologic grade of the meteorite (Van Schmus & Wood, 1967); "1" or "2" refers to the degree of hydration or aqueous alteration, whereas for a value of 3 or greater, higher numbers imply successively higher degrees of thermal metamorphism.

Fig. 4. Microscopy images of pristine presolar SiC grains, courtesy of T. Bernatowicz. Scale bar = 1 μm for all images except panel (d) = 0.5 μm.

#### **3. Laboratory astrophysics of silicon carbide**

262 Silicon Carbide – Materials, Processing and Applications in Electronic Devices

Fig. 3. Meteorite classification formalism, adapted from The Natural History Museum, London (http://www.nhm.ac.uk). Presolar SiC grains are dominantly found in the carbonaceous chondrite classes CM, CI, and CV, but occur over a range of subclasses. The numbers (e.g., the "2" in "CM2") represent the petrologic grade of the meteorite (Van Schmus & Wood, 1967); "1" or "2" refers to the degree of hydration or aqueous alteration, whereas for a value of 3 or greater, higher numbers imply successively higher degrees of thermal metamorphism.

Fig. 4. Microscopy images of pristine presolar SiC grains, courtesy of T. Bernatowicz. Scale

bar = 1 μm for all images except panel (d) = 0.5 μm.

For SiC, the major spectral features result from cation-anion charge transfer and/or electronic band gap transitions in the visible-UV, as well as from lattice vibrations in the IR. Vibrational motions involving a change in the dipole moment are IR active. The nearest-neighbor interaction between Si and C produces a strong band in the IR, regardless of polytype. The stacking disorder that exists for SiC lowers crystal symmetry, resulting in vibrational transitions that increase in number with polytype complexity. For all polytypes of SiC, the transverse optic mode (TO) is present at ~ 12.5 μm and the longitudinal optic mode (LO) is seen at ~ 10.3 μm (Nakashima & Harima, 1997). Electronic transitions occur throughout the visible-UV and are strongest at ~ 0.111 μm (Philipp & Taft, 1960). Laboratory astrophysics studies focus on low energy or IR wavelength SiC spectral features (at λ ~ 11 μm, 21 μm) to identify cosmic SiC in space, and also quantify the optical depth of and chemical impurities or defects in cosmic SiC via the general spectral behavior of the UV.

#### **3.1 Spectroscopic studies: Ultraviolet and infrared**

Past laboratory spectral studies utilized by astrophysicists are published across multiple disciplines. Although UV measurements for other sample types, e.g., extinction of light from SiC smoke particles (Stephens, 1980), have also been used in astrophysics, this paragraph reviews the state of single-crystal SiC spectroscopic studies in the UV and gives examples of UV SiC spectra in Figures 5 and 6. The polytypes that matter most to astrophysicists are 3C, 2H, and 4H, on the basis of the meteoritic record; data on other forms (e.g., 8H, 15R, 21R) have not been considered. Because the 6H form of α-SiC is available commercially with large faces perpendicular to c axis, for which unpolarized measurements provide data on E ⊥ c, there is a wealth of laboratory spectra on 6H in this orientation. The first α-SiC laboratory reflectance data (e.g., Philipp, 1958; Wheeler, 1966) were gathered at resolutions lower by at least a factor of two than can be attained with modern instrumentation. In the ultraviolet, modern commercial instruments exist and are inexpensive for wavelengths down to 0.192 μm (or, for a factor of x10 more in cost, down to 0.164 μm, the "vacuum UV"). However, spectral data for SiC used by astrophysicists does not extend much past 200 nm, as summarized in Figure 5. Early works on UV SiC spectroscopy studied in the astrophysics literature include Choyke & Patrick (1957), Philipp (1958), and Philipp & Taft (1960). Choyke & Patrick (1957) measured transmission (converted to absorption coefficient in cm-1) for one α-SiC plate, whereas Philipp (1958) measured absorption for yellow 3C and colorless 6H SiC single crystal samples of varying thicknesses. In both studies, samples were not well characterized in terms of SiC impurities, stacking faults, and defects, which are highly important in the UV-vis. Philipp & Taft (1960) presented reflectance spectra from ~ 0.11 to 0.62 μm for hexagonal SiC. Because reliable reflectivity standards were not available at that time, uncertainties in absolute R were large (i.e., > 5%). Hofmeister et al. (2009) published new data on the visible to soft UV range (1.11-0.303 μm) for α- and β-SiC single crystals with emphasis on impurities. In that study, absorbance spectra were provided for 6H and 3C SiC (E || c and E ⊥ c) as electronic tables for λ = 2.5-16.36 μm; figure 7 of that work provides absorbance spectra shortward of 2.5 μm. Additional laboratory UV absorption spectra (e.g., Choyke & Patrick 1968, 1969) and reflectivity spectra, including experimentally measured and calculated data (Wheeler, 1966; Belle et al., 1967; Lubinsky et al., 1975; Rehn et al., 1976; Gavrilenko, 1995; Logothetidis & Petalas, 1996; Adolph et al., 1997; Gavrilenko & Bechstedt,

Optical Properties and Applications of Silicon Carbide in Astrophysics 265

measurements should not be used for determining bulk optical functions. A wavelength shift (the KBr matrix correction, cf. Friedemann et al., 1981) has been applied to some laboratory spectra of sub-μm SiC grains dispersed in single-crystal matrices. Studies of thin films and isolated nanoparticles of β-SiC have shown that this wavelength shift is unnecessary when measurements are made carefully (Speck et al., 1999; Clément et al., 2003). Past astrophysical studies were also divided on whether the crystal structure of SiC can be determined from IR spectra (in favor: Borghesi et al., 1985; Speck et al., 1999; opposed: Spitzer et al., 1959a, 1959b; Papoular et al., 1998; Andersen et al., 1999; Mutschke et al., 1999). Pitman et al. (2008) showed that spectroscopic differences exist between α-SiC E || c, versus β-SiC or α-SiC (E ⊥ c). Pitman et al. (2008) provided electronic mid- and far-IR room temperature reflectance spectra of thin film 6H SiC (two orientations, several varieties)

Fig. 6. Comparing the effects of color impurities and polytype of SiC in the UV-vis. 1 nm =

The two SiC spectral features of greatest interest to astrophysicists are at 11 and 21 µm. The utility of the 11 µm feature (shown in Figure 7) will be discussed in Section 4. Among the Crich post-AGB stars (PPNe), approximately half exhibit a feature in their infrared spectra at 21 µm. This enigmatic feature has been widely discussed since its discovery (Kwok et al., 1989) and has been attributed to both transient molecular and long-lived solid-state species, but most of these species have been discarded. The most promising carrier is SiC (Speck & Hofmeister, 2004), on the basis of lab spectroscopy (Figure 8). The peak positions and profile shapes of the 21 µm band are remarkably constant, both in space (Volk et al., 1999) and in laboratory SiC spectra (Table 1). Kimura et al. (2005a, 2005b) produced nano-diamond

10-3 μm. d = thickness of sample. Vertical axis given in common log absorbance.

and semiconductor grade purity 3C SiC.

1997; Theodorou et al., 1999; Ismail & Abu-Safia, 2002; Xie et al., 2003; Lindquist et al., 2004) that extend into the vacuum UV are available in the semiconductor literature. In particular, the effect of SiC polytype on reflectivity was discussed by Lambrecht et al. (1993, 1994, 1997); we note that the reflectivity values from Lambrecht et al. (1997) are too low by 20%, caused by calibrating against a low value of real index of refraction (n=2.65) at ~ 0.31 μm (e.g., Petalas et al., 1998). The spectroscopic ellipsometry study by Petalas et al. (1998) provides reflectivity in agreement with Philipp & Taft (1960) and Wheeler (1966). The reflectivity data by Wheeler (1966) have been used extensively in comparison in the physics and materials literature but show structure on the spectral peaks that may not be real since those features were not observed subsequently; thus, those data are not shown explicitly in Figure 5. For further discussion, see the review by Devaty & Choyke (1997).

Fig. 5. UV-visible reflectance spectra and absorption coefficients. 1 nm = 10-3 μm. Panel (a): Open symbols: Philipp & Taft (1960), solid symbols and line: Petalas et al. (1998). Panel (b): Squares = 3C SiC, hexagons = 6H SiC. Inset: gem 6H SiC = synthetic moissanite.

In the infrared, many laboratory studies of SiC are available in astrophysics, some of which should be compared to semiconductor-relevant data with care. Spitzer et al. (1959a) obtained reflectivity data from a thin (0.06 µm) film of β-SiC that was vapor-deposited on a Si surface. Spitzer et al. (1959b) provided laboratory data for both polarizations of 6H single-crystals. Another widely cited source in astrophysics is the α-SiC E⊥c data shown in figure 9.6 of Bohren & Huffman (1983); that work did not provide experimental details, such as which polytype of α-SiC was used. Mutschke et al. (1999) presented averages of spectral parameters from many experimental studies of SiC from the 1960's to 1990's to obtain TO frequency positions, LO frequency positions or oscillator strengths, and full width at half maximum values for SiC. Other published works on SiC from astrophysics (e.g., Friedemann et al., 1981; Borghesi et al., 1985; Orofino et al., 1991; Papoular et al., 1998; Mutschke et al., 1999; Andersen et al., 1999, and references therein) are predominantly laboratory absorbance studies of powder samples, embedded in a (usually KBr) matrix. Strong differences in the spectra and optical properties obtained from powders (cf. Huffman, 1988; Mutschke et al., 1999) can be attributed to variations in clustering of grains, dilution, mean and distributions of grain size and shape. Laser pyrolysis has also been used to produce SiC particles most closely resembling those found in stellar environments (cf. Willacy & Cherchneff, 1998; Mutschke et al., 1999). Because the laser pyrolysis SiC samples are not of the order of several mm in diameter (cf. Hofmeister et al., 2003), those

1997; Theodorou et al., 1999; Ismail & Abu-Safia, 2002; Xie et al., 2003; Lindquist et al., 2004) that extend into the vacuum UV are available in the semiconductor literature. In particular, the effect of SiC polytype on reflectivity was discussed by Lambrecht et al. (1993, 1994, 1997); we note that the reflectivity values from Lambrecht et al. (1997) are too low by 20%, caused by calibrating against a low value of real index of refraction (n=2.65) at ~ 0.31 μm (e.g., Petalas et al., 1998). The spectroscopic ellipsometry study by Petalas et al. (1998) provides reflectivity in agreement with Philipp & Taft (1960) and Wheeler (1966). The reflectivity data by Wheeler (1966) have been used extensively in comparison in the physics and materials literature but show structure on the spectral peaks that may not be real since those features were not observed subsequently; thus, those data are not shown explicitly in

Fig. 5. UV-visible reflectance spectra and absorption coefficients. 1 nm = 10-3 μm. Panel (a): Open symbols: Philipp & Taft (1960), solid symbols and line: Petalas et al. (1998). Panel (b):

In the infrared, many laboratory studies of SiC are available in astrophysics, some of which should be compared to semiconductor-relevant data with care. Spitzer et al. (1959a) obtained reflectivity data from a thin (0.06 µm) film of β-SiC that was vapor-deposited on a Si surface. Spitzer et al. (1959b) provided laboratory data for both polarizations of 6H single-crystals. Another widely cited source in astrophysics is the α-SiC E⊥c data shown in figure 9.6 of Bohren & Huffman (1983); that work did not provide experimental details, such as which polytype of α-SiC was used. Mutschke et al. (1999) presented averages of spectral parameters from many experimental studies of SiC from the 1960's to 1990's to obtain TO frequency positions, LO frequency positions or oscillator strengths, and full width at half maximum values for SiC. Other published works on SiC from astrophysics (e.g., Friedemann et al., 1981; Borghesi et al., 1985; Orofino et al., 1991; Papoular et al., 1998; Mutschke et al., 1999; Andersen et al., 1999, and references therein) are predominantly laboratory absorbance studies of powder samples, embedded in a (usually KBr) matrix. Strong differences in the spectra and optical properties obtained from powders (cf. Huffman, 1988; Mutschke et al., 1999) can be attributed to variations in clustering of grains, dilution, mean and distributions of grain size and shape. Laser pyrolysis has also been used to produce SiC particles most closely resembling those found in stellar environments (cf. Willacy & Cherchneff, 1998; Mutschke et al., 1999). Because the laser pyrolysis SiC samples are not of the order of several mm in diameter (cf. Hofmeister et al., 2003), those

Squares = 3C SiC, hexagons = 6H SiC. Inset: gem 6H SiC = synthetic moissanite.

Figure 5. For further discussion, see the review by Devaty & Choyke (1997).

measurements should not be used for determining bulk optical functions. A wavelength shift (the KBr matrix correction, cf. Friedemann et al., 1981) has been applied to some laboratory spectra of sub-μm SiC grains dispersed in single-crystal matrices. Studies of thin films and isolated nanoparticles of β-SiC have shown that this wavelength shift is unnecessary when measurements are made carefully (Speck et al., 1999; Clément et al., 2003). Past astrophysical studies were also divided on whether the crystal structure of SiC can be determined from IR spectra (in favor: Borghesi et al., 1985; Speck et al., 1999; opposed: Spitzer et al., 1959a, 1959b; Papoular et al., 1998; Andersen et al., 1999; Mutschke et al., 1999). Pitman et al. (2008) showed that spectroscopic differences exist between α-SiC E || c, versus β-SiC or α-SiC (E ⊥ c). Pitman et al. (2008) provided electronic mid- and far-IR room temperature reflectance spectra of thin film 6H SiC (two orientations, several varieties) and semiconductor grade purity 3C SiC.

Fig. 6. Comparing the effects of color impurities and polytype of SiC in the UV-vis. 1 nm = 10-3 μm. d = thickness of sample. Vertical axis given in common log absorbance.

The two SiC spectral features of greatest interest to astrophysicists are at 11 and 21 µm. The utility of the 11 µm feature (shown in Figure 7) will be discussed in Section 4. Among the Crich post-AGB stars (PPNe), approximately half exhibit a feature in their infrared spectra at 21 µm. This enigmatic feature has been widely discussed since its discovery (Kwok et al., 1989) and has been attributed to both transient molecular and long-lived solid-state species, but most of these species have been discarded. The most promising carrier is SiC (Speck & Hofmeister, 2004), on the basis of lab spectroscopy (Figure 8). The peak positions and profile shapes of the 21 µm band are remarkably constant, both in space (Volk et al., 1999) and in laboratory SiC spectra (Table 1). Kimura et al. (2005a, 2005b) produced nano-diamond

Optical Properties and Applications of Silicon Carbide in Astrophysics 267

Amorphous SiC 450.172 0.1340 102.16 Nanocrystalline β-SiC 463.52 0.09291 34.3971

 Nanocrystalline α+β SiC 472.69 0.1274 60.794

Table 1. Peak parameters of λ ~ 21 μm feature in SiC. Values reported in frequency (cm-1 = 104/λ(μm)). Amorphous SiC spectrum was best fitted with a single Gaussian peak and multi-point baseline correction. Peaks in the IR actually tend to be Lorentzian in shape; the 21 μm feature in the nanocrystalline spectra were fitted with two Lorentzian peaks (for the

samples with Si replacing C from 10 to 50% by various methods; its IR spectrum exhibits bands at 9.5 and 21 µm, and the relative strength of the 21 µm band increases with C content. On this basis, Kimura et al. (2005a, 2005b) concluded that the 21 µm band in IR spectra of SiC samples also results from excess C. Jiang et al. (2005) calculated IR spectra of astronomical dust for various sub-µm grain sizes and a range of peak strengths for the 21 µm band at T ~ 70 K. That work concluded that the 21 µm feature was too weak to be SiC unless very high concentrations of impurity were observed. However, relative peak intensities are affected by factors not explored in that study. The intensity of emission at 21 µm would be enhanced relative to that at 11 µm by either lower temperature or larger (nonuniform) grain sizes. A more serious objection to the assignment is that the astronomy environment could possess Si-rich nano-diamond. Quantifying the strengths of the 21 µm SiC feature in both structures and low temperature measurements is needed to differentiate

Optical functions or "optical constants" are the real and imaginary parts of the complex index of refraction m = n + ik that vary as a function of wavelength, temperature, and dust species (composition, structure). n(λ) is the real index of refraction where the crystal is not strongly absorbing, and k(λ)= A/4πν represents the extinction or gradual loss of intensity due to absorption of photons as an electromagnetic wave interacts with matter. As discussed in the introduction, there is a substantial market for the optical functions of SiC within the astrophysics community. In the IR, the optical functions of SiC used in 20th century astronomical studies derive primarily from three studies: Bohren & Huffman (1983), Pégourié (1988), and Laor & Draine (1993). These data were for α-SiC, often in a single polarization, whereas SiC dust surrounding astronomical objects is β-SiC, and included a wavelength shift to "correct" for the KBr matrix. Pitman et al. (2008) derived and provided electronic tables of SiC optical functions out to λ~2000 μm for 6H (α-)SiC in both polarizations as well as 3C (β-)SiC; Hofmeister et al. (2009) extended these data shortward into the UV. For all spectral regions, the latter papers showed that 3C SiC and the E ⊥ c polarization of 6H SiC have almost identical optical functions that can be substituted for each other in modeling astronomical environments. This result agreed with previous work

TO and LO modes) and a two-point linear baseline correction.

between these possibilities.

**3.2 Optical functions of SiC** 

Position (cm-1) Height Width

424.75 0.07975 58.4357

433.09 0.03869 74.790

Fig. 7. λ ~ 11 μm feature in SiC. Panels (a, b): Mid- and mid+far-IR specular reflectivity spectra of bulk SiC, for different orientations. Panel (c): Laboratory (common log) absorbance, divided by thin film thickness for bulk versus nanocrystalline β-SiC, α-SiC, and a mixture of the two. Data from this work, K. M. Pitman et al., A&A, vol. 483, pp. 661-672, 2008, reproduced with permission © ESO.

Fig. 8. The λ ~ 21 μm feature in the SiC laboratory spectra is prominent in nanocrystalline and amorphous SiC, present but not as strong in bulk SiC. Laboratory IR absorbance spectra of SiC shown in bulk, nanocrystalline, amorphous, blends of α- and β-SiC. Some data from Speck & Hofmeister (2004); new β-SiC nanocrystalline data included longward of 20 μm. At 19.8 μm, a "S-shaped" beamsplitter artifact or spectral spike occurs. The amorphous SiC sample was polycard (i.e., this spectrum has a different baseline than the other 3 spectra, most noticeable at λ > 21 μm). The amorphous SiC spectrum was offset by - 0.19 in vertical axis; the other spectra were not offset. Instrumental noise was smoothed for amorphous SiC at λ < 20 μm and again for nanocrystalline β-SiC spectra at λ > 27 μm. The steep rise to short λ occurs because this feature is a shoulder on the main band near 11 μm.

Fig. 7. λ ~ 11 μm feature in SiC. Panels (a, b): Mid- and mid+far-IR specular reflectivity spectra of bulk SiC, for different orientations. Panel (c): Laboratory (common log)

2008, reproduced with permission © ESO.

absorbance, divided by thin film thickness for bulk versus nanocrystalline β-SiC, α-SiC, and a mixture of the two. Data from this work, K. M. Pitman et al., A&A, vol. 483, pp. 661-672,

Fig. 8. The λ ~ 21 μm feature in the SiC laboratory spectra is prominent in nanocrystalline and amorphous SiC, present but not as strong in bulk SiC. Laboratory IR absorbance spectra of SiC shown in bulk, nanocrystalline, amorphous, blends of α- and β-SiC. Some data from Speck & Hofmeister (2004); new β-SiC nanocrystalline data included longward of

20 μm. At 19.8 μm, a "S-shaped" beamsplitter artifact or spectral spike occurs. The amorphous SiC sample was polycard (i.e., this spectrum has a different baseline than the other 3 spectra, most noticeable at λ > 21 μm). The amorphous SiC spectrum was offset by - 0.19 in vertical axis; the other spectra were not offset. Instrumental noise was smoothed for amorphous SiC at λ < 20 μm and again for nanocrystalline β-SiC spectra at λ > 27 μm. The steep rise to short λ occurs because this feature is a shoulder on the main band near 11 μm.


Table 1. Peak parameters of λ ~ 21 μm feature in SiC. Values reported in frequency (cm-1 = 104/λ(μm)). Amorphous SiC spectrum was best fitted with a single Gaussian peak and multi-point baseline correction. Peaks in the IR actually tend to be Lorentzian in shape; the 21 μm feature in the nanocrystalline spectra were fitted with two Lorentzian peaks (for the TO and LO modes) and a two-point linear baseline correction.

samples with Si replacing C from 10 to 50% by various methods; its IR spectrum exhibits bands at 9.5 and 21 µm, and the relative strength of the 21 µm band increases with C content. On this basis, Kimura et al. (2005a, 2005b) concluded that the 21 µm band in IR spectra of SiC samples also results from excess C. Jiang et al. (2005) calculated IR spectra of astronomical dust for various sub-µm grain sizes and a range of peak strengths for the 21 µm band at T ~ 70 K. That work concluded that the 21 µm feature was too weak to be SiC unless very high concentrations of impurity were observed. However, relative peak intensities are affected by factors not explored in that study. The intensity of emission at 21 µm would be enhanced relative to that at 11 µm by either lower temperature or larger (nonuniform) grain sizes. A more serious objection to the assignment is that the astronomy environment could possess Si-rich nano-diamond. Quantifying the strengths of the 21 µm SiC feature in both structures and low temperature measurements is needed to differentiate between these possibilities.

#### **3.2 Optical functions of SiC**

Optical functions or "optical constants" are the real and imaginary parts of the complex index of refraction m = n + ik that vary as a function of wavelength, temperature, and dust species (composition, structure). n(λ) is the real index of refraction where the crystal is not strongly absorbing, and k(λ)= A/4πν represents the extinction or gradual loss of intensity due to absorption of photons as an electromagnetic wave interacts with matter. As discussed in the introduction, there is a substantial market for the optical functions of SiC within the astrophysics community. In the IR, the optical functions of SiC used in 20th century astronomical studies derive primarily from three studies: Bohren & Huffman (1983), Pégourié (1988), and Laor & Draine (1993). These data were for α-SiC, often in a single polarization, whereas SiC dust surrounding astronomical objects is β-SiC, and included a wavelength shift to "correct" for the KBr matrix. Pitman et al. (2008) derived and provided electronic tables of SiC optical functions out to λ~2000 μm for 6H (α-)SiC in both polarizations as well as 3C (β-)SiC; Hofmeister et al. (2009) extended these data shortward into the UV. For all spectral regions, the latter papers showed that 3C SiC and the E ⊥ c polarization of 6H SiC have almost identical optical functions that can be substituted for each other in modeling astronomical environments. This result agreed with previous work

Optical Properties and Applications of Silicon Carbide in Astrophysics 269

The first step in identifying the nature of dust grains in space is to match the positions and widths of astronomically observed spectral features with those seen in laboratory spectra. To do this we must consider what actually contributes to the spectrum when we look at a dusty star. The spectrum, Fλ, is made of contributions to the light from the star (which is essentially a blackbody, or perfect light absorber at all wavelengths) and the circumstellar material. In the infrared, the circumstellar material is dominated by the dust, the emission from which is determined by the species, i.e., composition, crystal structure, size, and shape

1 1

where Bλ(T) is the Planck function for a black body of temperature T, so that B*i* represents a single dust grain at a single temperature (of which there are *n* in total). Each Q*j* represents the extinction efficiency (or rate at which a dust particle absorbs, scatters, or extincts light divided by the incident power per unit area) for a single grain type as defined by its size, shape, composition and crystal structure. Each wj represents the weighting factor for a

For optically thin environments, where there is little or only single-scattering, the spectrum is dominated by starlight, and one can simply subtract a blackbody continuum relevant to the star (which for carbon stars is ~3000 K). However, for very dusty environments, starlight is largely absorbed by the dust and re-emitted in the infrared according to the dust grains' optical functions. Often the system is simplified so that the contributions to the spectrum

*F wQ BT*

 λλ

In this case one can fit a (blackbody) continuum to the observed spectrum and divide to

The circumstellar shells of carbon stars are expected to be dominated by amorphous or graphitic carbon grains (see Speck et al. 2009 and references therein). These dust species do not have diagnostic infrared features, and contribute to the dust continuum emission alone. However, SiC does exhibit a strong infrared feature around 11μm as discussed in Section I. The observed ~11 μm SiC feature has been used extensively to investigate the nature and evolution of dust around carbon stars (Little-Marenin, 1986; Baron et al., 1987; Willems, 1988; Chan & Kwok, 1990; Goebel et al., 1995; Speck et al., 1997; Sloan et al., 1998; Speck et al., 2005; Thompson et al., 2006; Speck et al., 2009), using datasets from both space-based instruments such as the Infrared Astronomical Satellite (IRAS) Low Resolution Spectrometer (LRS: Neugebauer et al., 1984), and the Infrared Space Observatory (ISO: Kessler et al., 1996) Short Wavelength Spectrometer (SWS: de Graauw et al., 1996), as well as instruments in ground-based observatories (e.g., CGS3 on the United Kingdom Infrared Telescope, UKIRT). In fact, the parameters most commonly used to make identifications of SiC dust in space are the strength and peak position of the ~11 μm feature. From ISO data, there is also a range in shapes and peak positions of the ~11 μm SiC feature that cannot be simply correlated with the apparent temperature of the

*j j i*

= ×× (1)

=× × ( ) (2)

,

= =

*i j F wQB*

λ

are dominated by a single dust species and Eq. 1 simplifies to Eq. 2,

λ

derive emissivities of the observed spectral features (e.g., Speck et al. 1997).

,

*n m*

**4.1 Matching spectral features** 

of the grains. The spectrum can be represented by Eq. 1,

single grain type (of which there are j in total).

by Mutschke et al. (1999). However, optical functions for the E || c orientation of 6H SiC can differ slightly (peaks shifted to lower frequency). Figure 9 presents optical functions for 4H SiC, with comparison to the other polytypes from Pitman et al. (2008), and optical functions comparing colored versus colorless samples of SiC from Hofmeister et al. (2009). In the UV, n and k were also calculated for 6H SiC at ~ 0.25-1.24 μm by Obarich (1971) and Ninomiya & Adachi (1994); works presented above also included calculated dielectric functions for other polytypes, from which one may further obtain n and k in the UV.

Fig. 9. UV-vis optical functions derived from experimental specular reflectance data via Lorentz-Lorenz classical dispersion analysis, showing the effect of polytype (top panels; 3C and 6H from Pitman et al. 2008, 4H from this work) and of impurities (bottom panels: Hofmeister et al. 2009, applicable to 3C or 6H E ⊥ c). Left: real index of refraction n. Right: imaginary index of refraction k. With the exception of 6H SiC E || c orientation, the optical functions for SiC are generally similar, regardless of polytype. As compared to 99.8% pure (colorless) SiC samples, the effect of impurities in colored SiC samples manifests in k.

#### **4. Application #1: Observational astronomy**

In this section, we outline the ways in which astrophysicists compare laboratory spectra and optical functions of SiC to determine the nature and evolution of SiC dust grains around classes of astronomical objects and environments, e.g., C-rich AGB stars (i.e., carbon stars).

#### **4.1 Matching spectral features**

268 Silicon Carbide – Materials, Processing and Applications in Electronic Devices

by Mutschke et al. (1999). However, optical functions for the E || c orientation of 6H SiC can differ slightly (peaks shifted to lower frequency). Figure 9 presents optical functions for 4H SiC, with comparison to the other polytypes from Pitman et al. (2008), and optical functions comparing colored versus colorless samples of SiC from Hofmeister et al. (2009). In the UV, n and k were also calculated for 6H SiC at ~ 0.25-1.24 μm by Obarich (1971) and Ninomiya & Adachi (1994); works presented above also included calculated dielectric

functions for other polytypes, from which one may further obtain n and k in the UV.

Fig. 9. UV-vis optical functions derived from experimental specular reflectance data via Lorentz-Lorenz classical dispersion analysis, showing the effect of polytype (top panels; 3C and 6H from Pitman et al. 2008, 4H from this work) and of impurities (bottom panels: Hofmeister et al. 2009, applicable to 3C or 6H E ⊥ c). Left: real index of refraction n. Right: imaginary index of refraction k. With the exception of 6H SiC E || c orientation, the optical functions for SiC are generally similar, regardless of polytype. As compared to 99.8% pure (colorless) SiC samples, the effect of impurities in colored SiC samples manifests in k.

In this section, we outline the ways in which astrophysicists compare laboratory spectra and optical functions of SiC to determine the nature and evolution of SiC dust grains around classes of astronomical objects and environments, e.g., C-rich AGB stars (i.e.,

**4. Application #1: Observational astronomy** 

carbon stars).

The first step in identifying the nature of dust grains in space is to match the positions and widths of astronomically observed spectral features with those seen in laboratory spectra. To do this we must consider what actually contributes to the spectrum when we look at a dusty star. The spectrum, Fλ, is made of contributions to the light from the star (which is essentially a blackbody, or perfect light absorber at all wavelengths) and the circumstellar material. In the infrared, the circumstellar material is dominated by the dust, the emission from which is determined by the species, i.e., composition, crystal structure, size, and shape of the grains. The spectrum can be represented by Eq. 1,

$$F\_{\lambda} = \sum\_{i=1, j=1}^{n,m} w\_j \times Q\_j \times B\_i \tag{1}$$

where Bλ(T) is the Planck function for a black body of temperature T, so that B*i* represents a single dust grain at a single temperature (of which there are *n* in total). Each Q*j* represents the extinction efficiency (or rate at which a dust particle absorbs, scatters, or extincts light divided by the incident power per unit area) for a single grain type as defined by its size, shape, composition and crystal structure. Each wj represents the weighting factor for a single grain type (of which there are j in total).

For optically thin environments, where there is little or only single-scattering, the spectrum is dominated by starlight, and one can simply subtract a blackbody continuum relevant to the star (which for carbon stars is ~3000 K). However, for very dusty environments, starlight is largely absorbed by the dust and re-emitted in the infrared according to the dust grains' optical functions. Often the system is simplified so that the contributions to the spectrum are dominated by a single dust species and Eq. 1 simplifies to Eq. 2,

$$F\_{\lambda} = w \times Q\_{\lambda} \times B\_{\lambda}(T) \tag{2}$$

In this case one can fit a (blackbody) continuum to the observed spectrum and divide to derive emissivities of the observed spectral features (e.g., Speck et al. 1997).

The circumstellar shells of carbon stars are expected to be dominated by amorphous or graphitic carbon grains (see Speck et al. 2009 and references therein). These dust species do not have diagnostic infrared features, and contribute to the dust continuum emission alone. However, SiC does exhibit a strong infrared feature around 11μm as discussed in Section I. The observed ~11 μm SiC feature has been used extensively to investigate the nature and evolution of dust around carbon stars (Little-Marenin, 1986; Baron et al., 1987; Willems, 1988; Chan & Kwok, 1990; Goebel et al., 1995; Speck et al., 1997; Sloan et al., 1998; Speck et al., 2005; Thompson et al., 2006; Speck et al., 2009), using datasets from both space-based instruments such as the Infrared Astronomical Satellite (IRAS) Low Resolution Spectrometer (LRS: Neugebauer et al., 1984), and the Infrared Space Observatory (ISO: Kessler et al., 1996) Short Wavelength Spectrometer (SWS: de Graauw et al., 1996), as well as instruments in ground-based observatories (e.g., CGS3 on the United Kingdom Infrared Telescope, UKIRT). In fact, the parameters most commonly used to make identifications of SiC dust in space are the strength and peak position of the ~11 μm feature. From ISO data, there is also a range in shapes and peak positions of the ~11 μm SiC feature that cannot be simply correlated with the apparent temperature of the

Optical Properties and Applications of Silicon Carbide in Astrophysics 271

codes used to solve the equation of radiative transfer are DUSTY (Nenkova et al. 2000) and 2-Dust (Ueta & Meixner 2003). The acquisition of new optical functions, for SiC and all materials posited to exist in space, is critical to these numerical efforts. Astrophysicists use RT modeling to determine the effects of grain size and shape distributions, chemical composition and mineralogies, temperature and density distributions on the expected astronomical spectrum, and to place constraints on the relative abundances of different grain types in a dust shell. In this way, astrophysicists can build a list of parameters that

In radiative transfer modeling, one simulates SiC dust in space by specifying best estimates for the optical functions, sizes, and shape distributions of the particles. The optical functions mentioned in Section 3 have been tested in a variety of radiative transfer applications. The optical functions of Bohren & Huffman (1983), Pégourié (1988), and Laor & Draine (1993) were used to place limits on the abundance of SiC dust in carbon stars (e.g., Martin & Rogers 1987; Lorenz-Martins & Lefevre 1993, 1994; Lorenz-Martins et al. 2001; Groenewegen 1995; Groenewegen et al. 1998, 2009; Griffin 1990, 1993; Bagnulo et al. 1995, 1997, 1998), Large Magellanic Cloud stars (Speck et al. 2006; Srinivasan et al. 2010), and (proto-)planetary nebulae (Clube & Gledhill 2004; Hoare 1990; Jiang et al. 2005). Those optical functions have also been used in studies of dust formation (e.g., Kozasa et al. 1996), hydrodynamics of circumstellar shells (e.g., Windsteig et al. 1997; Steffen et al. 1997), and mean opacities (Ferguson et al. 2005; Alexander & Ferguson 1994). In their radiative transfer models of dust around C-stars, Groenewegen et al. (2009) offered a comparison of the performance of the optical functions of Pitman et al. (2008), shown in Figure 3.5, against α-SiC from Pégourié (1988), and β-SiC from Borghesi et al. (1985) in matching observed 11 μm features in astronomical spectra. Ladjal et al. (2010) concluded that the Pitman et al. (2008) modeled the shape and peak position of the 11 μm feature well in evolved stars. The intrinsic shape for SiC grains in circumstellar environments is not known but distributions of complex, nonspherical shapes (Continuous Distribution of Ellipsoids, CDE, Bohren & Huffman 1983; Distribution of Hollow Spheres, Min et al. 2003; aggregates, Andersen et al. 2006, and references therein) are the best estimate at present. Most of these produce a feature at λ~11 μm that is broad as compared to laboratory SiC spectra, but matches astronomically observed spectra. There is no clear consensus on what the grain size distribution for SiC grains in space should be (see review by Speck et al. 2009). SiC dust is generally found in circumstellar, not interstellar, dust, which limits the assumptions on size. Strictly speaking, the SiC optical functions of Pégourié (1988) and Laor & Draine (1993) should be used with the corresponding grain size distribution of the ground and sedimented SiC sample measured in the lab (∝ diameter-2.1, with an average grain diameter = 0.04 µm). Bulk n and k datasets (e.g., Pitman et al. 2008; Hofmeister et al. 2009) can be used with any grain size

Once optical functions, sizes, and shape distributions have been selected for the SiC particles, astrophysicists are free to test the influence of percent SiC dust content on an astronomical spectrum. Figure 11 gives examples of synthetic spectra of SiC-bearing dust shells of varying optical thicknesses around a T=3000 K star using the radiative transfer code DUSTY. Simply changing the optical functions and/or shape distribution results in substantial differences in the modeled astronomical spectrum, and thus interpretations of

the self-absorption and emission in the circumstellar dust shell.

describes the circumstellar environment around a star.

distribution.

underlying continuum (Thompson et al., 2006). However, there remain several common trends that exist in the observed SiC features:

Fig. 10. The 11 μm SiC feature, observed in the spectra of carbon stars. Left hand panels represent stars that have the optically thinnest dust shells; optical depth increases to the right. Top panels: Ground-based observed spectra (black symbols: Speck et al. 1997) with best-fitting blackbody continua (red lines). Bottom panels: Continuum-divided spectra, following Eq. 2, provide the effective Q-values or extinction efficiencies for the dust shells. Blue lines: β-SiC absorbance data of Pitman et al. (2008), converted to absorptivity A = eabsorbance, is proportional to Q.


#### **5. Application #2: Radiative transfer modeling**

Radiative transfer (RT) modeling uses the optical functions of candidate minerals to model how a given object should look both spectroscopically and in images. Mineral candidates determined by spectral matching can then be input into numerical RT models; examples of

underlying continuum (Thompson et al., 2006). However, there remain several common

Fig. 10. The 11 μm SiC feature, observed in the spectra of carbon stars. Left hand panels represent stars that have the optically thinnest dust shells; optical depth increases to the right. Top panels: Ground-based observed spectra (black symbols: Speck et al. 1997) with best-fitting blackbody continua (red lines). Bottom panels: Continuum-divided spectra, following Eq. 2, provide the effective Q-values or extinction efficiencies for the dust shells. Blue lines: β-SiC absorbance data of Pitman et al. (2008), converted to absorptivity A =

i. Early in the AGB phase, when the mass-loss rate is low and the shell is optically thin,

ii. As the mass loss increases and the shell becomes optically thicker, the SiC emission

iii. Once the mass-loss rate is extremely high and the shell is optically thick, the SiC feature

iv. Once the AGB phase ends and the thinning dust shell cools, SiC is more rarely observed

Radiative transfer (RT) modeling uses the optical functions of candidate minerals to model how a given object should look both spectroscopically and in images. Mineral candidates determined by spectral matching can then be input into numerical RT models; examples of

the ~ 11 μm SiC emission feature is strong, narrow, and sharp.

but may be hidden by other emerging spectral features.

**5. Application #2: Radiative transfer modeling** 

trends that exist in the observed SiC features:

eabsorbance, is proportional to Q.

appears in absorption.

feature broadens, flattens, and weakens.

codes used to solve the equation of radiative transfer are DUSTY (Nenkova et al. 2000) and 2-Dust (Ueta & Meixner 2003). The acquisition of new optical functions, for SiC and all materials posited to exist in space, is critical to these numerical efforts. Astrophysicists use RT modeling to determine the effects of grain size and shape distributions, chemical composition and mineralogies, temperature and density distributions on the expected astronomical spectrum, and to place constraints on the relative abundances of different grain types in a dust shell. In this way, astrophysicists can build a list of parameters that describes the circumstellar environment around a star.

In radiative transfer modeling, one simulates SiC dust in space by specifying best estimates for the optical functions, sizes, and shape distributions of the particles. The optical functions mentioned in Section 3 have been tested in a variety of radiative transfer applications. The optical functions of Bohren & Huffman (1983), Pégourié (1988), and Laor & Draine (1993) were used to place limits on the abundance of SiC dust in carbon stars (e.g., Martin & Rogers 1987; Lorenz-Martins & Lefevre 1993, 1994; Lorenz-Martins et al. 2001; Groenewegen 1995; Groenewegen et al. 1998, 2009; Griffin 1990, 1993; Bagnulo et al. 1995, 1997, 1998), Large Magellanic Cloud stars (Speck et al. 2006; Srinivasan et al. 2010), and (proto-)planetary nebulae (Clube & Gledhill 2004; Hoare 1990; Jiang et al. 2005). Those optical functions have also been used in studies of dust formation (e.g., Kozasa et al. 1996), hydrodynamics of circumstellar shells (e.g., Windsteig et al. 1997; Steffen et al. 1997), and mean opacities (Ferguson et al. 2005; Alexander & Ferguson 1994). In their radiative transfer models of dust around C-stars, Groenewegen et al. (2009) offered a comparison of the performance of the optical functions of Pitman et al. (2008), shown in Figure 3.5, against α-SiC from Pégourié (1988), and β-SiC from Borghesi et al. (1985) in matching observed 11 μm features in astronomical spectra. Ladjal et al. (2010) concluded that the Pitman et al. (2008) modeled the shape and peak position of the 11 μm feature well in evolved stars. The intrinsic shape for SiC grains in circumstellar environments is not known but distributions of complex, nonspherical shapes (Continuous Distribution of Ellipsoids, CDE, Bohren & Huffman 1983; Distribution of Hollow Spheres, Min et al. 2003; aggregates, Andersen et al. 2006, and references therein) are the best estimate at present. Most of these produce a feature at λ~11 μm that is broad as compared to laboratory SiC spectra, but matches astronomically observed spectra. There is no clear consensus on what the grain size distribution for SiC grains in space should be (see review by Speck et al. 2009). SiC dust is generally found in circumstellar, not interstellar, dust, which limits the assumptions on size. Strictly speaking, the SiC optical functions of Pégourié (1988) and Laor & Draine (1993) should be used with the corresponding grain size distribution of the ground and sedimented SiC sample measured in the lab (∝ diameter-2.1, with an average grain diameter = 0.04 µm). Bulk n and k datasets (e.g., Pitman et al. 2008; Hofmeister et al. 2009) can be used with any grain size distribution.

Once optical functions, sizes, and shape distributions have been selected for the SiC particles, astrophysicists are free to test the influence of percent SiC dust content on an astronomical spectrum. Figure 11 gives examples of synthetic spectra of SiC-bearing dust shells of varying optical thicknesses around a T=3000 K star using the radiative transfer code DUSTY. Simply changing the optical functions and/or shape distribution results in substantial differences in the modeled astronomical spectrum, and thus interpretations of the self-absorption and emission in the circumstellar dust shell.

Optical Properties and Applications of Silicon Carbide in Astrophysics 273

5. Complimentary spectroscopic measurements of synthetic SiC made by the semiconductor and astrophysics communities have provided consistent values for optical functions, once different methodologies have been accounted for. Laboratory astrophysics studies of SiC focus on general UV spectral behavior and two specific IR spectral features (at λ ~ 11 μm, 21 μm) that can be matched to astronomical spectra. The effects of orientation, polytype, and impurities in SiC are all important to astronomical

6. Variations in optical functions with impurities and structure, as well as assumptions on size and shape distributions, strongly affects the amount of light scattering and

Optical properties of SiC warrant future study. Vacuum UV data from the semiconductor literature need to be better integrated into the astrophysics literature. Laboratory studies on SiC have considered the effect of varying temperature from early on (e.g., Choyke & Patrick 1957). However, most data were collected only at room temperature. Temperaturedependent spectra and optical functions are necessary, especially low-temperature measurements. Chemical vapor-deposited SiC samples are available from the semiconductor industry for β-SiC. For future work, other forms of β-SiC would be better for determining optical functions, e.g., single crystals for the non-absorbing near-IR to visible region. Further measurements of solid solutions of SiC and C, with focus on impurities likely to be incorporated in astrophysical environments rather than doped crystals, should be pursued in the UV. Although IR spectra of 2H SiC can be constructed from available data (e.g., Lambrecht et al. 1997) because folded modes are not present, 2H SiC also

Authors' laboratory and theoretical work shown in this chapter was kindly supported by the National Science Foundation under grants NSF-AST-1009544, NASA APRA04-000-0041, NSF-AST-0607341, and NSF-AST-0607418. Credit: K. M. Pitman et al., A&A, vol. 483, pp. 661-672, 2008, reproduced with permission © ESO. Data from Speck & Hofmeister (2004) and Hofmeister et al. (2009) reproduced with permission from the AAS. Figure 2.2 was kindly provided by T. Bernatowicz. The authors thank Jonas Goldsand for his assistance on

Adolph, B., Tenelsen, K., Gavrilenko, V. I., & Bechstedt, F. (1997). Optical and loss spectra of SiC polytypes from ab initio calculations, *Phys. Rev. B*, Vol. 55, pp. 1422-1429 Alexander, D. R., & Ferguson, J. W. (1994). Low-temperature Rosseland opacities, *Astrophys.* 

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Amari, S., Hoppe, P., Zinner, E., & Lewis, R. S. (1992). Interstellar SiC with unusual isotopic compositions - Grains from a supernova?, *Astrophys. J. Lett.,* Vol. 394, pp. L43-L46.

noble gases, *Geochim. Cosmochim. Ac.*, Vol. 58, p. 459.

SiC, graphite, and diamond, size distributions of SiC and graphite. II - SiC and its

laboratory sample preparation and data collection. This is PSI Contribution No. 506.

hollow spheres; fractal aggregates) are assumed.

warrants direct measurement for its importance in space.

*J.*, Vol. 437, No. 2, pp. 879-891

studies.

**7. Acknowledgment** 

**8. References** 

absorption inferred in space.

distributions of complex, nonspherical shapes (continuous distributions of ellipsoids or

Fig. 12. Synthetic spectra of stellar light flux generated with DUSTY code. Top panel: Pégourié (1988) α-SiC optical functions. Bottom panel: Pitman et al. (2008) SiC optical functions. Left hand versus right hand columns compare α-SiC (weighted average of 1/3 E||c, 2/3 E ⊥ c) versus β-SiC. Line styles compare different shape distributions (spherical, CDE, CDS = continuous distribution of ellipsoids; spheroids, DHS = distribution of hollow spheres). See Corman (2010) and Corman et al. (2011) for more examples.

#### **6. Conclusion**

Since the 1960s, laboratory and theoretical astrophysics investigations of SiC grains have culminated in several important findings:


distributions of complex, nonspherical shapes (continuous distributions of ellipsoids or hollow spheres; fractal aggregates) are assumed.


Optical properties of SiC warrant future study. Vacuum UV data from the semiconductor literature need to be better integrated into the astrophysics literature. Laboratory studies on SiC have considered the effect of varying temperature from early on (e.g., Choyke & Patrick 1957). However, most data were collected only at room temperature. Temperaturedependent spectra and optical functions are necessary, especially low-temperature measurements. Chemical vapor-deposited SiC samples are available from the semiconductor industry for β-SiC. For future work, other forms of β-SiC would be better for determining optical functions, e.g., single crystals for the non-absorbing near-IR to visible region. Further measurements of solid solutions of SiC and C, with focus on impurities likely to be incorporated in astrophysical environments rather than doped crystals, should be pursued in the UV. Although IR spectra of 2H SiC can be constructed from available data (e.g., Lambrecht et al. 1997) because folded modes are not present, 2H SiC also warrants direct measurement for its importance in space.

#### **7. Acknowledgment**

272 Silicon Carbide – Materials, Processing and Applications in Electronic Devices

Fig. 12. Synthetic spectra of stellar light flux generated with DUSTY code. Top panel: Pégourié (1988) α-SiC optical functions. Bottom panel: Pitman et al. (2008) SiC optical functions. Left hand versus right hand columns compare α-SiC (weighted average of 1/3 E||c, 2/3 E ⊥ c) versus β-SiC. Line styles compare different shape distributions (spherical, CDE, CDS = continuous distribution of ellipsoids; spheroids, DHS = distribution of hollow

Since the 1960s, laboratory and theoretical astrophysics investigations of SiC grains have

1. ~ 99% of meteoritic SiC grains were formed around carbon-rich Asymptotic Giant Branch stars, and that of these, > 95% originate around low-mass (<3M) carbon stars; 2. Nearly all SiC grains in space are crystalline, with > 80% of these occurring as the cubic 3C polytype, and the rest comprising the lower temperature 2H polytype or 3C/2H

3. The grain size distribution of SiC in space includes both very small and very large grains (1.5 nm - 26 μm), with most grains in the 0.1–1 μm range. Single-crystal SiC grains can exceed 20 μm in size. The sizes of individual SiC crystals are correlated with

4. There is no consensus on the shape of SiC particles in space. SEM and TEM imagery of presolar SiC grains provides a guide. In numerical radiative transfer model calculations,

spheres). See Corman (2010) and Corman et al. (2011) for more examples.

**6. Conclusion** 

combinations;

culminated in several important findings:

s-process element concentration.

Authors' laboratory and theoretical work shown in this chapter was kindly supported by the National Science Foundation under grants NSF-AST-1009544, NASA APRA04-000-0041, NSF-AST-0607341, and NSF-AST-0607418. Credit: K. M. Pitman et al., A&A, vol. 483, pp. 661-672, 2008, reproduced with permission © ESO. Data from Speck & Hofmeister (2004) and Hofmeister et al. (2009) reproduced with permission from the AAS. Figure 2.2 was kindly provided by T. Bernatowicz. The authors thank Jonas Goldsand for his assistance on laboratory sample preparation and data collection. This is PSI Contribution No. 506.

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Asymptotic Giant Branch Stars: Silicon Carbide as the Carrier of the 21 Micron


**12** 

*Japan* 

**Introducing Ohmic Contacts into** 

*WPI Research Center, Advanced Institute for Materials Research, Tohoku University* 

The promising mechanical and electronic properties of silicon carbide (SiC) are stimulating extensive investigations focused on the applications of its semiconducting and excellent structure properties. As a matter of fact, the interest toward SiC is twofold. On one hand, it is a high-strength composite and high-temperature structural ceramic, demonstrating the ability to function at high-power and caustic circumstances. On the other hand, it is an attractive semiconductor, which has excellent inherent characteristics such as a wide band gap (3.3 eV), high breakdown field (3 × 106 V/cm), more than double the high carrier mobility and electron saturation drift velocity (2.7 × 107 cm/s) of silicon (Morkoc et al., 1994). These intrinsic electronic properties together with the high thermal conductivity (5 W/cm K) and stability make it the most likely of all wide-band-gap semiconductors to succeed the current Si and GaAs as next-generation electronic devices, especially for high-temperature and highfrequency applications. Successful fabrication of SiC-based semiconductor devices includes Schottky barrier diodes, p-i-n diodes, metal-oxide-semiconductor field effect transistors, insulated gate bipolar transistors and so forth. Moreover, current significant improvements in its epitaxial and bulk crystal growth have paved the way for fabricating its electronic devices, which arouses further interest in developing device processing techniques so as to take full

One of the most critical issues currently limiting its device processing and hence its widespread application is the manufacturing of reliable and low-resistance Ohmic contacts (< 1 × 10-5 Ωcm2), especially to *p*-type SiC (Perez-Wurfl et al., 2003). The Ohmic contacts are primarily important in SiC devices because a Schottky barrier of high energy is inclined to form at an interface between metal and wide-band-gap semiconductor, which consequently results in low-current driving, slow switching speed, and increased power dissipation. Much of effort expended to date to realize the Ohmic contact has mainly focused on two techniques. One is the high-dose ion-implantation approach, which can increase the carrier density of SiC noticeably and lower its depletion layer width significantly so that increasing tunnelling current is able to flow across barrier region. Although the doping layers with high concentration (> 1020 cm-3) were formed, the key problem of this method is the easy formation of lattice defects or amorphization during the ion implantation. These defects are unfortunately very stable and need to be recovered via post-annealing at an extremely high

temperature (~ 2000 K), thereby complicating mass production of SiC devices.

**1. Introduction** 

advantage of its superior inherent properties.

**Silicon Carbide Technology** 

Zhongchang Wang, Susumu Tsukimoto, Mitsuhiro Saito and Yuichi Ikuhara

*2-1-1 Katahira, Aoba-ku,* 


### **Introducing Ohmic Contacts into Silicon Carbide Technology**

Zhongchang Wang, Susumu Tsukimoto, Mitsuhiro Saito and Yuichi Ikuhara *WPI Research Center, Advanced Institute for Materials Research, Tohoku University 2-1-1 Katahira, Aoba-ku, Japan* 

#### **1. Introduction**

282 Silicon Carbide – Materials, Processing and Applications in Electronic Devices

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The promising mechanical and electronic properties of silicon carbide (SiC) are stimulating extensive investigations focused on the applications of its semiconducting and excellent structure properties. As a matter of fact, the interest toward SiC is twofold. On one hand, it is a high-strength composite and high-temperature structural ceramic, demonstrating the ability to function at high-power and caustic circumstances. On the other hand, it is an attractive semiconductor, which has excellent inherent characteristics such as a wide band gap (3.3 eV), high breakdown field (3 × 106 V/cm), more than double the high carrier mobility and electron saturation drift velocity (2.7 × 107 cm/s) of silicon (Morkoc et al., 1994). These intrinsic electronic properties together with the high thermal conductivity (5 W/cm K) and stability make it the most likely of all wide-band-gap semiconductors to succeed the current Si and GaAs as next-generation electronic devices, especially for high-temperature and highfrequency applications. Successful fabrication of SiC-based semiconductor devices includes Schottky barrier diodes, p-i-n diodes, metal-oxide-semiconductor field effect transistors, insulated gate bipolar transistors and so forth. Moreover, current significant improvements in its epitaxial and bulk crystal growth have paved the way for fabricating its electronic devices, which arouses further interest in developing device processing techniques so as to take full advantage of its superior inherent properties.

One of the most critical issues currently limiting its device processing and hence its widespread application is the manufacturing of reliable and low-resistance Ohmic contacts (< 1 × 10-5 Ωcm2), especially to *p*-type SiC (Perez-Wurfl et al., 2003). The Ohmic contacts are primarily important in SiC devices because a Schottky barrier of high energy is inclined to form at an interface between metal and wide-band-gap semiconductor, which consequently results in low-current driving, slow switching speed, and increased power dissipation. Much of effort expended to date to realize the Ohmic contact has mainly focused on two techniques. One is the high-dose ion-implantation approach, which can increase the carrier density of SiC noticeably and lower its depletion layer width significantly so that increasing tunnelling current is able to flow across barrier region. Although the doping layers with high concentration (> 1020 cm-3) were formed, the key problem of this method is the easy formation of lattice defects or amorphization during the ion implantation. These defects are unfortunately very stable and need to be recovered via post-annealing at an extremely high temperature (~ 2000 K), thereby complicating mass production of SiC devices.

Introducing Ohmic Contacts into Silicon Carbide Technology 285

direct comparison of the total energies of such models is not physically meaningful since interfaces might have a different number of atoms. On the other hand, the ideal work of adhesion, or adhesion energy, *W*ad, which is key to predicting mechanical and thermodynamic properties of an interface is physically comparable. Generally, the *W*ad, which is defined as reversible energy required to separate an interface into two free surfaces, can be expressed by the difference in total energy between the interface and isolated slabs,

 Wad = (*E*1 + *E*2 – *E*IF)/*A*. (1) Here *E*1, *E*2, and *E*IF are total energies of isolated slab 1, slab 2, and their interface system, respectively, and *A* is the total interface area. To date, analytic models available for predicting *W*ad concerning SiC have mostly been restricted to SiC/metal heterojuctions such as SiC/Ni, SiC/Al and SiC/Ti. These models are motivated by the experimental deposition of metals on SiC. However, they neglect the complexity of situation; namely, the compounds (silicides or carbides) can be generated on SiC substrate after annealing and thus the models

Recent advances in the high-angle annular-dark-field (HAADF) microscopy, the highest resolution, have enabled an atomic-scale imaging of a buried interface (Nellist et al., 2004). However, a direct interpretation of the observed HAADF images is not always straightforward because there might be abrupt structural discontinuity, mixing of several species of elements on individual atomic columns, or missing contrasts of light elements. One possible way out to complement the microscopic data is via atomistic calculation, especially the first-principles calculation. As well known, the atomistic first-principles simulations have long been confirmed to be able to suggest plausible structures, elucidate the reason behind the observed images, and even provide a quantitative insight into how interface governs properties of materials. Consequently, a combination of state-of-the-art microcopy and accurate atomistic modeling is an important advance for determining interface atomic-scale structure and relating it to device properties, revealing, in this way,

In addition to determining atomic structure of 4H-SiC/Ti3SiC2 interface, the goal of this chapter is to clarify formation mechanism of the TiAl-based Ohmic contacts so as to provide suggestions for further improvement of the contacts. 4H-SiC will hereafter be referred to as SiC. First of all, we fabricated the TiAl-based contacts and measured their electric properties to confirm the formation of Ohmic contact. Next, the metals/SiC interface was analyzed using the XRD to identify reaction products and TEM, high-resolution TEM (HRTEM), and scanning TEM (STEM) to observe microstructures. Based on these observations, we finally performed systematic first-principles calculations, aimed at assisting the understanding of Ohmic contact formation at a quantum mechanical level. The remainder of this chapter is organized as follows: Section 2 presents the experimental procedures, observes the contact microstructure, and determines the orientation relationships between the generated Ti3SiC2 and SiC substrate. Section 3 describes the computational method, shows detailed results on bulk and surface calculations, outlines the geometries of the 96 candidate interfaces, and determine the structure, electronic states, local bonding, and nonequilibrium quantum

transport of the interface. We provide disscussion and concluding remarks in Sec. 4.

The *p*-type 4H-SiC epitaxial layers (5-μm thick) doped with aluminum (*N*A = 4.5 × 1018 cm-3) which were grown on undoped 4H-SiC wafers by chemical vapor deposition (manufactured

are only applicable to systems with as-deposited state.

physics origin of contact issues in SiC electronics.

**2. Experimental characterization** 

The other alternative is to generate an intermediate semiconductor layer with narrower band gap or higher carrier density at the contacts/SiC interface by deposition and annealing technique. To form such layers, many materials have been examined in a trial-and-error designing fashion, including metals, silicides, carbides, nitrides, and graphite. Of all these materials, metallic alloys have been investigated extensively, largely because the fabrication process is simple, standard, and requires no exotic substances. In particular, most of research activities have been focused on TiAl-based alloys, the only currently available materials that yield significantly low contact resistance (Ohmic contact) to the *p*-type SiC. Furthermore, they demonstrate high thermal stability. For example, Tanimoto et al. have developed the TiAl contacts with extremely low specific contact resistance in the range of 10- 7 to 10-6 Ωcm2 for the *p*-type 4H-SiC with an Al doping concentration of 1.2 × 1019 cm-3 (Tanimoto et al., 2002). Although a lot of intriguing results have been obtained regarding the TiAl-based contact systems, the mechanism whereby the Schottky becomes Ohmic after annealing has not been well clarified yet. In other words, the key factors to understanding the formation of origin of Ohmic contact remains controversial. Mohney et al. proposed that a high density of surface pits and spikes underneath the contacts contributes to the formation of Ohmic behaviour based on their observations using the scanning electron microscopy and atomic force microscopy (Mohney et al., 2002). Nakatsuka et al., however, concluded that the Al concentration in the TiAl alloys is fundamental for the contact formation (Nakatsuka et al., 2002). Using the liquid etch and ion milling techniques, John & Capano ruled out these possibilities and claimed that what matters in realizing the Ohmic nature is the carbides, Ti3SiC2 and Al4C3, formed between metals and semiconductor(John & Capano, 2004). This, however, differs, to some extent, from the X-ray diffraction (XRD) observations revealing that the compounds formed at the metal/SiC interface are silicides, TiSi2, TiSi and Ti3SiC2 (Chang et al., 2005). The formation of silicides or carbides on the surface of SiC substrate after annealing may serve as a primary current-transport pathway to lower the high Schottky barrier between the metal and the semiconductors. In addition, Ohyanagi et al. argued that carbon exists at the contacts/SiC interface and might play a crucial role in lowering Schottky barrier (Ohyanagi et al., 2008). These are just a few representative examples illustrating the obvious discrepancies in clarifying the formation mechanism of Ohmic contact. Taking the amount of speculations on the mechanism and the increasing needs for better device design and performance control, understanding the underlying formation origin is timely and relevant.

To develop an understanding of the origin in such a complex system, it is important to focus first on microstructure characterization. Tanimoto et al. examined the microstructure at the interface between TiAl contacts and the SiC using Auger electron spectroscopy and found that carbides containing Ti and Si were formed at interface (Tanimoto et al., 2002). Recently, transmission electron microscopy (TEM) studies by Tsukimoto et al. have provided useful information in this aspect due to possible high-resolution imaging (Tsukimoto et al., 2004). They have found that the majority of compounds generated on the surface of 4H-SiC substrate after annealing consist of a newly formed compound and hence proposed that the new interface is responsible for the lowering of Schottky barrier in the TiAl-based contact system. However, role of the interface in realizing the Ohmic nature remains unclear. It is not even clear how the two materials bond together atomically from these experiments, which is very important because it may strongly affect physical properties of the system.

To determine the most stable interface theoretically, one first has to establish feasible models on the basis of distinct terminations and contact sites and then compare them. However, a

The other alternative is to generate an intermediate semiconductor layer with narrower band gap or higher carrier density at the contacts/SiC interface by deposition and annealing technique. To form such layers, many materials have been examined in a trial-and-error designing fashion, including metals, silicides, carbides, nitrides, and graphite. Of all these materials, metallic alloys have been investigated extensively, largely because the fabrication process is simple, standard, and requires no exotic substances. In particular, most of research activities have been focused on TiAl-based alloys, the only currently available materials that yield significantly low contact resistance (Ohmic contact) to the *p*-type SiC. Furthermore, they demonstrate high thermal stability. For example, Tanimoto et al. have developed the TiAl contacts with extremely low specific contact resistance in the range of 10- 7 to 10-6 Ωcm2 for the *p*-type 4H-SiC with an Al doping concentration of 1.2 × 1019 cm-3 (Tanimoto et al., 2002). Although a lot of intriguing results have been obtained regarding the TiAl-based contact systems, the mechanism whereby the Schottky becomes Ohmic after annealing has not been well clarified yet. In other words, the key factors to understanding the formation of origin of Ohmic contact remains controversial. Mohney et al. proposed that a high density of surface pits and spikes underneath the contacts contributes to the formation of Ohmic behaviour based on their observations using the scanning electron microscopy and atomic force microscopy (Mohney et al., 2002). Nakatsuka et al., however, concluded that the Al concentration in the TiAl alloys is fundamental for the contact formation (Nakatsuka et al., 2002). Using the liquid etch and ion milling techniques, John & Capano ruled out these possibilities and claimed that what matters in realizing the Ohmic nature is the carbides, Ti3SiC2 and Al4C3, formed between metals and semiconductor(John & Capano, 2004). This, however, differs, to some extent, from the X-ray diffraction (XRD) observations revealing that the compounds formed at the metal/SiC interface are silicides, TiSi2, TiSi and Ti3SiC2 (Chang et al., 2005). The formation of silicides or carbides on the surface of SiC substrate after annealing may serve as a primary current-transport pathway to lower the high Schottky barrier between the metal and the semiconductors. In addition, Ohyanagi et al. argued that carbon exists at the contacts/SiC interface and might play a crucial role in lowering Schottky barrier (Ohyanagi et al., 2008). These are just a few representative examples illustrating the obvious discrepancies in clarifying the formation mechanism of Ohmic contact. Taking the amount of speculations on the mechanism and the increasing needs for better device design and performance control, understanding the

To develop an understanding of the origin in such a complex system, it is important to focus first on microstructure characterization. Tanimoto et al. examined the microstructure at the interface between TiAl contacts and the SiC using Auger electron spectroscopy and found that carbides containing Ti and Si were formed at interface (Tanimoto et al., 2002). Recently, transmission electron microscopy (TEM) studies by Tsukimoto et al. have provided useful information in this aspect due to possible high-resolution imaging (Tsukimoto et al., 2004). They have found that the majority of compounds generated on the surface of 4H-SiC substrate after annealing consist of a newly formed compound and hence proposed that the new interface is responsible for the lowering of Schottky barrier in the TiAl-based contact system. However, role of the interface in realizing the Ohmic nature remains unclear. It is not even clear how the two materials bond together atomically from these experiments, which is very important because it may strongly affect physical properties of the system. To determine the most stable interface theoretically, one first has to establish feasible models on the basis of distinct terminations and contact sites and then compare them. However, a

underlying formation origin is timely and relevant.

direct comparison of the total energies of such models is not physically meaningful since interfaces might have a different number of atoms. On the other hand, the ideal work of adhesion, or adhesion energy, *W*ad, which is key to predicting mechanical and thermodynamic properties of an interface is physically comparable. Generally, the *W*ad, which is defined as reversible energy required to separate an interface into two free surfaces, can be expressed by the difference in total energy between the interface and isolated slabs,

$$\mathbf{W}\_{\rm ad} = \left(E\_1 + E\_2 - E\_{\rm IF}\right) / A. \tag{1}$$

Here *E*1, *E*2, and *E*IF are total energies of isolated slab 1, slab 2, and their interface system, respectively, and *A* is the total interface area. To date, analytic models available for predicting *W*ad concerning SiC have mostly been restricted to SiC/metal heterojuctions such as SiC/Ni, SiC/Al and SiC/Ti. These models are motivated by the experimental deposition of metals on SiC. However, they neglect the complexity of situation; namely, the compounds (silicides or carbides) can be generated on SiC substrate after annealing and thus the models are only applicable to systems with as-deposited state.

Recent advances in the high-angle annular-dark-field (HAADF) microscopy, the highest resolution, have enabled an atomic-scale imaging of a buried interface (Nellist et al., 2004). However, a direct interpretation of the observed HAADF images is not always straightforward because there might be abrupt structural discontinuity, mixing of several species of elements on individual atomic columns, or missing contrasts of light elements. One possible way out to complement the microscopic data is via atomistic calculation, especially the first-principles calculation. As well known, the atomistic first-principles simulations have long been confirmed to be able to suggest plausible structures, elucidate the reason behind the observed images, and even provide a quantitative insight into how interface governs properties of materials. Consequently, a combination of state-of-the-art microcopy and accurate atomistic modeling is an important advance for determining interface atomic-scale structure and relating it to device properties, revealing, in this way, physics origin of contact issues in SiC electronics.

In addition to determining atomic structure of 4H-SiC/Ti3SiC2 interface, the goal of this chapter is to clarify formation mechanism of the TiAl-based Ohmic contacts so as to provide suggestions for further improvement of the contacts. 4H-SiC will hereafter be referred to as SiC. First of all, we fabricated the TiAl-based contacts and measured their electric properties to confirm the formation of Ohmic contact. Next, the metals/SiC interface was analyzed using the XRD to identify reaction products and TEM, high-resolution TEM (HRTEM), and scanning TEM (STEM) to observe microstructures. Based on these observations, we finally performed systematic first-principles calculations, aimed at assisting the understanding of Ohmic contact formation at a quantum mechanical level. The remainder of this chapter is organized as follows: Section 2 presents the experimental procedures, observes the contact microstructure, and determines the orientation relationships between the generated Ti3SiC2 and SiC substrate. Section 3 describes the computational method, shows detailed results on bulk and surface calculations, outlines the geometries of the 96 candidate interfaces, and determine the structure, electronic states, local bonding, and nonequilibrium quantum transport of the interface. We provide disscussion and concluding remarks in Sec. 4.

#### **2. Experimental characterization**

The *p*-type 4H-SiC epitaxial layers (5-μm thick) doped with aluminum (*N*A = 4.5 × 1018 cm-3) which were grown on undoped 4H-SiC wafers by chemical vapor deposition (manufactured

Introducing Ohmic Contacts into Silicon Carbide Technology 287

Fig. 1. Current-voltage properties of the TiAl contact system before and after thermal

To determine the chemical composition of the TiAl contact systems, we performed XRD analyses, as shown in Fig. 2, where textural orientations of the detected matters are shown as well. As expected from the preparation process, one can see in Fig. 2(a) peaks of deposited metals, Ti and Al, and the (0001)-oriented SiC in the system before annealing. It is worthy of mentioning that the detected Ti has a much weaker intensity of diffraction peak than Al, which can be attributed to its lower concentration and smaller grains. On the other hand, the XRD spectrum alters significantly after annealing (Fig. 2(b)), as the original Ti and Al peaks disappear and there emerge new peaks, suggesting that chemical reactions occur.

Fig. 2. XRD spectra of (a) as-deposited and (b) annealed TiAl contact systems. The TSC is an

From Fig. 2(b), the reaction products are found to be dominated by ternary Ti3SiC2 with a strongly (0001)-oriented texture, as only the (000*l*) diffraction peaks are detected. In addition to the Ti3SiC2, binary Al4C3 is also present in the annealed specimen. However, its amount is very small because the intensities of its diffraction peaks are comparatively much weaker. The formation of these compounds at elevated temperature is also supported by the Ti-Al-SiC equilibrium phase diagram, which predicts that four phases, SiC, Al4C3, Ti3SiC2, and liquid, can coexist in an equilibrium state when the aforementioned composition of TiAl alloy is adopted. Furthermore, the XRD results agree well with the experimental reports (Johnson and Capano,2004), but deviate somewhat from those of Nakatsuka et al. (2002) showing that binary Al3Ti is present as well. This slight difference is mainly because the intensity of Al3Ti peak is so low that might be overlapped by the strong peaks of SiC and

annealing at 1273 K for 2 min.

abbreviation of Ti3SiC2.

**2.1.1 Formation of Ti3SiC2 compound on SiC** 

by Cree Research, Inc.) were used as substrates. The 4H-SiC substrates had 8-off Siterminated (0001) surfaces inclined toward a [-2110] direction because only 4H-type structure of SiC with polymorph (e.g. 3C, 4H, 6H, 15R etc.) was controllable by lateral growth of the epitaxial layers parallel to (0001)-oriented surface. After chemical cleaning of the substrate surface, a 10 nm-thick sacrificial oxide (SiOx) layer was grown on the SiC substrate by dry-oxidation at 1423 K for 60 min. The electrode patterns were made by removing the SiOx layers, where contact metals were deposited by dipping in 5 % diluted hydrofluoric acid solution for 1 min using a photolithography technique. Prior to the deposition of contact materials, the substrates were cleaned by deionized water. Then, Ti and Al stacking layers with high purities were deposited sequentially on the substrate in a high vacuum chamber where the base pressure was below 5 × 10-6 Pa. The thicknesses of the Ti and Al layers investigated in this study are 100 nm and 380 nm, respectively, and these layer thicknesses were chosen to give the average composition of the Ti(20 at%) and Al(80 at%), where the layer thicknesses were measured by a quartz oscillator during deposition. The reasons to choose this average composition was that aluminum rich (more than 75 at%) in TiAl contacts were empirically found to be essential to yield low contact resistance, resulting from formation of the Ti3SiC2 compound layers. After depositing, the binary TiAl contact layers were annealed at 1273 K for a storage time of 2 min in an ultra-high vacuum chamber where the vacuum pressure was below 1×10-7 Pa.

The surface morphology of the TiAl contact layers on 4H-SiC after annealing was observed using a JEOL JSM-6060 scanning electron microscope (SEM). Microstructural analysis and identification of the Ti3SiC2 layers at the contact layers/4H-SiC interfaces after annealing was performed using X-ray diffraction (XRD) and cross-sectional TEM. For XRD analysis, Rigaku RINT-2500 with Cu *Kα* radiation operated at 30 kV and 100 mA was used. In particular, the interfacial structures and an orientation relationship between the contact layers and the 4H-SiC substrates were characterized by cross-sectional highresolution TEM observations and selected area diffraction pattern (SADP) analysis, respectively, using a JEOL JEM-4000EX electron microscope operated at an accelerating voltage of 400 kV, where the point-to-point resolution of this microscope was approximately 0.17 nm. Z-contrast images were obtained using a spherical aberration (C*s*) corrected scanning transmission electron microscope (STEM) (JEOL 2100F), which provides an unprecedented opportunity to investigated atomic-scale structure with a sub-Å electron probe. Thin foil specimens for the TEM and STEM observations were prepared by the standard procedures: cutting, gluing, mechanical grinding, dimple polishing, and argon ion sputter thinning techniques.

#### **2.1 Formation of Ohmic contacts**

To verify the formation of Ohmic contact, we measured the electric properties (*I−V* characteristics) for the TiAl contact systems before and after annealing (Fig. 1). For the system before annealing, its current almost maintains zero despite that the applied bias ranges from *−*3.0 to 3.0 V, which unambiguously reflects Schottky character of this system. This can be understood by considering that the potential induced by applied bias drops largely at an contact interface between metals and semiconductors, thus hindering the current flow. The annealed system, however, exhibits a typical Ohmic nature, as its *I−V* curve is nearly linear and the current increases sharply with the rise of applied bias. This drastic change of electric properties suggests that there might be substantial changes in microstructure during annealing.

by Cree Research, Inc.) were used as substrates. The 4H-SiC substrates had 8-off Siterminated (0001) surfaces inclined toward a [-2110] direction because only 4H-type structure of SiC with polymorph (e.g. 3C, 4H, 6H, 15R etc.) was controllable by lateral growth of the epitaxial layers parallel to (0001)-oriented surface. After chemical cleaning of the substrate surface, a 10 nm-thick sacrificial oxide (SiOx) layer was grown on the SiC substrate by dry-oxidation at 1423 K for 60 min. The electrode patterns were made by removing the SiOx layers, where contact metals were deposited by dipping in 5 % diluted hydrofluoric acid solution for 1 min using a photolithography technique. Prior to the deposition of contact materials, the substrates were cleaned by deionized water. Then, Ti and Al stacking layers with high purities were deposited sequentially on the substrate in a high vacuum chamber where the base pressure was below 5 × 10-6 Pa. The thicknesses of the Ti and Al layers investigated in this study are 100 nm and 380 nm, respectively, and these layer thicknesses were chosen to give the average composition of the Ti(20 at%) and Al(80 at%), where the layer thicknesses were measured by a quartz oscillator during deposition. The reasons to choose this average composition was that aluminum rich (more than 75 at%) in TiAl contacts were empirically found to be essential to yield low contact resistance, resulting from formation of the Ti3SiC2 compound layers. After depositing, the binary TiAl contact layers were annealed at 1273 K for a storage time of 2 min in an ultra-high vacuum

The surface morphology of the TiAl contact layers on 4H-SiC after annealing was observed using a JEOL JSM-6060 scanning electron microscope (SEM). Microstructural analysis and identification of the Ti3SiC2 layers at the contact layers/4H-SiC interfaces after annealing was performed using X-ray diffraction (XRD) and cross-sectional TEM. For XRD analysis, Rigaku RINT-2500 with Cu *Kα* radiation operated at 30 kV and 100 mA was used. In particular, the interfacial structures and an orientation relationship between the contact layers and the 4H-SiC substrates were characterized by cross-sectional highresolution TEM observations and selected area diffraction pattern (SADP) analysis, respectively, using a JEOL JEM-4000EX electron microscope operated at an accelerating voltage of 400 kV, where the point-to-point resolution of this microscope was approximately 0.17 nm. Z-contrast images were obtained using a spherical aberration (C*s*) corrected scanning transmission electron microscope (STEM) (JEOL 2100F), which provides an unprecedented opportunity to investigated atomic-scale structure with a sub-Å electron probe. Thin foil specimens for the TEM and STEM observations were prepared by the standard procedures: cutting, gluing, mechanical grinding, dimple polishing, and

To verify the formation of Ohmic contact, we measured the electric properties (*I−V* characteristics) for the TiAl contact systems before and after annealing (Fig. 1). For the system before annealing, its current almost maintains zero despite that the applied bias ranges from *−*3.0 to 3.0 V, which unambiguously reflects Schottky character of this system. This can be understood by considering that the potential induced by applied bias drops largely at an contact interface between metals and semiconductors, thus hindering the current flow. The annealed system, however, exhibits a typical Ohmic nature, as its *I−V* curve is nearly linear and the current increases sharply with the rise of applied bias. This drastic change of electric properties suggests that there might be substantial changes in

chamber where the vacuum pressure was below 1×10-7 Pa.

argon ion sputter thinning techniques.

**2.1 Formation of Ohmic contacts** 

microstructure during annealing.

Fig. 1. Current-voltage properties of the TiAl contact system before and after thermal annealing at 1273 K for 2 min.

#### **2.1.1 Formation of Ti3SiC2 compound on SiC**

To determine the chemical composition of the TiAl contact systems, we performed XRD analyses, as shown in Fig. 2, where textural orientations of the detected matters are shown as well. As expected from the preparation process, one can see in Fig. 2(a) peaks of deposited metals, Ti and Al, and the (0001)-oriented SiC in the system before annealing. It is worthy of mentioning that the detected Ti has a much weaker intensity of diffraction peak than Al, which can be attributed to its lower concentration and smaller grains. On the other hand, the XRD spectrum alters significantly after annealing (Fig. 2(b)), as the original Ti and Al peaks disappear and there emerge new peaks, suggesting that chemical reactions occur.

Fig. 2. XRD spectra of (a) as-deposited and (b) annealed TiAl contact systems. The TSC is an abbreviation of Ti3SiC2.

From Fig. 2(b), the reaction products are found to be dominated by ternary Ti3SiC2 with a strongly (0001)-oriented texture, as only the (000*l*) diffraction peaks are detected. In addition to the Ti3SiC2, binary Al4C3 is also present in the annealed specimen. However, its amount is very small because the intensities of its diffraction peaks are comparatively much weaker. The formation of these compounds at elevated temperature is also supported by the Ti-Al-SiC equilibrium phase diagram, which predicts that four phases, SiC, Al4C3, Ti3SiC2, and liquid, can coexist in an equilibrium state when the aforementioned composition of TiAl alloy is adopted. Furthermore, the XRD results agree well with the experimental reports (Johnson and Capano,2004), but deviate somewhat from those of Nakatsuka et al. (2002) showing that binary Al3Ti is present as well. This slight difference is mainly because the intensity of Al3Ti peak is so low that might be overlapped by the strong peaks of SiC and

Introducing Ohmic Contacts into Silicon Carbide Technology 289

To characterize the surface morphology of the TiAl contact layer after annealing, the SEM observation was employed. Figure 4 shows a plan-view SEM image from the TiAl contact layer after annealing at 1273 K. The surface is observed to have an uniformly scale-shaped contrast with hexagonal facets, although surface roughness after annealing is aggravated in comparison to that of the sample before annealing. Using a stylus surface profiler, the maximum typical roughness was measured to be about 1 μm. The surface facet planes are found to form parallel to <-2110> directions on the SiC(0001) substrate surface. The hillocks observed on the surface, which is due to formation of residual Al-based liquid droplet, is, however, absent for the samples annealed at temperatures lower than 1073 K. The surface morphology results from evaporation of the liquid phases with low melting points and high

Fig. 4. A plan-view SEM image of the Ti/Al contact layers deposited on SiC after annealing

Although the XRD can reveal detailed information on chemical composition of reaction products, it provides limited insight into matters concerning how the products distribute and contact the substrate. To observe the microstructure directly, we present in Fig. 5(a) a crosssectional bright-field TEM image of a representative region in the annealed TiAl contact system. The incident electron beam is along [0-110] direction of the SiC, which is parallel to the tilting axis of the 8º-off SiC(0001) surface. As seen in this figure, the SiC surface is covered entirely by the plate-shaped Ti3SiC2 with thickness ranging from 30 nm to 300 nm. This universal cover means that no any other compounds contact directly the SiC surface, thereby ensuring an exclusive contact of Ti3SiC2 to SiC. Consequently, the SiC/Ti3SiC2 interface might play an essential role in the formation of Ohmic contact. In addition, this interface is observed to have a sawtooth-like facet structure and the Ti3SiC2 surface inclines by nearly 8º toward the substrate surface, suggesting that the SiC surface affects significantly morphology of formed Ti3SiC2. To analyze the element species around interface, we further show in Fig. 5(b) the energydispersive X-ray spectroscopy (EDS) spectra for the interfacial SiC and Ti3SiC2 regions. The substrate is mainly composed of C and Si and the reaction products C, Si, and Ti, in accordance with chemical compositions of the substrate and the main reaction products, respectively. Unexpectedly, no Al peak is identified in either the interfacial SiC or Ti3SiC2 area, which seems to contravene the XRD analyses revealing that the Al4C3 compound is present in the annealed specimen. This discrepancy is mainly because the amount of Al4C3 is so small (Fig. 2(b)) that is hard to be detected by the EDS, or because Al might not distribute near the interface at all but around the Ti3SiC2 surface instead. Whatever the reason is, the Al should

vapor pressures during annealing at high temperatures in ultra high vacuum.

**2.1.2 Growth and microstructure of Ti3SiC2 layers on SiC** 

at 1273 K.

Ti3SiC2. Finally, the SiC retains (0001)-oriented texture after annealing, thereby facilitating development of hetero-epitaxy between reaction products and substrates.

Figure 3 shows an isothermal section of the pseudo-ternary phase diagram of Al-Ti-SiC system at 1273 K (Viala et al., 1997) based on the experimental measurements of Al-Ti-Si-C quaternary system, where a grey region indicates the existence of binary AlSi-based liquid phases, and thick and fine lines indicates sub-solidus lines and tie-lines, respectively. It is noted that the liquidus line would lie at near the composition region of pure Al, as denoted by a symbol *L* in Fig. 3. Based on this phase diagram, the liquid phase is predicted to form when the concentration of Al is more than 75 at% in the Ti/Al contacts at 1273 K . In general, both the solutes and solvents have high diffusibility in liquid, the liquid phase has high reactivity to solid (substrate) and hence the reaction products are easily formed at elevated temperatures. Formation of the liquid is believed to play an important role in the TiAl-based contact by rapid thermal anneal process. Here, the effective average composition of the present reaction system, which react Ti-80%Al and SiC, can assume to be at the point *a* within region (i) in the diagram. In this region, four phases of SiC, Al4C3, Ti3SiC2 and liquid with a composition of Al-12%Si (which is a eutectic composition of Al-Si binary alloy) is predicted to maintain constant and coexist in equilibrium. This prediction is consistent with the XRD results obtained from samples annealed at 1273 K for 2 min (Fig. 2(b)), although a small amount of Al3Ti and Al did not react completely with SiC and remained at this stage. Further annealing of the sample for longer time, for instance, 6 min, renders these unreacted Al3Ti and Al disappear due to additional reaction to form the carbides (Ti3SiC2 and a small amount of Al4C3) and to the evaporation of Al-Si liquid phase with a high vapor pressure during annealing in ultra high vacuum. Hence, the average composition of the reaction system seems to shift toward Al-poor area (region (ii), as indicated by an arrow), and reach the point *b* after annealing. In the region (ii), three phases, SiC, Ti3SiC2 and Al-Si liquid with the Si concentrations varied from 12% (at the point *c*) to 19% (at the point *d*) are coexisted with their volume being constituted by an array of tie-lines. However, it is not straightforward to control the compounds formed by the rapid thermal annealing process because of occurrence of non-equilibrium phenomena such as evaporation of the liquid phases in this reaction system. This might be the reason why the TiAl-based contacts have been fabricated empirically with no definite designing guidelines.

Fig. 3. Isothermal section of a pseudoternary phase diagram of Al-Ti-SiC system at 1273 K.

Ti3SiC2. Finally, the SiC retains (0001)-oriented texture after annealing, thereby facilitating

Figure 3 shows an isothermal section of the pseudo-ternary phase diagram of Al-Ti-SiC system at 1273 K (Viala et al., 1997) based on the experimental measurements of Al-Ti-Si-C quaternary system, where a grey region indicates the existence of binary AlSi-based liquid phases, and thick and fine lines indicates sub-solidus lines and tie-lines, respectively. It is noted that the liquidus line would lie at near the composition region of pure Al, as denoted by a symbol *L* in Fig. 3. Based on this phase diagram, the liquid phase is predicted to form when the concentration of Al is more than 75 at% in the Ti/Al contacts at 1273 K . In general, both the solutes and solvents have high diffusibility in liquid, the liquid phase has high reactivity to solid (substrate) and hence the reaction products are easily formed at elevated temperatures. Formation of the liquid is believed to play an important role in the TiAl-based contact by rapid thermal anneal process. Here, the effective average composition of the present reaction system, which react Ti-80%Al and SiC, can assume to be at the point *a* within region (i) in the diagram. In this region, four phases of SiC, Al4C3, Ti3SiC2 and liquid with a composition of Al-12%Si (which is a eutectic composition of Al-Si binary alloy) is predicted to maintain constant and coexist in equilibrium. This prediction is consistent with the XRD results obtained from samples annealed at 1273 K for 2 min (Fig. 2(b)), although a small amount of Al3Ti and Al did not react completely with SiC and remained at this stage. Further annealing of the sample for longer time, for instance, 6 min, renders these unreacted Al3Ti and Al disappear due to additional reaction to form the carbides (Ti3SiC2 and a small amount of Al4C3) and to the evaporation of Al-Si liquid phase with a high vapor pressure during annealing in ultra high vacuum. Hence, the average composition of the reaction system seems to shift toward Al-poor area (region (ii), as indicated by an arrow), and reach the point *b* after annealing. In the region (ii), three phases, SiC, Ti3SiC2 and Al-Si liquid with the Si concentrations varied from 12% (at the point *c*) to 19% (at the point *d*) are coexisted with their volume being constituted by an array of tie-lines. However, it is not straightforward to control the compounds formed by the rapid thermal annealing process because of occurrence of non-equilibrium phenomena such as evaporation of the liquid phases in this reaction system. This might be the reason why the TiAl-based contacts have been fabricated empirically with no definite designing guidelines.

Fig. 3. Isothermal section of a pseudoternary phase diagram of Al-Ti-SiC system at 1273 K.

development of hetero-epitaxy between reaction products and substrates.

#### **2.1.2 Growth and microstructure of Ti3SiC2 layers on SiC**

To characterize the surface morphology of the TiAl contact layer after annealing, the SEM observation was employed. Figure 4 shows a plan-view SEM image from the TiAl contact layer after annealing at 1273 K. The surface is observed to have an uniformly scale-shaped contrast with hexagonal facets, although surface roughness after annealing is aggravated in comparison to that of the sample before annealing. Using a stylus surface profiler, the maximum typical roughness was measured to be about 1 μm. The surface facet planes are found to form parallel to <-2110> directions on the SiC(0001) substrate surface. The hillocks observed on the surface, which is due to formation of residual Al-based liquid droplet, is, however, absent for the samples annealed at temperatures lower than 1073 K. The surface morphology results from evaporation of the liquid phases with low melting points and high vapor pressures during annealing at high temperatures in ultra high vacuum.

Fig. 4. A plan-view SEM image of the Ti/Al contact layers deposited on SiC after annealing at 1273 K.

Although the XRD can reveal detailed information on chemical composition of reaction products, it provides limited insight into matters concerning how the products distribute and contact the substrate. To observe the microstructure directly, we present in Fig. 5(a) a crosssectional bright-field TEM image of a representative region in the annealed TiAl contact system. The incident electron beam is along [0-110] direction of the SiC, which is parallel to the tilting axis of the 8º-off SiC(0001) surface. As seen in this figure, the SiC surface is covered entirely by the plate-shaped Ti3SiC2 with thickness ranging from 30 nm to 300 nm. This universal cover means that no any other compounds contact directly the SiC surface, thereby ensuring an exclusive contact of Ti3SiC2 to SiC. Consequently, the SiC/Ti3SiC2 interface might play an essential role in the formation of Ohmic contact. In addition, this interface is observed to have a sawtooth-like facet structure and the Ti3SiC2 surface inclines by nearly 8º toward the substrate surface, suggesting that the SiC surface affects significantly morphology of formed Ti3SiC2.

To analyze the element species around interface, we further show in Fig. 5(b) the energydispersive X-ray spectroscopy (EDS) spectra for the interfacial SiC and Ti3SiC2 regions. The substrate is mainly composed of C and Si and the reaction products C, Si, and Ti, in accordance with chemical compositions of the substrate and the main reaction products, respectively. Unexpectedly, no Al peak is identified in either the interfacial SiC or Ti3SiC2 area, which seems to contravene the XRD analyses revealing that the Al4C3 compound is present in the annealed specimen. This discrepancy is mainly because the amount of Al4C3 is so small (Fig. 2(b)) that is hard to be detected by the EDS, or because Al might not distribute near the interface at all but around the Ti3SiC2 surface instead. Whatever the reason is, the Al should

Introducing Ohmic Contacts into Silicon Carbide Technology 291

In support of this idea, we present in Fig. 7 a cross-sectional HRTEM image of the SiC/Ti3SiC2 interface observed from the [11-20] direction. One can see clearly well arranged (000*l*)-oriented lattice fringes along the direction parallel to the interface in both the Ti3SiC2 layer and SiC substrate. The points at which the phase contrast is no longer periodic in either the Ti3SiC2 or SiC define the interfacial region. Evidently, the interface is atomically abrupt and coherent without any secondary phase layers, amorphous layers, contaminants, or transition regions, which confirms a clean and direct contact of the Ti3SiC2 with SiC on atomic scale. The interface has (0001)-oriented terraces and ledges, as marked by letters *T*i (i = 1, 2, 3, 4) and *L*j (j = 1, 2, 3) in Fig. 7, respectively. The morphology of the terraces is observed to be atomically flat and abrupt as well. On the other hand, the ledge heights are found to be defined well as n × (a half unit cell height of 4H-SiC: 0.5 nm), where n represents the integer, e.g., n = 11 for *L*1, n = 2 for *L*2, and n = 1 for *L*3. This unique interface morphology is caused by the chemical reaction of TiAl and SiC, and anisotropic lateral growth of the epitaxial Ti3SiC2 layers along the directions parallel to SiC(0001), as indicated by arrows in Fig. 7. In addition, no misfit dislocations are clearly visible at interface in present HRTEM micrograph and further examination of other interfacial regions demonstrates that the density of misfit dislocations is extremely low in this system. This can be explained from the small lattice mismatch between the two materials (less than 0.5%). Unfortunately, it remains unclear from this figure how the two materials atomically bond together at interface, which is very important because the bonding nature is well known to be able to affect the physical

Fig. 7. A cross-sectional HRTEM micrograph of the interface between the Ti3SiC2 layer and

Figure 8 shows a typical HAADF image of the SiC/Ti3SiC2 interface. A simple looking at this figure confirms a clean and atomically sharp contact between the two materials, which means a successful growth of the epitaxially Ti3SiC2 on SiC. Brighter spots in the image represent atomic columns of Ti, while the comparatively darker ones are Si, since the intensity of an atomic column in the STEM, to good approximation, is directly proportional to the square of atomic number (Z) (Pennycook & Boatner, 1988). Not surprisingly, due to small atomic number of C, its columns are not scattered strongly enough to be visualized, thereby making the image incomplete. Further complementing of this image so as to relate

the 4H-SiC substrate, which is taken along the SiC [-2110] zone axis.

the atomic structure to property requires the first-principles calculations.

properties of interfacial systems significantly.

**2.1.3 Interface atomic-scale structures** 

not be the key to understanding the formation origin of Ohmic contact. That is, a large amount of Al diffuses into the SiC and introduces a heavily *p*-doped SiC, which result in narrower depletion area and thus more tunneling. As a matter of fact, this has also been suggested by analyzing interfacial chemical composition and local states, which shows that no additional Al segregates to interface, suggestive of a clean contact of Ti3SiC2 to SiC (Gao et al., 2007).

Fig. 5. (a) Cross-sectional bright-field TEM image of the annealed TiAl contact system showing exclusive reaction product of Ti3SiC2, and (b) EDS data obtained at the SiC and Ti3SiC2 region near to interface. The vertical axis in (b) denotes the counts (i.e., intensity).

Figure 6 shows a selected area diffraction pattern (SADP) at the contacts/SiC interface taken along the same electron-beam direction as in Fig. 5(a). A careful indexing of the pattern confirms again the plate-shaped layers as being ternary Ti3SiC2. The formed Ti3SiC2 layers are observed to have epitaxial orientation relationships, (0001)Ti3SiC2//(0001)SiC and [0-110]Ti3SiC2//[0-110]SiC with the SiC substrate, which agrees well with the XRD analyses demonstrating that both materials exhibit the (0001)-oriented textures. These orientation relationships are believed to be beneficial for forming a coherent and well matched interface between SiC and Ti3SiC2, since they both belong to the hexagonal space group with lattice constants of *a* = 3.081 Å and *c* = 10.085 Å for the SiC and *a* = 3.068 Å and *c* = 17.669 Å for the Ti3SiC2 (Harris, 1995).

Fig. 6. Selected-area diffraction pattern obtained at the annealed contacts/SiC interface. The arrays of diffraction spots from the SiC and contacts are marked by dashed and solid lines, respectively.

not be the key to understanding the formation origin of Ohmic contact. That is, a large amount of Al diffuses into the SiC and introduces a heavily *p*-doped SiC, which result in narrower depletion area and thus more tunneling. As a matter of fact, this has also been suggested by analyzing interfacial chemical composition and local states, which shows that no additional Al

Ti3SiC**<sup>2</sup> 8º** 

**Ti3SiC2**

**Ti**

0 2 4 6

**Si**

**Ti C**

**Ti**

segregates to interface, suggestive of a clean contact of Ti3SiC2 to SiC (Gao et al., 2007).

4H-SiC

**(a)**

**(b) 4H-SiC**

**Si**

0 2 4 6

**C**

Fig. 5. (a) Cross-sectional bright-field TEM image of the annealed TiAl contact system showing exclusive reaction product of Ti3SiC2, and (b) EDS data obtained at the SiC and Ti3SiC2 region near to interface. The vertical axis in (b) denotes the counts (i.e., intensity).

Ti3SiC2 (Harris, 1995).

respectively.

Figure 6 shows a selected area diffraction pattern (SADP) at the contacts/SiC interface taken along the same electron-beam direction as in Fig. 5(a). A careful indexing of the pattern confirms again the plate-shaped layers as being ternary Ti3SiC2. The formed Ti3SiC2 layers are observed to have epitaxial orientation relationships, (0001)Ti3SiC2//(0001)SiC and [0-110]Ti3SiC2//[0-110]SiC with the SiC substrate, which agrees well with the XRD analyses demonstrating that both materials exhibit the (0001)-oriented textures. These orientation relationships are believed to be beneficial for forming a coherent and well matched interface between SiC and Ti3SiC2, since they both belong to the hexagonal space group with lattice constants of *a* = 3.081 Å and *c* = 10.085 Å for the SiC and *a* = 3.068 Å and *c* = 17.669 Å for the

Energy (eV) Energy (eV)

Fig. 6. Selected-area diffraction pattern obtained at the annealed contacts/SiC interface. The arrays of diffraction spots from the SiC and contacts are marked by dashed and solid lines,

In support of this idea, we present in Fig. 7 a cross-sectional HRTEM image of the SiC/Ti3SiC2 interface observed from the [11-20] direction. One can see clearly well arranged (000*l*)-oriented lattice fringes along the direction parallel to the interface in both the Ti3SiC2 layer and SiC substrate. The points at which the phase contrast is no longer periodic in either the Ti3SiC2 or SiC define the interfacial region. Evidently, the interface is atomically abrupt and coherent without any secondary phase layers, amorphous layers, contaminants, or transition regions, which confirms a clean and direct contact of the Ti3SiC2 with SiC on atomic scale. The interface has (0001)-oriented terraces and ledges, as marked by letters *T*i (i = 1, 2, 3, 4) and *L*j (j = 1, 2, 3) in Fig. 7, respectively. The morphology of the terraces is observed to be atomically flat and abrupt as well. On the other hand, the ledge heights are found to be defined well as n × (a half unit cell height of 4H-SiC: 0.5 nm), where n represents the integer, e.g., n = 11 for *L*1, n = 2 for *L*2, and n = 1 for *L*3. This unique interface morphology is caused by the chemical reaction of TiAl and SiC, and anisotropic lateral growth of the epitaxial Ti3SiC2 layers along the directions parallel to SiC(0001), as indicated by arrows in Fig. 7. In addition, no misfit dislocations are clearly visible at interface in present HRTEM micrograph and further examination of other interfacial regions demonstrates that the density of misfit dislocations is extremely low in this system. This can be explained from the small lattice mismatch between the two materials (less than 0.5%). Unfortunately, it remains unclear from this figure how the two materials atomically bond together at interface, which is very important because the bonding nature is well known to be able to affect the physical properties of interfacial systems significantly.

Fig. 7. A cross-sectional HRTEM micrograph of the interface between the Ti3SiC2 layer and the 4H-SiC substrate, which is taken along the SiC [-2110] zone axis.

#### **2.1.3 Interface atomic-scale structures**

Figure 8 shows a typical HAADF image of the SiC/Ti3SiC2 interface. A simple looking at this figure confirms a clean and atomically sharp contact between the two materials, which means a successful growth of the epitaxially Ti3SiC2 on SiC. Brighter spots in the image represent atomic columns of Ti, while the comparatively darker ones are Si, since the intensity of an atomic column in the STEM, to good approximation, is directly proportional to the square of atomic number (Z) (Pennycook & Boatner, 1988). Not surprisingly, due to small atomic number of C, its columns are not scattered strongly enough to be visualized, thereby making the image incomplete. Further complementing of this image so as to relate the atomic structure to property requires the first-principles calculations.

Introducing Ohmic Contacts into Silicon Carbide Technology 293

Calculations of electronic structure and total energy were carried out using the Vienna *ab initio* simulation package (VASP) within the framework of density- functional theory (DFT) (Kresse & Hafner, 1993). The projector augmented wave (PAW) method was used for electron-ion interactions and the generalized gradient approximation (GGA) of Perdew and co-worker (PW91) was employed to describe the exchange-correlation functional. The single-particle Kohn-Sham wave function was expanded using the plane waves with different cutoff energies depending on calculated systems of either bulk or slab. Sampling of irreducible wedge of Brillion zone was performed with a regular Monkhorst-Pack grid of special *k* points, and electronic occupancies were determined according to a Methfessel-Paxton scheme with an energy smearing of 0.2 eV. All atoms were fully relaxed using the conjugate gradient (CG) algorithm until the magnitude of the Hellmann-Feynman force on

each atom was converged to less than 0.05 eV/Å, yielding optimized structures.

The electron transport properties of the above systems were explored with the fully selfconsistent nonequilibrium Green's function method implemented in Atomistix ToolKit (ATK) code. This method has been applied to many systems successfully. The local density approximation (LDA) and the Troullier-Martins nonlocal pseudopotential were adopted, and the valence electrons were expanded in a numerical atomic-orbital basis set of single zeta plus polarization (SZP). Trial calculations exhibit similar results by using double zeta plus polarization (DZP) basis sets for all atoms, thereby validating the use of SZP. Only Γpoint was employed in the *k*-point sampling in the surface Brillouin zone. A cutoff of 100 Ry for solving Poissons equation and various integrals is utilized to present charge density and a rather large k-point value, 200, is chosen for accurately describing electronic structure

We first assess accuracy of the computational methods by performing a series of bulk calculations. It is known that the 4H-SiC, one of the most common SiC polymorphs, belongs to hexagonal *P63mc* space group with *a* = 3.081Å and *c* = 10.085Å. A unit cell of SiC consists of four Si-C bilayers with a total of 8 atoms. The Ti3SiC2 also has a hexagonal crystal structure but within the *P63mmc* space group (*a* = 3.068Å and *c* = 17.669Å). The atomic positions of Ti correspond to the 2*a*, Si to the 2*b*, and C to the 4*f* Wyckoff sites of the space group and the phase is composed of a layered structure with a double Ti-C block, each made up of two edge-sharing CTi6 octahedra. Note that the Ti atoms of Ti3SiC2 occupy two types of structurally nonequivalent positions: one (Ti1, two per unit cell) has C atoms as nearest neighbors, while the other (Ti2, four per unit cell) has Si atoms (see Fig. 13(a)). The optimum lattice constants of bulk 4H-SiC calculated using the above parameters are *a* = 3.095Å and *c* = 10.131Å, 100.5% of the experimental value, while those of bulk Ti3SiC2 are *a* =

Figure 10(a) shows calculated band structure of 4H-SiC along the high-symmetry lines. The top of occupied valence band (VB) is located at Γ point and the bottom of conduction band (CB) is at M point, causing the SiC to be an indirect gap semiconductor. The calculated energy band gap is 2.25 eV, which is smaller than the experimental value of 3.26 eV, but close to the calculated value of 2.18 eV (Käckell et al., 1994) and 2.43 eV (Ching et al., 2006). Deviation from the experimental value is attributed to the well-known drawback of the DFT

3.076Å and *c* = 17.713Å, 100.25% of the experimental one (Harris, 1995).

**3. Atomistic modelling of the functional interface** 

along transport direction.

**3.1.1 Bulk properties** 

**3.1 Bulk and surface calculations** 

Fig. 8. A typical HAADF-STEM image of the SiC/Ti3SiC2 interface in the annealed TiAl contact system observed from the [11-20] direction. The position of interface is indicated by two arrows

To see the interface atomic-scale structure clearer, we magnify the cross-sectional HAADF image of the SiC/Ti3SiC2 interface in Fig. 9(a) and further filter it to reduce noise (Fig. 9(b)). The interface location is indicated by a horizontal line, which is determined based on the arrangement of atomic columns in bulk SiC and Ti3SiC2. The Si-terminated Ti3SiC2 is observed intuitively to make a direct contact with the Si-terminated SiC substrate with the interfacial Si atoms of Ti3SiC2 sitting above hollow sites of the interfacial Si plane of SiC. However, as we will see in the upcoming simulations, this interpretation is premature in that it neglects a possibility, namely, the unseen C might be trapped at interface. Another interesting feature in this figure is that no Al columns are detected surrounding interface, which eliminates the possibility of additional *p*-doping via Al diffusion into the top few SiC layers. Since there are also no pits, spikes, or dislocations which might act as pathways for current transport, we conclude that the clean and coherent SiC/Ti3SiC2 interface should be critical for the Ohmic contact formation. The ensuing question is how this interface lowers the Schottky barrier, which is rather difficult to investigate by experiment alone but can be suggested by calculations.

Fig. 9. A(a) Magnified HAADF image of the SiC/Ti3SiC2 interface. An overlay is shown as well for easy reference. The bigger balls denote Si and the smaller ones Ti. (b) The same image as in (a) but has been low-pass filtered to reduce the noise.

Fig. 8. A typical HAADF-STEM image of the SiC/Ti3SiC2 interface in the annealed TiAl contact system observed from the [11-20] direction. The position of interface is indicated by

To see the interface atomic-scale structure clearer, we magnify the cross-sectional HAADF image of the SiC/Ti3SiC2 interface in Fig. 9(a) and further filter it to reduce noise (Fig. 9(b)). The interface location is indicated by a horizontal line, which is determined based on the arrangement of atomic columns in bulk SiC and Ti3SiC2. The Si-terminated Ti3SiC2 is observed intuitively to make a direct contact with the Si-terminated SiC substrate with the interfacial Si atoms of Ti3SiC2 sitting above hollow sites of the interfacial Si plane of SiC. However, as we will see in the upcoming simulations, this interpretation is premature in that it neglects a possibility, namely, the unseen C might be trapped at interface. Another interesting feature in this figure is that no Al columns are detected surrounding interface, which eliminates the possibility of additional *p*-doping via Al diffusion into the top few SiC layers. Since there are also no pits, spikes, or dislocations which might act as pathways for current transport, we conclude that the clean and coherent SiC/Ti3SiC2 interface should be critical for the Ohmic contact formation. The ensuing question is how this interface lowers the Schottky barrier, which is rather difficult to investigate by experiment alone but can be

Fig. 9. A(a) Magnified HAADF image of the SiC/Ti3SiC2 interface. An overlay is shown as well for easy reference. The bigger balls denote Si and the smaller ones Ti. (b) The same

image as in (a) but has been low-pass filtered to reduce the noise.

two arrows

suggested by calculations.

#### **3. Atomistic modelling of the functional interface**

Calculations of electronic structure and total energy were carried out using the Vienna *ab initio* simulation package (VASP) within the framework of density- functional theory (DFT) (Kresse & Hafner, 1993). The projector augmented wave (PAW) method was used for electron-ion interactions and the generalized gradient approximation (GGA) of Perdew and co-worker (PW91) was employed to describe the exchange-correlation functional. The single-particle Kohn-Sham wave function was expanded using the plane waves with different cutoff energies depending on calculated systems of either bulk or slab. Sampling of irreducible wedge of Brillion zone was performed with a regular Monkhorst-Pack grid of special *k* points, and electronic occupancies were determined according to a Methfessel-Paxton scheme with an energy smearing of 0.2 eV. All atoms were fully relaxed using the conjugate gradient (CG) algorithm until the magnitude of the Hellmann-Feynman force on each atom was converged to less than 0.05 eV/Å, yielding optimized structures.

The electron transport properties of the above systems were explored with the fully selfconsistent nonequilibrium Green's function method implemented in Atomistix ToolKit (ATK) code. This method has been applied to many systems successfully. The local density approximation (LDA) and the Troullier-Martins nonlocal pseudopotential were adopted, and the valence electrons were expanded in a numerical atomic-orbital basis set of single zeta plus polarization (SZP). Trial calculations exhibit similar results by using double zeta plus polarization (DZP) basis sets for all atoms, thereby validating the use of SZP. Only Γpoint was employed in the *k*-point sampling in the surface Brillouin zone. A cutoff of 100 Ry for solving Poissons equation and various integrals is utilized to present charge density and a rather large k-point value, 200, is chosen for accurately describing electronic structure along transport direction.

#### **3.1 Bulk and surface calculations**

#### **3.1.1 Bulk properties**

We first assess accuracy of the computational methods by performing a series of bulk calculations. It is known that the 4H-SiC, one of the most common SiC polymorphs, belongs to hexagonal *P63mc* space group with *a* = 3.081Å and *c* = 10.085Å. A unit cell of SiC consists of four Si-C bilayers with a total of 8 atoms. The Ti3SiC2 also has a hexagonal crystal structure but within the *P63mmc* space group (*a* = 3.068Å and *c* = 17.669Å). The atomic positions of Ti correspond to the 2*a*, Si to the 2*b*, and C to the 4*f* Wyckoff sites of the space group and the phase is composed of a layered structure with a double Ti-C block, each made up of two edge-sharing CTi6 octahedra. Note that the Ti atoms of Ti3SiC2 occupy two types of structurally nonequivalent positions: one (Ti1, two per unit cell) has C atoms as nearest neighbors, while the other (Ti2, four per unit cell) has Si atoms (see Fig. 13(a)). The optimum lattice constants of bulk 4H-SiC calculated using the above parameters are *a* = 3.095Å and *c* = 10.131Å, 100.5% of the experimental value, while those of bulk Ti3SiC2 are *a* = 3.076Å and *c* = 17.713Å, 100.25% of the experimental one (Harris, 1995).

Figure 10(a) shows calculated band structure of 4H-SiC along the high-symmetry lines. The top of occupied valence band (VB) is located at Γ point and the bottom of conduction band (CB) is at M point, causing the SiC to be an indirect gap semiconductor. The calculated energy band gap is 2.25 eV, which is smaller than the experimental value of 3.26 eV, but close to the calculated value of 2.18 eV (Käckell et al., 1994) and 2.43 eV (Ching et al., 2006). Deviation from the experimental value is attributed to the well-known drawback of the DFT

Introducing Ohmic Contacts into Silicon Carbide Technology 295

To simulate a bulklike interface, it is essential to ensure that the two sides of the interface slabs used in calculations are thick enough to exhibit a bulklike interior because properties of a thin film may differ significantly from those of the bulk. To determine the minimum layer necessary for a bulklike slab, we first performed calculations on the convergence of surface energy with respect to slab thickness and then considered an additional series of surface relaxations as a function of slab layers. The surface energy of Ti3SiC2, *σ*T, under

<sup>1</sup> ( ) <sup>2</sup>

where, *total Eslab* denotes total energy of a relaxed and isolated slab, and *μ*X, *NX* , *A* represent chemical potential of *X* (*X* = Ti, Si, C), number of *X* atoms in the slab, and surface area, respectively. For Eq. (2), the *TS* term can be deleted at 0 K and meanwhile, the *PV* term is negligible for low pressure because we are considering a condensed matter system. Further, chemical potential of condensed phase of Ti3SiC2, *μ*Ti3SiC2, can be given by a sum of three

Since the total chemical potential of surface system, *μ*Ti3SiC2, is in equilibrium with that of its

32 32 . *bulk* μ = *Ti SiC Ti SiC <sup>E</sup>*

Replacing Eq. (4) with Eqs. (2) and (3), one can eliminate the *μ*Ti3SiC2 and *μ*C variables in the

*<sup>T</sup> E NE N N N N slab C Ti SiC Ti Ti C Si Si C <sup>A</sup>*

When the chemical potentials of the Ti and Si equal total energies of the hexagonal closepacked bulk Ti, *bulk ETi* , and fcc bulk Si, *bulk ESi* , respectively, the Eq. (5) can be redefined as

> <sup>0</sup> 1 1 3 1 [ ( ) ( )]. 2 2 2 2 *total bulk bulk bulk <sup>T</sup> E NE E N N E N N slab C Ti SiC Ti Ti C Si Si C <sup>A</sup>*

Similarly, the surface energy of the SiC, <sup>0</sup> σ*<sup>S</sup>* , can be given by the following equation under

<sup>0</sup> <sup>1</sup> [ ( )] <sup>2</sup> *total bulk bulk <sup>S</sup> E NE E N N slab C SiC Si Si C <sup>A</sup>*

Experimentally, the SiC(0001) plane was observed to be a favorable substrate surface that allows epitaxial growth of Ti3SiC2 with also a (0001)-oriented face. Four types of SiC terminations within the (0001) surface have been investigated, as shown in Fig. 12(b)**-**(e). In view of the unequal atom species at two sides of a stoichiometric slab, a non-stoichiometric

1 1 3 1 [ ( ) ( )]. 2 2 2 2

σ= − −μ − −μ − (5)

σ= − − − − − (6)

σ= − − − (7)

3 2

3 2

the condition that chemical potential of Si is equal to its bulk total energy.

*total bulk*

*<sup>T</sup> E N N N PV TS slab Ti Ti Si Si C C <sup>A</sup>* σ= − μ − μ − μ− − (2)

3 2 3 2. <sup>μ</sup>*Ti SiC Ti Si C* <sup>=</sup> <sup>μ</sup> <sup>+</sup> <sup>μ</sup> <sup>+</sup> <sup>μ</sup> (3)

(4)

**3.1.2 Surface properties** 

bulk, 3 2

*bulk ETi SiC* , we thus have

surface energy of Ti3SiC2, *σ*T, and obtain

pressure *P* and temperature *T* can be expressed as follows:

*total*

terms representing chemical potential of each species within the crystal:

which tends to underestimate band gap. The band gap in Fig. 10(a) can also be seen from the total DOS shown in Fig. 11(a). Besides this gap around the Fermi level (*E*F), there is also a gap of more than 1 eV located at about -10 eV below the *E*F, dividing the entire VB into two parts. The lower part of the VB originates mainly from the bonding between the *s* states of the Si and C, while the upper one is dominated by *p* orbitals of Si and C in a form of *sp3* hybridization. The CB part, however, shows a continuum state throughout the whole region, which is reflected from interweaving lines above *E*F (Fig. 10(a)).

Fig. 10. Energy band structure of (a) 4H-SiC and (b) Ti3SiC2 along the major symmetric directions. The dotted lines in red denote the Fermi level (*E*F).

In contrast, Ti3SiC2 exhibits clearly a metallic nature with bands crossing the *E*F, as shown in Fig. 10(b), thereby resulting in a peak in the total DOS at *E*F in Fig. 11(b). It is worth noting that the presence of the band at *E*F is caused by the energetic overlap of Ti *d* states with the gap levels of SiC (Fig. 11(b)), not an artifact due to the DFT underestimation of band gap. This metallic character is in agreement with reported experimental results and other theoretical studies. From Fig. 10(b), one can see that the VB of Ti3SiC2 is also separated into two parts at approximately 5.7 eV below *E*F, the lower part of which is composed of metalloid states having a typical *s* symmetry while the upper part of which consists of complex bands. It is also clear from Fig. 11(b) that these complicated states just below *E*F are dominated by strongly hybridized bonding states containing mainly *p* orbitals of both Si and C and *d* orbitals of Ti. The contribution to the CB, however, comes predominantly from antibonding *d* states of Ti, as shown in the PDOS of Ti in Fig. 11(b). The magnitude of DOS at *E*F is equal to 3.5 states/eV per unit cell, originating considerably from Ti *d* states together with a slight contribution from Si *p* states

Fig. 11. Calculated total and partial densities of states (PDOS) for (a) 4H-SiC and (b) Ti3SiC2. The Fermi level is set to zero and marked by a vertical dash line. The PDOS of Ti encompasses those of two types of nonequivalent Ti positions, Ti1 and Ti2.

#### **3.1.2 Surface properties**

294 Silicon Carbide – Materials, Processing and Applications in Electronic Devices

which tends to underestimate band gap. The band gap in Fig. 10(a) can also be seen from the total DOS shown in Fig. 11(a). Besides this gap around the Fermi level (*E*F), there is also a gap of more than 1 eV located at about -10 eV below the *E*F, dividing the entire VB into two parts. The lower part of the VB originates mainly from the bonding between the *s* states of the Si and C, while the upper one is dominated by *p* orbitals of Si and C in a form of *sp3* hybridization. The CB part, however, shows a continuum state throughout the whole

Fig. 10. Energy band structure of (a) 4H-SiC and (b) Ti3SiC2 along the major symmetric

considerably from Ti *d* states together with a slight contribution from Si *p* states

In contrast, Ti3SiC2 exhibits clearly a metallic nature with bands crossing the *E*F, as shown in Fig. 10(b), thereby resulting in a peak in the total DOS at *E*F in Fig. 11(b). It is worth noting that the presence of the band at *E*F is caused by the energetic overlap of Ti *d* states with the gap levels of SiC (Fig. 11(b)), not an artifact due to the DFT underestimation of band gap. This metallic character is in agreement with reported experimental results and other theoretical studies. From Fig. 10(b), one can see that the VB of Ti3SiC2 is also separated into two parts at approximately 5.7 eV below *E*F, the lower part of which is composed of metalloid states having a typical *s* symmetry while the upper part of which consists of complex bands. It is also clear from Fig. 11(b) that these complicated states just below *E*F are dominated by strongly hybridized bonding states containing mainly *p* orbitals of both Si and C and *d* orbitals of Ti. The contribution to the CB, however, comes predominantly from antibonding *d* states of Ti, as shown in the PDOS of Ti in Fig. 11(b). The magnitude of DOS at *E*F is equal to 3.5 states/eV per unit cell, originating

Fig. 11. Calculated total and partial densities of states (PDOS) for (a) 4H-SiC and (b) Ti3SiC2.

The Fermi level is set to zero and marked by a vertical dash line. The PDOS of Ti encompasses those of two types of nonequivalent Ti positions, Ti1 and Ti2.

region, which is reflected from interweaving lines above *E*F (Fig. 10(a)).

directions. The dotted lines in red denote the Fermi level (*E*F).

To simulate a bulklike interface, it is essential to ensure that the two sides of the interface slabs used in calculations are thick enough to exhibit a bulklike interior because properties of a thin film may differ significantly from those of the bulk. To determine the minimum layer necessary for a bulklike slab, we first performed calculations on the convergence of surface energy with respect to slab thickness and then considered an additional series of surface relaxations as a function of slab layers. The surface energy of Ti3SiC2, *σ*T, under pressure *P* and temperature *T* can be expressed as follows:

$$\sigma\_T = \frac{1}{2A} (E\_{slab}^{total} - N\_{Ti}\mu\_{Ti} - N\_{Si}\mu\_{Si} - N\_C\mu\_C - PV - TS) \tag{2}$$

where, *total Eslab* denotes total energy of a relaxed and isolated slab, and *μ*X, *NX* , *A* represent chemical potential of *X* (*X* = Ti, Si, C), number of *X* atoms in the slab, and surface area, respectively. For Eq. (2), the *TS* term can be deleted at 0 K and meanwhile, the *PV* term is negligible for low pressure because we are considering a condensed matter system. Further, chemical potential of condensed phase of Ti3SiC2, *μ*Ti3SiC2, can be given by a sum of three terms representing chemical potential of each species within the crystal:

$$
\mathfrak{\mu}\_{Ti\_3SiC\_2} = \mathfrak{3}\mathfrak{\mu}\_{Ti} + \mathfrak{\mu}\_{Si} + \mathfrak{2}\mathfrak{\mu}\_C. \tag{3}
$$

Since the total chemical potential of surface system, *μ*Ti3SiC2, is in equilibrium with that of its bulk, 3 2 *bulk ETi SiC* , we thus have

$$
\mu\_{Ti\_3SiC\_2} = E^{bulk}\_{Ti\_3SiC\_2} \,\text{.}\tag{4}
$$

Replacing Eq. (4) with Eqs. (2) and (3), one can eliminate the *μ*Ti3SiC2 and *μ*C variables in the surface energy of Ti3SiC2, *σ*T, and obtain

$$\boldsymbol{\sigma}\_{T} = \frac{1}{2\boldsymbol{A}} [\boldsymbol{E}\_{\text{slab}}^{\text{total}} - \frac{1}{2} \boldsymbol{N}\_{\text{C}} \boldsymbol{E}\_{\text{Ti}\_{\text{Si}}\text{Si}\_{\text{C}}}^{\text{bulk}} - \mu\_{\text{Ti}} (\boldsymbol{N}\_{\text{Ti}} - \frac{3}{2} \boldsymbol{N}\_{\text{C}}) - \mu\_{\text{Si}} (\boldsymbol{N}\_{\text{Si}} - \frac{1}{2} \boldsymbol{N}\_{\text{C}})].\tag{5}$$

When the chemical potentials of the Ti and Si equal total energies of the hexagonal closepacked bulk Ti, *bulk ETi* , and fcc bulk Si, *bulk ESi* , respectively, the Eq. (5) can be redefined as

$$\mathbf{G}\_{T}^{0} = \frac{1}{2A} [E\_{\text{slab}}^{\text{tstul}} - \frac{1}{2} N\_{\text{C}} E\_{Ti\_{3}\text{Sic}\_{2}}^{\text{bulk}} - E\_{Ti}^{\text{bulk}} \left( N\_{Ti} - \frac{3}{2} N\_{\text{C}} \right) - E\_{Si}^{\text{bulk}} \left( N\_{Si} - \frac{1}{2} N\_{\text{C}} \right)]. \tag{6}$$

Similarly, the surface energy of the SiC, <sup>0</sup> σ*<sup>S</sup>* , can be given by the following equation under the condition that chemical potential of Si is equal to its bulk total energy.

$$\mathbf{G}\_{\rm S}^{0} = \frac{1}{2A} \mathbf{I}\_{slab}^{total} - \mathbf{N}\_{\rm C} \mathbf{E}\_{\rm SiC}^{bulk} - \mathbf{E}\_{\rm Si}^{bulk} \left( \mathbf{N}\_{\rm Si} - \mathbf{N}\_{\rm C} \right) \tag{7}$$

Experimentally, the SiC(0001) plane was observed to be a favorable substrate surface that allows epitaxial growth of Ti3SiC2 with also a (0001)-oriented face. Four types of SiC terminations within the (0001) surface have been investigated, as shown in Fig. 12(b)**-**(e). In view of the unequal atom species at two sides of a stoichiometric slab, a non-stoichiometric

Introducing Ohmic Contacts into Silicon Carbide Technology 297

surface layers. Lastly, we also calculated the surface energies of the remaining terminations in Fig. 13(c)-(g) to be 4.10, 0.64, 1.12, 1.56 and 5.60 J/m2, respectively. In summary, we have calculated the bulk and surface properties for SiC and Ti3SiC2 and shown that these values are consistent with existing experimental and theoretical data, thereby offering not only detailed information but also a verification of applicability of the method and model for

A total of 96 possible candidate interface models have been considered within the above orientation relations, including four SiC terminations (Fig. 12(b)-(e)), six Ti3SiC2 terminations (Figs. 13(b)-(g)), and four different stacking sequences for each combination of SiC and Ti3SiC2 terminations. In the four stacking sequences, the interfacial Ti (C or Si) of Ti3SiC2 are located (i) on top (OT) of the surface atoms of SiC, (ii) at the center of the rhombic (RC) unit cell, (iii) above second-layer (SL) atoms of SiC, and (iv) above hollow sites (HS) of SiC, as shown in Fig. 14. These stacking sequences are of high symmetry and thus more likely to correspond to total-energy extrema. According to the surface calculations, our interface models are composed of a nine-layer symmetric SiC(0001) slab (bottom of Figs. 12(b)-(e)) connected to a symmetric Ti3SiC2(0001) slab (top of Fig. 13(b)-(g)) of at least 13 atomic layers. A 10 Å area of vacuum was added so as to minimize the coupling perpendicular to the interface. To form coherent interfaces, in-plane lattice constants of the Ti3SiC2 slab are expanded by 0.63% to match those of the harder SiC slab, while out-of-plane ones are fixed to their GGA optimized bulk values. Two steps were adopted to estimate *W*ad . First, total energies were calculated for various separations as two slabs were brought increasingly closer from a large initial separation. As a consequence, the total energy is found to behave likes a parabola, passing through a minimum at the equilibrium separation. The unrelaxed *W*ad was obtained by computing the energy difference between the interface at equilibrium separation and the unrelaxed isolated slabs. Next, full relaxation of each isolated slab and

further interface investigation.

**3.1.3 Interface construction and calculation process** 

interface slab was allowed, which yielded an estimate of relaxed *W*ad.

**3.1.4 Determination of interface atomic structure** 

Fig. 14. Schematic plots of four different stacking sequences. Only the Ti layer of Ti3SiC2 proximal to the interface is presented for clarity. The smallest red spheres, intermediate green spheres, and largest golden spheres represent C, Ti, and Si atoms, respectively. The dotted parallelogram outlines the SiC rhombic unit cell projected along the [0001] direction.

To clarify the mechanism theoretically, we first determined atomic structure of SiC/Ti3SiC2 interface via complementing the acquired HAADF image (Fig. 9). In light of bulk structures of 4H-SiC and Ti3SiC2, the aforementioned orientation relations, and the relative stacking order of Ti and Si, the observed image in Fig. 9 can be intuitively fitted by two models among all the 96 candidates: SiSi and SiCSi model (Fig. 15). In the SiSi model, the interfacial Si atoms of Ti3SiC2 sit above the hollow sites of interfacial Si plane of SiC, where the optimal distance between interfacial Si-Si planes (denoted as *d*1 in Fig. 15(a)) and that between

slab with identical surface layer must be used to extract surface energy of a particular termination. Initial convergence tests show that 10 Å of vacuum, 8×8×1 irreducible *k* points and a cut-off energy of 400 eV ensure total-energy convergence to less than 1 meV/atom. All of the atoms were fully relaxed until magnitude of force on every atom is smaller than 0.05 eV/Å. With these parameters, we first calculated surface energies of Si-terminated SiC with slabs varying from 5 to 17 layers using Eq. (7) and found that a 9-layer slab is enough to exhibit good convergence of surface energy. Next, we examined relaxation of the SiC(0001) surface slabs so as to ensure that they are reasonably converged with respect to slab layers. The SiC(0001) surface shows a low degree of interlayer relaxations with maximum of less than 3% of the bulk spacing for 9 or more layers thick.

Fig. 12. Schematic plot of 4H-SiC: (a) bulk, (b) Si1, (c) Si2, (d) C1, and (e) C2 terminations. The upper part shows the top view, while the lower one shows the side view. Only the top five of nine symmetric layers are presented for each termination.

Fig. 13. Top (upper part) and side (lower part) view of Ti3SiC2: (a) bulk, (b) Ti1(C), (c) C(Ti2), (d) Ti2(Si), (e) Si(Ti2), (f) Ti2(C), and (g) C(Ti1) termination. Only the top nine layers of each symmetric slab are presented for each termination.

The Ti3SiC2(0001) surface can be terminated with C, Si, any of two types of Ti (Ti1 and Ti2), or their combinations, yielding a total of six possible surface geometries. Figure 13(b)-(g) shows the six terminations: Ti1(C), C(Ti2), Ti2(Si), Si(Ti2), Ti2(C), and C(Ti1), where the letter in the brackets denotes sub-surface atom. The surface energies of Ti1(C) termination calculated using Eq. (6) is found to converge well to 0.84 J/m2 by a 13-layer-thick slab. Further, interlayer relaxations also show a good convergence for slabs having 13 layers or more. Contrast to the small relaxation presented in the SiC(0001), here there is a larger interlayer relaxation, especially for the first layer, which attenuates rapidly within two

slab with identical surface layer must be used to extract surface energy of a particular termination. Initial convergence tests show that 10 Å of vacuum, 8×8×1 irreducible *k* points and a cut-off energy of 400 eV ensure total-energy convergence to less than 1 meV/atom. All of the atoms were fully relaxed until magnitude of force on every atom is smaller than 0.05 eV/Å. With these parameters, we first calculated surface energies of Si-terminated SiC with slabs varying from 5 to 17 layers using Eq. (7) and found that a 9-layer slab is enough to exhibit good convergence of surface energy. Next, we examined relaxation of the SiC(0001) surface slabs so as to ensure that they are reasonably converged with respect to slab layers. The SiC(0001) surface shows a low degree of interlayer relaxations with maximum of less

Fig. 12. Schematic plot of 4H-SiC: (a) bulk, (b) Si1, (c) Si2, (d) C1, and (e) C2 terminations. The upper part shows the top view, while the lower one shows the side view. Only the top

**(0001)** 

**(d)**

**(e)** 

**Si Ti2**  **(f)** 

**Ti2 C**

**(g)** 

**C Ti1** 

**(0001)**

**(d) (e)**

**(b) (c)**

Fig. 13. Top (upper part) and side (lower part) view of Ti3SiC2: (a) bulk, (b) Ti1(C), (c) C(Ti2), (d) Ti2(Si), (e) Si(Ti2), (f) Ti2(C), and (g) C(Ti1) termination. Only the top nine layers of each

**Ti2 Si** 

The Ti3SiC2(0001) surface can be terminated with C, Si, any of two types of Ti (Ti1 and Ti2), or their combinations, yielding a total of six possible surface geometries. Figure 13(b)-(g) shows the six terminations: Ti1(C), C(Ti2), Ti2(Si), Si(Ti2), Ti2(C), and C(Ti1), where the letter in the brackets denotes sub-surface atom. The surface energies of Ti1(C) termination calculated using Eq. (6) is found to converge well to 0.84 J/m2 by a 13-layer-thick slab. Further, interlayer relaxations also show a good convergence for slabs having 13 layers or more. Contrast to the small relaxation presented in the SiC(0001), here there is a larger interlayer relaxation, especially for the first layer, which attenuates rapidly within two

five of nine symmetric layers are presented for each termination.

**(c)** 

**C Ti2** 

**Ti1 C** 

**Si C**

symmetric slab are presented for each termination.

**(a)**

**Ti1 Si Ti2 C** 

**(b)**

than 3% of the bulk spacing for 9 or more layers thick.

**(a)**

surface layers. Lastly, we also calculated the surface energies of the remaining terminations in Fig. 13(c)-(g) to be 4.10, 0.64, 1.12, 1.56 and 5.60 J/m2, respectively. In summary, we have calculated the bulk and surface properties for SiC and Ti3SiC2 and shown that these values are consistent with existing experimental and theoretical data, thereby offering not only detailed information but also a verification of applicability of the method and model for further interface investigation.

#### **3.1.3 Interface construction and calculation process**

A total of 96 possible candidate interface models have been considered within the above orientation relations, including four SiC terminations (Fig. 12(b)-(e)), six Ti3SiC2 terminations (Figs. 13(b)-(g)), and four different stacking sequences for each combination of SiC and Ti3SiC2 terminations. In the four stacking sequences, the interfacial Ti (C or Si) of Ti3SiC2 are located (i) on top (OT) of the surface atoms of SiC, (ii) at the center of the rhombic (RC) unit cell, (iii) above second-layer (SL) atoms of SiC, and (iv) above hollow sites (HS) of SiC, as shown in Fig. 14. These stacking sequences are of high symmetry and thus more likely to correspond to total-energy extrema. According to the surface calculations, our interface models are composed of a nine-layer symmetric SiC(0001) slab (bottom of Figs. 12(b)-(e)) connected to a symmetric Ti3SiC2(0001) slab (top of Fig. 13(b)-(g)) of at least 13 atomic layers. A 10 Å area of vacuum was added so as to minimize the coupling perpendicular to the interface. To form coherent interfaces, in-plane lattice constants of the Ti3SiC2 slab are expanded by 0.63% to match those of the harder SiC slab, while out-of-plane ones are fixed to their GGA optimized bulk values. Two steps were adopted to estimate *W*ad . First, total energies were calculated for various separations as two slabs were brought increasingly closer from a large initial separation. As a consequence, the total energy is found to behave likes a parabola, passing through a minimum at the equilibrium separation. The unrelaxed *W*ad was obtained by computing the energy difference between the interface at equilibrium separation and the unrelaxed isolated slabs. Next, full relaxation of each isolated slab and interface slab was allowed, which yielded an estimate of relaxed *W*ad.

Fig. 14. Schematic plots of four different stacking sequences. Only the Ti layer of Ti3SiC2 proximal to the interface is presented for clarity. The smallest red spheres, intermediate green spheres, and largest golden spheres represent C, Ti, and Si atoms, respectively. The dotted parallelogram outlines the SiC rhombic unit cell projected along the [0001] direction.

#### **3.1.4 Determination of interface atomic structure**

To clarify the mechanism theoretically, we first determined atomic structure of SiC/Ti3SiC2 interface via complementing the acquired HAADF image (Fig. 9). In light of bulk structures of 4H-SiC and Ti3SiC2, the aforementioned orientation relations, and the relative stacking order of Ti and Si, the observed image in Fig. 9 can be intuitively fitted by two models among all the 96 candidates: SiSi and SiCSi model (Fig. 15). In the SiSi model, the interfacial Si atoms of Ti3SiC2 sit above the hollow sites of interfacial Si plane of SiC, where the optimal distance between interfacial Si-Si planes (denoted as *d*1 in Fig. 15(a)) and that between

Introducing Ohmic Contacts into Silicon Carbide Technology 299

seen in Fig. 15(a), thus matching the HAADF image geometrically. Quantitatively, the *d*1 and *d*2 distances are now 2.53 Å and 2.81 Å (see Table I), respectively, very close to the obtained experimental values. Therefore, the introduction of interfacial C monolayer resolves the inconsistencies between simulations and experiments. Finally, we superimpose the calculation-inferred atomic structure of SiCSi interface (Fig. 15(b)) onto the HAADF

*W*ad (J/m2) 1.62 6.81 2.06 *d*1 (Å) 2.13 2.31 2.36 *d*2 (Å) 2.53 2.81 2.97 SBH (eV) 1.05 0.60 1.10

Table 1. Relaxed *W*ad (J/m2), optimal interfacial distances *d*1 and *d*2 (Å), and calculated *p*type Schottky barrier heights (SBH) (eV) for the SiC/Ti3SiC2 interfaces without (SiSi) and with interfacial C (SiCSi), and for the SiC/Ti interface (SiTi). Refer to Fig. 15 for their

To further examine whether the determined interface has a less Schottky character, we calculated *p*-type Schottky barrier height (SBH), an important quantity in analyzing electric properties of a metal/semiconductor contact interface. The *p*-type SBH is calculated from the difference between the *EF* of interface supercell and the valence-band top of bulk SiC region. It should be noted that due to the well-known problem of discontinuity in the exchange-correlation potential across heterointerface, an exact quantitative estimation of SBH is unlikely. However, the qualitative comparisons between the calculated SBHs for different interface configurations should be reliable. The *p*-type SBHs for the SiC/Ti3SiC2 interfaces with and without interfacial C are listed in Table I, where the SBH for the SiTi interface (Fig. 15(c)) is listed as well for comparison. From this Table, one can see that the

SiCSi interface shows the lowest SBH, meaning that it is of the least Schottky nature.

To shed light on origin of decrease in SBH and junction strengthening in the SiCSi interface, several analytic approaches were applied to characterize in detail interfacial electronic states and bonding nature. First, we calculated planar-averaged charge density and its difference along the interface normal. The density difference is evaluated by subtracting the sum of charge density of isolated SiC and Ti3SiC2 slabs from the total interface charge density. As seen in Fig. 16(a), after introducing the C, an interfacial Si-C pair is generated in the SiCSi case in a way similar to the pair in bulk SiC. As a result of the formation of the pair, there is a dramatic accumulation of charge within the interfacial region, in contrast to what is seen in either the SiSi or SiTi interface (Fig. 16(a)). This indicates that the covalent bonding is strengthened for the SiCSi. Evidently, the large degree of charge accumulation at interface is at the expense of depletion of charge in the sub-interfacial layers between Si and Ti, suggestive of weakened bonding between them. This is a short-range effect, however, since the charge density returns to its bulk value by the second layer. From Fig. 16(b), we note that the planar-averaged density difference for the SiCSi most prominently deviates from zero around the interface, reflecting the most significant charge transfer between SiC and Ti3SiC2 slabs. In addition, charge is

SiSi SiCSi SiTi

image (Fig. 9(a)) and find that they match very well.

**3.1.6 Electronic structure and chemical bonding** 

schematic configurations

**3.1.5 Schottky barrier height** 

interfacial Si-Si atoms projected onto paper plane (denoted as *d*2 in Fig. 15(a)) are calculated to be 2.13 and 2.53 Å (Table I), respectively. These distances, however, deviate severely from their average experimental values, 2.5 and 2.8 Å, which are obtained by characterizing quantitatively the HAADF image (Fig. 9(a)). In addition, an examination of interface stability by calculating the *W*ad indicates that the SiSi model is not favored at all (1.62 J/m2). It is even less stable than the model with interfacial Si of Ti3SiC2 resting straight atop the interfacial Si of SiC (2.58 J/m2), which contravenes again the observed image. Why does the less preferred interface predicted by our simulations emerge in experiments? It is worth noting that many other regions have been examined using the STEM but no other possibility is observed.

Fig. 15. Relaxed SiC(0001)/Ti3SiC2(0001) interface models (a) without interfacial C atoms (SiSi) and (b) with interfacial C atoms (SiCSi). (c) Optimized SiC(0001)/Ti(0001) interface model. The distance between interfacial Si-Si layers (Si-Ti layers for (c)) is represented by *d*1 and that between interfacial Si-Si atoms (Si-Ti atoms for (c)) projected onto the paper plane by *d*2. The interfaces are represented by dotted lines.

Could these pronounced discrepancies between results of experiment and calculation be ascribed to computational inaccuracies? Since the calculation parameters described above are verified to be sufficient to ensure a total energy precision of better than 1 meV/atom, one might be concerned that another numerical inaccuracy arises from size effect of the used slabs. However, we found this inaccuracy to be within 0.1 J/m2 via enlarging the slabs along the interface, so that it does not affect our simulated *W*ad. In addition, convergence tests show that the used slab thickness yields surface energy convergence to smaller than 0.02 J/m2. Furthermore, the used GGA functional was tested to evaluate bulk lattice constants and distances between atoms within an error of less than 0.5%. Finally, there is a small lattice mismatch of 0.63% at interface, which can be damped out by structural optimization. Moreover, Wang et al. have reported that a lattice mismatch as large as 3.9% at an interface varies the *W*ad only by less than 5% (Wang et al., 2002). Therefore, it seems that the discrepancies should not simply be attributed to the computational error.

To resolve these paradoxes, we noticed that a possibility might be ignored, that is, the unseen C might be trapped at interface, altering the local environment there. To test this hypothesis, the other SiCSi model was established by introducing C into the interfacial layer from the consideration of crystal extension and stacking sequences. The calculated *W*ad of this SiCSi model is listed in Table I, where the interface is strengthened substantially after the incorporation of C. Investigation into its fully optimized atomic configuration (Fig. 15(b)) reveals that the incorporation of C does not induce significant interface reconstruction. Namely, the two Si layers proximal to the interface maintain the stacking seen in Fig. 15(a), thus matching the HAADF image geometrically. Quantitatively, the *d*1 and *d*2 distances are now 2.53 Å and 2.81 Å (see Table I), respectively, very close to the obtained experimental values. Therefore, the introduction of interfacial C monolayer resolves the inconsistencies between simulations and experiments. Finally, we superimpose the calculation-inferred atomic structure of SiCSi interface (Fig. 15(b)) onto the HAADF image (Fig. 9(a)) and find that they match very well.


Table 1. Relaxed *W*ad (J/m2), optimal interfacial distances *d*1 and *d*2 (Å), and calculated *p*type Schottky barrier heights (SBH) (eV) for the SiC/Ti3SiC2 interfaces without (SiSi) and with interfacial C (SiCSi), and for the SiC/Ti interface (SiTi). Refer to Fig. 15 for their schematic configurations

#### **3.1.5 Schottky barrier height**

298 Silicon Carbide – Materials, Processing and Applications in Electronic Devices

interfacial Si-Si atoms projected onto paper plane (denoted as *d*2 in Fig. 15(a)) are calculated to be 2.13 and 2.53 Å (Table I), respectively. These distances, however, deviate severely from their average experimental values, 2.5 and 2.8 Å, which are obtained by characterizing quantitatively the HAADF image (Fig. 9(a)). In addition, an examination of interface stability by calculating the *W*ad indicates that the SiSi model is not favored at all (1.62 J/m2). It is even less stable than the model with interfacial Si of Ti3SiC2 resting straight atop the interfacial Si of SiC (2.58 J/m2), which contravenes again the observed image. Why does the less preferred interface predicted by our simulations emerge in experiments? It is worth noting that many other regions have been examined using the STEM but no other possibility

**(a) (b) (c)**

Fig. 15. Relaxed SiC(0001)/Ti3SiC2(0001) interface models (a) without interfacial C atoms (SiSi) and (b) with interfacial C atoms (SiCSi). (c) Optimized SiC(0001)/Ti(0001) interface model. The distance between interfacial Si-Si layers (Si-Ti layers for (c)) is represented by *d*1 and that between interfacial Si-Si atoms (Si-Ti atoms for (c)) projected onto the paper plane

*d1 d2*

Could these pronounced discrepancies between results of experiment and calculation be ascribed to computational inaccuracies? Since the calculation parameters described above are verified to be sufficient to ensure a total energy precision of better than 1 meV/atom, one might be concerned that another numerical inaccuracy arises from size effect of the used slabs. However, we found this inaccuracy to be within 0.1 J/m2 via enlarging the slabs along the interface, so that it does not affect our simulated *W*ad. In addition, convergence tests show that the used slab thickness yields surface energy convergence to smaller than 0.02 J/m2. Furthermore, the used GGA functional was tested to evaluate bulk lattice constants and distances between atoms within an error of less than 0.5%. Finally, there is a small lattice mismatch of 0.63% at interface, which can be damped out by structural optimization. Moreover, Wang et al. have reported that a lattice mismatch as large as 3.9% at an interface varies the *W*ad only by less than 5% (Wang et al., 2002). Therefore, it seems that the

To resolve these paradoxes, we noticed that a possibility might be ignored, that is, the unseen C might be trapped at interface, altering the local environment there. To test this hypothesis, the other SiCSi model was established by introducing C into the interfacial layer from the consideration of crystal extension and stacking sequences. The calculated *W*ad of this SiCSi model is listed in Table I, where the interface is strengthened substantially after the incorporation of C. Investigation into its fully optimized atomic configuration (Fig. 15(b)) reveals that the incorporation of C does not induce significant interface reconstruction. Namely, the two Si layers proximal to the interface maintain the stacking

discrepancies should not simply be attributed to the computational error.

by *d*2. The interfaces are represented by dotted lines.

is observed.

To further examine whether the determined interface has a less Schottky character, we calculated *p*-type Schottky barrier height (SBH), an important quantity in analyzing electric properties of a metal/semiconductor contact interface. The *p*-type SBH is calculated from the difference between the *EF* of interface supercell and the valence-band top of bulk SiC region. It should be noted that due to the well-known problem of discontinuity in the exchange-correlation potential across heterointerface, an exact quantitative estimation of SBH is unlikely. However, the qualitative comparisons between the calculated SBHs for different interface configurations should be reliable. The *p*-type SBHs for the SiC/Ti3SiC2 interfaces with and without interfacial C are listed in Table I, where the SBH for the SiTi interface (Fig. 15(c)) is listed as well for comparison. From this Table, one can see that the SiCSi interface shows the lowest SBH, meaning that it is of the least Schottky nature.

#### **3.1.6 Electronic structure and chemical bonding**

To shed light on origin of decrease in SBH and junction strengthening in the SiCSi interface, several analytic approaches were applied to characterize in detail interfacial electronic states and bonding nature. First, we calculated planar-averaged charge density and its difference along the interface normal. The density difference is evaluated by subtracting the sum of charge density of isolated SiC and Ti3SiC2 slabs from the total interface charge density. As seen in Fig. 16(a), after introducing the C, an interfacial Si-C pair is generated in the SiCSi case in a way similar to the pair in bulk SiC. As a result of the formation of the pair, there is a dramatic accumulation of charge within the interfacial region, in contrast to what is seen in either the SiSi or SiTi interface (Fig. 16(a)). This indicates that the covalent bonding is strengthened for the SiCSi. Evidently, the large degree of charge accumulation at interface is at the expense of depletion of charge in the sub-interfacial layers between Si and Ti, suggestive of weakened bonding between them. This is a short-range effect, however, since the charge density returns to its bulk value by the second layer. From Fig. 16(b), we note that the planar-averaged density difference for the SiCSi most prominently deviates from zero around the interface, reflecting the most significant charge transfer between SiC and Ti3SiC2 slabs. In addition, charge is

Introducing Ohmic Contacts into Silicon Carbide Technology 301

further confirmed from the density-difference plot (Fig. 19(c)) displaying charge accumulation along the interfacial Si-Ti bonds. The amount of charge accumulated on the Si-Ti bonds is larger than that on the interfacial Si-Si bonds of SiSi (Fig. 19(a)) but far less significant than that on the interfacial Si-C bonds of SiCSi (Fig. 19(b)). This heaviest charge accumulation along the interfacial Si-C bonds, together with the mixed covalent-ionic character at the SiCSi interface, explains the largest *W*ad associated with the SiCSi interface (Table I). Finally, we note from both figures that charge variations due to the interface are screened rapidly with distance from interface, suggesting that the interface effect is confined to within a short range, in agreement

Fig. 17. PDOS (states/eV atom) projected on the atomic layers close to the relaxed SiCSi interface. The left panel shows PDOSs of SiC layers and the right one those of Ti3SiC2 layers.

Fig. 18. Contour plots of charge densities for (a) SiSi, (b) SiCSi, and (c) SiTi interfaces taken along the (11-20) plane. The interface is represented by a horizontal line and the atoms that

**0.00**

**0.17** 

**0.33**

**0.50**

intersect the contour plane are labeled.

The first layer is the atomic layer proximal to interface. The *EF* is set to zero.

**(a) (b) (c)**

with the previous analyses on PDOS and planar-averaged charge.

observed to be depleted noticeably in both the sub-interfacial SiC and Ti3SiC2 region for the SiCSi, suggesting that the atoms second nearest to the interface contribute to the interfacial bonding. These missing charges, to a large extent, make their way onto the more electronegative C ions, indicative of formation of ionic bonding.

Fig. 16. Planar-averaged (a) total charge density and (b) charge-density difference for the relaxed SiSi, SiCSi, and SiTi interfaces along [0001] direction. The solid rectangles, circles, and triangles give the locations of C, Si, and Ti atoms, respectively. The interface position is set to zero and indicated by a vertical line

Figure 17 presents DOS projected on selected atomic layers of the SiCSi interface in order to gain insight into electronic states. Overall PDOS shape of interfacial Si of Ti3SiC2 resembles to some extent that of a Si layer deeper in SiC but deviates remarkably from that of a Si layer deeper in Ti3SiC2 (7th layer), which can be reflected from the formation of Si-C pair. Moreover, this suggests that the substrate has a fundamental effect on the interface electronically. A key feature in this figure is that a strong interaction is observed between the sub-interfacial Ti *d* and Si *p* states below *EF*, which continues well into the SiC surface, inducing noticeable gap states in the interfacial C at *EF*. This means that the interfacial C layer, the first monolayer on the substrate, is metallized, indicative of possible electric conductivity. In fact, the gap states can extend as far as they can into deeper layers of SiC, as there appear weak but visible peaks at *EF* in the PDOSs of the 2nd and 3rd layers of SiC. Consequently, a local weak metallicity might occur in top few layers of the semiconductor surface, which could enable current flow through the SiC. Apart from the peaks in SiC, all of the Ti3SiC2 layers exhibit notable peaks at *EF*, which can be attributed to the large degree of overlap between Ti *d* and C (Si) *p* states. Finally, we note significant hybridization between the interfacial C *sp* and Si *sp* states, suggestive of covalent bonding at interface.

To identify the bonding type directly, we further show contour plots of charge densities (Fig. 18) and their differences (Fig. 19) along the (11-20) plane for the optimized SiSi, SiCSi and SiTi interfaces. From Fig. 18, we notice first that the bonding interaction between the interfacial Si and C for the SiCSi interface is remarkably similar to the Si-C interaction deeper into SiC: the majority of charge is localized on C with humps directed towards their adjacent Si. We thus conclude that the interfacial bonding for the SiCSi is of mixed covalent-ionic nature. The interfacial bonds for the SiSi interface, however, exhibit covalent character with a small amount of charge accumulated within the interfacial region (Fig. 18(a)), in consistence with our analyses on planar-averaged density-difference (Fig. 16). As for the SiTi, the charge distribution of interfacial Ti is almost identical to that of Ti away from interface, having a character of weakly but broadly distributed charge density. This indicates that the interfacial bonds for the SiTi take on weakly metallic nature, yet maintain a small degree of covalency. The covalency can be

observed to be depleted noticeably in both the sub-interfacial SiC and Ti3SiC2 region for the SiCSi, suggesting that the atoms second nearest to the interface contribute to the interfacial bonding. These missing charges, to a large extent, make their way onto the more

Fig. 16. Planar-averaged (a) total charge density and (b) charge-density difference for the relaxed SiSi, SiCSi, and SiTi interfaces along [0001] direction. The solid rectangles, circles, and triangles give the locations of C, Si, and Ti atoms, respectively. The interface position is

Figure 17 presents DOS projected on selected atomic layers of the SiCSi interface in order to gain insight into electronic states. Overall PDOS shape of interfacial Si of Ti3SiC2 resembles to some extent that of a Si layer deeper in SiC but deviates remarkably from that of a Si layer deeper in Ti3SiC2 (7th layer), which can be reflected from the formation of Si-C pair. Moreover, this suggests that the substrate has a fundamental effect on the interface electronically. A key feature in this figure is that a strong interaction is observed between the sub-interfacial Ti *d* and Si *p* states below *EF*, which continues well into the SiC surface, inducing noticeable gap states in the interfacial C at *EF*. This means that the interfacial C layer, the first monolayer on the substrate, is metallized, indicative of possible electric conductivity. In fact, the gap states can extend as far as they can into deeper layers of SiC, as there appear weak but visible peaks at *EF* in the PDOSs of the 2nd and 3rd layers of SiC. Consequently, a local weak metallicity might occur in top few layers of the semiconductor surface, which could enable current flow through the SiC. Apart from the peaks in SiC, all of the Ti3SiC2 layers exhibit notable peaks at *EF*, which can be attributed to the large degree of overlap between Ti *d* and C (Si) *p* states. Finally, we note significant hybridization between

the interfacial C *sp* and Si *sp* states, suggestive of covalent bonding at interface.

To identify the bonding type directly, we further show contour plots of charge densities (Fig. 18) and their differences (Fig. 19) along the (11-20) plane for the optimized SiSi, SiCSi and SiTi interfaces. From Fig. 18, we notice first that the bonding interaction between the interfacial Si and C for the SiCSi interface is remarkably similar to the Si-C interaction deeper into SiC: the majority of charge is localized on C with humps directed towards their adjacent Si. We thus conclude that the interfacial bonding for the SiCSi is of mixed covalent-ionic nature. The interfacial bonds for the SiSi interface, however, exhibit covalent character with a small amount of charge accumulated within the interfacial region (Fig. 18(a)), in consistence with our analyses on planar-averaged density-difference (Fig. 16). As for the SiTi, the charge distribution of interfacial Ti is almost identical to that of Ti away from interface, having a character of weakly but broadly distributed charge density. This indicates that the interfacial bonds for the SiTi take on weakly metallic nature, yet maintain a small degree of covalency. The covalency can be

electronegative C ions, indicative of formation of ionic bonding.

set to zero and indicated by a vertical line

further confirmed from the density-difference plot (Fig. 19(c)) displaying charge accumulation along the interfacial Si-Ti bonds. The amount of charge accumulated on the Si-Ti bonds is larger than that on the interfacial Si-Si bonds of SiSi (Fig. 19(a)) but far less significant than that on the interfacial Si-C bonds of SiCSi (Fig. 19(b)). This heaviest charge accumulation along the interfacial Si-C bonds, together with the mixed covalent-ionic character at the SiCSi interface, explains the largest *W*ad associated with the SiCSi interface (Table I). Finally, we note from both figures that charge variations due to the interface are screened rapidly with distance from interface, suggesting that the interface effect is confined to within a short range, in agreement with the previous analyses on PDOS and planar-averaged charge.

Fig. 17. PDOS (states/eV atom) projected on the atomic layers close to the relaxed SiCSi interface. The left panel shows PDOSs of SiC layers and the right one those of Ti3SiC2 layers. The first layer is the atomic layer proximal to interface. The *EF* is set to zero.

Fig. 18. Contour plots of charge densities for (a) SiSi, (b) SiCSi, and (c) SiTi interfaces taken along the (11-20) plane. The interface is represented by a horizontal line and the atoms that intersect the contour plane are labeled.

Introducing Ohmic Contacts into Silicon Carbide Technology 303

Although the charge-distribution analysis can reveal valuable information on interfacial bonding, it provides restrained insight into how electrons distribute around *EF*, which matters because density around *EF* directly determines the current transmission. Figure 21 illustrates an electron-density isosurface and its slice along the (11-20) plane for the optimized SiCSi interface around *EF*. From Fig. 21(a), one can see that charges surrounding interfacial Si are connected and broadly distributed in a sheet-like fashion, which suggests a possible electrical conductivity through this region. In addition, there also appear heavily accumulated electrons within the interfacial area, which are connected along the interface and extended as far as several atomic layers into the SiC. These characters can also be confirmed from the slice plot in Fig. 21(b), meaning that current might flow over the top few atomic layers of semiconductor, thereby causing Ohmic property. As expected, the electron density at *EF* is extremely high for the Ti3SiC2 (i.e., sea of electrons) but becomes nil for the SiC layers away from interface (Fig. 21(b)), which can be understood from their intrinsic

To examine electrical conductivity and gain insight into how the interface influences current transport, we devised a two-probe system, Ti/Ti3SiC2/SiC/Ti3SiC2/Ti, and investigated nonequilibrium quantum transport properties. Figure 22(a) schematically shows a model of the sandwich transport system, which can be divided into a left semi-infinite electrode, a scattering region, and a right semi-infinite electrode. The scattering region consists of hexagonal SiC and Ti3SiC2 layers and the periodic boundary conditions are imposed along the directions parallel to the interface. The SiC/Ti3SiC2 interface could be either the SiSi or SiCSi, whereas other interfaces are maintained identical for the sandwich systems. In this sense, the difference between the two systems can be mainly attributed to their differing SiC/Ti3SiC2 interfaces. Furthermore, we also calculated the Ti/SiC/Ti system, wherein the

Fig. 21. Isosurface and (b) electron density plot along the (11-20) plane in the energy window

(*EF*-0.5 eV, *EF*) for the SiCSi interface. The interface is marked by two arrows.

**3.1.7 Electron density near fermi level** 

metallic and semiconducting nature.

**3.1.8 Quantum electron transport property** 

SiTi model shown in Fig. 15(c) was taken as the SiC/Ti interface.

To further explain the decrease in SBH for the SiCSi, we plotted the variation of electrostatic potential along the interface normal in Fig. 20, where potential changes for the SiSi and SiTi interfaces are shown as well. As a result of the large interface dipole generated by the considerable charge transfer (Fig. 16(b)) and the partial ionicity (Fig. 18(b)), the electrostatic potential of interfacial Si in the SiCSi is lowered significantly relative to its adjacent SiC region (Fig. 20(b)), which consequently enables the reduction of SBH. This is contrary to the SiSi (Fig. 20(a)) and SiTi (Fig. 20(c)) cases, as their electrostatic potentials are high at interface. These high potentials indicate that electrons might be transferred from the SiC surface to the interface, resulting in electron depletion on substrate surface. Moreover, we note in Fig. 20 that electrostatic potential for Si atoms is always lower than that for the Ti or C atoms, which explains the lower electron density of Si shown in the charge-distribution plot (Fig. 18).

Fig. 19. Contour plots of charge-density differences for (a) SiSi, (b) SiCSi, and (c) SiTi interfaces taken along the (11-20) plane. The difference of charge density presents redistribution of charge in the interface relative to its isolated system.

Fig. 20. Electrostatic potential as a function of distance from interface along the [0001] direction for (a) SiSi, (b) SiCSi, and (c) SiTi interfaces. Interface position is set to zero.

#### **3.1.7 Electron density near fermi level**

302 Silicon Carbide – Materials, Processing and Applications in Electronic Devices

To further explain the decrease in SBH for the SiCSi, we plotted the variation of electrostatic potential along the interface normal in Fig. 20, where potential changes for the SiSi and SiTi interfaces are shown as well. As a result of the large interface dipole generated by the considerable charge transfer (Fig. 16(b)) and the partial ionicity (Fig. 18(b)), the electrostatic potential of interfacial Si in the SiCSi is lowered significantly relative to its adjacent SiC region (Fig. 20(b)), which consequently enables the reduction of SBH. This is contrary to the SiSi (Fig. 20(a)) and SiTi (Fig. 20(c)) cases, as their electrostatic potentials are high at interface. These high potentials indicate that electrons might be transferred from the SiC surface to the interface, resulting in electron depletion on substrate surface. Moreover, we note in Fig. 20 that electrostatic potential for Si atoms is always lower than that for the Ti or C atoms, which

explains the lower electron density of Si shown in the charge-distribution plot (Fig. 18).

**(a) (b) (c)**

Fig. 19. Contour plots of charge-density differences for (a) SiSi, (b) SiCSi, and (c) SiTi interfaces taken along the (11-20) plane. The difference of charge density presents

**-0.25** 

**-0.10**

**0.05**

**0.20**

Fig. 20. Electrostatic potential as a function of distance from interface along the [0001] direction for (a) SiSi, (b) SiCSi, and (c) SiTi interfaces. Interface position is set to zero.

redistribution of charge in the interface relative to its isolated system.

Although the charge-distribution analysis can reveal valuable information on interfacial bonding, it provides restrained insight into how electrons distribute around *EF*, which matters because density around *EF* directly determines the current transmission. Figure 21 illustrates an electron-density isosurface and its slice along the (11-20) plane for the optimized SiCSi interface around *EF*. From Fig. 21(a), one can see that charges surrounding interfacial Si are connected and broadly distributed in a sheet-like fashion, which suggests a possible electrical conductivity through this region. In addition, there also appear heavily accumulated electrons within the interfacial area, which are connected along the interface and extended as far as several atomic layers into the SiC. These characters can also be confirmed from the slice plot in Fig. 21(b), meaning that current might flow over the top few atomic layers of semiconductor, thereby causing Ohmic property. As expected, the electron density at *EF* is extremely high for the Ti3SiC2 (i.e., sea of electrons) but becomes nil for the SiC layers away from interface (Fig. 21(b)), which can be understood from their intrinsic metallic and semiconducting nature.

#### **3.1.8 Quantum electron transport property**

To examine electrical conductivity and gain insight into how the interface influences current transport, we devised a two-probe system, Ti/Ti3SiC2/SiC/Ti3SiC2/Ti, and investigated nonequilibrium quantum transport properties. Figure 22(a) schematically shows a model of the sandwich transport system, which can be divided into a left semi-infinite electrode, a scattering region, and a right semi-infinite electrode. The scattering region consists of hexagonal SiC and Ti3SiC2 layers and the periodic boundary conditions are imposed along the directions parallel to the interface. The SiC/Ti3SiC2 interface could be either the SiSi or SiCSi, whereas other interfaces are maintained identical for the sandwich systems. In this sense, the difference between the two systems can be mainly attributed to their differing SiC/Ti3SiC2 interfaces. Furthermore, we also calculated the Ti/SiC/Ti system, wherein the SiTi model shown in Fig. 15(c) was taken as the SiC/Ti interface.

Fig. 21. Isosurface and (b) electron density plot along the (11-20) plane in the energy window (*EF*-0.5 eV, *EF*) for the SiCSi interface. The interface is marked by two arrows.

Introducing Ohmic Contacts into Silicon Carbide Technology 305

the possible enhancement of electric field at these features and semiconductor doping at these locations, (3) formation of intermediate semiconductor layer between the deposited metals and semiconductor, which consists of silicides or carbides, could divide the high

The findings presented first demonstrate that no Al is clearly segregated around the interfacial region, in particular at the top few layers of SiC, which rules out the possibility of additional Al doping. Though a small amount of residual Al is found to be present, mostly in a form of Al4C3 compound, it may locate on the surface of annealed contacts rather than in the layer directly contacted to the SiC, thus playing a negligible role in Ohmic contact formation. The majority of deposited Al is evaporated during annealing because of its low melting point and high equilibrium vapor pressure. The dominant role played by Al in the TiAl system is to assist the formation of liquid alloy so as to facilitate chemical reaction. Furthermore, careful characterization of the interfacial region reveals that the substrate and the generated compound are epitaxially oriented and well matched at interface with no clear evidence of high density of defects. This suggests that the morphology might not be the key to understanding the contact formation. In support of this speculation, it has been observed previously that Ti Ohmic contacts can be possibly generated without any pitting and that

One remaining theory is the alloy-assisted Ohmic contact formation. This alloy is determined to be ternary Ti3SiC2, which has also been corroborated by other expriments. Since the bulk Ti3SiC2 has already been found to be of metallic nature both in experiment and theory, the contact between Ti3SiC2 and its covered metals should show Ohmic character and thus the SiC/Ti3SiC2 interface should play a significant role in Ohmic contact formation. This idea is supported by the fact that the determined interface has a lowered SBH due to the large dipole shift at interface induced by the partial ionicity and the considerable charge transfer. In addition, the interfacial states, as indicated by the electron distribution at *EF*, are also viewed as a contributing factor in reducing the SBH. These states might be further enhanced by the possible presence of point defects at interface, although

The calculations predict that an atomic layer of carbon emerges as the first monolayer of Ohmic contacts, which eventually affects interface electronic structure. Such trapped carbon was previously studied in both other interfacial systems theoretically by DFT and the TiNi Ohmic contacts on 4H-SiC experimentally by Auger electron spectroscopy (Ohyanagi et al., 2008). It was proposed that the carbon could be segregated to interfacial area, strengthening interface substantially and reducing Schottky barrier dramatically. Further, it was reported that the Ohmic contact can be realized by depositing carbon films only onto the SiC substrate, indicative of the determinative role of carbon in the Ohmic contact formation (Lu et al., 2003). The important role played by carbon can be traced to the two interfacial Si layers, which provide possible sites for carbon segregation due to the strong Si-C interaction. Finally, recent observation shows that atomic-scale Ti3SiC2-like bilayer can be embeded in the SiC interior, forming an atomically ordered multilayer that exhibits an unexpected electronic state with the point Fermi surface. The valence charge is found to be confined largely within the bilayer in a spatially connected way, which serves as a possible

Several experimental methods can be used to probe the Ohmic character of Ti3SiC2 contacts on SiC discussed in this chapter. For example, based on the results regarding morphology of grown layers, epitaxial Ti3SiC2 layers can be deposited directly onto the SiC substrate by

barrier height into lower ones, thus reducing the effective barrier height.

these structural defects have not been detected by the TEM study.

conducting channel to enhance the current flow over the semiconductor.

pit-free Ohmic contacts can be fabricated.

Fig. 22. Schematic plot of a two-probe Ti/Ti3SiC2/SiC/Ti3SiC2/Ti transport system. The system has infinite extent in the (*x*, *y*) directions and extends to ± ∞ in the *z* direction. (b) Transmission spectra under 0 V and (c) *I-V* curves for the two relaxed systems including the SiSi and SiCSi interfaces. The *I-V* curve for the system including the SiTi interface is also shown for comparison. Difference in effective potential along the (11-20) plane under an applied bias voltage of 0.4 V for (d) SiSi and (e) SiCSi cases

Figure 22(b) shows transmission spectra for the relaxed SiSi, SiCSi, and SiTi systems, where one can see that the spectra differ from one another suggesting variations in electronic structures with interface geometries. The most interesting feature is the presence of transmission peaks at *EF* for the SiCSi, which is attributable to the electrons distributed around the interface at *EF*. Further calculations on electrical properties (e.g., *I−V* curve) for the three systems reveal that the current in the SiCSi case increases much faster than either the SiSi or SiTi case as the applied bias voltage increases (Fig. 22(b)), which can be explained by its lowest SBH (Table I). Finally, in comparing the general trend of the calculated *I−V* with that of the experimental curve (Fig. 1), we find that they agree qualitatively: both the annealed specimen and the SiCSi model clearly show Ohmic behavior, thereby validating the application of the SiCSi model to describe the Ohmic contacts in the TiAl-based system. Finally, we examined how applied bias voltages vary from the interface to the SiC region. Figure 22(d) and (e) illustrate the difference in effective potential along the (11-20) plane between the bias voltage of 0.4 V and the one of 0.0 V for the two relaxed systems including SiSi and SiCSi. One can see that the voltage drops less intensively from interface to SiC in the SiCSi case, suggestive of a less Schottky nature.

#### **4. Discussion and conclusion**

The current understanding of formation origin of Ohmic contact, which is based mainly on experimental studies of property measurement and structure characterization, can be summarized in three main points: (1) the deposited Al (80 at%) might diffuse in part into the SiC and dope heavily the semiconductor because Al is well-known to act as a *p*-type dopant for SiC, (2) the high density of pits, spikes, or dislocations may be generated underneath the contacts after annealing so that current can transport primarily through these defects due to

Fig. 22. Schematic plot of a two-probe Ti/Ti3SiC2/SiC/Ti3SiC2/Ti transport system. The system has infinite extent in the (*x*, *y*) directions and extends to ± ∞ in the *z* direction. (b) Transmission spectra under 0 V and (c) *I-V* curves for the two relaxed systems including the SiSi and SiCSi interfaces. The *I-V* curve for the system including the SiTi interface is also shown for comparison. Difference in effective potential along the (11-20) plane under an

Figure 22(b) shows transmission spectra for the relaxed SiSi, SiCSi, and SiTi systems, where one can see that the spectra differ from one another suggesting variations in electronic structures with interface geometries. The most interesting feature is the presence of transmission peaks at *EF* for the SiCSi, which is attributable to the electrons distributed around the interface at *EF*. Further calculations on electrical properties (e.g., *I−V* curve) for the three systems reveal that the current in the SiCSi case increases much faster than either the SiSi or SiTi case as the applied bias voltage increases (Fig. 22(b)), which can be explained by its lowest SBH (Table I). Finally, in comparing the general trend of the calculated *I−V* with that of the experimental curve (Fig. 1), we find that they agree qualitatively: both the annealed specimen and the SiCSi model clearly show Ohmic behavior, thereby validating the application of the SiCSi model to describe the Ohmic contacts in the TiAl-based system. Finally, we examined how applied bias voltages vary from the interface to the SiC region. Figure 22(d) and (e) illustrate the difference in effective potential along the (11-20) plane between the bias voltage of 0.4 V and the one of 0.0 V for the two relaxed systems including SiSi and SiCSi. One can see that the voltage drops less intensively from interface to SiC in

The current understanding of formation origin of Ohmic contact, which is based mainly on experimental studies of property measurement and structure characterization, can be summarized in three main points: (1) the deposited Al (80 at%) might diffuse in part into the SiC and dope heavily the semiconductor because Al is well-known to act as a *p*-type dopant for SiC, (2) the high density of pits, spikes, or dislocations may be generated underneath the contacts after annealing so that current can transport primarily through these defects due to

applied bias voltage of 0.4 V for (d) SiSi and (e) SiCSi cases

the SiCSi case, suggestive of a less Schottky nature.

**4. Discussion and conclusion** 

the possible enhancement of electric field at these features and semiconductor doping at these locations, (3) formation of intermediate semiconductor layer between the deposited metals and semiconductor, which consists of silicides or carbides, could divide the high barrier height into lower ones, thus reducing the effective barrier height.

The findings presented first demonstrate that no Al is clearly segregated around the interfacial region, in particular at the top few layers of SiC, which rules out the possibility of additional Al doping. Though a small amount of residual Al is found to be present, mostly in a form of Al4C3 compound, it may locate on the surface of annealed contacts rather than in the layer directly contacted to the SiC, thus playing a negligible role in Ohmic contact formation. The majority of deposited Al is evaporated during annealing because of its low melting point and high equilibrium vapor pressure. The dominant role played by Al in the TiAl system is to assist the formation of liquid alloy so as to facilitate chemical reaction. Furthermore, careful characterization of the interfacial region reveals that the substrate and the generated compound are epitaxially oriented and well matched at interface with no clear evidence of high density of defects. This suggests that the morphology might not be the key to understanding the contact formation. In support of this speculation, it has been observed previously that Ti Ohmic contacts can be possibly generated without any pitting and that pit-free Ohmic contacts can be fabricated.

One remaining theory is the alloy-assisted Ohmic contact formation. This alloy is determined to be ternary Ti3SiC2, which has also been corroborated by other expriments. Since the bulk Ti3SiC2 has already been found to be of metallic nature both in experiment and theory, the contact between Ti3SiC2 and its covered metals should show Ohmic character and thus the SiC/Ti3SiC2 interface should play a significant role in Ohmic contact formation. This idea is supported by the fact that the determined interface has a lowered SBH due to the large dipole shift at interface induced by the partial ionicity and the considerable charge transfer. In addition, the interfacial states, as indicated by the electron distribution at *EF*, are also viewed as a contributing factor in reducing the SBH. These states might be further enhanced by the possible presence of point defects at interface, although these structural defects have not been detected by the TEM study.

The calculations predict that an atomic layer of carbon emerges as the first monolayer of Ohmic contacts, which eventually affects interface electronic structure. Such trapped carbon was previously studied in both other interfacial systems theoretically by DFT and the TiNi Ohmic contacts on 4H-SiC experimentally by Auger electron spectroscopy (Ohyanagi et al., 2008). It was proposed that the carbon could be segregated to interfacial area, strengthening interface substantially and reducing Schottky barrier dramatically. Further, it was reported that the Ohmic contact can be realized by depositing carbon films only onto the SiC substrate, indicative of the determinative role of carbon in the Ohmic contact formation (Lu et al., 2003). The important role played by carbon can be traced to the two interfacial Si layers, which provide possible sites for carbon segregation due to the strong Si-C interaction. Finally, recent observation shows that atomic-scale Ti3SiC2-like bilayer can be embeded in the SiC interior, forming an atomically ordered multilayer that exhibits an unexpected electronic state with the point Fermi surface. The valence charge is found to be confined largely within the bilayer in a spatially connected way, which serves as a possible conducting channel to enhance the current flow over the semiconductor.

Several experimental methods can be used to probe the Ohmic character of Ti3SiC2 contacts on SiC discussed in this chapter. For example, based on the results regarding morphology of grown layers, epitaxial Ti3SiC2 layers can be deposited directly onto the SiC substrate by

Introducing Ohmic Contacts into Silicon Carbide Technology 307

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To summarize, we have determined in this chapter atomic-scale structure of Ohmic contacts on SiC and related it to electronic structure and electric property, aimed at understanding the formation mechanism of Ohmic contact in TiAl-based system. The combined HAADF-DFT study represents an important advance in relating structures to device properties at an atomic scale and is not limited to the contacts in SiC electronics. Our results show that the main product generated by chemical reaction can be epitaxial and have atomic bonds to the substrate. The contact interface, which could trap an atomic layer of carbon, enables lowered Schottky barrier due to the large interfacial dipole shift associated with the considerable charge transfer. These findings are relevant for technological improvement of contacts in SiC devices, and this chapter presents an important step towards addressing the current contact issues in wide-band-gap electronics.

#### **5. Acknowledgment**

We thank S. Watanabe (Univ. of Tokyo) for allowing our use of computational resources. The present study was supported in part by a Grant-in-Aid for Scientific Research on Priority Area, "Atomic Scale Modification (474)" from the Ministry of Education, Culture, Sports, Science, and Technology of Japan. Z. W acknowledges financial supports from the Grant-in-Aid for Young Scientists (B) (Grant No. 22760500), the IKETANI Science and Technology Foundation (Grant No. 0221047-A), and the IZUMI Science and Technology Foundation. S. T. thanks the supports from Nippon Sheet Glass Foundation and the MURATA Science Foundation. The calculations were carried out on a parallel SR11000 supercomputer at the Institute for Solid State Physics, Univ. of Tokyo.

#### **6. References**


means of sputtering, molecular bean epitaxy (MBE), or pulsed-laser deposition (PLD). In particular, the crucial effect of interfacial carbon can be possibly examined using the MBE and PLD techniques, which allow a layer-by-layer deposition of crystalline thin films. If the outcome of such investigations is positive for Ohmic contact formation, direct deposition of epitaxial Ti3SiC2 thin films rather than the metals would be a potential processing technique

To summarize, we have determined in this chapter atomic-scale structure of Ohmic contacts on SiC and related it to electronic structure and electric property, aimed at understanding the formation mechanism of Ohmic contact in TiAl-based system. The combined HAADF-DFT study represents an important advance in relating structures to device properties at an atomic scale and is not limited to the contacts in SiC electronics. Our results show that the main product generated by chemical reaction can be epitaxial and have atomic bonds to the substrate. The contact interface, which could trap an atomic layer of carbon, enables lowered Schottky barrier due to the large interfacial dipole shift associated with the considerable charge transfer. These findings are relevant for technological improvement of contacts in SiC devices, and this chapter presents an important step towards addressing the current contact

We thank S. Watanabe (Univ. of Tokyo) for allowing our use of computational resources. The present study was supported in part by a Grant-in-Aid for Scientific Research on Priority Area, "Atomic Scale Modification (474)" from the Ministry of Education, Culture, Sports, Science, and Technology of Japan. Z. W acknowledges financial supports from the Grant-in-Aid for Young Scientists (B) (Grant No. 22760500), the IKETANI Science and Technology Foundation (Grant No. 0221047-A), and the IZUMI Science and Technology Foundation. S. T. thanks the supports from Nippon Sheet Glass Foundation and the MURATA Science Foundation. The calculations were carried out on a parallel SR11000

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for easier realization of ordered structure and better control of Ohmic property.

issues in wide-band-gap electronics.

**5. Acknowledgment** 

**6. References** 

0921-5093

Kingdom


**13** 

Piotr Klimczyk

*Poland* 

**SiC-Based Composites Sintered with** 

Silicon carbide-based materials usually have high hardness (2500 – 2800 HV) and thus have superior wear resistance. Nevertheless, the tribological performance of SiC is determined by many factors, such as the grain size of mated materials or the reactions in the presence of oxygen and humidity in the surrounding atmosphere. For example, in unlubricated sliding, wear resistance of SiC ceramics can be greater in air than in inert atmosphere owing to thin soft oxide films reducing friction and local surface pressure. (Gahr et al., 2001; Guicciardi et al., 2007). The friction and wear properties of SiC materials (both in dry and lubricating conditions) have been studied extensively because they are used in applications like

Silicon carbide-based ceramics have high melting point (~2500 °C), high thermal conductivity (43 – 145 W/m·K – depending on a temperature and phase composition), low thermal expansion (~4,5×10-6·K-1), and high temperature capability. Silicon carbide is a semiconductor which can be doped n-type by nitrogen or phosphorus and p-type by aluminium, boron, gallium or beryllium. Due to the combination of its thermal and electrical properties, SiC is applied in a resistance heating, flame igniters and electronic components. Relatively pure SiC has also an excellent corrosion resistance in the presence of hot acids

Silicon carbide powder compacts are difficult to densify without additives because of the covalent nature of the Si–C bonds and the associated low self-diffusion coefficient. Therefore, Reaction Sintering (RS) in the presence of liquid silicon as well as Hot Isotactic Pressing (HIP) are frequently used to obtain a high quality, full dense SiC ceramics. Typical room temperature flexural strength of SiC-based materials is about 350-550 MPa. High-strength RS-SiC (over 1000 MPa in a 3-point bending test) was developed by controlling the residual Si size under 100 nm. (Magnani et al., 2000; Suyama et al., 2003). Silicon carbide ceramics have the ability to increase in strength with increase of temperature. It was reported that flexural strength of some kind of commercial SiC ceramic increase is from 413 MPa at the room temperature to around 580 MPa at 1800 °C (Richerson, 2004). For hot-pressed silicon carbide with addition of 0.15-1.0 wt% Al2O3, the high-temperature strength has been improved from 200 MPa to 700 MPa by decreasing the grain boundary concentration of both Al and O at 1500 °C (Kinoshita et

bearings, cylinder liners and mechanical seals (Murthy et al., 2004).

**1. Introduction** 

and bases (Richerson, 2004).

al., 1997).

**High Pressure Method** 

*Institute of Advanced Manuacturing Technology* 

Wang, X. G.; Smith, J. R. & Evans, A. (2002), Fundamental Inflenence of C on Adhesion of the Al2O3/Al Interface, *Physical Review Letters,* Vol.89, No.28, (December 2002), pp. 286102-1-4, ISSN 0031-9007

### **SiC-Based Composites Sintered with High Pressure Method**

Piotr Klimczyk

*Institute of Advanced Manuacturing Technology Poland* 

#### **1. Introduction**

308 Silicon Carbide – Materials, Processing and Applications in Electronic Devices

Wang, X. G.; Smith, J. R. & Evans, A. (2002), Fundamental Inflenence of C on Adhesion of

286102-1-4, ISSN 0031-9007

the Al2O3/Al Interface, *Physical Review Letters,* Vol.89, No.28, (December 2002), pp.

Silicon carbide-based materials usually have high hardness (2500 – 2800 HV) and thus have superior wear resistance. Nevertheless, the tribological performance of SiC is determined by many factors, such as the grain size of mated materials or the reactions in the presence of oxygen and humidity in the surrounding atmosphere. For example, in unlubricated sliding, wear resistance of SiC ceramics can be greater in air than in inert atmosphere owing to thin soft oxide films reducing friction and local surface pressure. (Gahr et al., 2001; Guicciardi et al., 2007). The friction and wear properties of SiC materials (both in dry and lubricating conditions) have been studied extensively because they are used in applications like bearings, cylinder liners and mechanical seals (Murthy et al., 2004).

Silicon carbide-based ceramics have high melting point (~2500 °C), high thermal conductivity (43 – 145 W/m·K – depending on a temperature and phase composition), low thermal expansion (~4,5×10-6·K-1), and high temperature capability. Silicon carbide is a semiconductor which can be doped n-type by nitrogen or phosphorus and p-type by aluminium, boron, gallium or beryllium. Due to the combination of its thermal and electrical properties, SiC is applied in a resistance heating, flame igniters and electronic components. Relatively pure SiC has also an excellent corrosion resistance in the presence of hot acids and bases (Richerson, 2004).

Silicon carbide powder compacts are difficult to densify without additives because of the covalent nature of the Si–C bonds and the associated low self-diffusion coefficient. Therefore, Reaction Sintering (RS) in the presence of liquid silicon as well as Hot Isotactic Pressing (HIP) are frequently used to obtain a high quality, full dense SiC ceramics. Typical room temperature flexural strength of SiC-based materials is about 350-550 MPa. High-strength RS-SiC (over 1000 MPa in a 3-point bending test) was developed by controlling the residual Si size under 100 nm. (Magnani et al., 2000; Suyama et al., 2003). Silicon carbide ceramics have the ability to increase in strength with increase of temperature. It was reported that flexural strength of some kind of commercial SiC ceramic increase is from 413 MPa at the room temperature to around 580 MPa at 1800 °C (Richerson, 2004). For hot-pressed silicon carbide with addition of 0.15-1.0 wt% Al2O3, the high-temperature strength has been improved from 200 MPa to 700 MPa by decreasing the grain boundary concentration of both Al and O at 1500 °C (Kinoshita et al., 1997).

SiC-Based Composites Sintered with High Pressure Method 311

toughness compared to the monolithic materials. (Ando et al., 2002; Lojanová et al., 2010;

The combination of the fair fracture toughness with high hardness, wear resistance and mechanical strength at elevated temperatures makes SiC/Si3N4 ceramics a promising material for cutting tools (Eblagon et al., 2007). Despite many studies on materials based on silicon carbide and silicon nitride, there is a lack of knowledge about the SiC/Si3N4 composites where the predominant phase is SiC. In the presented work, the materials

The purpose of the presented experiment was to study the influence of High Pressure - High Temperature (HPHT) sintering on the phase composition, microstructure and selected properties of SiC/Si3N4 composites as well as to study the effect of the addition of thirdphase particles selected from metals (Ti) or ceramics (TiB2, cBN - cubic Boron Nitride) to the SiC – Si3N4 system. The main goal was to improve fracture toughness and wear resistance of

The composites were manufactured and tested in two stages. The first stage consisted in sintering of materials having, in its initial composition, only SiC and/or Si3N4 powder(s). Samples sintered from nano-, sub-micro- and micropowders with various silicon carbide to

At the second stage the best SiC/Si3N4 composite manufactured at the first stage was

All materials were sintered with the HPHT method. The parameters of sintering: time and temperature were chosen individually for each composition. The obtained samples were subjected to a series of studies, which included: phase composition and crystallite size analysis by X-ray diffraction, measurements of density by hydrostatic method and Young's modulus by the ultrasonic method, measurement of hardness and and fracture toughness using Vickers indentation as well as studies of tribological properties using the Ball-On-Disk

Pressure is a versatile tool in solid state physics, materials engineering and geological sciences. Under the influence of high pressure and temperature there are a lot of changes in physical, chemical and structural properties of materials (Eremets, 1996). It gives a possibility to generate of new, non-existent in nature phases, or phases which occur only in inaccessible places, such as the earth core (Manghnani et al., 1980). The use of pressure as a parameter in the study of materials was pioneered principally by Professor P. W. Bridgman, who for forty years investigated most of the elements and many other materials using diverse techniques (Bridgman, 1964). There are many design solutions to ensure High Pressure - High Temperature (HPHT) conditions for obtaining and examination of materials. Depending on the design assumptions, it is possible to achieve very high pressures, up to several hundred gigapascals, as in the case of Diamond Anvils Cell (DAC).

Sajgalík et al., 2000; Takahashi et al., 2010).

**2. Description of experiment** 

the investigated materials.

contained from 0 to 100% of silicon carbide were investigated.

silicon nitride ratios were investigated at this stage.


subjected to modification, consisting of:


**2.1 HPHT method of sintering** 

method.

A favorable combination of properties makes SiC materials suitable for many engineering applications, including parts of machines and devices exposed to the abrasion, the high temperature, the corrosive environment, etc. A major disadvantage of SiC ceramic materials is their low fracture toughness, which usually does not exceed about 3.5 MPa·m1/2(Lee et al., 2007; Suyama et al., 2003). Low values of KIc coefficient exclude these materials from numerous applications with dynamic loads, e.g. in machining processes.

There are various ways to improve the fracture toughness of ceramic materials. One of them involves obtaining a composite material by the introduction of the additional phases in the form of nano-, micro- or sub-micro-sized particles to the base material. Some papers indicate that nanosized structures have great potential to essentially improve the mechanical performance of ceramic materials even at high temperatures (Awaji et al., 2002; Derby, 1998; Kim et al., 2006; Niihara et al., 1999). Depending on the type of introduced particles, composites can take advantage of different strengthening mechanisms, such as the crack deflection, crack bridging, crack branching, crack bowing, crack pinning, microcracking, thermal residual stress toughening, transformation toughening and synergism toughening. For example, metallic particles are capable of plastic deformation, thus absorption of energy and bridging of a growing crack, resulting in increased strengthening (Fig. 1a) (Yeomans, 2008). On the other hand, hard ceramic particles, like borides or nitrides, can introduce a favorable stress state which can cause a toughening effect by crack deflection and crack bifurcation (Fig. 1b) (Xu, 2005). An addition of metal borides such as ZrB2, TaB2, NbB2 or TiB2, promote densification of SiC powder as well as improve hardness and other mechanical properties of the material as a whole (Tanaka et al., 2003).

Fig. 1. Example of strengthening mechanisms which can occur in ceramic matrix composites with dispersed "soft" metallic or/and "hard" ceramic particles: a) crack bridging, b) crack deflection and crack bifurcation

The wide group of materials containing the silicon carbide are SiC/Si3N4 composites. In such materials predominant phase is silicon nitride, while SiC content does not usually exceed 30 vol.%. Silicon nitride has a lower hardness but a higher fracture toughness than silicon carbide. If SiC particles are uniformly dispersed in the Si3N4 ceramics, high strength can be obtained from room temperature to elevated temperature. It was reported that the strength of 1000 MPa at 1400°C is obtained in nano-composites having ultra-fine SiC particles added into the Si3N4 matrix. This improvement was mainly attributed to the suppression of a grain boundary sliding by intergranular SiC particles bonded directly with the Si3N4 grain in the atomic scale without any impurity phases (Hirano & Niihara, 1995; Yamada & Kamiya, 1999). SiC/Si3N4 composites have an ability to crack healing under high temperature and applied stress, to exhibit a significantly higher creep resistance and fracture toughness compared to the monolithic materials. (Ando et al., 2002; Lojanová et al., 2010; Sajgalík et al., 2000; Takahashi et al., 2010).

The combination of the fair fracture toughness with high hardness, wear resistance and mechanical strength at elevated temperatures makes SiC/Si3N4 ceramics a promising material for cutting tools (Eblagon et al., 2007). Despite many studies on materials based on silicon carbide and silicon nitride, there is a lack of knowledge about the SiC/Si3N4 composites where the predominant phase is SiC. In the presented work, the materials contained from 0 to 100% of silicon carbide were investigated.

#### **2. Description of experiment**

310 Silicon Carbide – Materials, Processing and Applications in Electronic Devices

A favorable combination of properties makes SiC materials suitable for many engineering applications, including parts of machines and devices exposed to the abrasion, the high temperature, the corrosive environment, etc. A major disadvantage of SiC ceramic materials is their low fracture toughness, which usually does not exceed about 3.5 MPa·m1/2(Lee et al., 2007; Suyama et al., 2003). Low values of KIc coefficient exclude these materials from

There are various ways to improve the fracture toughness of ceramic materials. One of them involves obtaining a composite material by the introduction of the additional phases in the form of nano-, micro- or sub-micro-sized particles to the base material. Some papers indicate that nanosized structures have great potential to essentially improve the mechanical performance of ceramic materials even at high temperatures (Awaji et al., 2002; Derby, 1998; Kim et al., 2006; Niihara et al., 1999). Depending on the type of introduced particles, composites can take advantage of different strengthening mechanisms, such as the crack deflection, crack bridging, crack branching, crack bowing, crack pinning, microcracking, thermal residual stress toughening, transformation toughening and synergism toughening. For example, metallic particles are capable of plastic deformation, thus absorption of energy and bridging of a growing crack, resulting in increased strengthening (Fig. 1a) (Yeomans, 2008). On the other hand, hard ceramic particles, like borides or nitrides, can introduce a favorable stress state which can cause a toughening effect by crack deflection and crack bifurcation (Fig. 1b) (Xu, 2005). An addition of metal borides such as ZrB2, TaB2, NbB2 or TiB2, promote densification of SiC powder as well as improve hardness and other

Fig. 1. Example of strengthening mechanisms which can occur in ceramic matrix composites with dispersed "soft" metallic or/and "hard" ceramic particles: a) crack bridging, b) crack

The wide group of materials containing the silicon carbide are SiC/Si3N4 composites. In such materials predominant phase is silicon nitride, while SiC content does not usually exceed 30 vol.%. Silicon nitride has a lower hardness but a higher fracture toughness than silicon carbide. If SiC particles are uniformly dispersed in the Si3N4 ceramics, high strength can be obtained from room temperature to elevated temperature. It was reported that the strength of 1000 MPa at 1400°C is obtained in nano-composites having ultra-fine SiC particles added into the Si3N4 matrix. This improvement was mainly attributed to the suppression of a grain boundary sliding by intergranular SiC particles bonded directly with the Si3N4 grain in the atomic scale without any impurity phases (Hirano & Niihara, 1995; Yamada & Kamiya, 1999). SiC/Si3N4 composites have an ability to crack healing under high temperature and applied stress, to exhibit a significantly higher creep resistance and fracture

numerous applications with dynamic loads, e.g. in machining processes.

mechanical properties of the material as a whole (Tanaka et al., 2003).

deflection and crack bifurcation

The purpose of the presented experiment was to study the influence of High Pressure - High Temperature (HPHT) sintering on the phase composition, microstructure and selected properties of SiC/Si3N4 composites as well as to study the effect of the addition of thirdphase particles selected from metals (Ti) or ceramics (TiB2, cBN - cubic Boron Nitride) to the SiC – Si3N4 system. The main goal was to improve fracture toughness and wear resistance of the investigated materials.

The composites were manufactured and tested in two stages. The first stage consisted in sintering of materials having, in its initial composition, only SiC and/or Si3N4 powder(s). Samples sintered from nano-, sub-micro- and micropowders with various silicon carbide to silicon nitride ratios were investigated at this stage.

At the second stage the best SiC/Si3N4 composite manufactured at the first stage was subjected to modification, consisting of:


All materials were sintered with the HPHT method. The parameters of sintering: time and temperature were chosen individually for each composition. The obtained samples were subjected to a series of studies, which included: phase composition and crystallite size analysis by X-ray diffraction, measurements of density by hydrostatic method and Young's modulus by the ultrasonic method, measurement of hardness and and fracture toughness using Vickers indentation as well as studies of tribological properties using the Ball-On-Disk method.

#### **2.1 HPHT method of sintering**

Pressure is a versatile tool in solid state physics, materials engineering and geological sciences. Under the influence of high pressure and temperature there are a lot of changes in physical, chemical and structural properties of materials (Eremets, 1996). It gives a possibility to generate of new, non-existent in nature phases, or phases which occur only in inaccessible places, such as the earth core (Manghnani et al., 1980). The use of pressure as a parameter in the study of materials was pioneered principally by Professor P. W. Bridgman, who for forty years investigated most of the elements and many other materials using diverse techniques (Bridgman, 1964). There are many design solutions to ensure High Pressure - High Temperature (HPHT) conditions for obtaining and examination of materials. Depending on the design assumptions, it is possible to achieve very high pressures, up to several hundred gigapascals, as in the case of Diamond Anvils Cell (DAC).

SiC-Based Composites Sintered with High Pressure Method 313

synthetic diamonds and for sintering of wide range of superhard composites based on polycrystalline diamond (PCD) or polycrystalline cubic boron nitride (PcBN). Under the influence of a simultaneous action of pressure and temperature the sintering process occurs much faster than in the case of free sintering. A typical duration of sintering process with HPHT method is about 0.5 – 2 minutes (Fig. 3) while the free sintering requires several hours. Short duration of the process contributes to the grain growth limitation, which is essential in the case of sintering of nanopowdes. The materials obtained with HPHT method are characterized by almost a 100% level of densification, isotropy of properties and sometimes by a completely different phase composition in relation to the same free-sintered materials, due to the different thermodynamic conditions of the manufacturing process.

0 30 60 90 120 150 180 210 240 270 300 330 360 390

0

10

20

30

40

50

Load, ×0.2 MN

60

70

80

90

100

1 2 3

Time, s

Fig. 3. Three stages of an example process of HPHT sintering: 1 – loading, 2 – sintering,

0

3 – unloading

1

2

Power, kVA

3

4

5

 Load Power

Such devices, due to their small size, are intended solely for laboratory investigations (XRD in-situ study, neutron diffraction etc.) (Piermarini, 2008). For the purposes of industrial and semi-industrial production of materials the most frequently the "Belt" or "Bridgman" type of equipment is used (Eremets, 1996; Hall, 1960; Khvostantsev et al., 2004). These apparatuses provide a relatively large working volume, the optimum pressure distribution and the possibility of achieving high temperatures.

In the toroidal type of Bridgman apparatus the quasi-hydrostatic compression of the material is achieved as a result of plastic deformation of the so called "gasket" (Fig. 2).

Fig. 2. Sintering process in a Bridgman-type HPHT system. Quasi-hydrostatic compression of the preliminary consolidated powders (sample - 1) is achieved as a result of plastic deformation of the gasket material (2) between anvils (3); electrical heating is provided by a high-power transformer (4) and graphite resistive heater (5)

Gaskets are made of special kinds of metamorphic rocks such as pyrophyllite, "lithographic stone" or catlinite (Filonenko & Zibrov, 2001; Prikhna, 2008). The toroidal chamber, depending on its volume (usually from od 0.3 do 1 cm3), can generate pressures up to 12 GPa and temperature up to ~2500 °C. The presented system is used often for production of

Such devices, due to their small size, are intended solely for laboratory investigations (XRD in-situ study, neutron diffraction etc.) (Piermarini, 2008). For the purposes of industrial and semi-industrial production of materials the most frequently the "Belt" or "Bridgman" type of equipment is used (Eremets, 1996; Hall, 1960; Khvostantsev et al., 2004). These apparatuses provide a relatively large working volume, the optimum pressure distribution

In the toroidal type of Bridgman apparatus the quasi-hydrostatic compression of the material is achieved as a result of plastic deformation of the so called "gasket" (Fig. 2).

Fig. 2. Sintering process in a Bridgman-type HPHT system. Quasi-hydrostatic compression of the preliminary consolidated powders (sample - 1) is achieved as a result of plastic deformation of the gasket material (2) between anvils (3); electrical heating is provided by a

Gaskets are made of special kinds of metamorphic rocks such as pyrophyllite, "lithographic stone" or catlinite (Filonenko & Zibrov, 2001; Prikhna, 2008). The toroidal chamber, depending on its volume (usually from od 0.3 do 1 cm3), can generate pressures up to 12 GPa and temperature up to ~2500 °C. The presented system is used often for production of

high-power transformer (4) and graphite resistive heater (5)

and the possibility of achieving high temperatures.

synthetic diamonds and for sintering of wide range of superhard composites based on polycrystalline diamond (PCD) or polycrystalline cubic boron nitride (PcBN). Under the influence of a simultaneous action of pressure and temperature the sintering process occurs much faster than in the case of free sintering. A typical duration of sintering process with HPHT method is about 0.5 – 2 minutes (Fig. 3) while the free sintering requires several hours. Short duration of the process contributes to the grain growth limitation, which is essential in the case of sintering of nanopowdes. The materials obtained with HPHT method are characterized by almost a 100% level of densification, isotropy of properties and sometimes by a completely different phase composition in relation to the same free-sintered materials, due to the different thermodynamic conditions of the manufacturing process.

Fig. 3. Three stages of an example process of HPHT sintering: 1 – loading, 2 – sintering, 3 – unloading

SiC-Based Composites Sintered with High Pressure Method 315

After drying, the mixtures were preliminarily compressed into a disc of r 15 mm diameter and 5 mm height under pressure of ~200 MPa. The green bodies with the addition of TiH2 were additionally annealed in a vacuum at a temperature of 800 °C for 1h in order to remove the hydrogen and obtain pure metallic titanium. The materials were obtained at high pressure (6 GPa) in the wide range of temperatures ( 430 – 2150 °C depending of composition) using a Bridgman-type toroidal apparatus (Fig. 2). The sintering temperatures were established experimentally for each material to obtain crack-free samples with the highest values of density and mechanical properties. The duration of the sintering process

The sintered compacts were subsequently ground to remove remains of graphite after the technological process of sintering and to obtain the required quality and surface parallelism for Young's modulus determination. The samples provided for microscopic investigations

Densities of the sintered samples were measured by the hydrostatic method. The uncertainty of the measurements was below 0.02 g/cm3, which gave a relative error value of below 0.5 % (excluding measurements of small pieces of broken samples, where the error

Young's modulus of the samples obtained by HPHT sintering was measured by means of transmission velocity of ultrasonic waves through the sample, using a Panametrics Epoch III

2

*C C E C*

where: *E* - Young's modulus, *CL* - velocity of the longitudinal wave, *CT* - velocity of the

The velocities of transverse and longitudinal waves were determined as a ratio of sample thickness and relevant transition time. The accuracy of calculated Young's modulus (Eq. 1)

Hardness of sintered samples was determined by the Vickers method using a digital Vickers Hardness Tester (FUTURE-TECH FV-700). Five hardness measurements, with indentation loads of 2.94, 9.81 and 98.1 N, were carried out for each sample. Standard deviations of HV

Indentation fracture toughness was calculated from the length of cracks which developed in a Vickers indentation test (with indentation load - 98.1 N) using Niihara's

> <sup>5</sup> <sup>2</sup> 0 129 . *<sup>K</sup> H c Ic H a E a*

2 3

values were relatively high but usually no more than 5 % of the average values.

ϕ

ϕ

*T*

2 2

2 2 3 -4 - *L T*

*C C* = ⋅ *<sup>ρ</sup>* (1)

<sup>−</sup> = ⋅ (2)

*L T*

and for mechanical tests were additionally polished using diamond slurries.

ultrasonic flaw detector. Calculations were carried out according to (Eq. 1):

was up to 0.1 g/cm3, due to their insufficient volume and mass).

**70SiC/30Si3N4 composite + cBN** (modification by addition of the third, nitride phase)

70 SiC(sub-micro)/30 Si3N4 (sub-micro, Starck) + 8 vol.% cBN(micro) 70 SiC(sub-micro)/30 Si3N4 (sub-micro, Goodfellow) + 8 vol.% cBN(nano) 70 SiC(sub-micro)/30 Si3N4 (sub-micro, Starck) + 30 vol.% cBN(micro)

was 40s for nanopowders and 60 s for the others.

transversal wave, *ρ* - density of the material.

was estimated to be below 2 %.

equation (Eq. 2):

**2.3 Investigation methods** 

#### **2.2 Samples preparation**

Powders used for the preparation of mixtures for sintering of SiC/Si3N4 materials are listed in Table 1.


Table 1. Powders used for preparation of mixtures for sintering of SiC/Si3N4 materials

The following mixtures were prepared by mixing the appropriate powders (Table. 1) in an isopropanol environment using the Fritsch Pulverisette 6 planetary mill.

**nano-SiC/Si3N4 materials** 

100 % SiC(nano) 100 % Si3N4(nano) 50 SiC(nano)/50 Si3N4(nano) – vol.% **sub-micro-SiC/Si3N4 materials**  95 SiC(sub-micro)/5 Si3N4(sub-micro, Starck) – vol.% 70 SiC(sub-micro)/30 Si3N4(sub-micro, Starck) – vol.% 50 SiC(sub-micro)/50 Si3N4(sub-micro, Starck) – vol.% 100 % Si3N4(sub-micro, Starck) **micro-SiC/Si3N4 materials**  70 SiC(micro)/30 Si3N4(micro) – vol.% 100 % Si3N4(micro) **70SiC/30Si3N4 composite** (modification by using various SiC and Si3N4 powders) 70 SiC(sub-micro)/30 Si3N4(sub-micro, Starck) – vol.% 70 SiC(sub-micro)/30 Si3N4(sub-micro, Goodfellow) – vol.% 70 SiC(micro)/30 Si3N4(micro) – vol.% 70 SiC(sub-micro)/30 Si3N4(micro) – vol.% **70SiC/30Si3N4 composite + Ti** (modification by addition of the third, metallic phase) 70 SiC(sub-micro)/30 Si3N4(sub-micro, Starck) + 8 vol.% Ti - from TiH2(micro) **70SiC/30Si3N4 composite + TiB2** (modification by addition of the third, boride phase) 70 SiC(sub-micro)/30 Si3N4(sub-micro, Starck) + 8 vol.% TiB2(micro) 70 SiC(sub-micro)/30 Si3N4(sub-micro, Starck) + 30 vol.% TiB2(micro)

**70SiC/30Si3N4 composite + cBN** (modification by addition of the third, nitride phase)

70 SiC(sub-micro)/30 Si3N4 (sub-micro, Starck) + 8 vol.% cBN(micro)

70 SiC(sub-micro)/30 Si3N4 (sub-micro, Goodfellow) + 8 vol.% cBN(nano)

70 SiC(sub-micro)/30 Si3N4 (sub-micro, Starck) + 30 vol.% cBN(micro)

After drying, the mixtures were preliminarily compressed into a disc of r 15 mm diameter and 5 mm height under pressure of ~200 MPa. The green bodies with the addition of TiH2 were additionally annealed in a vacuum at a temperature of 800 °C for 1h in order to remove the hydrogen and obtain pure metallic titanium. The materials were obtained at high pressure (6 GPa) in the wide range of temperatures ( 430 – 2150 °C depending of composition) using a Bridgman-type toroidal apparatus (Fig. 2). The sintering temperatures were established experimentally for each material to obtain crack-free samples with the highest values of density and mechanical properties. The duration of the sintering process was 40s for nanopowders and 60 s for the others.

The sintered compacts were subsequently ground to remove remains of graphite after the technological process of sintering and to obtain the required quality and surface parallelism for Young's modulus determination. The samples provided for microscopic investigations and for mechanical tests were additionally polished using diamond slurries.

#### **2.3 Investigation methods**

314 Silicon Carbide – Materials, Processing and Applications in Electronic Devices

Powders used for the preparation of mixtures for sintering of SiC/Si3N4 materials are listed

SiC nano <5 nm France beta SiC sub-micro 0.1 – 1 Goodfellow, UK alpha

Si3N4 sub-micro 0.1 – 0.8 Goodfellow, UK alpha

Si3N4 nano <20nm Goodfellow, UK amorphous

Si3N4 micro 1 – 5 AEE, USA alpha>85%

TiB2 micro 2.5 – 3.5 H.C. Starck, Germany F-grade

isopropanol environment using the Fritsch Pulverisette 6 planetary mill.

Si3N4 sub-micro 0.6 H.C. Starck, Germany alpha>90%, M11-grade

cBN nano 0 – 0.1 Element6, South Africa Micron+ABN, M0.10-grade cBN micro 3 – 6 Element6, South Africa Micron+ABN, M36-grade

The following mixtures were prepared by mixing the appropriate powders (Table. 1) in an

Table 1. Powders used for preparation of mixtures for sintering of SiC/Si3N4 materials

**70SiC/30Si3N4 composite** (modification by using various SiC and Si3N4 powders)

**70SiC/30Si3N4 composite + Ti** (modification by addition of the third, metallic phase) 70 SiC(sub-micro)/30 Si3N4(sub-micro, Starck) + 8 vol.% Ti - from TiH2(micro)

**70SiC/30Si3N4 composite + TiB2** (modification by addition of the third, boride phase)

70 SiC(sub-micro)/30 Si3N4(sub-micro, Starck) + 8 vol.% TiB2(micro) 70 SiC(sub-micro)/30 Si3N4(sub-micro, Starck) + 30 vol.% TiB2(micro)

SiC micro 1.2 AGH, Poland

TiH2 micro <44 Fluka, Switzerland

[µm] Manufacturer Description

**2.2 Samples preparation** 

**nano-SiC/Si3N4 materials** 

50 SiC(nano)/50 Si3N4(nano) – vol.% **sub-micro-SiC/Si3N4 materials** 

70 SiC(micro)/30 Si3N4(micro) – vol.%

70 SiC(micro)/30 Si3N4(micro) – vol.% 70 SiC(sub-micro)/30 Si3N4(micro) – vol.%

100 % Si3N4(sub-micro, Starck) **micro-SiC/Si3N4 materials** 

95 SiC(sub-micro)/5 Si3N4(sub-micro, Starck) – vol.% 70 SiC(sub-micro)/30 Si3N4(sub-micro, Starck) – vol.% 50 SiC(sub-micro)/50 Si3N4(sub-micro, Starck) – vol.%

70 SiC(sub-micro)/30 Si3N4(sub-micro, Starck) – vol.% 70 SiC(sub-micro)/30 Si3N4(sub-micro, Goodfellow) – vol.%

100 % SiC(nano) 100 % Si3N4(nano)

100 % Si3N4(micro)

Powder Category Particle size

in Table 1.

Densities of the sintered samples were measured by the hydrostatic method. The uncertainty of the measurements was below 0.02 g/cm3, which gave a relative error value of below 0.5 % (excluding measurements of small pieces of broken samples, where the error was up to 0.1 g/cm3, due to their insufficient volume and mass).

Young's modulus of the samples obtained by HPHT sintering was measured by means of transmission velocity of ultrasonic waves through the sample, using a Panametrics Epoch III ultrasonic flaw detector. Calculations were carried out according to (Eq. 1):

$$E = \rho \cdot \mathbf{C}\_T^2 \frac{\mathbf{3C}\_L^2 \cdot \mathbf{4C}\_T^2}{\mathbf{C}\_L^2 \cdot \mathbf{C}\_T^2} \tag{1}$$

where: *E* - Young's modulus, *CL* - velocity of the longitudinal wave, *CT* - velocity of the transversal wave, *ρ* - density of the material.

The velocities of transverse and longitudinal waves were determined as a ratio of sample thickness and relevant transition time. The accuracy of calculated Young's modulus (Eq. 1) was estimated to be below 2 %.

Hardness of sintered samples was determined by the Vickers method using a digital Vickers Hardness Tester (FUTURE-TECH FV-700). Five hardness measurements, with indentation loads of 2.94, 9.81 and 98.1 N, were carried out for each sample. Standard deviations of HV values were relatively high but usually no more than 5 % of the average values.

Indentation fracture toughness was calculated from the length of cracks which developed in a Vickers indentation test (with indentation load - 98.1 N) using Niihara's equation (Eq. 2):

$$\frac{K\_{IC}\rho}{H\sqrt{a}}\left(\frac{H}{E\rho}\right)^{\frac{2}{5}} = 0.129 \cdot \left(\frac{c}{a}\right)^{-\frac{3}{2}}\tag{2}$$

SiC-Based Composites Sintered with High Pressure Method 317

*n <sup>V</sup> <sup>W</sup>*

*F L* <sup>=</sup> <sup>⋅</sup> (4)

Composite: 50 SiC/50 Si3N4 - vol.%


β-SiC (8.0 nm) + orthorhombic Si1.8Al0.2O1.2N1.8 (20.0 nm)

*s*

**3. Materials sintered from nano-, sub-micro-, and micro-SiC/Si3N4 powders**  A macroscopic view, phase composition and crystallite size of materials sintered from nanopowders under the pressure of 6 GPa at temperatures ranging from 430 to 1880 ° C in

> Si3N4 amorphous powder, < 20 nm

of sintering Sintered material: appearance, phase composition, crystallite size

amorphous Si3N4

<sup>β</sup>-SiC (4.4 nm) orthorhombic

Si1.8Al0.2O1.2N1.8 (77)

β-SiC (4.1 nm) amorphous Si3N4 β-SiC (4.5 nm) + amorphous Si3N4

β-SiC (4.1 nm) amorphous Si3N4 β-SiC (11.1 nm) + amorphous Si3N4

where: *Ws* - specific wear rate, *V* – volume of removed material, *L* – sliding distance.

the period of time 40s are shown in Table 2.

β-SiC powder, 4.1 nm

Initial powders

Temperature

650°C

890°C

1170°C

430°C -

where: *KIc* - critical stress intensity factor, ϕ - constrain factor, *H* - Vickers hardness, *E* - Young's modulus, *a* - half of indent diagonal, *c* - length of crack.

Microstructural observations were carried out on the densified materials using a JEOL JXA-50A Scanning electron Microscope equipped with back scattering electron (BSE) imaging.

In the Ball-On-Disc tests, the coefficient of friction and the specific wear rate of the sintered samples in contact with Si3N4 ball were determined using a CETR UMT-2MT (USA) universal mechanical tester. In the Ball-On-Disc method, sliding contact is brought about by pushing a ball specimen onto a rotating disc specimen under a constant load (Fig. 4). The loading mechanism applied a controlled load *Fn* to the ball holder and the friction force was measured continuously during the test using an extensometer. For each test, a new ball was used or the ball was rotated so that a new surface was in contact with the disc. The ball and disc samples were washed in ethyl alcohol and dried.

Fig. 4. Material pair for the Ball-On-Disc method: 1 – Si3N4 ball; 2 – sample (disc)

The size of the disc-shaped samples was ~13.5 in diameter and ~3.8 mm in height with the surfaces flatness and parallelism within 0.02 mm. The roughness of the tested surface was not more than 0.1 µm Ra. The following test conditions were established: ball diameter – 2 mm, applied load – 4 N, sliding speed – 0.1 m/s, diameter of the sliding circle – 2 ÷ 5 mm, sliding distance – 100 m, calculated duration of the test – 1000 s. The tests were carried out without lubricant at room temperature. Each test was repeated at least three times. Coefficient of friction was calculated from (Eq. 3):

$$
\mu = \frac{F\_f}{F\_n} \tag{3}
$$

where: *µ* – coefficient of friction, *Ff* – measured friction force, *Fn* – applied normal force. After completing the test, according to ISO 20808:2004 E standard, the cross-sectional profile of the wear track at four places at intervals of 90° was measured using a contact stylus profilometer PRO500 (CETR, USA). Then the average cross-sectional area of the wear track was calculated. The volume of material removed was calculated as a product of crosssectional area of the wear track and their circumference. Specific wear rate was calculated from (Eq. 4):

ϕ

Microstructural observations were carried out on the densified materials using a JEOL JXA-50A Scanning electron Microscope equipped with back scattering electron (BSE) imaging. In the Ball-On-Disc tests, the coefficient of friction and the specific wear rate of the sintered samples in contact with Si3N4 ball were determined using a CETR UMT-2MT (USA) universal mechanical tester. In the Ball-On-Disc method, sliding contact is brought about by pushing a ball specimen onto a rotating disc specimen under a constant load (Fig. 4). The loading mechanism applied a controlled load *Fn* to the ball holder and the friction force was measured continuously during the test using an extensometer. For each test, a new ball was used or the ball was rotated so that a new surface was in contact with the disc. The ball and

Fig. 4. Material pair for the Ball-On-Disc method: 1 – Si3N4 ball; 2 – sample (disc)

The size of the disc-shaped samples was ~13.5 in diameter and ~3.8 mm in height with the surfaces flatness and parallelism within 0.02 mm. The roughness of the tested surface was not more than 0.1 µm Ra. The following test conditions were established: ball diameter – 2 mm, applied load – 4 N, sliding speed – 0.1 m/s, diameter of the sliding circle – 2 ÷ 5 mm, sliding distance – 100 m, calculated duration of the test – 1000 s. The tests were carried out without lubricant at room temperature. Each test was repeated at least three times.

> *f n F F* μ

where: *µ* – coefficient of friction, *Ff* – measured friction force, *Fn* – applied normal force. After completing the test, according to ISO 20808:2004 E standard, the cross-sectional profile of the wear track at four places at intervals of 90° was measured using a contact stylus profilometer PRO500 (CETR, USA). Then the average cross-sectional area of the wear track was calculated. The volume of material removed was calculated as a product of crosssectional area of the wear track and their circumference. Specific wear rate was calculated

= (3)


where: *KIc* - critical stress intensity factor,

disc samples were washed in ethyl alcohol and dried.

Coefficient of friction was calculated from (Eq. 3):

from (Eq. 4):

*E* - Young's modulus, *a* - half of indent diagonal, *c* - length of crack.

$$\mathcal{W}\_s = \frac{V}{F\_n \cdot L} \tag{4}$$

where: *Ws* - specific wear rate, *V* – volume of removed material, *L* – sliding distance.

#### **3. Materials sintered from nano-, sub-micro-, and micro-SiC/Si3N4 powders**

A macroscopic view, phase composition and crystallite size of materials sintered from nanopowders under the pressure of 6 GPa at temperatures ranging from 430 to 1880 ° C in the period of time 40s are shown in Table 2.


SiC-Based Composites Sintered with High Pressure Method 319

The comparison of physical-mechanical properties of nano-, sub-micro- and micro-SiC/Si3N4 materials sintered at different temperatures is presented in Fig. 5 and Table 3. Generally, nanocomposites are characterized by the lowest physical-mechanical properties of the three granulometric types of the investigated materials. Densities and Young's modulus values of the best nanostructured samples do not exceed 2.55 g/cm3 and 135 GPa respectively. In most cases, nanostructured SiC/Si3N4 samples are characterized by a lot of cracks (see Table 2). Cracking of such ceramics occurs as a result of the presence in their structure of residual micro- and macro-stresses which overcome the strength of the produced material. The fine powder is characterized by a very large specific surface and high gas content in the sample due to the absorption process of the material particles. During heating, as a result of the increase in temperature, the volume of gases increases, which causes cracking or even permanent fragmentation of the sample. In order to prevent the cracking phenomena in the samples, various conditions of the sintering process were tested. Depending on composition, materials characterized by the highest level of densification and the best mechanical properties were obtained at different temperatures: 890 °C for pure Si3N4 and 1880 °C for 50 Si3N4/50 SiC – vol.% composite. Unfortunately, some of these samples had cracks as well. Different kinds of internal cracks, delamination and other defects of microstructure occurred in most of the nanostructured samples. These defects cause a scattering of caustic waves propagated through the material and, in consequence, the impossibility of Young's modulus measurements using

Composites without cracks were obtained only from micro- and sub-micro-structured powders. Only for these composites hardness and fracture toughness were measured.

ultrasonic probes (marked as \*\*nm in Table 3).

2.30 2.40 2.50 2.60 2.70 2.80 2.90 3.00 3.10 3.20 3.30

Density, g/ccm

400

600

800

sintered at different temperatures

1000

Sintering temperature, °C

1200

1400

1600

1800

2000

2200

Fig. 5. Density and Young modulus of nano-, sub-micro-, and micro-SiC/Si3N4 materials

Youngs modulus, GPa

400

600

800

1000

1200

Sintering temperature, °C

1400

1600

1800

2000

2200

Table 2. A macroscopic view, phase composition and crystallite size of SiC/Si3N4 materials sintered from nanopowders under the pressure of 6 GPa at temperatures ranging from 430 to 1880 ° C in the period of time 40s

The initial crystallite size of sintered SiC nanopowder was about 4.1 nm and did not change until the sintering temperature of 1170 °C. At the sintering temperature of 1450°C crystallites reached an average size of 10.6 nm while at the maximum applied temperature (1880 °C) their size was 110 nm. This material showed no phase transformation. The sinters obtained at 1880 °C as well as the initial powder have the cubic structure of β-SiC phase.

Sintered Si3N4 powder remained amorphous until the temperature of 890 °C. At the temperature of 1170 °C a new phase crystallized. The X-ray diffraction pattern of this phase corresponds to the o'-sialon with orthorhombic structure and Si1.8Al0.2O1.2N1.8 stoichiometry. As evidenced by the chemical formula, this compound has a low content of aluminum with reference to silicon while the quantities of nitrogen and oxygen are comparable. It can be assumed that o'-sialon is a transition phase between the amorphous silicon nitride and a completely crystalline β-Si3N4 phase. O'-sialon was formed probably due to embedding a certain amount of oxygen and impurities adsorbed on the surface of powder to an atomic lattice of crystallizing silicon nitride. The crystallite size of this phase was estimated to around be 77 nm. The samples obtained at temperatures of 1450 and 1880 °C contain only β-Si3N4 phase with the crystallite size 77.4 and 143 nm respectively.

50 SiC/50 Si3N4 – vol.% nanocomposite was sintered at the same temperatures as silicon carbide powder without additions. The phase composition of sintered composites did not differ qualitatively from the sum of their components sintered separately. There was no formation of new phases in the reaction between silicon carbide and silicon nitride. Sintering of composites, especially at higher temperatures, leads to lower grain growth than it is in single-phase powders sintered separately. This indicates a favorable effect of inhibiting grain growth in the composite.

Composite: 50 SiC/50 Si3N4 - vol.%

Si1.8Al0.2O1.2N1.8 (31.0 nm)

Si3N4 amorphous powder, < 20 nm

of sintering Sintered material: appearance, phase composition, crystallite size

<sup>β</sup>-SiC (10.6 nm) <sup>β</sup>-Si3N4 (77.4 nm) β-SiC (10.2 nm) + orthorhombic

β-SiC (110 nm) β-Si3N4 (143 nm) β-SiC (51.8 nm) + β-Si3N4 (86.9 nm)

Table 2. A macroscopic view, phase composition and crystallite size of SiC/Si3N4 materials sintered from nanopowders under the pressure of 6 GPa at temperatures ranging from

The initial crystallite size of sintered SiC nanopowder was about 4.1 nm and did not change until the sintering temperature of 1170 °C. At the sintering temperature of 1450°C crystallites reached an average size of 10.6 nm while at the maximum applied temperature (1880 °C) their size was 110 nm. This material showed no phase transformation. The sinters obtained at 1880 °C as well as the initial powder have the cubic structure of β-SiC phase. Sintered Si3N4 powder remained amorphous until the temperature of 890 °C. At the temperature of 1170 °C a new phase crystallized. The X-ray diffraction pattern of this phase corresponds to the o'-sialon with orthorhombic structure and Si1.8Al0.2O1.2N1.8 stoichiometry. As evidenced by the chemical formula, this compound has a low content of aluminum with reference to silicon while the quantities of nitrogen and oxygen are comparable. It can be assumed that o'-sialon is a transition phase between the amorphous silicon nitride and a completely crystalline β-Si3N4 phase. O'-sialon was formed probably due to embedding a certain amount of oxygen and impurities adsorbed on the surface of powder to an atomic lattice of crystallizing silicon nitride. The crystallite size of this phase was estimated to around be 77 nm. The samples obtained at temperatures of 1450 and 1880 °C contain only β-

50 SiC/50 Si3N4 – vol.% nanocomposite was sintered at the same temperatures as silicon carbide powder without additions. The phase composition of sintered composites did not differ qualitatively from the sum of their components sintered separately. There was no formation of new phases in the reaction between silicon carbide and silicon nitride. Sintering of composites, especially at higher temperatures, leads to lower grain growth than it is in single-phase powders sintered separately. This indicates a favorable effect of inhibiting

Initial powders

Temperature

1450°C

1880°C

430 to 1880 ° C in the period of time 40s

grain growth in the composite.

Si3N4 phase with the crystallite size 77.4 and 143 nm respectively.

β-SiC powder, 4.1 nm

The comparison of physical-mechanical properties of nano-, sub-micro- and micro-SiC/Si3N4 materials sintered at different temperatures is presented in Fig. 5 and Table 3. Generally, nanocomposites are characterized by the lowest physical-mechanical properties of the three granulometric types of the investigated materials. Densities and Young's modulus values of the best nanostructured samples do not exceed 2.55 g/cm3 and 135 GPa respectively. In most cases, nanostructured SiC/Si3N4 samples are characterized by a lot of cracks (see Table 2). Cracking of such ceramics occurs as a result of the presence in their structure of residual micro- and macro-stresses which overcome the strength of the produced material. The fine powder is characterized by a very large specific surface and high gas content in the sample due to the absorption process of the material particles. During heating, as a result of the increase in temperature, the volume of gases increases, which causes cracking or even permanent fragmentation of the sample. In order to prevent the cracking phenomena in the samples, various conditions of the sintering process were tested. Depending on composition, materials characterized by the highest level of densification and the best mechanical properties were obtained at different temperatures: 890 °C for pure Si3N4 and 1880 °C for 50 Si3N4/50 SiC – vol.% composite. Unfortunately, some of these samples had cracks as well. Different kinds of internal cracks, delamination and other defects of microstructure occurred in most of the nanostructured samples. These defects cause a scattering of caustic waves propagated through the material and, in consequence, the impossibility of Young's modulus measurements using ultrasonic probes (marked as \*\*nm in Table 3).

Composites without cracks were obtained only from micro- and sub-micro-structured powders. Only for these composites hardness and fracture toughness were measured.

Fig. 5. Density and Young modulus of nano-, sub-micro-, and micro-SiC/Si3N4 materials sintered at different temperatures

SiC-Based Composites Sintered with High Pressure Method 321

**Si3N4 based ceramics SiC based ceramics** 

StarCeram N 7000

Density,

Young's modulus, GPa

Vickers hardness, HV

Fracture toughness, MPam1/2

Ceramics – commercial data sheets)

H.C. Starck

StarCeram N 8000

H.C. Starck

1500 1520 <sup>1450</sup>

EKatherm

(300g)

structured 70 SiC/30 Si3N4 – vol.% composites obtained by HPHT sintering

method of sintering is the critical factor in achieving good quality of ceramics.

1 Data from: H.C. Starck Ceramics GmbH& Co. KG, Ceradyne Inc. and Saint – Gobain Advanced

properties than comparable commercial materials (Table 4).

Ceradyne

Ceralloy 147-A

Ceradyne

g/ccm >3.22 >3.23 >3.24 3.18 3.10 3.10 3.20 **3.14 3.18** 

1650 (300g) <sup>2500</sup>

Table 4. Comparison of commercial advanced SiC/Si3N4-based ceramics1 with sub-micro-

The composites obtained from submicron powders are characterized by the best properties. Density and Young's modulus of the best 70 SiC/30 Si3N4 – vol.% compacts sintered at 1880 °C were 3.18 g/cm3 and 377 GPa respectively (over 99% and 90% of the theoretical values). This material is also characterized by the highest hardness (HV1 ~3000) and relatively good fracture toughness (4.9 MPam1/2). The same material sintered at a lower temperature (1690 °C) has slightly lower values of density (3.14 g/cm3), Young's modulus (363 GPa) and hardness (HV1 2626) but higher fracture toughness (5.6 MPam1/2) - Table 3. HPHT sintered sub-micro-70 SiC/30 Si3N4 – vol.% composites have a better combination of mechanical

The composites obtained from the micro-sized powders have their properties intermediate between the nano- and sub-micro-structured materials. Even though the best micro-SiC/Si3N4 samples are crack free and have fairly good density (>94% of theoretical values) and indentation fracture toughness (4.6 – 4.8 MPam1/2), their Young's modulus and hardness are much lower than for the sub-micro-structured samples. The insufficient mechanical properties of microstructured Si3N4–SiC materials can be attributed not only to grain size but also to specific properties of the initial powder resulting from their production method (e.g. shape of the grains, impurities, oxidation etc.). The choice of suitable initial powders for the given

StarCeram S

H.C. Starck

290 310 310 310 395 410 430 **363 377** 

6.7 6.0 7.0 4.5 3.0 4.6 4.3 **5.6 4.9** 

Hexoloy SA

Saint Gobain

2800 (100g Konopp )

Ceralloy 146-S5

Ceradyne

2600 (300g)

**2812 (300g)** 

**3132 (300g )** 

**Sub-micro-70SiC/30Si3N4 composites (this work)** 


Table 3. Physical-mechanical properties of selected nano-, sub-micro- and micro-SiC/Si3N4 materials sintered at optimal temperatures; \*optimum temperature for selected properties, e.g. *1690 (KIc)* - the best fracture toughness; \*\*nm - non measurable with ultrasonic method

g/ccm

**sub-micro-structured materials** (powders: α-SiC 0.1-1µm, α-Si3N4 0.6µm) sintered at 6GPa

**micro-structured materials** (initial powders: SiC 1.2 µm, α-Si3N4 1-5 µm,) sintered at 6GPa

Table 3. Physical-mechanical properties of selected nano-, sub-micro- and micro-SiC/Si3N4 materials sintered at optimal temperatures; \*optimum temperature for selected properties, e.g. *1690 (KIc)* - the best fracture toughness; \*\*nm - non measurable with ultrasonic method

**nanomaterials** (initial powders: β-SiC<5nm, amorphous Si3N4 <20nm) sintered at 6GPa

Density Youngs

% of theoretic

GPa

% of theoretic

/cracks 2.78 87 172 38 0.24 - - - -

/cracks 3.18 99 407 92 0.17 - - - -

*(KIc)* 3.14 98 363 87 0.19 2810 2630 2240 *5.6* 

*E, HV) 3.18 99 377 90 0.19 3130 2970 2400* 4.9

*\*1450 (ρ*) *3.03 95* 167 52 0.2 - 1250 1060 4.8

3.02 94 243 58 0.16 - 1880 1510 4.6

2.95 92 *223 70* 0.22 - - - -

<sup>1880</sup> 1690 3.18 99 349 91 0.21 2700 2560 2140 5

<sup>1690</sup> /cracs - - - - - - - - -

<sup>1880</sup> 890 2.54 80 135 42 0.24 - - - -

2.49 78 \*\*nm - \*\*nm - - - -

modulus

Poisson's ratio

Hardness


Fracture toughness

MPam1/2

Sintering temp.

1880

650- 1880

1690- 2150

1690- 2030

1450-

1170-

1450- 1880

1880

1450

1880 /small chipping

1880

*\*1690* 

1450 /small cracks

*\*1690 (E) /small chipping*

*\*1880 (ρ,* 

vol.% °C °C

100 SiC(nano) 650-

100 Si3N4(nano) 430-

range

)

\*Sintering temp. optimal for (properties

/descripttion

Sample composition

for 40s

for 60s

for 60s

70 SiC(micro) /30 Si3N4(micro)

50 SiC(nano) /50 Si3N4(nano)

95 SiC(sub-micro) /5 Si3N4(sub-micro, Starck)

70 SiC(sub-micro) /30Si3N4(sub-micro, Starck)

50 SiC(sub-micro) /50Si3N4(sub-micro, Starck)

100Si3N4(sub-micro, Starck)

100 Si3N4(micro) 890-


Table 4. Comparison of commercial advanced SiC/Si3N4-based ceramics1 with sub-microstructured 70 SiC/30 Si3N4 – vol.% composites obtained by HPHT sintering

The composites obtained from submicron powders are characterized by the best properties. Density and Young's modulus of the best 70 SiC/30 Si3N4 – vol.% compacts sintered at 1880 °C were 3.18 g/cm3 and 377 GPa respectively (over 99% and 90% of the theoretical values). This material is also characterized by the highest hardness (HV1 ~3000) and relatively good fracture toughness (4.9 MPam1/2). The same material sintered at a lower temperature (1690 °C) has slightly lower values of density (3.14 g/cm3), Young's modulus (363 GPa) and hardness (HV1 2626) but higher fracture toughness (5.6 MPam1/2) - Table 3. HPHT sintered sub-micro-70 SiC/30 Si3N4 – vol.% composites have a better combination of mechanical properties than comparable commercial materials (Table 4).

The composites obtained from the micro-sized powders have their properties intermediate between the nano- and sub-micro-structured materials. Even though the best micro-SiC/Si3N4 samples are crack free and have fairly good density (>94% of theoretical values) and indentation fracture toughness (4.6 – 4.8 MPam1/2), their Young's modulus and hardness are much lower than for the sub-micro-structured samples. The insufficient mechanical properties of microstructured Si3N4–SiC materials can be attributed not only to grain size but also to specific properties of the initial powder resulting from their production method (e.g. shape of the grains, impurities, oxidation etc.). The choice of suitable initial powders for the given method of sintering is the critical factor in achieving good quality of ceramics.

 1 Data from: H.C. Starck Ceramics GmbH& Co. KG, Ceradyne Inc. and Saint – Gobain Advanced Ceramics – commercial data sheets)

SiC-Based Composites Sintered with High Pressure Method 323

3.10 3.12 3.14 3.16 3.18 3.20 3.22 3.24 3.26 3.28 3.30 3.32 3.34

> 3.16 3.18 3.20 3.22 3.24 3.26 3.28 3.30 3.32

Density, g/ccm

1600

1700

Sintering temperature, °C

1800

with cracks; white symbols placed on temperature axis – broken samples

Density, g/ccm

700

800

900

1000

1100

1200

1300

Sintering temperature, °C

1400

1500

1600

1700

with cracks; white symbols placed on temperature axis – broken samples

1800

1900

2000

Fig. 7. Density and Young's modulus of 70 SiC/30 Si3N4 + 8 vol.% Ti composites sintered at different temperatures. Dark symbols – samples without cracks; white symbols – samples

1900

Fig. 8. Density and Young's modulus of 70 SiC/30 Si3N4 + 8 vol.% TiB2 composites sintered at different temperatures. Dark symbols – samples without cracks; white symbols – samples

Young modulus, GPa

1600

1700

1800

Sintering temperature, °C

1900

Young modulus, GPa

700

800

900

1000

1100

1200

1300

1400

Sintering temperature, °C

1500

1600

1700

1800

1900

2000

For all the investigated samples, independently of their grain size, a strong influence of indentation load on hardness values can be observed. Increasing the indentation load causes a decrease in hardness values (Table 3).

#### **4. Modifications of 70 SiC/30 Si3N4 composite**

Density and Young's modulus of various 70 SiC/30 Si3N4 – vol.% composites sintered at different temperatures with and without additions of Ti, TiB2 and cBN phases are presented in Figs 6-11 and in Table 5.

Fig. 6. Density and Young's modulus of various kinds of 70 SiC/30 Si3N4 – vol.% composites sintered at different temperatures. Colored symbols – samples without cracks; white symbols – samples with cracks; white symbols placed on temperature axis – broken samples

For all the investigated samples, independently of their grain size, a strong influence of indentation load on hardness values can be observed. Increasing the indentation load causes

Density and Young's modulus of various 70 SiC/30 Si3N4 – vol.% composites sintered at different temperatures with and without additions of Ti, TiB2 and cBN phases are presented

a decrease in hardness values (Table 3).

in Figs 6-11 and in Table 5.

2.90 2.92 2.94 2.96 2.98 3.00 3.02 3.04 3.06 3.08 3.10 3.12 3.14 3.16 3.18 3.20 3.22

Density, g/ccm

1400

1500

1600

1700

Sintering temperature, °C

1800

1900

2000

2100

Fig. 6. Density and Young's modulus of various kinds of 70 SiC/30 Si3N4 – vol.% composites

symbols – samples with cracks; white symbols placed on temperature axis – broken samples

sintered at different temperatures. Colored symbols – samples without cracks; white

Young modulus, GPa

1400

1500

1600

1700

1800

Sintering temperature, °C

1900

2000

2100

**4. Modifications of 70 SiC/30 Si3N4 composite** 

Fig. 7. Density and Young's modulus of 70 SiC/30 Si3N4 + 8 vol.% Ti composites sintered at different temperatures. Dark symbols – samples without cracks; white symbols – samples with cracks; white symbols placed on temperature axis – broken samples

Fig. 8. Density and Young's modulus of 70 SiC/30 Si3N4 + 8 vol.% TiB2 composites sintered at different temperatures. Dark symbols – samples without cracks; white symbols – samples with cracks; white symbols placed on temperature axis – broken samples

SiC-Based Composites Sintered with High Pressure Method 325

3.25 3.30 3.35 3.40 3.45 3.50 3.55 3.60 3.65 3.70 3.75 3.80 3.85 3.90 3.95

(Fig. 7).

Density, g/ccm

1600

samples with cracks

1700

cracking of the samples (Fig. 9).

1800

Sintering temperature, °C

1900

2000

Among the composites sintered without additional phases, the highest degree of densification and best mechanical properties were demonstrated by composite obtained from submicron powders 70 SiC(sub-micro)/30 Si3N4(sub-micro, Starck) – vol%. (Fig. 6 and Table 5). This

The modification of the 70 SiC/30 Si3N4 composite by the addition of Ti was not successful. The samples with the addition of 8 vol.% Ti introduced in the form of TiH2, sintered at low temperatures, were characterized by a very low Young's modulus, whilst all the samples sintered at temperatures above ~1200 °C were cracked. A decrease in density was observed with increasing sintering temperature, whilst Young's modulus showed an upward trend

The composites with the addition of TiB2 were characterized by a high degree of densification, a high Young's modulus and improved KIc as compared to the unmodified composite. No improvement in hardness was observed (Table 5). In the case of 70 SiC/30 Si3N4 material with the addition of 8 vol.% TiB2, there is some increase in density and Young's modulus with increasing temperature (Fig. 8). Composite with the addition of 30 vol.% TiB2, shows an increase in density with sintering temperature up to a maximum value, and then its stabilization. A further increase of the sintering temperature results in

The composites modified by the addition of 8 vol.% cBN micropowder have better properties than the composites with TiB2 but a tendency to cracking of this material is noticeable. The use of nano-cBN particles as a modifier causes the deterioration of the properties and cracking of samples (Fig. 10). The composites modified by the addition of 30 vol.% cBN micropowder, showed the best mechanical properties (Fig. 11 and Table 5).

Fig. 11. Density and Young's modulus of 70 SiC/30 Si3N4 + 30 vol.% cBN composites sintered at different temperatures. Dark symbols – samples without cracks; white symbols –

composite was selected for modification by the addition of the third phase particles.

Young modulus, GPa

1600

1700

1800

Sintering temperature, °C

1900

2000

Fig. 9. Density and Young's modulus of 70 SiC/30 Si3N4 + 30 vol.% TiB2 composites sintered at different temperatures. Dark symbols – samples without cracks; white symbols – samples with cracks; white symbols placed on temperature axis – broken samples

Fig. 10. Density and Young's modulus of 70 SiC/30 Si3N4 + 8 vol.% cBN composites sintered at different temperaturesDark symbols – samples without cracks; white symbols – samples with cracks; white symbols placed on temperature axis – broken samples

3.40 3.42 3.44 3.46 3.48 3.50 3.52 3.54 3.56 3.58 3.60 3.62

2.90

1600

1700

1800

Sintering temperature, °C

1900

with cracks; white symbols placed on temperature axis – broken samples

2000

Fig. 10. Density and Young's modulus of 70 SiC/30 Si3N4 + 8 vol.% cBN composites sintered at different temperaturesDark symbols – samples without cracks; white symbols – samples

320

1600

1700

1800

Sintering temperature, °C

1900

2000

340

360

380

Young modulus, GPa

400

420

440

460

2.95

3.00

3.05

Density, g/ccm

3.10

3.15

3.20

3.25

Density, g/ccm

1600

1700

1800

1900

Sintering temperature, °C

2000

2100

with cracks; white symbols placed on temperature axis – broken samples

2200

Fig. 9. Density and Young's modulus of 70 SiC/30 Si3N4 + 30 vol.% TiB2 composites sintered at different temperatures. Dark symbols – samples without cracks; white symbols – samples

320

1600

1700

1800

1900

Sintering temperature, °C

2000

2100

2200

340

360

380

Young modulus, GPa

400

420

440

460

Fig. 11. Density and Young's modulus of 70 SiC/30 Si3N4 + 30 vol.% cBN composites sintered at different temperatures. Dark symbols – samples without cracks; white symbols – samples with cracks

Among the composites sintered without additional phases, the highest degree of densification and best mechanical properties were demonstrated by composite obtained from submicron powders 70 SiC(sub-micro)/30 Si3N4(sub-micro, Starck) – vol%. (Fig. 6 and Table 5). This composite was selected for modification by the addition of the third phase particles.

The modification of the 70 SiC/30 Si3N4 composite by the addition of Ti was not successful. The samples with the addition of 8 vol.% Ti introduced in the form of TiH2, sintered at low temperatures, were characterized by a very low Young's modulus, whilst all the samples sintered at temperatures above ~1200 °C were cracked. A decrease in density was observed with increasing sintering temperature, whilst Young's modulus showed an upward trend (Fig. 7).

The composites with the addition of TiB2 were characterized by a high degree of densification, a high Young's modulus and improved KIc as compared to the unmodified composite. No improvement in hardness was observed (Table 5). In the case of 70 SiC/30 Si3N4 material with the addition of 8 vol.% TiB2, there is some increase in density and Young's modulus with increasing temperature (Fig. 8). Composite with the addition of 30 vol.% TiB2, shows an increase in density with sintering temperature up to a maximum value, and then its stabilization. A further increase of the sintering temperature results in cracking of the samples (Fig. 9).

The composites modified by the addition of 8 vol.% cBN micropowder have better properties than the composites with TiB2 but a tendency to cracking of this material is noticeable. The use of nano-cBN particles as a modifier causes the deterioration of the properties and cracking of samples (Fig. 10). The composites modified by the addition of 30 vol.% cBN micropowder, showed the best mechanical properties (Fig. 11 and Table 5).

SiC-Based Composites Sintered with High Pressure Method 327

Starck) – vol.% 70 SiC(micro)/30 Si3N4(micro) – vol.%

70 SiC(sub-micro)/30 Si3N4(sub-micro,

70 SiC(sub-micro)/30 Si3N4(sub-micro,

Starck) + 30 vol.% cBN(micro)

Fig. 12. SEM microstructures of selected 70 SiC/30 Si3N4 composites with and without the

Starck) + 30 vol.%TiB2(micro)

70 SiC(sub-micro)/30 Si3N4(sub-micro,

70 SiC(sub-micro)/30 Si3N4(sub-micro,

70 SiC(sub-micro)/30 Si3N4(sub-micro,

Starck) + 8 vol.% cBN(micro)

addition of TiB2 and cBN

Starck) + 8 vol.% TiB2(micro)


Table 5. Physical-mechanical properties of the best samples selected from different modifications of 70 SiC/30 Si3N4 composites; \*optimum temperature for selected properties, e.g. *1690 (KIc)* - the best value of fracture toughness

SEM microstructures of 70 SiC/30 Si3N4 with and without the addition of TiB2 and cBN are presented in Fig. 12. The microstructures of the investigated samples are compact and dense, with the ingredients uniformly distributed in the volume of the composite. This demonstrates successful blending, using a planetary mill; EDS analysis, however, showed a

g/ccm

% of theoretic

GPa

Density Youngs

modulus

% of theoretic

*HV) 3.18 99 377 92 0.19 2970 2400* 4.9 *\*1690 (KIc)* 3.14 98 363 87 0.19 2630 2240 *5.6* 

/cracks 3.13 97 368 89 0.20 2772 2268 5.7

cracks 3.02 94 243 58 0.16 1880 1510 4.6

*HV) 3.10 97 368 90 0.20 2748 2392* 5.6

*/small cracks* 3.06 95 345 84 0.20 2576 2278 *6.0* 

*\*790 (ρ) 3.21 97* 119 31 0.13 - - - *\*1170 (E)* 3.13 94 *176 46* 0.10 - - -

*\*1810 (ρ, E) 3.27 99 381 90* 0.20 2488 2364 4.2 *\*1690 (KIc)* 3.23 97 356 84 0.18 2526 2324 *6.1* 

*(ρ, HV) 3.55 99* 374 83 0.17 *2564 2318* 5.8 *\*1730 (KIc)* 3.50 97 374 83 0.17 2390 2260 *6.4* 

/cracks 3.17 98 387 86 0.19 2850 2408 6.4

/cracks 3.07 95 379 84 0.17 - - -

*(ρ, E) /cracks 3.88 118 473 84* 0.18 3038 2612 7.4

*(HV, KIc)* 3.80 116 457 82 0.18 *3190 2790 7.5* 

Poisson's ratio

Hardness

GPa HV1 HV10

Fracture

MPam1/2

toughness

Sintering temp. optimal for (properties) /descrip tion

*\*1880 (ρ, E,* 

1810

1450 /small

*\*1810 (ρ, E,* 

*\*1730 (KIc)*

*\*1810* 

1950

1880

*\*1810* 

*\*1880* 

modifications of 70 SiC/30 Si3N4 composites; \*optimum temperature for selected properties,

SEM microstructures of 70 SiC/30 Si3N4 with and without the addition of TiB2 and cBN are presented in Fig. 12. The microstructures of the investigated samples are compact and dense, with the ingredients uniformly distributed in the volume of the composite. This demonstrates successful blending, using a planetary mill; EDS analysis, however, showed a

Table 5. Physical-mechanical properties of the best samples selected from different

Sintering temp.

1450- 2030

1650- 1810

1450- 1880

1650- 1810

790- 1810

1650- 1810

1650- 2150

1650- 1950

1730- 1880

1650- 1950

e.g. *1690 (KIc)* - the best value of fracture toughness

vol.% °C °C

range

Sample composition

**70SiC/30Si3N4 composite** 70 SiC(sub-micro)/ 30 Si3N4(sub-micro, Starck)

30 Si3N4(sub-micro, oodfellow)

**70SiC/30Si3N4 composite + Ti**

**70SiC/30Si3N4 composite + TiB2**

**70SiC/30Si3N4 composite + cBN**

30 Si3N4(sub-micro, Goodfellow)

70 SiC(sub-micro)/

70 SiC(sub-micro)/ 30 Si3N4(micro)

70 SiC(sub-micro)/ 30 Si3N4(sub-micro, Starck) + 8 Ti – from TiH2 (micro)

70 SiC(sub-micro)/ 30 Si3N4(sub-micro, Starck)

70 SiC(sub-micro)/ 30 Si3N4(sub-micro, Starck)

70 SiC(sub-micro)/ 30 Si3N4(sub-micro, Starck)

70 SiC(sub-micro)/

70 SiC(sub-micro)/ 30 Si3N4(sub-micro, Starck)

+ 30cBN(micro)

+ 8 TiB2(micro)

+ 30 TiB2(micro)

+ 8cBN(micro)

+ 8cBN(nano)

70 SiC(micro)/ 30 Si3N4(micro)

70 SiC(sub-micro)/30 Si3N4(sub-micro, Starck) – vol.% 70 SiC(micro)/30 Si3N4(micro) – vol.%

70 SiC(sub-micro)/30 Si3N4(sub-micro, Starck) + 8 vol.% TiB2(micro)

70 SiC(sub-micro)/30 Si3N4(sub-micro, Starck) + 30 vol.%TiB2(micro)

70 SiC(sub-micro)/30 Si3N4(sub-micro, Starck) + 30 vol.% cBN(micro)

Fig. 12. SEM microstructures of selected 70 SiC/30 Si3N4 composites with and without the addition of TiB2 and cBN

SiC-Based Composites Sintered with High Pressure Method 329

Additionally, for comparison, the commercial Si3N4 based cutting tool material (ISCAR, IS9-grade) was also tested. The mean curves of friction coefficient for investigated materials in a sliding contact with the Si3N4 ball are presented in Fig. 14. A comparison of the specific

22 °C, ball φ 2mm, 4N, 100m

(micro)

(micro)

0 100 200 300 400 500 600 700 800 900 1000

Time, t [s]

70 SiC/30 Si3N4 composites, sintered without additional phases, as well as the commercial material had the highest coefficients of friction. Average values of the friction coefficient for 70 SiC(sub-micro)/30 Si3N4(sub-micro, Starck), 70 SiC(sub-micro)/30 Si3N4(micro) composites and for commercial Si3N4 based cutting tool material were 0.60, 0.56 and 0.62 respectively. The composites modified by the addition of a TiB2 phase were characterized by intermediate values of the friction coefficient. Average values of the friction coefficient for 70 SiC(sub-micro)/30 Si3N4(sub-micro, Starck) + 8 vol.% TiB2(micro) and 70 SiC(submicro)/30 Si3N4(sub-micro, Starck) + 30 vol.% TiB2(micro) materials were 0.48 and 0.46 respectively. The composite with the addition of 30% cBN was characterized by the lowest average coefficient of friction, at only 0.36. High coefficients of friction generate thermal stress, which is detrimental to the wear behavior of materials. Hard ceramic bodies – possessing high fracture toughness and low coefficients of friction – used in mechanical

Fig. 14. Coefficient of friction of selected 70 SiC/30 Si3N4 – vol.% composites with and

0.0

without the addition of TiB2 and cBN

0.1

0.2

0.3

0.4

0.5

0.6

Coefficient of friction, μ [-]

0.7

0.8

0.9

1.0

wear rate determined by the wear tracks measurement is presented in Fig. 15.

N4

N4

N4

N4

N4

(sub-micro, Starck) - vol.%

(sub-micro, Starck) + 8 vol.% TiB2

(sub-micro, Starck) + 30 vol.% TiB2

(sub-micro, Starck) + 30 vol.% cBN(micro)

(micro) - vol.%

70 SiC(sub-micro)/30 Si3

70 SiC(sub-micro)/30 Si3

70 SiC(sub-micro)/30 Si3

70 SiC(sub-micro)/30 Si3

70 SiC(sub-micro)/30 Si3


Si3 N4

high content of tungsten carbide and zirconium dioxide from the vessel and grinding media used to prepare the mixtures (white areas visible in the microstructures - Fig. 12). The highest quantity of WC was admixed to composite containing 30% of cBN super-abrasive powder. WC has density of 15.7 g/cm3. It explains too high value (118%) of relative density of 70 SiC/30 Si3N4 + 30vol.% cBN composite.

An example of a crack which developed in a Vickers indentation test in the composite modified by addition 30% of cBN is presented in Fig. 13. In this material the mixed mode of crack propagation can be observed. Some parts of fracture are of an intra-crystalline character (indicated as **1** in Fig. 13) while some are inter-crystalline (indicated as **2** in Fig. 13). In both cases the change of direction of crack propagation is visible. A similar effect can be observed in the composites modified by the TiB2 phase. This indicates that the crack deflection mechanism influences on toughening of composites modified by ceramic particles.

Fig. 13. SEM microstructure of 70 SiC/30 Si3N4 composite modified by addition of 30 vol.% cBN phase (the darkest areas). Mixed mode of crack propagation visible: 1) crack propagates through the cBN grains, 2) crack propagates around the cBN grains

High-quality composites, characterized by the homogeneous microstructure, without cracks (formed during the third stage of HPHT sintering process - cooling and releasing of the pressure) and high values of Young's modulus, hardness and fracture toughness were subjected to the tribological tests. The above criteria were fulfilled for following materials:

70 SiC(sub-micro)/30 Si3N4(sub-micro, Starck) – vol.%,

70 SiC(sub-micro)/30 Si3N4(micro) – vol.%,

70 SiC(sub-micro)/30 Si3N4(sub-micro, Starck) + 8 vol.% TiB2(micro),

70 SiC(sub-micro)/30 Si3N4(sub-micro, Starck)+ 30 vol.% TiB2(micro),

70 SiC(sub-micro)/30 Si3N4 (sub-micro, Starck) + 30 vol.% cBN(micro).

high content of tungsten carbide and zirconium dioxide from the vessel and grinding media used to prepare the mixtures (white areas visible in the microstructures - Fig. 12). The highest quantity of WC was admixed to composite containing 30% of cBN super-abrasive powder. WC has density of 15.7 g/cm3. It explains too high value (118%) of relative density

An example of a crack which developed in a Vickers indentation test in the composite modified by addition 30% of cBN is presented in Fig. 13. In this material the mixed mode of crack propagation can be observed. Some parts of fracture are of an intra-crystalline character (indicated as **1** in Fig. 13) while some are inter-crystalline (indicated as **2** in Fig. 13). In both cases the change of direction of crack propagation is visible. A similar effect can be observed in the composites modified by the TiB2 phase. This indicates that the crack deflection mechanism

Fig. 13. SEM microstructure of 70 SiC/30 Si3N4 composite modified by addition of 30 vol.% cBN phase (the darkest areas). Mixed mode of crack propagation visible: 1) crack propagates

High-quality composites, characterized by the homogeneous microstructure, without cracks (formed during the third stage of HPHT sintering process - cooling and releasing of the pressure) and high values of Young's modulus, hardness and fracture toughness were subjected to the tribological tests. The above criteria were fulfilled for following materials:

through the cBN grains, 2) crack propagates around the cBN grains

70 SiC(sub-micro)/30 Si3N4(sub-micro, Starck) + 8 vol.% TiB2(micro), 70 SiC(sub-micro)/30 Si3N4(sub-micro, Starck)+ 30 vol.% TiB2(micro), 70 SiC(sub-micro)/30 Si3N4 (sub-micro, Starck) + 30 vol.% cBN(micro).

70 SiC(sub-micro)/30 Si3N4(sub-micro, Starck) – vol.%,

70 SiC(sub-micro)/30 Si3N4(micro) – vol.%,

influences on toughening of composites modified by ceramic particles.

of 70 SiC/30 Si3N4 + 30vol.% cBN composite.

Additionally, for comparison, the commercial Si3N4 based cutting tool material (ISCAR, IS9-grade) was also tested. The mean curves of friction coefficient for investigated materials in a sliding contact with the Si3N4 ball are presented in Fig. 14. A comparison of the specific wear rate determined by the wear tracks measurement is presented in Fig. 15.

Fig. 14. Coefficient of friction of selected 70 SiC/30 Si3N4 – vol.% composites with and without the addition of TiB2 and cBN

70 SiC/30 Si3N4 composites, sintered without additional phases, as well as the commercial material had the highest coefficients of friction. Average values of the friction coefficient for 70 SiC(sub-micro)/30 Si3N4(sub-micro, Starck), 70 SiC(sub-micro)/30 Si3N4(micro) composites and for commercial Si3N4 based cutting tool material were 0.60, 0.56 and 0.62 respectively. The composites modified by the addition of a TiB2 phase were characterized by intermediate values of the friction coefficient. Average values of the friction coefficient for 70 SiC(sub-micro)/30 Si3N4(sub-micro, Starck) + 8 vol.% TiB2(micro) and 70 SiC(submicro)/30 Si3N4(sub-micro, Starck) + 30 vol.% TiB2(micro) materials were 0.48 and 0.46 respectively. The composite with the addition of 30% cBN was characterized by the lowest average coefficient of friction, at only 0.36. High coefficients of friction generate thermal stress, which is detrimental to the wear behavior of materials. Hard ceramic bodies – possessing high fracture toughness and low coefficients of friction – used in mechanical

SiC-Based Composites Sintered with High Pressure Method 331

Specific wear rates of investigated materials, in most cases, show a similar trend to the trends exhibited by their coefficients of friction. Only 70 SiC/30 Si3N4 composites without addition of third phase and commercial material show some deviations from this trend. 70 SiC(sub-micro)/30 Si3N4(sub-micro, Starck) composite is the least wear resistant. Their specific wear rate reached value of 17.1 × 10-6 mm3/N·m. Subsequently 70 SiC(submicro)/30 Si3N4(micro) and commercial material are classified. Their specific wear rates are 8.7 × 10-6 and 7.2 × 10-6 mm3/N·m respectively. Significantly better are composites modified by addition of TiB2 particels. The specific wear rate of 70 SiC(sub-micro)/30 Si3N4(submicro, Starck) + 8 vol.% TiB2(micro) and 70 SiC(sub-micro)/30 Si3N4(sub-micro, Starck)+ 30 vol.% TiB2(micro) samples equal 3.7 × 10-6 and 2.3 × 10-6 mm3/N·m respectively. The highest wear resistant is exhibited by 70 SiC(sub-micro)/30 Si3N4 (sub-micro, Starck) + 30 vol.% cBN(micro) composite with its specific wear rate value equals only 1.2×10-6 mm3/N·m.

The performed research proves that the HPHT sintering is a method of the future for compacting SiC/Si3N4 nanopowders, due to the short time of the process amounting to 40 seconds that permits the grain growth limitations. The obtained compacts were characterized by the crystallites sizes of 4 to 143 nm, depending on the sintering parameters. SiC and SiC/Si3N4 samples sintered from nanopowders are characterized by the presence of cracks. Cracking of such ceramics occurs as a result of residual micro- and macro-stresses in their structure which overcome the strength of the produced material. The fine powder is characterized by a very large specific surface and high gas content in the sample due to the absorption process of the material particles. During heating, as a result of the increase in temperature, the volume of gases increases, which causes cracking or even permanent fragmentation of the sample. The research regarding the mechanical properties of SiC/Si3N4 composites indicates that materials obtained from submicron powders display the best properties. Density and Young's modulus of the best 70 SiC/30 Si3N4 – vol.% compacts, sintered at 1880 °C, were 3.18 g/cm3 (over 99% the theoretical values) and 377 GPa respectively. This material is also characterized by the highest hardness (HV1 ~3000) and relatively good fracture toughness (4.9 MPa·m1/2). The same material sintered at a lower temperature (1690 °C) has slightly lower values of density (3.14 g/cm3), Young's modulus (363 GPa) and hardness (HV1 2626) but higher fracture toughness (5.6 MPa·m1/2). HPHT sintered sub-micro-70 SiC/30 Si3N4 – vol.% composites have a better combination of

The research concerning mmodification of sub-micro-70 SiC/30 Si3N4 – vol.% composites proves that the addition of the third phase in the form of TiB2 or cBN particles contribute to their further improvement. Composites modified by the addition of 30vol.% cBN micropowder are characterized by the best combination of Young's modulus, hardness, fracture toughness, coefficient of friction and the specific wear rate. Such properties predispose 70 SiC/30 Si3N4 + 30vol.% cBN composites to various advanced engineering

This study was carried out within the framework of the project funded by the Polish Ministry of Science and Higher Education (Project number: DPN/N111/BIALORUS/2009).

mechanical properties than comparable commercial materials.

applications including their use for wear parts and cutting tools.

**5. Conclusions** 

**6. Acknowledgments** 

systems that involve high loads, velocities and temperatures, will reduce costs and be less harmful to the environment.

Fig. 15. Wear rate of selected 70 SiC/30 Si3N4 – vol.% composites with and without the addition of TiB2 and cBN

Specific wear rates of investigated materials, in most cases, show a similar trend to the trends exhibited by their coefficients of friction. Only 70 SiC/30 Si3N4 composites without addition of third phase and commercial material show some deviations from this trend. 70 SiC(sub-micro)/30 Si3N4(sub-micro, Starck) composite is the least wear resistant. Their specific wear rate reached value of 17.1 × 10-6 mm3/N·m. Subsequently 70 SiC(submicro)/30 Si3N4(micro) and commercial material are classified. Their specific wear rates are 8.7 × 10-6 and 7.2 × 10-6 mm3/N·m respectively. Significantly better are composites modified by addition of TiB2 particels. The specific wear rate of 70 SiC(sub-micro)/30 Si3N4(submicro, Starck) + 8 vol.% TiB2(micro) and 70 SiC(sub-micro)/30 Si3N4(sub-micro, Starck)+ 30 vol.% TiB2(micro) samples equal 3.7 × 10-6 and 2.3 × 10-6 mm3/N·m respectively. The highest wear resistant is exhibited by 70 SiC(sub-micro)/30 Si3N4 (sub-micro, Starck) + 30 vol.% cBN(micro) composite with its specific wear rate value equals only 1.2×10-6 mm3/N·m.

### **5. Conclusions**

330 Silicon Carbide – Materials, Processing and Applications in Electronic Devices

systems that involve high loads, velocities and temperatures, will reduce costs and be less

22 °C, ball φ 2mm, 4N, 100m

harmful to the environment.

70 SiC(sub-micro)/30 Si

N3 70 SiC(sub-micro)/30 Si

70 SiC(sub-micro)/30 Si

Fig. 15. Wear rate of selected 70 SiC/30 Si3N4 – vol.% composites with and without the

70 SiC(sub-micro)/30 Si

70 SiC(sub-micro)/30 Si

N3

Si

N3

4 - commercial material

4(sub-micro, Starck)

+ **30 vol.% cBN**

N3

4(sub-micro, Starck)

+ **30 vol.% TiB2**

N3

4(sub-micro, Starck)

+ **8 vol.% TiB2**

N3

4**(micro)**

4**(sub-micro, Starck)**

0

addition of TiB2 and cBN

2

4

6

8

10

Wear rate, Ws(disc) x 10-6 [mm

3/N\*m]

12

14

16

18

20

The performed research proves that the HPHT sintering is a method of the future for compacting SiC/Si3N4 nanopowders, due to the short time of the process amounting to 40 seconds that permits the grain growth limitations. The obtained compacts were characterized by the crystallites sizes of 4 to 143 nm, depending on the sintering parameters. SiC and SiC/Si3N4 samples sintered from nanopowders are characterized by the presence of cracks. Cracking of such ceramics occurs as a result of residual micro- and macro-stresses in their structure which overcome the strength of the produced material. The fine powder is characterized by a very large specific surface and high gas content in the sample due to the absorption process of the material particles. During heating, as a result of the increase in temperature, the volume of gases increases, which causes cracking or even permanent fragmentation of the sample. The research regarding the mechanical properties of SiC/Si3N4 composites indicates that materials obtained from submicron powders display the best properties. Density and Young's modulus of the best 70 SiC/30 Si3N4 – vol.% compacts, sintered at 1880 °C, were 3.18 g/cm3 (over 99% the theoretical values) and 377 GPa respectively. This material is also characterized by the highest hardness (HV1 ~3000) and relatively good fracture toughness (4.9 MPa·m1/2). The same material sintered at a lower temperature (1690 °C) has slightly lower values of density (3.14 g/cm3), Young's modulus (363 GPa) and hardness (HV1 2626) but higher fracture toughness (5.6 MPa·m1/2). HPHT sintered sub-micro-70 SiC/30 Si3N4 – vol.% composites have a better combination of mechanical properties than comparable commercial materials.

The research concerning mmodification of sub-micro-70 SiC/30 Si3N4 – vol.% composites proves that the addition of the third phase in the form of TiB2 or cBN particles contribute to their further improvement. Composites modified by the addition of 30vol.% cBN micropowder are characterized by the best combination of Young's modulus, hardness, fracture toughness, coefficient of friction and the specific wear rate. Such properties predispose 70 SiC/30 Si3N4 + 30vol.% cBN composites to various advanced engineering applications including their use for wear parts and cutting tools.

#### **6. Acknowledgments**

This study was carried out within the framework of the project funded by the Polish Ministry of Science and Higher Education (Project number: DPN/N111/BIALORUS/2009).

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**Part 2** 

**Silicon Carbide:** 

**Electronic Devices and Applications** 

