**High-Quality Epitaxy of Functional Heterostructures with Strain Engineering**

**Chapter 1**

**Provisional chapter**

(a highly

**Strain Effect in Epitaxial Oxide Heterostructures**

**Strain Effect in Epitaxial Oxide Heterostructures**

DOI: 10.5772/intechopen.70125

In recent decades, extensive studies have been conducted on controlling and engineering novel functionalities in transition metal oxide (TMO) heterostructures by epitaxial strain. In this chapter, we discuss popular transition metal oxide thin films in the context of various research fields that are extensively studied in condensed matter physics. These

properties from imposing epitaxial strain (compressive or tensile strain caused by the use of various lattice-mismatched substrates) on these films that cannot be observed in their bulk form. Subsequently, the intrinsic mechanisms for these novel phenomena are discussed based on experimental observations and theoretical modelling. We conclude that by using epitaxial strain, not only can thin film functionalities be tuned but many novel correlated phenomena can also be created. We believe that our collective efforts on the strain engineering of various transition metal oxide thin films will provide an insightful description of this emerging subject from a fundamental physics and nanoscale device

(a high temperature superconductor), SrRuO3


(a strongly correlated metal). We focus on the appearance of novel functional

(a colossal magnetoresistive ferromag-

(a conductive oxide interface),

© 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution,

© 2018 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

and reproduction in any medium, provided the original work is properly cited.

Matter can primarily be classified into three states: (1) gaseous, (2) liquid, and (3) solid (or condensed). In gaseous phases, the interactions among particles (atoms, molecules and ions) are very weak, and therefore they move freely. In liquid phases, the interactions between particles are comparatively strong. In solids, particles are closely packed or condensed, making the interactions between them the strongest compared to the other two states of matter.

Abhijit Biswas and Yoon Hee Jeong

Abhijit Biswas and Yoon Hee Jeong

http://dx.doi.org/10.5772/intechopen.70125

materials include La1.85Sr0.15CuO4

netic metal), BiFeO3

applications point of view.

and LaNiO3

**1. Introduction**

conductive ferromagnetic metal), La0.67Sr0.33MnO3

(a multiferroic oxide), LaAlO3

**Keywords:** oxides, substrates, thin films, strain effect, transport properties

**Abstract**

Additional information is available at the end of the chapter

Additional information is available at the end of the chapter

**Provisional chapter**

## **Strain Effect in Epitaxial Oxide Heterostructures Strain Effect in Epitaxial Oxide Heterostructures**

DOI: 10.5772/intechopen.70125

### Abhijit Biswas and Yoon Hee Jeong Abhijit Biswas and Yoon Hee Jeong

Additional information is available at the end of the chapter Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/intechopen.70125

#### **Abstract**

In recent decades, extensive studies have been conducted on controlling and engineering novel functionalities in transition metal oxide (TMO) heterostructures by epitaxial strain. In this chapter, we discuss popular transition metal oxide thin films in the context of various research fields that are extensively studied in condensed matter physics. These materials include La1.85Sr0.15CuO4 (a high temperature superconductor), SrRuO3 (a highly conductive ferromagnetic metal), La0.67Sr0.33MnO3 (a colossal magnetoresistive ferromagnetic metal), BiFeO3 (a multiferroic oxide), LaAlO3 -SrTiO3 (a conductive oxide interface), and LaNiO3 (a strongly correlated metal). We focus on the appearance of novel functional properties from imposing epitaxial strain (compressive or tensile strain caused by the use of various lattice-mismatched substrates) on these films that cannot be observed in their bulk form. Subsequently, the intrinsic mechanisms for these novel phenomena are discussed based on experimental observations and theoretical modelling. We conclude that by using epitaxial strain, not only can thin film functionalities be tuned but many novel correlated phenomena can also be created. We believe that our collective efforts on the strain engineering of various transition metal oxide thin films will provide an insightful description of this emerging subject from a fundamental physics and nanoscale device applications point of view.

**Keywords:** oxides, substrates, thin films, strain effect, transport properties

## **1. Introduction**

Matter can primarily be classified into three states: (1) gaseous, (2) liquid, and (3) solid (or condensed). In gaseous phases, the interactions among particles (atoms, molecules and ions) are very weak, and therefore they move freely. In liquid phases, the interactions between particles are comparatively strong. In solids, particles are closely packed or condensed, making the interactions between them the strongest compared to the other two states of matter.

© 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. © 2018 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Condensed matters (solids) are mostly crystalline; i.e., they have a periodic arrangement of atoms, ions or molecules. Depending on the periodicity of the atoms, they form different crystal structures. In nature, there are seven types of lattice structures: cubic (e.g., SrTiO<sup>3</sup> ), triclinic (e.g., FeSiO3 ), monoclinic (e.g., BiMnO3 ), orthorhombic (e.g., GdFeO3 ), tetragonal (e.g., BaTiO3 ), rhombohedral (e.g., BiFeO3 ), and hexagonal (e.g., YMnO3 ). Moreover, completely disordered systems displaying non-periodicity of atoms are called non-crystalline amorphous solids (e.g., glass). In reality, both types of systems show complex physics and chemistry with an immense number of functionalities [1].

this chapter. Thin films are those with thicknesses ranging from a few angstroms to several nanometers (~4 Å to 1000 nm). Most thin films are made of oxides, particularly transition

TMO thin films are one of the most investigated research topics in condensed matter physics as they show a variety of phenomena, e.g., metal insulator transitions (MIT), high-temperature superconductivity (HTSC), colossal magnetoresistance (CMR), and multiferrocity (coexistence of magnetism and ferroelectricity), as well as those exhibited by high-mobility two-dimensional electron gases (2DEGs), topological insulators (TI), and quantum spin-liquids (QSL) [6–20]. In TMOs, the *d*-orbital electrons of transition metal elements play a crucial role in determining the physical properties of a compound through the interplay between spin, lattice, charge, and orbital degrees of freedom (**Figure 2a**) [21–24]. Among the various types of TMOs, perovskites are a class of materials that shows almost all the properties mentioned above. They have been a deeply researched topic among physicists owing to their simple crystal structure

Perovskites, named after the Russian Mineralogist Count Lev Aleksevich von Perovski, have

or rare earth metal and the B-site is a transition metal element (e.g., Fe, Co, Ni, Mn, Ti, Ru, and Ir). The structure can easily accommodate a wide range of valence states in both A- and

ited; for example, manganites, ruthenates, nickelates, titanates, and iridates [25]. CaTiO3 was the first perovskite discovered by Gustav Rose in 1839 from samples found in the Ural

tant part of the crystal structure of these materials because the hopping of electrons from one *d*-orbital of the transition metal element to another *d*-orbital depends on the shape, size and position of this octahedron; thus, it affects the physics and chemistry of the material and the

**Figure 2.** (a)-(b) Electronic and structural degrees of freedom in transition metal oxides and their interplay show a variety of correlated multifunctional phenomena in perovskite oxides, for both bulk and heterostructure thin films.

Elsevier Ltd; Copyright 2014 Annual Reviews; Copyright 2008 IOP Publishing Group.

perovskite structure (e.g., SrTiO3

, and A+3B+3O3

type, where the A-site is an alkaline earth

Strain Effect in Epitaxial Oxide Heterostructures http://dx.doi.org/10.5772/intechopen.70125 5

); so the variety of perovskite oxides is unlim-

octahedron (**Figure 2c**). This octahedral cage is the most impor-

octahedra cage. Reprinted with permission from [11, 20, 26]. Copyright 2012

perovskites is surrounded by six O anions,

). Sr-cation is at the center; Ti-cation is

metal oxides (TMOs).

(**Figure 2b**) [25, 26].

B-sites (e.g. A+1B+5O3

forming a corner-shared BO6

a general unit cell crystal structure of the ABO3

, A+2B+4O3

Mountains in Russia. The B-site cation of ABO3

appearance of variety of phenomena [21–24].

(c) Schematic representation of a typical ABO3

surrounded by six O-anion forming TiO6

Irrespective of their structural symmetry, three types of crystalline solids can be found either naturally or artificially, i.e., made in the laboratory. These include polycrystals, single crystals, and thin films. Polycrystalline materials are composed of many crystallites of various sizes that are oriented randomly (**Figure 1a**). Due to the random orientation of crystallites, they have many crystallite grains (~1 μm in size) with grain boundaries, twin boundaries and high porosity. As a result, polycrystals are occasionally considered dirty materials, and they show unusual behaviors at low temperature due to disorder. Polycrystals can be nearly several centimeters in size. Typically, the "solid-state reaction" method is used to synthesize polycrystalline materials [2].

Single crystals, in contrast, contain uniform orientations of their crystal lattices up to their edges, even at the macroscopic level; hence, there are no grain boundaries (**Figure 1b**). Therefore, it becomes easy to determine the various directions of a crystal and measure its properties along a particular direction. As a result, single crystals are regarded to be the cleanest and are very popular among the material science community as they reflect the exact properties of a material. Single crystals are nearly a few mm in size. For the most part, the floating-zone method, Czochralski method and Bridgman-Stockbarger method are used to grow high-quality single crystals [3]. A detailed analysis of these methods is beyond the scope of this chapter.

Thin films consist of very few layers of a solid material. They are typically deposited on structurally compatible metal oxide substrate surfaces (**Figure 1c**) by various thin-film deposition techniques [5]. Details about various thin-film deposition techniques are discussed later in

**Figure 1.** Schematics of a (a) polycrystal, (b) single crystal, and (c) thin film. Polycrystals have many grains, whereas the crystal orientation in single crystals is uniform. Moreover, thin films are grown on structurally compatible metal oxide substrates. Polycrystalline figure was taken from Ref. [4].

this chapter. Thin films are those with thicknesses ranging from a few angstroms to several nanometers (~4 Å to 1000 nm). Most thin films are made of oxides, particularly transition metal oxides (TMOs).

Condensed matters (solids) are mostly crystalline; i.e., they have a periodic arrangement of atoms, ions or molecules. Depending on the periodicity of the atoms, they form different crystal structures. In nature, there are seven types of lattice structures: cubic (e.g., SrTiO<sup>3</sup>

disordered systems displaying non-periodicity of atoms are called non-crystalline amorphous solids (e.g., glass). In reality, both types of systems show complex physics and chemistry with

Irrespective of their structural symmetry, three types of crystalline solids can be found either naturally or artificially, i.e., made in the laboratory. These include polycrystals, single crystals, and thin films. Polycrystalline materials are composed of many crystallites of various sizes that are oriented randomly (**Figure 1a**). Due to the random orientation of crystallites, they have many crystallite grains (~1 μm in size) with grain boundaries, twin boundaries and high porosity. As a result, polycrystals are occasionally considered dirty materials, and they show unusual behaviors at low temperature due to disorder. Polycrystals can be nearly several centimeters in size. Typically, the "solid-state reaction" method is used to synthesize

Single crystals, in contrast, contain uniform orientations of their crystal lattices up to their edges, even at the macroscopic level; hence, there are no grain boundaries (**Figure 1b**). Therefore, it becomes easy to determine the various directions of a crystal and measure its properties along a particular direction. As a result, single crystals are regarded to be the cleanest and are very popular among the material science community as they reflect the exact properties of a material. Single crystals are nearly a few mm in size. For the most part, the floating-zone method, Czochralski method and Bridgman-Stockbarger method are used to grow high-quality single

crystals [3]. A detailed analysis of these methods is beyond the scope of this chapter.

Thin films consist of very few layers of a solid material. They are typically deposited on structurally compatible metal oxide substrate surfaces (**Figure 1c**) by various thin-film deposition techniques [5]. Details about various thin-film deposition techniques are discussed later in

**Figure 1.** Schematics of a (a) polycrystal, (b) single crystal, and (c) thin film. Polycrystals have many grains, whereas the crystal orientation in single crystals is uniform. Moreover, thin films are grown on structurally compatible metal oxide

), orthorhombic (e.g., GdFeO3

), and hexagonal (e.g., YMnO3

), monoclinic (e.g., BiMnO3

), rhombohedral (e.g., BiFeO3

an immense number of functionalities [1].

substrates. Polycrystalline figure was taken from Ref. [4].

polycrystalline materials [2].

clinic (e.g., FeSiO3

BaTiO3

4 Epitaxy

), tri-

), tetragonal (e.g.,

). Moreover, completely

TMO thin films are one of the most investigated research topics in condensed matter physics as they show a variety of phenomena, e.g., metal insulator transitions (MIT), high-temperature superconductivity (HTSC), colossal magnetoresistance (CMR), and multiferrocity (coexistence of magnetism and ferroelectricity), as well as those exhibited by high-mobility two-dimensional electron gases (2DEGs), topological insulators (TI), and quantum spin-liquids (QSL) [6–20]. In TMOs, the *d*-orbital electrons of transition metal elements play a crucial role in determining the physical properties of a compound through the interplay between spin, lattice, charge, and orbital degrees of freedom (**Figure 2a**) [21–24]. Among the various types of TMOs, perovskites are a class of materials that shows almost all the properties mentioned above. They have been a deeply researched topic among physicists owing to their simple crystal structure (**Figure 2b**) [25, 26].

Perovskites, named after the Russian Mineralogist Count Lev Aleksevich von Perovski, have a general unit cell crystal structure of the ABO3 type, where the A-site is an alkaline earth or rare earth metal and the B-site is a transition metal element (e.g., Fe, Co, Ni, Mn, Ti, Ru, and Ir). The structure can easily accommodate a wide range of valence states in both A- and B-sites (e.g. A+1B+5O3 , A+2B+4O3 , and A+3B+3O3 ); so the variety of perovskite oxides is unlimited; for example, manganites, ruthenates, nickelates, titanates, and iridates [25]. CaTiO3 was the first perovskite discovered by Gustav Rose in 1839 from samples found in the Ural Mountains in Russia. The B-site cation of ABO3 perovskites is surrounded by six O anions, forming a corner-shared BO6 octahedron (**Figure 2c**). This octahedral cage is the most important part of the crystal structure of these materials because the hopping of electrons from one *d*-orbital of the transition metal element to another *d*-orbital depends on the shape, size and position of this octahedron; thus, it affects the physics and chemistry of the material and the appearance of variety of phenomena [21–24].

**Figure 2.** (a)-(b) Electronic and structural degrees of freedom in transition metal oxides and their interplay show a variety of correlated multifunctional phenomena in perovskite oxides, for both bulk and heterostructure thin films. (c) Schematic representation of a typical ABO3 perovskite structure (e.g., SrTiO3 ). Sr-cation is at the center; Ti-cation is surrounded by six O-anion forming TiO6 octahedra cage. Reprinted with permission from [11, 20, 26]. Copyright 2012 Elsevier Ltd; Copyright 2014 Annual Reviews; Copyright 2008 IOP Publishing Group.

In bulk polycrystals and single crystals, the shape, size and position of the BO6 octahedra can be manipulated externally by inducing chemical pressure (replacing A-site or B-site cations with other transition metal elements), or by partial oxygen pressure (changing the pressure from the atmospheric one) [6]. Ceramic materials fail structurally under modest strain (typically < 0.1% under strain) as these materials are brittle and thus will crack under this magnitude of strain, limiting the ability of routes involving chemical substitutions to control these materials. Cations with different sizes lead to the distortion of the crystal lattice, which is usually quantified as the Goldsmith tolerance factor [27] *t f* , given by

$$t\_f = \frac{r\_\Lambda + r\_\alpha}{\sqrt{2}(r\_\mu + r\_\alpha)}\tag{1}$$

as it provided an alternative method for making thin-film materials in the laboratory [29]. The PLD technique is probably the most commonly used method for growing oxide thin films [5, 30–32]. Films are grown inside a high-vacuum chamber. A homemade or commercially available polycrystalline target is ablated by an energy source (typically a KrF laser with a wavelength of 248 nm or a frequency-doubled Nd:YAG laser with a wavelength of 532 nm). When the target is ablated, it produces a highly energetic plasma plume from the target. This highly energetic plume contains ions and molecules that are then deposited onto the substrate surface, which is attached on a substrate holder and placed opposite the target along the same out-ofplane axis. The substrate temperature, which is controlled by a heater, is determined from outside the chamber using a pyrometer. The target-to-substrate distance is kept at ~40–50 mm as the dynamics and kinetics of the plume species are limited to a maximum critical distance from the target because of collisions. A schematic diagram of a PLD chamber is shown (**Figure 3a**) [33]. Gaseous atoms condense on a template created by the substrate to form a single crystal. During this process, one needs to fulfill the growing conditions, e.g., optimize the base pres-

Strain Effect in Epitaxial Oxide Heterostructures http://dx.doi.org/10.5772/intechopen.70125 7

, or Ar) pressure, substrate temperature, laser density, spot size, and substrate

surface flatness. Since the whole process is a thermally non-equilibrium one, by tuning all these parameters and ultimately optimizing them, one can grow the highest quality atomically controlled epitaxial oxide thin films (**Figure 3b**) [15]. The *in-situ* growth process can be monitored

The advantages of the PLD technique are: (1) *in-situ* stoichiometric transfer of composition from target to substrate; (2) compatible materials can be grown under oxygen pressures ranging from ultra-high vacuum (UHV) to atmospheric pressure; (3) materials ranging from ultra-thin homoepitaxial thin films to artificial superlattices can be grown with nanometer precision; (4) depending on the availability of the target material, a wide variety of films can be grown; and (5) materials are grown in a compact and inexpensive chamber. Furthermore, the disadvantages are: (1) sub-optimized growth conditions can lead to the non-stoichiometric films; and (2) due to the highly energetic plumes, macroparticles called "droplets" can be deposited on a substrate surfaces within a micrometer range [30]. Therefore, to grow the highest quality epitaxial thin films, one should be aware of these facts. There are many groups around the world who have been pioneers in growing artificial epitaxial single-crystalline thin films of the highest quality.

**Figure 3.** (a) Schematic diagram of a PLD chamber used for growing epitaxial oxide thin films. (b) Schematic of a layerby-layer view of two different materials grown on a substrate. Reprinted with permission from Refs. [15, 33]. Copyright

2013 Materials Research Society; Copyright 2012 IOP Publishing Ltd.

in real time by using the reflection high-energy electron diffraction (RHEED) method.

sure, gas (O<sup>2</sup>

, O3

where *r*A, *r*B, and *r*O represent the ionic radii of ions A, B and O, respectively. The stability and distortion of a crystal structure is indicated by the value of *t f* . For a perfect cubic structure, *tf* is 1. Structure still remains cubic for 0.89 ≤ *tf* ≤ 1.0 [26]. For more lower value of *tf* it forms other types of crystal structures, resulting in structural transitions to orthorhombic, or rhombohedral states that have lower symmetry than the cubic state.

However, as a result of chemical substitutions, disorder is introduced into the materials, which in most cases suppresses and even destroys the properties of a material. These difficulties can be overcome in a unique way in thin films by a disorder-free clean route approach. This can be achieved by growing thin films on substrates that are structurally compatible but have different cubic (pseudo-cubic) lattice constants. This is termed "strain engineering" in epitaxial thin films [28]. Once a strain effect is induced in a film, due to the change of energy scales of various degrees of freedoms (lattice, charge, spin, and orbital), it shows novel properties that cannot be found in parent bulk compound. This means that novel quantum-correlated phenomena can be obtained by the strain engineering of oxide heterostructures, which broadens the field and our understanding of condensed matter physics. In the next section, we will discuss how to grow such atomically controlled high-quality thin films and induce the strain effect in TMO heterostructure.

## **2. Thin film growth methods and substrates**

In recent decades, significant advances have been made in synthesizing epitaxial thin films in the laboratory using various deposition techniques [5]. These methods are: (1) pulsed laser deposition (PLD), (2) molecular beam epitaxy (MBE), (3) off-axis radio frequency magnetron sputtering (RFMS), (4) metal-organic chemical vapor deposition (MOCVD), and (5) chemical solution deposition (CSD). By using these techniques, atomically controlled epitaxial thin films (*epi* means "above" and *taxy* means "in an ordered manner" in Greek), heterostructures and artificial superlattices can be grown. Among these techniques, PLD and MBE are the most popular ones adopted by the thin film community.

#### **2.1. Pulsed laser deposition (PLD)**

In 1986, the successful growth of HTSC YBa2 Cu3 O7−δ (YBCO, *T*SC ~90 K) thin films by the PLD technique by Dijkkamp et al., generated great interest among the material science community, as it provided an alternative method for making thin-film materials in the laboratory [29]. The PLD technique is probably the most commonly used method for growing oxide thin films [5, 30–32]. Films are grown inside a high-vacuum chamber. A homemade or commercially available polycrystalline target is ablated by an energy source (typically a KrF laser with a wavelength of 248 nm or a frequency-doubled Nd:YAG laser with a wavelength of 532 nm). When the target is ablated, it produces a highly energetic plasma plume from the target. This highly energetic plume contains ions and molecules that are then deposited onto the substrate surface, which is attached on a substrate holder and placed opposite the target along the same out-ofplane axis. The substrate temperature, which is controlled by a heater, is determined from outside the chamber using a pyrometer. The target-to-substrate distance is kept at ~40–50 mm as the dynamics and kinetics of the plume species are limited to a maximum critical distance from the target because of collisions. A schematic diagram of a PLD chamber is shown (**Figure 3a**) [33]. Gaseous atoms condense on a template created by the substrate to form a single crystal. During this process, one needs to fulfill the growing conditions, e.g., optimize the base pressure, gas (O<sup>2</sup> , O3 , or Ar) pressure, substrate temperature, laser density, spot size, and substrate surface flatness. Since the whole process is a thermally non-equilibrium one, by tuning all these parameters and ultimately optimizing them, one can grow the highest quality atomically controlled epitaxial oxide thin films (**Figure 3b**) [15]. The *in-situ* growth process can be monitored in real time by using the reflection high-energy electron diffraction (RHEED) method.

In bulk polycrystals and single crystals, the shape, size and position of the BO6

1. Structure still remains cubic for 0.89 ≤ *tf* ≤ 1.0 [26]. For more lower value of *tf*

usually quantified as the Goldsmith tolerance factor [27] *t*

distortion of a crystal structure is indicated by the value of *t*

dral states that have lower symmetry than the cubic state.

**2. Thin film growth methods and substrates**

popular ones adopted by the thin film community.

In 1986, the successful growth of HTSC YBa2

**2.1. Pulsed laser deposition (PLD)**

*t*

6 Epitaxy

be manipulated externally by inducing chemical pressure (replacing A-site or B-site cations with other transition metal elements), or by partial oxygen pressure (changing the pressure from the atmospheric one) [6]. Ceramic materials fail structurally under modest strain (typically < 0.1% under strain) as these materials are brittle and thus will crack under this magnitude of strain, limiting the ability of routes involving chemical substitutions to control these materials. Cations with different sizes lead to the distortion of the crystal lattice, which is

> *<sup>f</sup>* <sup>=</sup> *<sup>r</sup>*<sup>A</sup> <sup>+</sup> *<sup>r</sup>* \_\_\_\_\_\_\_O √ \_\_

where *r*A, *r*B, and *r*O represent the ionic radii of ions A, B and O, respectively. The stability and

types of crystal structures, resulting in structural transitions to orthorhombic, or rhombohe-

However, as a result of chemical substitutions, disorder is introduced into the materials, which in most cases suppresses and even destroys the properties of a material. These difficulties can be overcome in a unique way in thin films by a disorder-free clean route approach. This can be achieved by growing thin films on substrates that are structurally compatible but have different cubic (pseudo-cubic) lattice constants. This is termed "strain engineering" in epitaxial thin films [28]. Once a strain effect is induced in a film, due to the change of energy scales of various degrees of freedoms (lattice, charge, spin, and orbital), it shows novel properties that cannot be found in parent bulk compound. This means that novel quantum-correlated phenomena can be obtained by the strain engineering of oxide heterostructures, which broadens the field and our understanding of condensed matter physics. In the next section, we will discuss how to grow such atomically controlled high-quality thin films and induce the strain effect in TMO heterostructure.

In recent decades, significant advances have been made in synthesizing epitaxial thin films in the laboratory using various deposition techniques [5]. These methods are: (1) pulsed laser deposition (PLD), (2) molecular beam epitaxy (MBE), (3) off-axis radio frequency magnetron sputtering (RFMS), (4) metal-organic chemical vapor deposition (MOCVD), and (5) chemical solution deposition (CSD). By using these techniques, atomically controlled epitaxial thin films (*epi* means "above" and *taxy* means "in an ordered manner" in Greek), heterostructures and artificial superlattices can be grown. Among these techniques, PLD and MBE are the most

Cu3

technique by Dijkkamp et al., generated great interest among the material science community,

*f*

*f*

, given by

<sup>2</sup>(*r*<sup>B</sup> <sup>+</sup> *<sup>r</sup>*O) (1)

O7−δ (YBCO, *T*SC ~90 K) thin films by the PLD

. For a perfect cubic structure, *tf*

octahedra can

is

it forms other

The advantages of the PLD technique are: (1) *in-situ* stoichiometric transfer of composition from target to substrate; (2) compatible materials can be grown under oxygen pressures ranging from ultra-high vacuum (UHV) to atmospheric pressure; (3) materials ranging from ultra-thin homoepitaxial thin films to artificial superlattices can be grown with nanometer precision; (4) depending on the availability of the target material, a wide variety of films can be grown; and (5) materials are grown in a compact and inexpensive chamber. Furthermore, the disadvantages are: (1) sub-optimized growth conditions can lead to the non-stoichiometric films; and (2) due to the highly energetic plumes, macroparticles called "droplets" can be deposited on a substrate surfaces within a micrometer range [30]. Therefore, to grow the highest quality epitaxial thin films, one should be aware of these facts. There are many groups around the world who have been pioneers in growing artificial epitaxial single-crystalline thin films of the highest quality.

**Figure 3.** (a) Schematic diagram of a PLD chamber used for growing epitaxial oxide thin films. (b) Schematic of a layerby-layer view of two different materials grown on a substrate. Reprinted with permission from Refs. [15, 33]. Copyright 2013 Materials Research Society; Copyright 2012 IOP Publishing Ltd.

## **2.2. Molecular beam epitaxy (MBE)**

Molecular beam epitaxy (MBE) is also a method used to grow high-quality epitaxial thin films [5, 34]. It was invented in 1960s at Bell Labs by Arthur and Alfred Y. Cho [35]. The overall schematic of MBE is very similar to that of PLD thin film deposition. The only difference is the target material. Instead of a ceramic target, one uses "guns" called effusion cells (**Figure 4a**) [28, 36]. At the same time, one generates molecules from each cell using a highly intense laser beam (termed "atomic spray painting" by D. G. Schlom, a famous MBE thin film scientist) (**Figure 4b**) [28]. The spray duration is individually controlled for each beam by shutters. Once all the deposition conditions are satisfied, the ejected molecules travel to the substrate surface, condenses and form a single-crystalline thin film compatible with the substrate crystal structure. One of the main advantages of MBE thin film growth is its extreme cleanliness; i.e., no dirt particles (highly energetic species) or unwanted gas molecules can interfere with or contaminate the single-crystal thin film growth.

between the substrate and film [38]. When choosing a metal oxide substrate for growing epi-

**1.** Lattice matching between the substrate and film, which is important for the growth of

**2.** No chemical reaction between the elements of the substrate and film (chemically

**3.** Thermal-expansion matching between the substrate and film, as films are generally grown

**4.** Surface quality of the substrate (e.g., free of cracks, unwanted particles, defects, and im-

In most cases, the lattice constant and structure of a thin film should be compatible with those of the substrate to grow epitaxial films in their most natural state (**Figure 5a**). For most ABO3 perovskites, their lattice constants range from 3.80 to 4.00 Å [39]. Fortunately, there are many perovskite single-crystal metal oxide substrates available commercially with lattice constants

**Figure 5.** (a) Structural relationship between the substrate and film. For the most natural growth state of a film, a film's

(b) List of cubic (pseudo-cubic) substrates and thin films within the lattice constant range from 3.70 to 4.00 Å. With a judicial choice of substrate, various atomically controlled high-quality thin films can be grown. Reprinted and adapted

), and the two should have structural compatibility.

Strain Effect in Epitaxial Oxide Heterostructures http://dx.doi.org/10.5772/intechopen.70125 9

) should be similar to the substrate's lattice constant (*a*<sup>s</sup>

with permission from Ref. [41]. Copyright 2014 Materials Research Society.

taxial films, one should consider the following factors:

most natural state films (structural compatibility).

at high temperatures (good thermal-expansion match).

compatibility).

pure phases).

lattice constant (*a*<sup>f</sup>

#### **2.3. Substrate selection for epitaxial thin films**

Substrates seem to be the basis of all thin film growth. Choosing a suitable metal oxide substrate is an important factor for growing high-quality epitaxial thin films as the structure and properties of a thin film depends on the underlying substrate and the interfacial interaction

**Figure 4.** (a) Schematic diagram of a laser-MBE chamber for growing epitaxial thin films. (b) Schematic illustration of layer-by-layer MBE thin film growth, i.e., "atomic spray painting." Reprinted with permission from [28, 37]. Copyright 2008 The American Ceramic Society; Copyright 2014 Macmillan Publishers Limited.

between the substrate and film [38]. When choosing a metal oxide substrate for growing epitaxial films, one should consider the following factors:

**2.2. Molecular beam epitaxy (MBE)**

8 Epitaxy

or contaminate the single-crystal thin film growth.

**2.3. Substrate selection for epitaxial thin films**

Molecular beam epitaxy (MBE) is also a method used to grow high-quality epitaxial thin films [5, 34]. It was invented in 1960s at Bell Labs by Arthur and Alfred Y. Cho [35]. The overall schematic of MBE is very similar to that of PLD thin film deposition. The only difference is the target material. Instead of a ceramic target, one uses "guns" called effusion cells (**Figure 4a**) [28, 36]. At the same time, one generates molecules from each cell using a highly intense laser beam (termed "atomic spray painting" by D. G. Schlom, a famous MBE thin film scientist) (**Figure 4b**) [28]. The spray duration is individually controlled for each beam by shutters. Once all the deposition conditions are satisfied, the ejected molecules travel to the substrate surface, condenses and form a single-crystalline thin film compatible with the substrate crystal structure. One of the main advantages of MBE thin film growth is its extreme cleanliness; i.e., no dirt particles (highly energetic species) or unwanted gas molecules can interfere with

Substrates seem to be the basis of all thin film growth. Choosing a suitable metal oxide substrate is an important factor for growing high-quality epitaxial thin films as the structure and properties of a thin film depends on the underlying substrate and the interfacial interaction

**Figure 4.** (a) Schematic diagram of a laser-MBE chamber for growing epitaxial thin films. (b) Schematic illustration of layer-by-layer MBE thin film growth, i.e., "atomic spray painting." Reprinted with permission from [28, 37]. Copyright

2008 The American Ceramic Society; Copyright 2014 Macmillan Publishers Limited.


In most cases, the lattice constant and structure of a thin film should be compatible with those of the substrate to grow epitaxial films in their most natural state (**Figure 5a**). For most ABO3 perovskites, their lattice constants range from 3.80 to 4.00 Å [39]. Fortunately, there are many perovskite single-crystal metal oxide substrates available commercially with lattice constants

**Figure 5.** (a) Structural relationship between the substrate and film. For the most natural growth state of a film, a film's lattice constant (*a*<sup>f</sup> ) should be similar to the substrate's lattice constant (*a*<sup>s</sup> ), and the two should have structural compatibility. (b) List of cubic (pseudo-cubic) substrates and thin films within the lattice constant range from 3.70 to 4.00 Å. With a judicial choice of substrate, various atomically controlled high-quality thin films can be grown. Reprinted and adapted with permission from Ref. [41]. Copyright 2014 Materials Research Society.

ranging from 3.70 to 4.20 Å [28, 33, 40–42]. Among various available perovskite substrates, insulating SrTiO3 is the most popular one. It has a cubic structure with a lattice constant of ~3.905 Å. There are also a broad range of substrates available with similar structures to that of SrTiO3 while possessing different lattice constants and crystal orientations. These commercially available substrates include *RE*ScO3 (*RE* = rare earths), La0.18Sr0.82Al0.59Ta0.41O3 (LSAT), NdGaO3 , SrLaAlO4 , LaAlO3 , SrLaAlO4 , and YAlO3 (**Figure 5b**). Thus, after careful consideration of all the important factors listed above and a film's lattice constant, it is easy to choose a substrate suitable for the epitaxial growth of thin films.

## **3. Strain in perovskite thin films**

#### **3.1. Strain engineering of perovskite thin films**

Strain engineering is a unique way to create the novel functionalities in epitaxial oxide thin films [40–43]. From substrate-thin film relation point of view, when the lattice constant of a film (*a*<sup>f</sup> ) is dissimilar to the lattice constant a substrate (*a*<sup>s</sup> ), compression or elongation occurs within the film's crystal structure and thus elastic strain is induced in the film [41]. For cases of dissimilar lattice constants (*a*<sup>f</sup> ≠ *a*<sup>s</sup> ), the structure of the thin film tries to take the structure of the substrate, causing structural changes (mainly the change in BO6 octahedron rotation, tilting, and distortion, and/or the change in B─O bond length) to occur from the original atomic position. This is defined as the typical strain effect in thin films. Quantitatively, the amount of strain (*ε*) induced in a film is defined as

$$\mathbf{c} = \begin{pmatrix} \frac{a\_s - a\_i}{a\_i} \end{pmatrix} \tag{2}$$

generate from multifunctionality may create an economically viable path superseding the miniaturization limit of silicon electronic devices. In this perspective, oxide electronics based on multifunctional properties of transition metal oxides looks promising [46, 47]. Even more exciting is the fact that advanced thin film growth techniques with atomic controllability provide further opportunities to design and synthesize artificial complex transition metal oxide heterostructures and superlattices to bring forth emergent physical properties, normally not seen in bulk states. However, despite the rapid progress and tremendous success in obtaining novel functionalities by the strain engineering of epitaxial oxide heterostructures, there is no general rule or theory available till date for predicting a material's electronic, magnetic, or other functional properties. This is perhaps due to a lack of knowledge about fully resolved atomic structures, especially the position of non-trivial oxygen atoms, as no experimental tool has yet been developed for the direct observation of oxygen atoms. In view of the lack of an experimental tool of this kind for transition metal oxides, electronic structure calculations could play a role instead. J. M. Rondinelli and N. A. Spaldin's recent article is particularly

**Figure 6.** "*Strain engineering*" of perovskite heterostructures. (a) Compressive and (b) tensile strain is induced in a film

In principle, for compressive strain, a thin film's lattice is compressed along the in-plane direction, and expanded along the out-of-plane direction. On the other hand, for tensile strained films, lattices expand along the in-plane direction and shrink along the out-of-pane direction. Reprinted with permission from Ref. [41]. Copyright 2014 Materials Research

> *a*<sup>s</sup>

, whereas for tensile strain, *a*<sup>f</sup>

Strain Effect in Epitaxial Oxide Heterostructures http://dx.doi.org/10.5772/intechopen.70125

> < *a*<sup>s</sup> .

11

through the use of various lattice-mismatched substrates. For compressive strain, *a*<sup>f</sup>

The detailed structural distortion obtained by the movement of oxygen atoms due to strain is highly significant and it has a strong influence on the electronic properties of TMOs. In fact, just a small modification in an atomic structure would change the relevant energy scales (lattice, charge, spin, and orbital) and it is hard to predict functionalities as material properties are strongly dependent on the competition between these energy scales. To illustrate the

chain with a 180° B─O─B bond angle (**Figure 7a**). There are very few systems that adopt this

perovskite struc-

3*m*. The most important part of this struc-

(*B* = transition metal) octahedron, which results in an O─B─O─B

); however, in practice, most perovskites show structural distor-

insightful in this regard, and we follow them briefly in this section [48].

effects of structural distortions in thin films, let us start with the ideal ABO<sup>3</sup>

tions that lower their symmetry from that of a highly symmetric cubic structure.

ture which is a simple cubic one with space group Pm¯

ture is its corner-shared BO6

Society.

cubic structure (e.g., SrTiO3

where *a*<sup>s</sup> is the substrate lattice constant and *a*<sup>f</sup> is the film lattice constant.

Generally, compressive strain (**Figure 6a**) is induced in a film when *a*<sup>f</sup> > *a*<sup>s</sup> , whereas tensile strain (**Figure 6b**) is induced in a film when *a*<sup>f</sup> < *a*<sup>s</sup> . Under these epitaxial strain scenarios, the properties of functional oxide thin films can be drastically altered. Currently, the strain (*ε*) of ~2–3% is quite common in epitaxial oxide thin films, with highest strain to date of ~6.5% being imposed on multiferroic BiFeO3 films grown on a highly lattice-mismatched (1 1 0) YAlO<sup>3</sup> substrate [43]. Thus, elastic strain is a viable route to observe materials with exceptional properties that cannot be observed in their bulk form by any other means [44, 45]. Although it looks simple, the intrinsic mechanism of the appearance of novel functionalities induced by the strain effect is quite complex to understand. In the next section, we briefly discuss about the intrinsic mechanism of the strain effect in perovskite thin films.

#### **3.2. Mechanism of the strain effect in perovskite thin films**

In post-Moore era, electronic devices with multifunctionality may offer a new alternative to replace the current silicon-based technology because the additional value the devices would

ranging from 3.70 to 4.20 Å [28, 33, 40–42]. Among various available perovskite substrates,

~3.905 Å. There are also a broad range of substrates available with similar structures to that

ation of all the important factors listed above and a film's lattice constant, it is easy to choose

Strain engineering is a unique way to create the novel functionalities in epitaxial oxide thin films [40–43]. From substrate-thin film relation point of view, when the lattice constant of a

within the film's crystal structure and thus elastic strain is induced in the film [41]. For cases

ing, and distortion, and/or the change in B─O bond length) to occur from the original atomic position. This is defined as the typical strain effect in thin films. Quantitatively, the amount of

*<sup>a</sup>*<sup>s</sup> - *<sup>a</sup>* \_\_\_\_f

< *a*<sup>s</sup>

properties of functional oxide thin films can be drastically altered. Currently, the strain (*ε*) of ~2–3% is quite common in epitaxial oxide thin films, with highest strain to date of ~6.5% being

strate [43]. Thus, elastic strain is a viable route to observe materials with exceptional properties that cannot be observed in their bulk form by any other means [44, 45]. Although it looks simple, the intrinsic mechanism of the appearance of novel functionalities induced by the strain effect is quite complex to understand. In the next section, we briefly discuss about the

In post-Moore era, electronic devices with multifunctionality may offer a new alternative to replace the current silicon-based technology because the additional value the devices would

, and YAlO3

while possessing different lattice constants and crystal orientations. These commer-

is the most popular one. It has a cubic structure with a lattice constant of

(*RE* = rare earths), La0.18Sr0.82Al0.59Ta0.41O3

), the structure of the thin film tries to take the structure of

is the film lattice constant.

films grown on a highly lattice-mismatched (1 1 0) YAlO<sup>3</sup>

*<sup>a</sup>*<sup>f</sup> ) (2)

> *a*<sup>s</sup>

. Under these epitaxial strain scenarios, the

(**Figure 5b**). Thus, after careful consider-

), compression or elongation occurs

octahedron rotation, tilt-

, whereas tensile

sub-

(LSAT),

insulating SrTiO3

, SrLaAlO4

cially available substrates include *RE*ScO3

**3. Strain in perovskite thin films**

of dissimilar lattice constants (*a*<sup>f</sup> ≠ *a*<sup>s</sup>

strain (*ε*) induced in a film is defined as

ϵ = (

strain (**Figure 6b**) is induced in a film when *a*<sup>f</sup>

imposed on multiferroic BiFeO3

is the substrate lattice constant and *a*<sup>f</sup>

, LaAlO3

**3.1. Strain engineering of perovskite thin films**

a substrate suitable for the epitaxial growth of thin films.

, SrLaAlO4

) is dissimilar to the lattice constant a substrate (*a*<sup>s</sup>

the substrate, causing structural changes (mainly the change in BO6

Generally, compressive strain (**Figure 6a**) is induced in a film when *a*<sup>f</sup>

intrinsic mechanism of the strain effect in perovskite thin films.

**3.2. Mechanism of the strain effect in perovskite thin films**

of SrTiO3

10 Epitaxy

NdGaO3

film (*a*<sup>f</sup>

where *a*<sup>s</sup>

**Figure 6.** "*Strain engineering*" of perovskite heterostructures. (a) Compressive and (b) tensile strain is induced in a film through the use of various lattice-mismatched substrates. For compressive strain, *a*<sup>f</sup> > *a*<sup>s</sup> , whereas for tensile strain, *a*<sup>f</sup> < *a*<sup>s</sup> . In principle, for compressive strain, a thin film's lattice is compressed along the in-plane direction, and expanded along the out-of-plane direction. On the other hand, for tensile strained films, lattices expand along the in-plane direction and shrink along the out-of-pane direction. Reprinted with permission from Ref. [41]. Copyright 2014 Materials Research Society.

generate from multifunctionality may create an economically viable path superseding the miniaturization limit of silicon electronic devices. In this perspective, oxide electronics based on multifunctional properties of transition metal oxides looks promising [46, 47]. Even more exciting is the fact that advanced thin film growth techniques with atomic controllability provide further opportunities to design and synthesize artificial complex transition metal oxide heterostructures and superlattices to bring forth emergent physical properties, normally not seen in bulk states. However, despite the rapid progress and tremendous success in obtaining novel functionalities by the strain engineering of epitaxial oxide heterostructures, there is no general rule or theory available till date for predicting a material's electronic, magnetic, or other functional properties. This is perhaps due to a lack of knowledge about fully resolved atomic structures, especially the position of non-trivial oxygen atoms, as no experimental tool has yet been developed for the direct observation of oxygen atoms. In view of the lack of an experimental tool of this kind for transition metal oxides, electronic structure calculations could play a role instead. J. M. Rondinelli and N. A. Spaldin's recent article is particularly insightful in this regard, and we follow them briefly in this section [48].

The detailed structural distortion obtained by the movement of oxygen atoms due to strain is highly significant and it has a strong influence on the electronic properties of TMOs. In fact, just a small modification in an atomic structure would change the relevant energy scales (lattice, charge, spin, and orbital) and it is hard to predict functionalities as material properties are strongly dependent on the competition between these energy scales. To illustrate the effects of structural distortions in thin films, let us start with the ideal ABO<sup>3</sup> perovskite structure which is a simple cubic one with space group Pm¯ 3*m*. The most important part of this structure is its corner-shared BO6 (*B* = transition metal) octahedron, which results in an O─B─O─B chain with a 180° B─O─B bond angle (**Figure 7a**). There are very few systems that adopt this cubic structure (e.g., SrTiO3 ); however, in practice, most perovskites show structural distortions that lower their symmetry from that of a highly symmetric cubic structure.

This structural distortion is imposed on a thin film by the appropriate choice of lattice-mismatched substrates. It is widely believed that the strain imposed by film-substrate lattice mismatch generally changes the in-plane lattice parameter, but exactly what occurs still remains unclear and moreover is difficult to determine experimentally. Two possibilities remain: (1) changes in the in-plane lattice parameter are offset by changes in the in-plane metal-oxygen B─O bond lengths (**Figure 8a** and **b**), or (2) while keeping the B─O distance fixed, the lattice mismatch is offset by a change in magnitude of the tilt patterns through the rigid rotation of

octahedron (**Figure 8c** and **d**). This is highly significant as, for example, the magni-

*<sup>d</sup>*3.5 (3)

Strain Effect in Epitaxial Oxide Heterostructures http://dx.doi.org/10.5772/intechopen.70125 13

tude and symmetry of a crystal field are affected by changes in the B─O bond length, whereas the strength and sign of a superexchange interaction are affected by changes in the B─O─B

Quantitatively, changes in the B─O bond length and B─O─B bond angles of octahedra affect

where *ψ* = (*π − φ*)/2 is the buckling deviation of the B─O─B bond angle *φ* from *π* and *d* is the B─O bond length (**Figure 8e**) [54]. Due to rigidity, it is hard to change the B─O bond-length. Thus, as a result of imposed strain, octahedral rotation and tilt angle changes, the electron hopping changes within the *d*-orbitals and thus changes a material's functionalities. Changes in the bandwidth also affect the effective correlation as in general changes in these energy scales cause the appearance of novel functionalities in oxide heterostructures under strain.

**Figure 8.** (a) Contraction and (b) elongation of B─O bond lengths, *d*, in a coherently strained perovskite film. Contraction is due to compressive strain, whereas elongation is due to tensile strain. Alternatively, change in the in-plane lattice parameters are due to the rotation of octahedra (c) perpendicular to the plane of the substrate or (d) about an axis parallel to the plane of the substrate. (e) Rotation (*θ*) and tilt (*φ*) angle used to describe the substrate-induced changes of octahedra. Reprinted with permission from Ref. [48]. Copyright 2011 WILEY-VCH Verlag GmbH & Co. KGaA,

perovskites as follows:

the BO6

Weinheim.

bond angle [48].

the bandwidth (*W*) of ABO3

*<sup>W</sup>* <sup>∝</sup> cos*<sup>ψ</sup>* \_\_\_\_\_

**Figure 7.** (a) The ideal ABO3 perovskite crystal structure showing tilt in all three directions. (b) Distortion of BO6 octahedra along various directions, lowering the symmetry of the cubic structure and forming other crystal structure. The +ve sign indicates in-phase rotation (*c*<sup>+</sup> ), and the −ve sign indicates out-of-phase rotation (*c*<sup>−</sup> ). Reprinted with permission from Ref. [48]. Copyright 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Rotations or tilts of BO6 octahedra around the high-symmetry axes are the most common distortions in perovskite structures [49–51]. These are conveniently described by the Glazer notation [52, 53] and written as *a*# *b*# *c*# , where *a*, *b*, and *c* are the axes around which rotation occurs and the superscripts indicate whether the octahedral rotation is in phase (+) or out of phase (−). Thus, *a*, *b*, and *c* are not identical with the lattice constants; instead, they indicate that the nearest neighbor transition metal distances along that direction are equivalent. As perovskites are three-dimensional systems, a rotation or tilt in one direction restricts the rotation or tilt in other directions. Depending on the rotation or tilt of the BO6 octahedra, the cubic structure can deform, leading to the symmetry lowering of other crystal structures (**Figure 7b**) [48–51].

This structural distortion is imposed on a thin film by the appropriate choice of lattice-mismatched substrates. It is widely believed that the strain imposed by film-substrate lattice mismatch generally changes the in-plane lattice parameter, but exactly what occurs still remains unclear and moreover is difficult to determine experimentally. Two possibilities remain: (1) changes in the in-plane lattice parameter are offset by changes in the in-plane metal-oxygen B─O bond lengths (**Figure 8a** and **b**), or (2) while keeping the B─O distance fixed, the lattice mismatch is offset by a change in magnitude of the tilt patterns through the rigid rotation of the BO6 octahedron (**Figure 8c** and **d**). This is highly significant as, for example, the magnitude and symmetry of a crystal field are affected by changes in the B─O bond length, whereas the strength and sign of a superexchange interaction are affected by changes in the B─O─B bond angle [48].

Quantitatively, changes in the B─O bond length and B─O─B bond angles of octahedra affect the bandwidth (*W*) of ABO3 perovskites as follows:

$$\mathcal{W} \propto \frac{\cos \psi}{d^{1.8}} \tag{3}$$

where *ψ* = (*π − φ*)/2 is the buckling deviation of the B─O─B bond angle *φ* from *π* and *d* is the B─O bond length (**Figure 8e**) [54]. Due to rigidity, it is hard to change the B─O bond-length. Thus, as a result of imposed strain, octahedral rotation and tilt angle changes, the electron hopping changes within the *d*-orbitals and thus changes a material's functionalities. Changes in the bandwidth also affect the effective correlation as in general changes in these energy scales cause the appearance of novel functionalities in oxide heterostructures under strain.

Rotations or tilts of BO6

**Figure 7.** (a) The ideal ABO3

12 Epitaxy

indicates in-phase rotation (*c*<sup>+</sup>

(**Figure 7b**) [48–51].

notation [52, 53] and written as *a*#

octahedra around the high-symmetry axes are the most common

perovskite crystal structure showing tilt in all three directions. (b) Distortion of BO6

, where *a*, *b*, and *c* are the axes around which rotation

octahedra,

octahedra

). Reprinted with permission from Ref.

distortions in perovskite structures [49–51]. These are conveniently described by the Glazer

along various directions, lowering the symmetry of the cubic structure and forming other crystal structure. The +ve sign

), and the −ve sign indicates out-of-phase rotation (*c*<sup>−</sup>

occurs and the superscripts indicate whether the octahedral rotation is in phase (+) or out of phase (−). Thus, *a*, *b*, and *c* are not identical with the lattice constants; instead, they indicate that the nearest neighbor transition metal distances along that direction are equivalent. As perovskites are three-dimensional systems, a rotation or tilt in one direction restricts the

the cubic structure can deform, leading to the symmetry lowering of other crystal structures

rotation or tilt in other directions. Depending on the rotation or tilt of the BO6

*b*# *c*#

[48]. Copyright 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

**Figure 8.** (a) Contraction and (b) elongation of B─O bond lengths, *d*, in a coherently strained perovskite film. Contraction is due to compressive strain, whereas elongation is due to tensile strain. Alternatively, change in the in-plane lattice parameters are due to the rotation of octahedra (c) perpendicular to the plane of the substrate or (d) about an axis parallel to the plane of the substrate. (e) Rotation (*θ*) and tilt (*φ*) angle used to describe the substrate-induced changes of octahedra. Reprinted with permission from Ref. [48]. Copyright 2011 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Along with these changes in bond length, bond-angle and crystal symmetry that determine changes in the in-plane lattice parameters, another possibility for substrate-induced changes in lattice parameter remains: the defect stoichiometry or defect concentration of the material. Defect concentration, especially the oxygen concentration, is particularly important as films are generally grown under the high oxygen pressure or high vacuum. To accommodate the strain energy, it is easy to form oxygen vacancies. It is known that the higher the concentration of oxygen vacancies, the larger the lattice constants [55]. Since strain is induced by various lattice-mismatched substrates, it is difficult to establish whether changes in defect concentration are an intrinsic thermodynamic response due to strain or if they arise due to an extrinsic effect during the growth process.

## **4. Material properties tuned by epitaxial strain**

## **4.1. A high temperature superconductor: La1.85Sr0.15CuO4**

In 1986, the discovery of HTSC in the cuprate oxide family by Bednorz and Müller generated considerable interest within the material science community, both in fundamental and applied research, due to the possibility obtaining oxides that are room-temperature superconductors [56]. La1.85Sr0.15CuO4 (LSCO) is one example of these oxides. La<sup>2</sup> CuO4 is an antiferromagnetic insulator, but upon doping divalent Sr2+ ions in the trivalent La3+ site, magnetism is suppressed, and the compound makes a transition from an insulating to a superconducting state [57]. LSCO has a K2 NiF4 -type tetragonal structure with bulk lattice constants of *a* = 3.777 Å and *c* = 13.226 Å and space group *P42*/*ncm* (**Figure 9a**) [58]. It has quasi-two-dimensional copper-oxygen (Cu─O) planes, and superconductivity occurs within these planes [59]. In the bulk, around the optimal doping region, its maximum superconducting transition temperature is *T*C ~25 K (**Figure 9b** and **c**) [60]. Its carrier doping remains within the Cu─O planes and the formation of electron pairs due to coupling between electrons and phonons seem to play a major role in achieving superconductivity [61]. Its critical temperature is controlled by either the density of electron pairs or the strength of electron pairing interactions [62].

In principle, external perturbation is applied to a material to enhance its functional properties, suggesting that substrate-induced strain might be a way to enhance the superconducting *T*C of cuprates (**Figure 10a**) [63–70]. Indeed, Sato et al., and Locquet et al., grew La2−*<sup>x</sup>* Sr*x* CuO4 (LSCO; *x* = 0.1, 0.15) thin films on two different substrates, such as (0 0 1) SrTiO<sup>3</sup> and (0 0 1) SrLaAlO4 [63, 64]. Surprisingly, Locquet et al., observed that when films are grown on highly strained (0 0 1) SrLaAlO4 substrates (*a*<sup>s</sup> = 3.75 Å), which produces ~0.5% compressive strain onto these films, this amount of strain is enough to modify the superconducting *T*C, making *T*C almost double to its value found in the bulk, i.e., *T*C ~49.1 K (**Figure 10b**) [64]. Independently, Sato, also reported the same study (**Figure 10c**) [69]. This is thought to be associated with straininduced lattice deformation, which modifies the energy scales, leading to the formation and condensation of superconducting pairs. It was also observed that the residual resistivity value (*ρ* (0 K)) decreases as *T*C increases [69]. More specifically, increasing *T*C has a clear correlation with low residual resistivity. As stated by Sato, an increase in Cu─O bond length enhances the electrostatic potential at the Cu site relative to that at the oxygen site in the Cu─O plane.

**Figure 9.** (a) Schematic representation of the K2

NiF4

Copyright 1992 American Physical Society; Copyright 2013 Macmillan Publishers Limited.

constants of *a* = 3.777 Å and *c* = 13.226 Å. (b) Resistivity of bulk single LSCO, showing the appearance of superconducting *TSC* upon divalent Sr hole doping. (c) Sr hole doping dependence temperature vs. the material properties phase diagram of LSCO, showing that the system makes a transition from an antiferromagnetic insulator to a superconducting phase with the increase in Sr doping. Crystal structure was drawn using VESTA software. Reprinted with permission [57, 60].


Sr*x* CuO4

Strain Effect in Epitaxial Oxide Heterostructures http://dx.doi.org/10.5772/intechopen.70125 15

(LSCO) with lattice

Along with these changes in bond length, bond-angle and crystal symmetry that determine changes in the in-plane lattice parameters, another possibility for substrate-induced changes in lattice parameter remains: the defect stoichiometry or defect concentration of the material. Defect concentration, especially the oxygen concentration, is particularly important as films are generally grown under the high oxygen pressure or high vacuum. To accommodate the strain energy, it is easy to form oxygen vacancies. It is known that the higher the concentration of oxygen vacancies, the larger the lattice constants [55]. Since strain is induced by various lattice-mismatched substrates, it is difficult to establish whether changes in defect concentration are an intrinsic thermodynamic response due to strain or if they arise due to an extrinsic

In 1986, the discovery of HTSC in the cuprate oxide family by Bednorz and Müller generated considerable interest within the material science community, both in fundamental and applied research, due to the possibility obtaining oxides that are room-temperature superconductors

insulator, but upon doping divalent Sr2+ ions in the trivalent La3+ site, magnetism is suppressed, and the compound makes a transition from an insulating to a superconducting state [57]. LSCO

and space group *P42*/*ncm* (**Figure 9a**) [58]. It has quasi-two-dimensional copper-oxygen (Cu─O) planes, and superconductivity occurs within these planes [59]. In the bulk, around the optimal doping region, its maximum superconducting transition temperature is *T*C ~25 K (**Figure 9b** and **c**) [60]. Its carrier doping remains within the Cu─O planes and the formation of electron pairs due to coupling between electrons and phonons seem to play a major role in achieving superconductivity [61]. Its critical temperature is controlled by either the density of electron

In principle, external perturbation is applied to a material to enhance its functional properties, suggesting that substrate-induced strain might be a way to enhance the superconducting *T*C of

[63, 64]. Surprisingly, Locquet et al., observed that when films are grown on highly strained

films, this amount of strain is enough to modify the superconducting *T*C, making *T*C almost double to its value found in the bulk, i.e., *T*C ~49.1 K (**Figure 10b**) [64]. Independently, Sato, also reported the same study (**Figure 10c**) [69]. This is thought to be associated with straininduced lattice deformation, which modifies the energy scales, leading to the formation and condensation of superconducting pairs. It was also observed that the residual resistivity value (*ρ* (0 K)) decreases as *T*C increases [69]. More specifically, increasing *T*C has a clear correlation with low residual resistivity. As stated by Sato, an increase in Cu─O bond length enhances the electrostatic potential at the Cu site relative to that at the oxygen site in the Cu─O plane.

substrates (*a*<sup>s</sup> = 3.75 Å), which produces ~0.5% compressive strain onto these

cuprates (**Figure 10a**) [63–70]. Indeed, Sato et al., and Locquet et al., grew La2−*<sup>x</sup>*

*x* = 0.1, 0.15) thin films on two different substrates, such as (0 0 1) SrTiO<sup>3</sup>


CuO4

is an antiferromagnetic

Sr*x* CuO4

and (0 0 1) SrLaAlO4

(LSCO;

(LSCO) is one example of these oxides. La<sup>2</sup>

effect during the growth process.

[56]. La1.85Sr0.15CuO4

NiF4

(0 0 1) SrLaAlO4

has a K2

14 Epitaxy

**4. Material properties tuned by epitaxial strain**

**4.1. A high temperature superconductor: La1.85Sr0.15CuO4**

pairs or the strength of electron pairing interactions [62].

**Figure 9.** (a) Schematic representation of the K2 NiF4 -type tetragonal crystal structure of La2−*<sup>x</sup>* Sr*x* CuO4 (LSCO) with lattice constants of *a* = 3.777 Å and *c* = 13.226 Å. (b) Resistivity of bulk single LSCO, showing the appearance of superconducting *TSC* upon divalent Sr hole doping. (c) Sr hole doping dependence temperature vs. the material properties phase diagram of LSCO, showing that the system makes a transition from an antiferromagnetic insulator to a superconducting phase with the increase in Sr doping. Crystal structure was drawn using VESTA software. Reprinted with permission [57, 60]. Copyright 1992 American Physical Society; Copyright 2013 Macmillan Publishers Limited.

SrTiO3

SrRuO3

*c*<sup>c</sup> = *c*/2 = *d*002). Bulk SrRuO3

with the occurrence of RuO6

from the ideal cubic perovskites.

of ~10 Å at *T* = 300 K (**Figure 11b**) [73]. SrRuO3

ing for its usefulness as a bottom electrode for BiFeO<sup>3</sup>

**Figure 11.** (a) Schematic view of the crystal structure SrRuO3

(b–c) Resistivity (*ρ*) and magnetization of SrRuO3

Copyright 1999, American Institute of Physics.

films used in electronic applications [79].

substrates and ~51.5 K for compressive-strained films grown on (0 0 1) LaSrAlO<sup>4</sup>

strates [68]. Recently, Lee et al., also showed that oxygen vacancies and thickness-dependent strain relaxation indeed play a crucial role in increasing the superconducting *T*C as lattice

is one of the most promising oxide material among those used by thin-film research-

shows structural phase transitions from orthorhombic to tetrag-

octahedral rotation, leading to a lowered structural symmetry

, BaTiO3

shows a ferromagnetic transition at the Curie

, or Pb(Zr,Ti)O<sup>3</sup>

showing both the orthorhombic and pseudo-cubic unit

. The material was found be metal over the whole temperature range

ers [71]. It is an itinerant ferromagnetic bad metal [72, 73]. Structurally, it has a GdFeO3

orthorhombic distorted perovskite structure at *T* = 300 K with lattice parameters of *a* = 5.5670 Å, *b* = 5.5304 Å, and *c* = 7.8446 Å and space group *Pbnm* (**Figure 11a**) [74]. This structure is con-

onal at *T* = 547°C and then to cubic symmetry at *T* = 677°C, respectively [75]. This is associated

In high-quality bulk single crystals, the *ρ* is ~200 μΩ cm with a mean free path of electrons

temperature *T*C ~165 K (**Figure 11c**) with a magnetic moment of ~1.6 μB per Ru atom [76]. Although extensively studied, but the origin of its ferromagnetism, Stoner-type itinerant ferromagnetism vs. localized moment picture, is still under fierce debate because of contradicting experimental results and theoretical calculations [77, 78]. Due to its highly conductive nature and structural compatibility with other perovskite thin films, it is particularly interest-

ous substrates [80]. The ferromagnetic transition temperature for these thin films were found be lower than the bulk value, *T*C ~150 K, which is probably caused by the dimensionality and

cell. Lattice parameters are *a* = 5.5670 Å, *b* = 5.5304 Å, and *c* = 7.8446 Å, with the pseudo-cubic (*a*pc) one being ~3.93 Å.

with *ρ* ~200 μΩ cm at *T* = 300 K. Magnetization measurement shows ferromagnetic ordering at *T*<sup>C</sup> = 165 K. Reprinted with permission from Refs. [72–74]. Copyright 1996 IOP Publishing Ltd.; Copyright 1996, American Physical Society;

structures are highly sensitive to oxygen stoichiometry (**Figure 10d**) [70].

verted into a pseudo-cubic (pc) lattice with a constant of *a*pc ~ 3.93 Å (*a*<sup>c</sup> = *b*<sup>c</sup> = √

Eom et al. were the first to synthesize high quality metallic epitaxial SrRuO<sup>3</sup>

**4.2. A highly conductive ferromagnetic metal: SrRuO<sup>3</sup>**

sub-

17


/2 = *d*<sup>110</sup> and

ferroelectric thin

thin films on vari-

\_\_\_\_\_\_\_ *a* <sup>2</sup> + *b*<sup>2</sup>

Strain Effect in Epitaxial Oxide Heterostructures http://dx.doi.org/10.5772/intechopen.70125

**Figure 10.** (a) In-plane strain and lattice parameters of the LSCO thin film and other perovskite substrates studied. (b) Strain-dependent resistivity (*ρ*) and superconductivity of LSCO films, showing that for tensile-strained films (on SrTiO<sup>3</sup> substrates), superconductivity occurs at *T*C ~10 K, whereas for compressive-strained films (on SrLaAlO<sup>4</sup> substrates), the superconductivity transition temperature is doubled from the bulk value; i.e., *T*C becomes ~49.1 K. (c) Superconductivity at *T*C ~50 K for films grown on LaSrAlO<sup>4</sup> substrates with various amount of hole doping scenarios. (d) Changes in the *c*-axis lattice parameter and out-of-plane strain as a function of in-plane strain. The gray oval shape is the region where films do not show superconductivity. Reprinted with permission from Refs. [64, 69, 70]. Copyright 1998 Macmillan Publisher Ltd.; Copyright 2008 Elsevier Ltd.; Copyright 2015, AIP Publishing LLC.

Therefore, hole carriers are distributed more preferentially in itinerant states originating from the O 2p orbitals. As a result, antiferromagnetic spin fluctuation in the Cu─O plane is suppressed due to the reduction of the superexchange interaction between two adjacent Cu spins. Reduced spin fluctuation is the possible origin for reduction in *ρ* (0 K) and increase in *T*C [69].

For compressively strained films grown on (0 0 1) SrTiO<sup>3</sup> substrate, which induced ~3% tensile strain on films, the *T*C was found to be ~10 K [64]. Later, Božović et al., showed that with higher quality films (with much more oxygen intake as the films were annealed under an ozone atmosphere), *T*C could reach up to ~40 K for tensile-strained films grown on (0 0 1) SrTiO3 substrates and ~51.5 K for compressive-strained films grown on (0 0 1) LaSrAlO<sup>4</sup> substrates [68]. Recently, Lee et al., also showed that oxygen vacancies and thickness-dependent strain relaxation indeed play a crucial role in increasing the superconducting *T*C as lattice structures are highly sensitive to oxygen stoichiometry (**Figure 10d**) [70].

## **4.2. A highly conductive ferromagnetic metal: SrRuO<sup>3</sup>**

Therefore, hole carriers are distributed more preferentially in itinerant states originating from the O 2p orbitals. As a result, antiferromagnetic spin fluctuation in the Cu─O plane is suppressed due to the reduction of the superexchange interaction between two adjacent Cu spins. Reduced spin fluctuation is the possible origin for reduction in *ρ* (0 K) and increase in *T*C [69].

**Figure 10.** (a) In-plane strain and lattice parameters of the LSCO thin film and other perovskite substrates studied. (b) Strain-dependent resistivity (*ρ*) and superconductivity of LSCO films, showing that for tensile-strained films (on SrTiO<sup>3</sup>

superconductivity transition temperature is doubled from the bulk value; i.e., *T*C becomes ~49.1 K. (c) Superconductivity

*c*-axis lattice parameter and out-of-plane strain as a function of in-plane strain. The gray oval shape is the region where films do not show superconductivity. Reprinted with permission from Refs. [64, 69, 70]. Copyright 1998 Macmillan

substrates with various amount of hole doping scenarios. (d) Changes in the

substrates), superconductivity occurs at *T*C ~10 K, whereas for compressive-strained films (on SrLaAlO<sup>4</sup>

sile strain on films, the *T*C was found to be ~10 K [64]. Later, Božović et al., showed that with higher quality films (with much more oxygen intake as the films were annealed under an ozone atmosphere), *T*C could reach up to ~40 K for tensile-strained films grown on (0 0 1)

substrate, which induced ~3% ten-

substrates), the

For compressively strained films grown on (0 0 1) SrTiO<sup>3</sup>

Publisher Ltd.; Copyright 2008 Elsevier Ltd.; Copyright 2015, AIP Publishing LLC.

at *T*C ~50 K for films grown on LaSrAlO<sup>4</sup>

16 Epitaxy

SrRuO3 is one of the most promising oxide material among those used by thin-film researchers [71]. It is an itinerant ferromagnetic bad metal [72, 73]. Structurally, it has a GdFeO3 -type orthorhombic distorted perovskite structure at *T* = 300 K with lattice parameters of *a* = 5.5670 Å, *b* = 5.5304 Å, and *c* = 7.8446 Å and space group *Pbnm* (**Figure 11a**) [74]. This structure is converted into a pseudo-cubic (pc) lattice with a constant of *a*pc ~ 3.93 Å (*a*<sup>c</sup> = *b*<sup>c</sup> = √ \_\_\_\_\_\_\_ *a* <sup>2</sup> + *b*<sup>2</sup> /2 = *d*<sup>110</sup> and *c*<sup>c</sup> = *c*/2 = *d*002). Bulk SrRuO3 shows structural phase transitions from orthorhombic to tetragonal at *T* = 547°C and then to cubic symmetry at *T* = 677°C, respectively [75]. This is associated with the occurrence of RuO6 octahedral rotation, leading to a lowered structural symmetry from the ideal cubic perovskites.

In high-quality bulk single crystals, the *ρ* is ~200 μΩ cm with a mean free path of electrons of ~10 Å at *T* = 300 K (**Figure 11b**) [73]. SrRuO3 shows a ferromagnetic transition at the Curie temperature *T*C ~165 K (**Figure 11c**) with a magnetic moment of ~1.6 μB per Ru atom [76]. Although extensively studied, but the origin of its ferromagnetism, Stoner-type itinerant ferromagnetism vs. localized moment picture, is still under fierce debate because of contradicting experimental results and theoretical calculations [77, 78]. Due to its highly conductive nature and structural compatibility with other perovskite thin films, it is particularly interesting for its usefulness as a bottom electrode for BiFeO<sup>3</sup> , BaTiO3 , or Pb(Zr,Ti)O<sup>3</sup> ferroelectric thin films used in electronic applications [79].

Eom et al. were the first to synthesize high quality metallic epitaxial SrRuO<sup>3</sup> thin films on various substrates [80]. The ferromagnetic transition temperature for these thin films were found be lower than the bulk value, *T*C ~150 K, which is probably caused by the dimensionality and

**Figure 11.** (a) Schematic view of the crystal structure SrRuO3 showing both the orthorhombic and pseudo-cubic unit cell. Lattice parameters are *a* = 5.5670 Å, *b* = 5.5304 Å, and *c* = 7.8446 Å, with the pseudo-cubic (*a*pc) one being ~3.93 Å. (b–c) Resistivity (*ρ*) and magnetization of SrRuO3 . The material was found be metal over the whole temperature range with *ρ* ~200 μΩ cm at *T* = 300 K. Magnetization measurement shows ferromagnetic ordering at *T*<sup>C</sup> = 165 K. Reprinted with permission from Refs. [72–74]. Copyright 1996 IOP Publishing Ltd.; Copyright 1996, American Physical Society; Copyright 1999, American Institute of Physics.

strain effects [81]. Along with its electrode applications, due to its high metallicity upon ferromagnetic ordering, strain engineering of SrRuO3 has become a popular research topic among thin-film scientists. Later, it has been found that the structural, metallic, and magnetic properties of SrRuO3 thin films are highly sensitive to the substrate-induced strain (**Figure 12a**) [81–92].

Strain has definite effect on the magnetic properties of SrRuO<sup>3</sup>

LSAT and *T*C ~128 K for films grown on (0 0 1) SrTiO<sup>3</sup>

caused by the twin structure of (0 0 1) LaAlO3

), the *M*<sup>S</sup>

by using various lattice-mismatched substrates, e.g., (0 0 1) SrTiO<sup>3</sup>

netic *T*C has a strong substrate dependence as it was found be *T*C ~124 K for films grown on

films grown on (0 0 1) LSAT substrates (**Figure 12e**). For more compressive-strained films

strained case is associated with the better alignment of moments in a low Ru4+ spin state. This higher value of magnetic moment was also expected based on the theoretical calculations [77]. Compressive and tensile strain-dependent physical properties have also been examined for

been found that tensile-strained films show low ferromagnetic ordering at *T*C ~100 K, whereas compressively strained films show an almost bulk-like ferromagnetic transition at *T*C ~155 K (**Figure 13**). Similar to the orthorhombic phase, compressive strain causes a lower residual resistivity ratio. The observations described above are associated with the deformation rather

ics [7, 94]. At *T* = 300 K, LSMO forms a rhombohedral crystal structure (*a* = 3.869 Å) with

*T*<sup>N</sup> = 139.5 K [95]. Upon hole doping with divalent Sr2+ in place of La3+, it becomes a ferromagnetic metal (**Figure 14b**) [96]. Doped LSMO is a mixed valence compound with Mn3+ (3*d*<sup>4</sup>

ping mechanism [96]. It is a highly conductive oxide that is useful as a bottom electrode for thin film device applications. It shows ferromagnetic ordering above room temperature with *T*C ~360 K (**Figure 14c**) [97], having a magnetic moment of ~3.6 μB per Mn ion [98]. Its *ρ* changes greatly with the application of a magnetic field and shows colossal magnetoresistance (CMR;

netic field sensors, "read" heads of magnetic hard-disk drives and non-volatile magnetic random access memory (MRAM). Its half metallic behavior—i.e., spins are fully polarized within one band structure whereas others are empty—is highly important for spintronic applications

Due to its rich electronic and magnetic phase diagram (**Figure 14e**) [99], it is highly desirable to investigate the change in functionalities or appearance of novel states in LSMO by inducing the strain effect. Several groups have reported on the effect of strain on the electronic and magnetic properties of LSMO [100–111]. To observe the strain-dependent magnetic phase diagram, Tsui et al., grew epitaxial LSMO thin films on various substrates, such as (0 0 1) LaAlO<sup>3</sup>

[98]. It also shows compositional- and temperature-dependent MITs (**Figure 14e**) [99].

). The change in its magnetism was well explained by the double-exchange hop-

%) (**Figure 14d**) [97], which is important in commercial applications, including mag-

octahedra and thus the change in effective correlation [90–93].

(LSMO) is an extremely important class of material in condensed matter phys-

. (1 1 0) NaGaO3

**4.3. A colossal magnetoresistive ferromagnetic metal: La0.67Sr0.33MnO3**

3*c* (**Figure 14a**) [94]. Undoped LaMnO<sup>3</sup>

, (0 0 1) LSAT, and (0 0 1) SrTiO3

, and its effect on magnetic properties has been investigated. The ferromag-

) increases from its bulk value and maximum of ~2 μB per Ru atom for

increases, possibly due to the deterioration in film quality

substrates were used to induce tensile strain [90]. It has

substrates. The increase in *M*<sup>S</sup>

on SrRuO3

and (0 0 1) LaAlO3

magnetic moment (*M*<sup>S</sup>

(those on (0 0 1) LaAlO3

the tetragonal phase of SrRuO3

than the tilting of RuO6

La0.67Sr0.33MnO3

space group *<sup>R</sup>*¯

Mn4+ (3*d*<sup>3</sup>

Δ*ρ*/*ρ* > 106

(1 1 0) NdGaO3

sive strain, whereas (1 1 0) GdScO3

. Inducing compressive strain

[85]. It has been found that the saturated

Strain Effect in Epitaxial Oxide Heterostructures http://dx.doi.org/10.5772/intechopen.70125

substrates were used for imposing compres-

is an antiferromagnetic insulator below

[103]. By using four different substrates, the

, (0 0 1) LSAT,

19

in compressive

) and

,

The structural phase transition temperature (*T*<sup>S</sup> ) of SrRuO3 is strongly affected by epitaxial strain. After imposing tensile strain on SrRuO3 by growing films on (1 1 0) DyScO<sup>3</sup> substrates, an orthorhombic (stable in bulk phase) to tetragonal phase (stable at high temperature) transition could be observed at *T* = 300 K [84]. Strain imposed by substrates, induces additional rotation of RuO6 octahedra, thus reducing the *T*<sup>S</sup> [84, 86].

Transport wise, *ρ* at *T* = 300 K increases with the induced tensile strain (films grown on (1 1 0) GdScO3 and (1 1 0) DyScO3 substrates). The Ru─O─Ru bond angle is reduced when exerting tensile strain, which increases the effective correlation and thus reduces the bandwidth (*W*) (**Figure 12b**) [84]. Consequently, in the case of tensile-strained films, *ρ* has a higher value at *T* = 300 K compared to that of the most natural state of a film. On the other hand, it has also been found that for compressive-strained films (films grown on (0 0 1) SrTiO<sup>3</sup> , (0 0 1) LSAT, and (0 0 1) LaAlO3 substrates), *ρ* decreases, which is consistent with the increase in the Ru─O─Ru bond angle, decrease in effective correlation, and increase in bandwidth (*W*) (**Figure 12c**) [85]. The slight increase in the *ρ* of films grown on (0 0 1) LaAlO<sup>3</sup> substrates is associated with either the rough surface quality of the films caused by the twin structure of (0 0 1) LaAlO3 or the films being fully relaxed on this substrate (**Figure 12d**) [85].

**Figure 12.** (a) Schematic illustration of the strain effect in epitaxial orthorhombic SrRuO<sup>3</sup> thin films. Films on DyScO<sup>3</sup> are subject to tensile strain, whereas films on SrTiO<sup>3</sup> , LSAT, and LaAlO3 undergo compressive strain. (b) Schematic representation of RuO6 octahedral rotation from the bulk, due to both compressive and tensile strain. (c–d) Effect of tensile strain and compressive strain on the resistivity of SrRuO3 . For the tensile strain case, overall resistivity increases, while for the compressive-strained case, resistivity decreases from its bulk value. (e) Increase in saturation magnetization following the induction of compressive strain. The magnetic moment becomes ~2 μB per Ru atom, which is close to the theoretical value. Reprinted with permission from Refs. [84–86]. Copyright 2008 AIP Publishing LLC; Copyright 2010 AIP Publishing LLC; Copyright 2010 Wiley-VCH Gmbh & Co. KGaA.

Strain has definite effect on the magnetic properties of SrRuO<sup>3</sup> . Inducing compressive strain on SrRuO3 by using various lattice-mismatched substrates, e.g., (0 0 1) SrTiO<sup>3</sup> , (0 0 1) LSAT, and (0 0 1) LaAlO3 , and its effect on magnetic properties has been investigated. The ferromagnetic *T*C has a strong substrate dependence as it was found be *T*C ~124 K for films grown on LSAT and *T*C ~128 K for films grown on (0 0 1) SrTiO<sup>3</sup> [85]. It has been found that the saturated magnetic moment (*M*<sup>S</sup> ) increases from its bulk value and maximum of ~2 μB per Ru atom for films grown on (0 0 1) LSAT substrates (**Figure 12e**). For more compressive-strained films (those on (0 0 1) LaAlO3 ), the *M*<sup>S</sup> increases, possibly due to the deterioration in film quality caused by the twin structure of (0 0 1) LaAlO3 substrates. The increase in *M*<sup>S</sup> in compressive strained case is associated with the better alignment of moments in a low Ru4+ spin state. This higher value of magnetic moment was also expected based on the theoretical calculations [77].

Compressive and tensile strain-dependent physical properties have also been examined for the tetragonal phase of SrRuO3 . (1 1 0) NaGaO3 substrates were used for imposing compressive strain, whereas (1 1 0) GdScO3 substrates were used to induce tensile strain [90]. It has been found that tensile-strained films show low ferromagnetic ordering at *T*C ~100 K, whereas compressively strained films show an almost bulk-like ferromagnetic transition at *T*C ~155 K (**Figure 13**). Similar to the orthorhombic phase, compressive strain causes a lower residual resistivity ratio. The observations described above are associated with the deformation rather than the tilting of RuO6 octahedra and thus the change in effective correlation [90–93].

## **4.3. A colossal magnetoresistive ferromagnetic metal: La0.67Sr0.33MnO3**

strain effects [81]. Along with its electrode applications, due to its high metallicity upon ferro-

thin-film scientists. Later, it has been found that the structural, metallic, and magnetic proper-

an orthorhombic (stable in bulk phase) to tetragonal phase (stable at high temperature) transition could be observed at *T* = 300 K [84]. Strain imposed by substrates, induces additional

Transport wise, *ρ* at *T* = 300 K increases with the induced tensile strain (films grown on (1 1 0)

tensile strain, which increases the effective correlation and thus reduces the bandwidth (*W*) (**Figure 12b**) [84]. Consequently, in the case of tensile-strained films, *ρ* has a higher value at *T* = 300 K compared to that of the most natural state of a film. On the other hand, it has

the Ru─O─Ru bond angle, decrease in effective correlation, and increase in bandwidth (*W*)

associated with either the rough surface quality of the films caused by the twin structure of

or the films being fully relaxed on this substrate (**Figure 12d**) [85].

, LSAT, and LaAlO3

while for the compressive-strained case, resistivity decreases from its bulk value. (e) Increase in saturation magnetization following the induction of compressive strain. The magnetic moment becomes ~2 μB per Ru atom, which is close to the theoretical value. Reprinted with permission from Refs. [84–86]. Copyright 2008 AIP Publishing LLC; Copyright 2010

octahedral rotation from the bulk, due to both compressive and tensile strain. (c–d) Effect of

also been found that for compressive-strained films (films grown on (0 0 1) SrTiO<sup>3</sup>

(**Figure 12c**) [85]. The slight increase in the *ρ* of films grown on (0 0 1) LaAlO<sup>3</sup>

**Figure 12.** (a) Schematic illustration of the strain effect in epitaxial orthorhombic SrRuO<sup>3</sup>

are subject to tensile strain, whereas films on SrTiO<sup>3</sup>

tensile strain and compressive strain on the resistivity of SrRuO3

AIP Publishing LLC; Copyright 2010 Wiley-VCH Gmbh & Co. KGaA.

representation of RuO6

thin films are highly sensitive to the substrate-induced strain (**Figure 12a**) [81–92].

) of SrRuO3

[84, 86].

has become a popular research topic among

by growing films on (1 1 0) DyScO<sup>3</sup>

substrates). The Ru─O─Ru bond angle is reduced when exerting

substrates), *ρ* decreases, which is consistent with the increase in

is strongly affected by epitaxial

substrates,

, (0 0 1)

substrates is

thin films. Films on DyScO<sup>3</sup>

undergo compressive strain. (b) Schematic

. For the tensile strain case, overall resistivity increases,

magnetic ordering, strain engineering of SrRuO3

The structural phase transition temperature (*T*<sup>S</sup>

octahedra, thus reducing the *T*<sup>S</sup>

strain. After imposing tensile strain on SrRuO3

and (1 1 0) DyScO3

LSAT, and (0 0 1) LaAlO3

ties of SrRuO3

18 Epitaxy

rotation of RuO6

(0 0 1) LaAlO3

GdScO3

La0.67Sr0.33MnO3 (LSMO) is an extremely important class of material in condensed matter physics [7, 94]. At *T* = 300 K, LSMO forms a rhombohedral crystal structure (*a* = 3.869 Å) with space group *<sup>R</sup>*¯ 3*c* (**Figure 14a**) [94]. Undoped LaMnO<sup>3</sup> is an antiferromagnetic insulator below *T*<sup>N</sup> = 139.5 K [95]. Upon hole doping with divalent Sr2+ in place of La3+, it becomes a ferromagnetic metal (**Figure 14b**) [96]. Doped LSMO is a mixed valence compound with Mn3+ (3*d*<sup>4</sup> ) and Mn4+ (3*d*<sup>3</sup> ). The change in its magnetism was well explained by the double-exchange hopping mechanism [96]. It is a highly conductive oxide that is useful as a bottom electrode for thin film device applications. It shows ferromagnetic ordering above room temperature with *T*C ~360 K (**Figure 14c**) [97], having a magnetic moment of ~3.6 μB per Mn ion [98]. Its *ρ* changes greatly with the application of a magnetic field and shows colossal magnetoresistance (CMR; Δ*ρ*/*ρ* > 106 %) (**Figure 14d**) [97], which is important in commercial applications, including magnetic field sensors, "read" heads of magnetic hard-disk drives and non-volatile magnetic random access memory (MRAM). Its half metallic behavior—i.e., spins are fully polarized within one band structure whereas others are empty—is highly important for spintronic applications [98]. It also shows compositional- and temperature-dependent MITs (**Figure 14e**) [99].

Due to its rich electronic and magnetic phase diagram (**Figure 14e**) [99], it is highly desirable to investigate the change in functionalities or appearance of novel states in LSMO by inducing the strain effect. Several groups have reported on the effect of strain on the electronic and magnetic properties of LSMO [100–111]. To observe the strain-dependent magnetic phase diagram, Tsui et al., grew epitaxial LSMO thin films on various substrates, such as (0 0 1) LaAlO<sup>3</sup> , (1 1 0) NdGaO3 , (0 0 1) LSAT, and (0 0 1) SrTiO3 [103]. By using four different substrates, the

**Figure 13.** Compressive (on NdGaO3 ) and tensile (on GdScO3 ) strain-dependent resistivity of tetragonal phase SrRuO3 thin films. A striking feature was obtained in magnetic ordering. For tensile-strained films (on GdScO<sup>3</sup> ), resistivity is higher than the bulk value and the magnetic ordering temperature is reduced with ferromagnetic *T*C ~124 K. For compressive-strained film (on NdGaO<sup>3</sup> ), resistivity and magnetic ordering are very close to the bulk values with ferromagnetic *T*C ~155 K. Reprinted with permission from Ref. [90]. Copyright 2013 AIP Publishing LLC.

grown on (0 0 1) LSAT and (1 1 0) NdGaO3

firmed by magnetization measurements [103].

following substrates: (1 0 0)*pc* LaAlO3

(0 0 1) SrTiO3

SrTiO3

LSAT and (1 1 0) NdGaO3

, (1 1 0) DyScO3

magnetic anisotropy for films grown on (0 0 1) LaAlO<sup>3</sup>

**Figure 14.** (a) Rhombohedral crystal structure of La0.67Sr0.33MnO3

, (1 1 0) GdScO3

substrates, show magnetic ordering below *T*<sup>C</sup>

substrates, whereas films grown on

Strain Effect in Epitaxial Oxide Heterostructures http://dx.doi.org/10.5772/intechopen.70125 21

, (0 0 1) LSAT, (0 0 1)

octahedra. (b) Sr hole

is around

(**Figure 15a–c**) [108]. *ρ*

~340 K. Field-dependent magnetization measurements confirm the presence of perpendicular

doping-dependent resistivity of bulk LSMO single crystals showing insulator-to-metal transitions with the kink in resistivity; appearance of magnetic ordering. (c) Magnetization measurements show ferromagnetic ordering above room temperature at *T*C ~360 K. (d) Magnetoresistance measurements, i.e., magnetic field-dependent resistivity, show a marked change in resistivity upon the application of a magnetic field, which is defined as the appearance of "colossal magnetoresistance" in LSMO. (e) Temperature- and compositional-dependent phase diagram of LSMO, showing that as Sr hole doping increases, various novel phases can appear in LSMO, making it a rich material that shows complex physics. Adapted and reprinted with permission from Refs. [94, 96, 97, 99]. Copyright 2001 Elsevier Ltd.; Copyright 1995 American Physical Society; Copyright 1996 American Physical Society; Copyright 1996 American Physical Society.

Recently, Adamo et al., performed a comprehensive study on the strain effect on the electronic and magnetic properties of LSMO with biaxial strain ranging from −2.3 to +3.2% by using the

, (0 0 1) LaSrGaO4

show a strong strain dependency on the MIT temperature. For low strain values, low temperature *ρ* is closer to the single-crystal value. The MIT value for films grown on (1 1 0) NdGaO<sup>3</sup>

*T*MIT = 370 ± 10 K. Films with high compressive strain show fully insulating behavior over the entire *T* range (**Figure 15d**). For films under higher tensile strain, at *T* = 300 K, *ρ* is nearly 1 Ω cm. The magnetization behavior of these films are quite similar to that observed by Tsui et al., The observed magnetic behavior and change in *T*C exhibit a strong strain dependence (**Figure 15e**), which is in good agreement with the theoretical predictions of Millis et al. [112].

, (1 1 0) SmScO3

is *T*MIT > 390 K, whereas the MIT transition value for films grown on (0 0 1) SrTiO<sup>3</sup>

exhibit easy-plane magnetic anisotropy at low *T*. For the films grown on (0 0 1)

substrates, the presence of distorted easy-pane anisotropy was con-

, (1 1 0) NdGaO3

(LSMO) showing MnO6

and (1 1 0) NdScO3

strain ranged from compressive to tensile strain as follow; −2.0% compressive strain for films grown on (0 0 1) LaAlO3 , −0.25% compressive strain for films grown on (1 1 0) NdGaO<sup>3</sup> , +0.25% tensile strain for films grown on (0 0 1) LSAT, and +0.85% tensile strain for films grown on (0 0 1) SrTiO3 . Compressively strained films on (0 0 1) LaAlO<sup>3</sup> substrates show in-plane compression and out-of-plane expansion in their lattice parameters. In contrast, tensile-strained films on (0 0 1) SrTiO<sup>3</sup> show the opposite effect. For films grown on the other two substrates with very low strain, they show very weak out-of-plane expansion in their lattice parameters. For compressively strained films on (0 0 1) LaAlO<sup>3</sup> substrates, there is a strong suppression of *T*C from its bulk value; i.e., *T*C is reduced from 360 to 300 K. There is an increase in in-plane magnetization compared to out-of-plane magnetization, which indicates the presence of easyplane anisotropy. Films grown on (0 0 1) SrTiO3 substrates show magnetic ordering below *T*<sup>C</sup> ~320 K. On the other hand, films grown on the almost lattice-matched substrates, i.e., films

**Figure 14.** (a) Rhombohedral crystal structure of La0.67Sr0.33MnO3 (LSMO) showing MnO6 octahedra. (b) Sr hole doping-dependent resistivity of bulk LSMO single crystals showing insulator-to-metal transitions with the kink in resistivity; appearance of magnetic ordering. (c) Magnetization measurements show ferromagnetic ordering above room temperature at *T*C ~360 K. (d) Magnetoresistance measurements, i.e., magnetic field-dependent resistivity, show a marked change in resistivity upon the application of a magnetic field, which is defined as the appearance of "colossal magnetoresistance" in LSMO. (e) Temperature- and compositional-dependent phase diagram of LSMO, showing that as Sr hole doping increases, various novel phases can appear in LSMO, making it a rich material that shows complex physics. Adapted and reprinted with permission from Refs. [94, 96, 97, 99]. Copyright 2001 Elsevier Ltd.; Copyright 1995 American Physical Society; Copyright 1996 American Physical Society; Copyright 1996 American Physical Society.

grown on (0 0 1) LSAT and (1 1 0) NdGaO3 substrates, show magnetic ordering below *T*<sup>C</sup> ~340 K. Field-dependent magnetization measurements confirm the presence of perpendicular magnetic anisotropy for films grown on (0 0 1) LaAlO<sup>3</sup> substrates, whereas films grown on (0 0 1) SrTiO3 exhibit easy-plane magnetic anisotropy at low *T*. For the films grown on (0 0 1) LSAT and (1 1 0) NdGaO3 substrates, the presence of distorted easy-pane anisotropy was confirmed by magnetization measurements [103].

strain ranged from compressive to tensile strain as follow; −2.0% compressive strain for films

is higher than the bulk value and the magnetic ordering temperature is reduced with ferromagnetic *T*C ~124 K. For

tensile strain for films grown on (0 0 1) LSAT, and +0.85% tensile strain for films grown on

pression and out-of-plane expansion in their lattice parameters. In contrast, tensile-strained

with very low strain, they show very weak out-of-plane expansion in their lattice parameters.

of *T*C from its bulk value; i.e., *T*C is reduced from 360 to 300 K. There is an increase in in-plane magnetization compared to out-of-plane magnetization, which indicates the presence of easy-

~320 K. On the other hand, films grown on the almost lattice-matched substrates, i.e., films

. Compressively strained films on (0 0 1) LaAlO<sup>3</sup>

) and tensile (on GdScO3

thin films. A striking feature was obtained in magnetic ordering. For tensile-strained films (on GdScO<sup>3</sup>

ferromagnetic *T*C ~155 K. Reprinted with permission from Ref. [90]. Copyright 2013 AIP Publishing LLC.

For compressively strained films on (0 0 1) LaAlO<sup>3</sup>

plane anisotropy. Films grown on (0 0 1) SrTiO3

, −0.25% compressive strain for films grown on (1 1 0) NdGaO<sup>3</sup>

show the opposite effect. For films grown on the other two substrates

, +0.25%

), resistivity

substrates show in-plane com-

substrates, there is a strong suppression

) strain-dependent resistivity of tetragonal phase SrRuO3

), resistivity and magnetic ordering are very close to the bulk values with

substrates show magnetic ordering below *T*<sup>C</sup>

grown on (0 0 1) LaAlO3

**Figure 13.** Compressive (on NdGaO3

compressive-strained film (on NdGaO<sup>3</sup>

films on (0 0 1) SrTiO<sup>3</sup>

(0 0 1) SrTiO3

20 Epitaxy

Recently, Adamo et al., performed a comprehensive study on the strain effect on the electronic and magnetic properties of LSMO with biaxial strain ranging from −2.3 to +3.2% by using the following substrates: (1 0 0)*pc* LaAlO3 , (0 0 1) LaSrGaO4 , (1 1 0) NdGaO3 , (0 0 1) LSAT, (0 0 1) SrTiO3 , (1 1 0) DyScO3 , (1 1 0) GdScO3 , (1 1 0) SmScO3 and (1 1 0) NdScO3 (**Figure 15a–c**) [108]. *ρ* show a strong strain dependency on the MIT temperature. For low strain values, low temperature *ρ* is closer to the single-crystal value. The MIT value for films grown on (1 1 0) NdGaO<sup>3</sup> is *T*MIT > 390 K, whereas the MIT transition value for films grown on (0 0 1) SrTiO<sup>3</sup> is around *T*MIT = 370 ± 10 K. Films with high compressive strain show fully insulating behavior over the entire *T* range (**Figure 15d**). For films under higher tensile strain, at *T* = 300 K, *ρ* is nearly 1 Ω cm. The magnetization behavior of these films are quite similar to that observed by Tsui et al., The observed magnetic behavior and change in *T*C exhibit a strong strain dependence (**Figure 15e**), which is in good agreement with the theoretical predictions of Millis et al. [112].

**Figure 15.** (a) Epitaxial growth of compressive- and tensile-strained La0.67Sr0.33MnO3 (LSMO) films. Films grown on LaAlO3 , LaSrGaO4 , NdGaO3 , and LSAT are subject to compressive strain, whereas films grown on SrTiO<sup>3</sup> , DyScO3 , GdScO3 , SmScO3 , and NdScO3 are subject to tensile strain. The appearance of thickness fringes in the X-ray diffraction patterns shows the high crystallinity of each film. (b) Change in lattice parameter and (c) evolution of biaxial strain with the judicial choice of substrates for LSMO thin films. (d and e) Resistivity and magnetization of compressive- and tensile-strained films. Highly tensile- or compressive-strained films show insulating behavior (due to the strain and intrinsic atomic disorder effect), whereas metallic behavior was obtained for films that were exposed to moderate tensile or compressive strain. Magnetization measurements show that the ferromagnetic ordering temperature decreases as the tensile strain increases. Reprinted with permission from Ref. [108]. Copyright 2009 AIP Publishing LLC.

multiferroic properties above *T* = 300 K, it is a very promising candidate for room-tempera-

polarization along the [1 1 1]*C* and magnetization plane is perpendicular to the polarization direction. (b) Polarization-

loop. Reprinted and adapted with permission [114, 115]. Copyright 2011 The Royal Society; Copyright 2003 American

magnitude higher than the bulk value. After this finding, it has been shown that the structural,

of various substrates, compressive (−) or tensile (+) strain can be induced on the film, which changes its structural symmetry as octahedral tilt is highly sensitive to strain. Commercially

, (1 1 0) NdScO3

being the compressive strain and +ve sign corresponds to tensile strain. For cases of low com-

a value of ~1.23 [124, 128]. This high *c*/*a* value can be regarded as being similar to a tetragonal

134]. The transition from *R*-phase to *TG*-phase was thought to be an isosymmetric monoclinic symmetry phase transition [128]. However, it was actually shown that octahedral tilt disappears, and the sudden jump in the *c*/*a* ratio can be attributed to structural relaxation through an out-of-plane shift. In contrast, imposing moderate tensile strain by using high lattice-mis-

substrates results in BiFeO3

of −6.5%, −4.5%, −2.6%, −0.5%, −0.1%, +0.2%, +0.9% and +1.2%, respectively, -ve sign

strain, i.e., the strain promoted by using different lattice-mismatched substrates [121–137].

substrates by using the PLD method and observed multiferroic properties [115].

heterostructures on

along the

23

at *T* = 300 K, an order of

showing rhombohedral distortion with easy-axis

Strain Effect in Epitaxial Oxide Heterostructures http://dx.doi.org/10.5772/intechopen.70125

, showing that the system is antiferromagnetic

, (0 0 1) LAST, (1 1 0)

impose a strain on

thin films are highly sensitive to substrate-induced

adopts rhombohedral symmetry (*R*-phase). With the availability

is ferroelectric with a polarization value of ~60 μC/cm<sup>2</sup>

. Blue: in-plane, and red: out-of-plane magnetization-magnetic field

, (0 0 1) LaAlO3

shows monoclinic (*M*) phases (**Figure 17a–f**) [120]. In general,

. Upon imposing even higher compressive strain by

in a novel orthorhombic (*O*) phase [132].

makes a transition to a fully *TG*-phase (**Figure 17g**) [124,

, the ratio of lattice parameters *c*/*a* is ~1. When grown on high lattice-mis-

substrate, the ratio of lattice parameters *c*/*a* shows a large increase to

and (1 1 0) PrScO<sup>3</sup>

Wang et al., were the first to synthesize high quality epitaxial BiFeO<sup>3</sup>

They observed that these films display a spontaneous *P* ~ 60 μC/cm<sup>2</sup>

ture magnetoelectric device applications [120].

electric field hysteresis loop showing that BiFeO<sup>3</sup>

with a saturation magnetization of ~150 emu/cm3

Association for the Advancement of Science.

**Figure 16.** (a) Atomic and magnetic structure of rhombohedral BiFeO3

[1 1 1]*C*. (c) Magnetization vs. magnetic field hysteresis loop of BiFeO<sup>3</sup>

polar, and magnetic behavior of BiFeO3

available perovskite substrates such as (1 1 0) YAlO3

substrates, BiFeO3

, (1 1 0) SmScO3

As said, at *T* = 300 K, BiFeO<sup>3</sup>

, (1 1 0) GdScO3

pressive or tensile strain, BiFeO3

(*TG*)-phase or super *TG*-phase of BiFeO3

for *R*-phase BiFeO3

using (1 1 0) YAlO3

matched (0 0 1) LaAlO3

matched (1 1 0) NdScO3

(0 0 1) SrTiO3

DyScO3

BiFeO3

## **4.4. A multiferroic oxide: BiFeO<sup>3</sup>**

Bismuth ferrite, BiFeO3 (BFO), is probably the most promising compound in condensed matter physics [9]. It possess a rhombohedral distorted perovskite structure (*a* = *b* = *c* = 5.63 Å, *α* = *<sup>β</sup>* = *γ* = 59.4°) with space group *<sup>R</sup>*¯ 3*c* at *T* = 300 K (**Figure 16a**) [113–115]. There is a coexistence of its magnetism and ferroelectricity, that's why BiFeO<sup>3</sup> is called a multiferroic (**Figure 16b** and **c**) [115]. In principle, the coexistence of ferroelectricity and magnetism is a very rare phenomenon as ferroelectricity requires B-site ions with *d*<sup>0</sup> electronic configurations, whereas magnetism requires B-site ions with d*<sup>n</sup>* (*n* > 0) electronic configurations [116]. Therefore, multiferrocity is a very unique phenomenon in condensed matter physics. Bulk single-crystal BiFeO3 shows G-type antiferromagnetic ordering below the Néel temperature at *T*<sup>N</sup> = 643 K [117]. In BiFeO3 , Fe moments are coupled ferromagnetically with the pseudo-cubic {1 1 1}*<sup>C</sup>* planes, whereas they are antiferromagnetically coupled between neighboring planes. In the bulk, an additional long-range cycloidal magnetic modulation is superimposed on the antiferromagnetic ordering, which results in a rotation of the spin axis through the crystal [43]. It also exhibits ferroelectricity below *T*C ~ 1103 K with a polarization (*P*) value of ~3.5 μC/cm<sup>2</sup> along (001)C and ~6.1 μC/cm<sup>2</sup> along [1 1 1]*C* [118]. Recently, the polarization value of highly pure single-crystal BiFeO3 was found to be ~100 μC/cm<sup>2</sup> along the [1 1 1]*C* [119]. Due to its

**Figure 16.** (a) Atomic and magnetic structure of rhombohedral BiFeO3 showing rhombohedral distortion with easy-axis polarization along the [1 1 1]*C* and magnetization plane is perpendicular to the polarization direction. (b) Polarizationelectric field hysteresis loop showing that BiFeO<sup>3</sup> is ferroelectric with a polarization value of ~60 μC/cm<sup>2</sup> along the [1 1 1]*C*. (c) Magnetization vs. magnetic field hysteresis loop of BiFeO<sup>3</sup> , showing that the system is antiferromagnetic with a saturation magnetization of ~150 emu/cm3 . Blue: in-plane, and red: out-of-plane magnetization-magnetic field loop. Reprinted and adapted with permission [114, 115]. Copyright 2011 The Royal Society; Copyright 2003 American Association for the Advancement of Science.

multiferroic properties above *T* = 300 K, it is a very promising candidate for room-temperature magnetoelectric device applications [120].

Wang et al., were the first to synthesize high quality epitaxial BiFeO<sup>3</sup> heterostructures on (0 0 1) SrTiO3 substrates by using the PLD method and observed multiferroic properties [115]. They observed that these films display a spontaneous *P* ~ 60 μC/cm<sup>2</sup> at *T* = 300 K, an order of magnitude higher than the bulk value. After this finding, it has been shown that the structural, polar, and magnetic behavior of BiFeO3 thin films are highly sensitive to substrate-induced strain, i.e., the strain promoted by using different lattice-mismatched substrates [121–137].

**4.4. A multiferroic oxide: BiFeO<sup>3</sup>**

, NdGaO3

, and NdScO3

*<sup>β</sup>* = *γ* = 59.4°) with space group *<sup>R</sup>*¯

magnetism requires B-site ions with d*<sup>n</sup>*

along (001)C and ~6.1 μC/cm<sup>2</sup>

pure single-crystal BiFeO3

of its magnetism and ferroelectricity, that's why BiFeO<sup>3</sup>

**Figure 15.** (a) Epitaxial growth of compressive- and tensile-strained La0.67Sr0.33MnO3

phenomenon as ferroelectricity requires B-site ions with *d*<sup>0</sup>

(BFO), is probably the most promising compound in condensed mat-

, and LSAT are subject to compressive strain, whereas films grown on SrTiO<sup>3</sup>

are subject to tensile strain. The appearance of thickness fringes in the X-ray diffraction

3*c* at *T* = 300 K (**Figure 16a**) [113–115]. There is a coexistence

along [1 1 1]*C* [118]. Recently, the polarization value of highly

(*n* > 0) electronic configurations [116]. Therefore, mul-

is called a multiferroic (**Figure 16b**

(LSMO) films. Films grown on

, DyScO3 ,

electronic configurations, whereas

along the [1 1 1]*C* [119]. Due to its

ter physics [9]. It possess a rhombohedral distorted perovskite structure (*a* = *b* = *c* = 5.63 Å, *α* =

patterns shows the high crystallinity of each film. (b) Change in lattice parameter and (c) evolution of biaxial strain with the judicial choice of substrates for LSMO thin films. (d and e) Resistivity and magnetization of compressive- and tensile-strained films. Highly tensile- or compressive-strained films show insulating behavior (due to the strain and intrinsic atomic disorder effect), whereas metallic behavior was obtained for films that were exposed to moderate tensile or compressive strain. Magnetization measurements show that the ferromagnetic ordering temperature decreases as the

tensile strain increases. Reprinted with permission from Ref. [108]. Copyright 2009 AIP Publishing LLC.

and **c**) [115]. In principle, the coexistence of ferroelectricity and magnetism is a very rare

tiferrocity is a very unique phenomenon in condensed matter physics. Bulk single-crystal

planes, whereas they are antiferromagnetically coupled between neighboring planes. In the bulk, an additional long-range cycloidal magnetic modulation is superimposed on the antiferromagnetic ordering, which results in a rotation of the spin axis through the crystal [43]. It also exhibits ferroelectricity below *T*C ~ 1103 K with a polarization (*P*) value of ~3.5 μC/cm<sup>2</sup>

was found to be ~100 μC/cm<sup>2</sup>

shows G-type antiferromagnetic ordering below the Néel temperature at *T*<sup>N</sup> = 643 K

, Fe moments are coupled ferromagnetically with the pseudo-cubic {1 1 1}*<sup>C</sup>*

Bismuth ferrite, BiFeO3

, LaSrGaO4

, SmScO3

BiFeO3

LaAlO3

22 Epitaxy

GdScO3

[117]. In BiFeO3

As said, at *T* = 300 K, BiFeO<sup>3</sup> adopts rhombohedral symmetry (*R*-phase). With the availability of various substrates, compressive (−) or tensile (+) strain can be induced on the film, which changes its structural symmetry as octahedral tilt is highly sensitive to strain. Commercially available perovskite substrates such as (1 1 0) YAlO3 , (0 0 1) LaAlO3 , (0 0 1) LAST, (1 1 0) DyScO3 , (1 1 0) GdScO3 , (1 1 0) SmScO3 , (1 1 0) NdScO3 and (1 1 0) PrScO<sup>3</sup> impose a strain on BiFeO3 of −6.5%, −4.5%, −2.6%, −0.5%, −0.1%, +0.2%, +0.9% and +1.2%, respectively, -ve sign being the compressive strain and +ve sign corresponds to tensile strain. For cases of low compressive or tensile strain, BiFeO3 shows monoclinic (*M*) phases (**Figure 17a–f**) [120]. In general, for *R*-phase BiFeO3 , the ratio of lattice parameters *c*/*a* is ~1. When grown on high lattice-mismatched (0 0 1) LaAlO3 substrate, the ratio of lattice parameters *c*/*a* shows a large increase to a value of ~1.23 [124, 128]. This high *c*/*a* value can be regarded as being similar to a tetragonal (*TG*)-phase or super *TG*-phase of BiFeO3 . Upon imposing even higher compressive strain by using (1 1 0) YAlO3 substrates, BiFeO3 makes a transition to a fully *TG*-phase (**Figure 17g**) [124, 134]. The transition from *R*-phase to *TG*-phase was thought to be an isosymmetric monoclinic symmetry phase transition [128]. However, it was actually shown that octahedral tilt disappears, and the sudden jump in the *c*/*a* ratio can be attributed to structural relaxation through an out-of-plane shift. In contrast, imposing moderate tensile strain by using high lattice-mismatched (1 1 0) NdScO3 substrates results in BiFeO3 in a novel orthorhombic (*O*) phase [132].

**Figure 17.** (a–f) Summary of the various crystal structures of BiFeO3 thin films under epitaxial strain, i.e., both compressive and tensile strain. Under different amounts of strain, bulk rhombohedral (*R*) phase to monoclinic (*M*), tetragonal (*TG*), and orthorhombic (*O*) phase transitions can be observed in BiFeO3 . (g) Calculated overall energy of the system and *c*/*a* ratio for strained BiFeO3 . Reprinted with permission from Refs. [120, 124]. Copyright 2014 IOP Publishing Ltd; Copyright 2009 American Association for the Advancement of Science.

tilt favors an increase in *P*, whereas the presence of tilts instead favors a change in the direction without changing the *P* [130]. Recent theoretical calculations suggest that if highly

films grown on LSAT substrates was attributed to a leakage problem. (b) Magnetic phase diagram shows that with the

stable magnetic states (blue: antiferromagnetic; red: type-1 cycloid; orange: type-2 cycloid). The different substrates used for the study are shown above with different colors corresponding to the different magnetic structures of BiFeO<sup>3</sup>

spins are denoted by green arrows. Reprinted with permission from Refs. [133, 135]. Copyright 2012 IOP Publishing Ltd;

To address how G-type antiferromagnetism is affected by strain effects, Sando et al., studied the strain effect within the range from −2.6% (compressive strain) to +1.0 (tensile strain)

pies combined with Landau–Ginzburg theory and effective Hamiltonian calculations, they observed different magnetic structures for different amounts of strain. For low compressive strain, there exists a bulk-like cycloidal spin modulation with non-collinear order, whereas for moderate tensile strain, they observed a new cycloidal phase with a propagation wave vector

is grown with *P4mm* structure, then it would show a high *P* of ~150 μC/cm<sup>2</sup>

along the [1 1 1]*C*, which has been found experimentally in

thin films. The large value of polarization for compressively strained

thin films. The colors correspond to different

Strain Effect in Epitaxial Oxide Heterostructures http://dx.doi.org/10.5772/intechopen.70125 25

. The

(**Figure 18b**) [135]. By using Mössbauer and Raman spectrosco-

strained BiFeO3

along the [0 0 1]*C* and ~100 μC/cm<sup>2</sup>

Copyright 2013 Macmillan Publisher Limited.

for the *R*-phase of BiFeO3

the super tetragonal-phase [137, 138].

**Figure 18.** (a) Polarization values of strained BiFeO<sup>3</sup>

evolution of strain, various novel magnetic phases can appear in BiFeO3

First-principle calculations also suggested that with a tensile strain of 2% or more, the orthorhombic phase in BiFeO3 can be stabilized. This is associated with the oxygen octahedral tilt exhibiting short atomic bonds and zig-zag cation displacement patterns. Consequently, the strain effect in BiFeO<sup>3</sup> induces very high structural flexibility, which changes the structure from *R*-phase to *M*-, *TG*- and *O*-phases or even mixed (*R* + *O*) ones [43, 128, 131].

One of the key aspects of the strain-induced scenario is to increase the out-of-plane *P* in strained BiFeO3 thin films. One of the goals is to induce strain and raise the *P* above 100 μC/cm<sup>2</sup> at *T* = 300 K. However, in the rhombohedral phase, whatever the growth direction is, the projected *P* along the [1 1 1]*C* increases by only up to ~20% compared to its initial value (**Figure 18a**) [133]. First-principle calculations suggested that suppressing octahedral

**Figure 18.** (a) Polarization values of strained BiFeO<sup>3</sup> thin films. The large value of polarization for compressively strained films grown on LSAT substrates was attributed to a leakage problem. (b) Magnetic phase diagram shows that with the evolution of strain, various novel magnetic phases can appear in BiFeO3 thin films. The colors correspond to different stable magnetic states (blue: antiferromagnetic; red: type-1 cycloid; orange: type-2 cycloid). The different substrates used for the study are shown above with different colors corresponding to the different magnetic structures of BiFeO<sup>3</sup> . The spins are denoted by green arrows. Reprinted with permission from Refs. [133, 135]. Copyright 2012 IOP Publishing Ltd; Copyright 2013 Macmillan Publisher Limited.

tilt favors an increase in *P*, whereas the presence of tilts instead favors a change in the direction without changing the *P* [130]. Recent theoretical calculations suggest that if highly strained BiFeO3 is grown with *P4mm* structure, then it would show a high *P* of ~150 μC/cm<sup>2</sup> along the [0 0 1]*C* and ~100 μC/cm<sup>2</sup> along the [1 1 1]*C*, which has been found experimentally in the super tetragonal-phase [137, 138].

First-principle calculations also suggested that with a tensile strain of 2% or more, the ortho-

compressive and tensile strain. Under different amounts of strain, bulk rhombohedral (*R*) phase to monoclinic (*M*),

exhibiting short atomic bonds and zig-zag cation displacement patterns. Consequently, the

One of the key aspects of the strain-induced scenario is to increase the out-of-plane *P* in

tion is, the projected *P* along the [1 1 1]*C* increases by only up to ~20% compared to its initial value (**Figure 18a**) [133]. First-principle calculations suggested that suppressing octahedral

from *R*-phase to *M*-, *TG*- and *O*-phases or even mixed (*R* + *O*) ones [43, 128, 131].

**Figure 17.** (a–f) Summary of the various crystal structures of BiFeO3

Ltd; Copyright 2009 American Association for the Advancement of Science.

tetragonal (*TG*), and orthorhombic (*O*) phase transitions can be observed in BiFeO3

can be stabilized. This is associated with the oxygen octahedral tilt

. Reprinted with permission from Refs. [120, 124]. Copyright 2014 IOP Publishing

thin films under epitaxial strain, i.e., both

. (g) Calculated overall energy of the

induces very high structural flexibility, which changes the structure

thin films. One of the goals is to induce strain and raise the *P* above

at *T* = 300 K. However, in the rhombohedral phase, whatever the growth direc-

rhombic phase in BiFeO3

system and *c*/*a* ratio for strained BiFeO3

strain effect in BiFeO<sup>3</sup>

strained BiFeO3

100 μC/cm<sup>2</sup>

24 Epitaxy

To address how G-type antiferromagnetism is affected by strain effects, Sando et al., studied the strain effect within the range from −2.6% (compressive strain) to +1.0 (tensile strain) for the *R*-phase of BiFeO3 (**Figure 18b**) [135]. By using Mössbauer and Raman spectroscopies combined with Landau–Ginzburg theory and effective Hamiltonian calculations, they observed different magnetic structures for different amounts of strain. For low compressive strain, there exists a bulk-like cycloidal spin modulation with non-collinear order, whereas for moderate tensile strain, they observed a new cycloidal phase with a propagation wave vector along [110]. For the high compressive- or tensile-strained case, the magnetic state was found to be a pseudo-collinear antiferromagnetic one.

#### **4.5. A conductive oxide interface: LaAlO<sup>3</sup> -SrTiO3**

SrTiO3 and LaAlO3 are both band insulators with band gaps of ~3.25 eV and ~5.6 eV, respectively [139, 140]. Along [0 0 1], SrTiO3 unit cells consist of charge-neutral layers of SrO0 and TiO<sup>2</sup> 0 , whereas LaAlO3 consists of polar layers of LaO1+ and AlO<sup>2</sup> 1− (**Figure 19a** and **b**) [14]. In 2004, Ohtomo and Hwang discovered that if band insulator LaAlO<sup>3</sup> (LAO) is grown on top of another band insulator, SrTiO3 (STO), with atomic precision, the interface of LAO-STO can be highly conducting, which results in a two-dimensional electron gas (2DEG) at the interface [14]. Surprisingly, conductivity was observed for only one type of interface: LaO-TiO2 (n-type), whereas insulating characteristics were observed for AlO<sup>2</sup> -SrO (p-type) interfaces (**Figure 19c**) [141]. With this discovery, a tremendous interest has emerged among the thinfilm community to deposit each and every thin film material with atomically controlled interfaces. Later, it was found that the LAO-STO interface not only is highly conductive but can also show coexistence of superconductivity and magnetism, the quantum Hall effect, and the Rashba effect [18, 142–145]. Based on various experimental observations, the origin of 2DEG, interfacial charge distribution vs. oxygen vacancy scenario is still under debate [146, 147].

Since the atomic configuration of a substrate's topmost layer plays a key role in forming 2DEGs at interfaces between two non-conducting oxides, it would be highly desirable to study the formation of 2DEGs at oxide interfaces with the strain effects [148–155]. Bark et al., grew LAO-STO interfaces on various substrates, such as (1 1 0) NdGaO3 , (0 0 1) LSAT, (1 1 0) DyScO3 , and (1 1 0) GdScO3 (**Figure 20a**) [148]. By using four different substrates, the strain ranged from compressive to tensile strain as follow; −1.21% compressive strain for films grown on (1 1 0) NdGaO3 , −0.96% compressive strain for films grown on (0 0 1) LSAT, +1.11% tensile strain for films grown on (1 1 0) DyScO<sup>3</sup> , and +1.59% tensile strain for films grown on (1 1 0) GdScO<sup>3</sup> . They have shown that imposing tensile strain on SrTiO3 destroys the 2DEG, whereas exerting compressive strain leads to the 2DEG nature being retained but with a reduction of carrier concentration compared to that of unstrained LAO-STO interfaces (**Figure 20b**). Using theoretical calculations, they suggested that this behavior is associated with the built-in polarization in SrTiO3 , as it was observed that with induced strain, polarization can have built up in pure SrTiO3 as well [44]. This polarization is directed away from the interface and creates a negative polarization opposing that of the polar LaAlO3 layer. It has also been calculated that the distortion of interfacial Ti─O octahedra enhances with increases in in-plane compressive strain, which also modulates the carrier concentration [152]. Applied in-plane compressive strain also reduces the carrier concentration. On the other hand, under tensile strain, the interfacial charge carrier density increases, which is consistent with the theoretical calculations [155]. It has been found that when moving from the compressive-strained to the tensile-strained scenario at the LAO-STO interface, the Ti─O bond length becomes elongated, which confines the Ti *d*xy orbital electrons at the interface, thus increasing the sheet carrier concentration (*ns* ) at the interface. For the compressively strained scenario, the Ti─O bond length decreases and the Ti *d*xy orbital cannot hold all the electrons at the interface; hence, the remaining electrons are transferred to a deeper layer, reducing the carrier concentration at the interface.

To observe the correlation and strain effect induced by the topmost polar layer, Ariando et al.,

interfaces show insulating characteristics at the interface. Reprinted with permission from Refs. [14, 141]. Copyright 2004

the formation of 2-dimesnioanl electron gas (2DEG) with n-type charge carriers at the interface, whereas AlO2

(band insulator) materials showing the composition and ionic distribution. Depending on the topmost

substrate, two possible interfaces can form: (1) LaO1+-TiO<sup>2</sup>

**Figure 19.** (a) and (b) Schematic representation of two possible interfaces between change neutral SrTiO3

(c) Temperature-dependent resistivity of these two types of interfaces. LaO1+-TiO<sup>2</sup>

Nature Publishing Group; Copyright 2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

ing and form 2DEGs. They also claimed that the interfacial strain and electron correlation caused by the polar layers seem to control the carrier density and mobility at the interface (**Figure 20d**). The presence of large octahedral distortion due to strain also plays an important role in observing

perovskites, e.g., NaAlO3

0

(**Figure 20c**) [150]. They found that these interfaces are also conduct-

/SrTiO3

, and (2) AlO2

interfaces show metallicity and

0

Strain Effect in Epitaxial Oxide Heterostructures http://dx.doi.org/10.5772/intechopen.70125 27

, PrAlO<sup>3</sup> /

(band insulator)

1−-SrO0 .

1−-SrO0

grew various combination of polar/non-polar ABO3

/SrTiO3

SrTiO3

and polar LaAlO3

, and NdGaO3

layer termination of the (0 0 1) SrTiO3

along [110]. For the high compressive- or tensile-strained case, the magnetic state was found

**-SrTiO3**

be highly conducting, which results in a two-dimensional electron gas (2DEG) at the interface [14]. Surprisingly, conductivity was observed for only one type of interface: LaO-TiO2

(**Figure 19c**) [141]. With this discovery, a tremendous interest has emerged among the thinfilm community to deposit each and every thin film material with atomically controlled interfaces. Later, it was found that the LAO-STO interface not only is highly conductive but can also show coexistence of superconductivity and magnetism, the quantum Hall effect, and the Rashba effect [18, 142–145]. Based on various experimental observations, the origin of 2DEG, interfacial charge distribution vs. oxygen vacancy scenario is still under debate [146, 147].

Since the atomic configuration of a substrate's topmost layer plays a key role in forming 2DEGs at interfaces between two non-conducting oxides, it would be highly desirable to study the formation of 2DEGs at oxide interfaces with the strain effects [148–155]. Bark et al., grew LAO-

compressive to tensile strain as follow; −1.21% compressive strain for films grown on (1 1 0)

compressive strain leads to the 2DEG nature being retained but with a reduction of carrier concentration compared to that of unstrained LAO-STO interfaces (**Figure 20b**). Using theoretical calculations, they suggested that this behavior is associated with the built-in polarization in

tortion of interfacial Ti─O octahedra enhances with increases in in-plane compressive strain, which also modulates the carrier concentration [152]. Applied in-plane compressive strain also reduces the carrier concentration. On the other hand, under tensile strain, the interfacial charge carrier density increases, which is consistent with the theoretical calculations [155]. It has been found that when moving from the compressive-strained to the tensile-strained scenario at the LAO-STO interface, the Ti─O bond length becomes elongated, which confines the Ti *d*xy orbital electrons at the interface, thus increasing the sheet carrier concentration (*ns*

at the interface. For the compressively strained scenario, the Ti─O bond length decreases and the Ti *d*xy orbital cannot hold all the electrons at the interface; hence, the remaining electrons

are transferred to a deeper layer, reducing the carrier concentration at the interface.

(**Figure 20a**) [148]. By using four different substrates, the strain ranged from

, and +1.59% tensile strain for films grown on (1 1 0) GdScO<sup>3</sup>

, −0.96% compressive strain for films grown on (0 0 1) LSAT, +1.11% tensile strain for

, as it was observed that with induced strain, polarization can have built up in pure

as well [44]. This polarization is directed away from the interface and creates a negative

consists of polar layers of LaO1+ and AlO<sup>2</sup>

2004, Ohtomo and Hwang discovered that if band insulator LaAlO<sup>3</sup>

(n-type), whereas insulating characteristics were observed for AlO<sup>2</sup>

STO interfaces on various substrates, such as (1 1 0) NdGaO3

They have shown that imposing tensile strain on SrTiO3

polarization opposing that of the polar LaAlO3

are both band insulators with band gaps of ~3.25 eV and ~5.6 eV, respec-

unit cells consist of charge-neutral layers of SrO0

(STO), with atomic precision, the interface of LAO-STO can

and

, and

.

)

1− (**Figure 19a** and **b**) [14]. In

(LAO) is grown on top


, (0 0 1) LSAT, (1 1 0) DyScO3

destroys the 2DEG, whereas exerting

layer. It has also been calculated that the dis-

to be a pseudo-collinear antiferromagnetic one.

**4.5. A conductive oxide interface: LaAlO<sup>3</sup>**

tively [139, 140]. Along [0 0 1], SrTiO3

and LaAlO3

, whereas LaAlO3

of another band insulator, SrTiO3

SrTiO3

26 Epitaxy

TiO<sup>2</sup> 0

(1 1 0) GdScO3

films grown on (1 1 0) DyScO<sup>3</sup>

NdGaO3

SrTiO3

SrTiO3

**Figure 19.** (a) and (b) Schematic representation of two possible interfaces between change neutral SrTiO3 (band insulator) and polar LaAlO3 (band insulator) materials showing the composition and ionic distribution. Depending on the topmost layer termination of the (0 0 1) SrTiO3 substrate, two possible interfaces can form: (1) LaO1+-TiO<sup>2</sup> 0 , and (2) AlO2 1−-SrO0 . (c) Temperature-dependent resistivity of these two types of interfaces. LaO1+-TiO<sup>2</sup> 0 interfaces show metallicity and the formation of 2-dimesnioanl electron gas (2DEG) with n-type charge carriers at the interface, whereas AlO2 1−-SrO0 interfaces show insulating characteristics at the interface. Reprinted with permission from Refs. [14, 141]. Copyright 2004 Nature Publishing Group; Copyright 2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

To observe the correlation and strain effect induced by the topmost polar layer, Ariando et al., grew various combination of polar/non-polar ABO3 perovskites, e.g., NaAlO3 /SrTiO3 , PrAlO<sup>3</sup> / SrTiO3 , and NdGaO3 /SrTiO3 (**Figure 20c**) [150]. They found that these interfaces are also conducting and form 2DEGs. They also claimed that the interfacial strain and electron correlation caused by the polar layers seem to control the carrier density and mobility at the interface (**Figure 20d**). The presence of large octahedral distortion due to strain also plays an important role in observing

nickelates, more specifically LaNiO<sup>3</sup>

LaNiO3

(0 0 1) LaAlO3

distorted NiO6

tensile strain increases, LaNiO3

no long-range magnetic ordering [156–158].

, (0 0 1) SrLaGaO4

its strain-dependent transport properties.

(b) Resistivity of bulk polycrystalline LaNiO3

Ltd.; Copyright 2014 American Physical Society.

It is the only member in the perovskite nickelate family (*RE*NiO3

lattice-mismatched substrates) to obtain novel functionalities in LaNiO<sup>3</sup>

reported the strain dependent transport properties in epitaxial LaNiO3

systems. They grew 10-unit cell ultra-thin LaNiO3

is a strongly correlated Mott metal [159, 160]. LaNiO3

films on (1 1 0) YAlO<sup>3</sup>

gradually evolves from the Mott to the Mott-Anderson regime;

, and (1 1 0) GdScO3

highly distorted rhombohedral structure with lattice parameters of *a* = *b* = 5.4573 Å, *c* = 13.1462 Å, and *α* = *β* = *γ* = 60.49° and with space group *R*3¯*<sup>c</sup>* (**Figure 21a**) [161]. Its pseudo-cubic lattice constant is *a*pc = 3.84 Å. It is highly metallic over the entire temperature range (**Figure 21b**) [162].

The functionalities of strongly correlated rare-earth nickelates are highly sensitive to external perturbation, e.g., chemical pressure and atmospheric pressure [156–158]. Thus, it would be very interesting to investigate the ability of strain-based perturbation (i.e., by using various

Moon et al., investigated in detail the transport properties of tensile- and compressive-strained

, (0 0 1) LSAT, (0 0 1) SrTiO3

(**Figure 22a**) [167–169]. They investigated *ρ* of tensile-strained films and observed that when the

The authors have also investigated the Hall effect (1/*R*<sup>H</sup> ∝ *T*; *R*<sup>H</sup> = Hall coefficient) in both the compressive- and tensile-strained cases (**Figure 22c**) [168]. They claimed that the evolution of the linear *T* dependent transport coefficient is quite similar to that of hole-doped cuprate superconductors. By using density functional theoretical (DFT) calculations, they claimed that strain-induced changes in transport properties arise from changes in the low-energy electronic band structure that induces self-doping, i.e., a transfer of charge between the O p and Ni d states. Using detailed quantitative structural analysis and theoretical calculations May et al., found that strain systematically modifies both the Ni─O─Ni bond angles and Ni─O lengths in this functional perovskite oxide (**Figure 22d**) [164, 172], which has strong effect on

i.e., correlation and disorder play a crucial role at low temperature (**Figure 22b**) [163, 167].

**Figure 21.** (a) Schematic representation of the distorted rhombohedral crystal structure of LaNiO3

octahedra with lattice parameters of *a* = *b* = 5.4573 Å and *c* = 13.1462 Å. The pseudo-cubic unit cell is ~3.84 Å.

ordering over the entire temperature range. Reprinted with permission from Refs. [161, 162]. Copyright 2015 Elsevier B. V.

showing it is a paramagnetic metal without any indication of magnetic

has a

29

, *RE* = rare earths) which shows

Strain Effect in Epitaxial Oxide Heterostructures http://dx.doi.org/10.5772/intechopen.70125

. Several groups have

thin films [163–172].

, (0 0 1) SrLaAlO4

substrates

showing highly

,

**Figure 20.** (a) Schematic representation of a LaAlO3 -SrTiO3 interface grown on various substrates (i.e., on GdScO3 , DyScO3 , LSAT and NdGaO3 ). (b) Carrier concentration at room temperature at the LAO-STO interface under various epitaxial strains. For tensile-strained films, the carrier concentration is below the measurement limit. (c) The strain effect at the interface and lattice parameters of various perovskites. (d) Sheet resistance (*R*<sup>S</sup> ), carrier concentration (*n*s ), and mobility (*μ*) of various polar/non-polar interfaces. (e) Carrier concentration at the interface of LAO-STO with monolayer growth of rare earth oxides. For some rare earth cases, the interfaces are conductive, whereas insulating interfaces are formed in some cases involving rare-earth oxides, showing the effect of correlation on the formation of 2DEGs at interfaces. Reprinted with the permission from Refs. [148–150]. Copyright 2011 National Academy of Sciences; Copyright 2011 American Association for the Advancement of Science; Copyright 2012 American Physical Society.

these novel phases. Instead of growing various rare earth-based polar ABO3 perovskites, Jang et al., directly grew monolayers of rare-earth oxides (*R*O, R = La, Pr, Nd, Sm, and Y) to observe the correlation effect at interfaces (**Figure 20e**) [149]. Surprisingly, they found that some oxides (La, Pr, and Nd) forms 2DEGs at the interface, whereas an insulating interface is formed in the case of SmO and YO. Based on the observations and theoretical calculations, they claimed that this is due to the correlation effect at the interface. Independent theoretical calculation also suggest that in-plane strain can induce metal-insulator transitions at oxide interfaces [155].

## **4.6. A strongly correlated metal: LaNiO<sup>3</sup>**

The physics of strongly correlated materials, i.e., those having strong electronic correlations, is remarkably rich and complex and cannot be understood within the framework of conventional theories of metals and insulators [21, 22]. For example, in strongly correlated nickelate materials, spin, lattice charge, and orbital degrees of freedom result in competing interactions. Due to this, these materials show exotic phases [156–158]. Among strongly correlated materials, nickelates, more specifically LaNiO<sup>3</sup> is a strongly correlated Mott metal [159, 160]. LaNiO3 has a highly distorted rhombohedral structure with lattice parameters of *a* = *b* = 5.4573 Å, *c* = 13.1462 Å, and *α* = *β* = *γ* = 60.49° and with space group *R*3¯*<sup>c</sup>* (**Figure 21a**) [161]. Its pseudo-cubic lattice constant is *a*pc = 3.84 Å. It is highly metallic over the entire temperature range (**Figure 21b**) [162]. It is the only member in the perovskite nickelate family (*RE*NiO3 , *RE* = rare earths) which shows no long-range magnetic ordering [156–158].

The functionalities of strongly correlated rare-earth nickelates are highly sensitive to external perturbation, e.g., chemical pressure and atmospheric pressure [156–158]. Thus, it would be very interesting to investigate the ability of strain-based perturbation (i.e., by using various lattice-mismatched substrates) to obtain novel functionalities in LaNiO<sup>3</sup> . Several groups have reported the strain dependent transport properties in epitaxial LaNiO3 thin films [163–172]. Moon et al., investigated in detail the transport properties of tensile- and compressive-strained LaNiO3 systems. They grew 10-unit cell ultra-thin LaNiO3 films on (1 1 0) YAlO<sup>3</sup> , (0 0 1) SrLaAlO4 , (0 0 1) LaAlO3 , (0 0 1) SrLaGaO4 , (0 0 1) LSAT, (0 0 1) SrTiO3 , and (1 1 0) GdScO3 substrates (**Figure 22a**) [167–169]. They investigated *ρ* of tensile-strained films and observed that when the tensile strain increases, LaNiO3 gradually evolves from the Mott to the Mott-Anderson regime; i.e., correlation and disorder play a crucial role at low temperature (**Figure 22b**) [163, 167].

The authors have also investigated the Hall effect (1/*R*<sup>H</sup> ∝ *T*; *R*<sup>H</sup> = Hall coefficient) in both the compressive- and tensile-strained cases (**Figure 22c**) [168]. They claimed that the evolution of the linear *T* dependent transport coefficient is quite similar to that of hole-doped cuprate superconductors. By using density functional theoretical (DFT) calculations, they claimed that strain-induced changes in transport properties arise from changes in the low-energy electronic band structure that induces self-doping, i.e., a transfer of charge between the O p and Ni d states. Using detailed quantitative structural analysis and theoretical calculations May et al., found that strain systematically modifies both the Ni─O─Ni bond angles and Ni─O lengths in this functional perovskite oxide (**Figure 22d**) [164, 172], which has strong effect on its strain-dependent transport properties.

these novel phases. Instead of growing various rare earth-based polar ABO3

effect at the interface and lattice parameters of various perovskites. (d) Sheet resistance (*R*<sup>S</sup>

in-plane strain can induce metal-insulator transitions at oxide interfaces [155].

**4.6. A strongly correlated metal: LaNiO<sup>3</sup>**

**Figure 20.** (a) Schematic representation of a LaAlO3

, LSAT and NdGaO3

DyScO3

(*n*s

28 Epitaxy

al., directly grew monolayers of rare-earth oxides (*R*O, R = La, Pr, Nd, Sm, and Y) to observe the correlation effect at interfaces (**Figure 20e**) [149]. Surprisingly, they found that some oxides (La, Pr, and Nd) forms 2DEGs at the interface, whereas an insulating interface is formed in the case of SmO and YO. Based on the observations and theoretical calculations, they claimed that this is due to the correlation effect at the interface. Independent theoretical calculation also suggest that


epitaxial strains. For tensile-strained films, the carrier concentration is below the measurement limit. (c) The strain

), and mobility (*μ*) of various polar/non-polar interfaces. (e) Carrier concentration at the interface of LAO-STO with monolayer growth of rare earth oxides. For some rare earth cases, the interfaces are conductive, whereas insulating interfaces are formed in some cases involving rare-earth oxides, showing the effect of correlation on the formation of 2DEGs at interfaces. Reprinted with the permission from Refs. [148–150]. Copyright 2011 National Academy of Sciences; Copyright 2011 American Association for the Advancement of Science; Copyright 2012 American Physical Society.

The physics of strongly correlated materials, i.e., those having strong electronic correlations, is remarkably rich and complex and cannot be understood within the framework of conventional theories of metals and insulators [21, 22]. For example, in strongly correlated nickelate materials, spin, lattice charge, and orbital degrees of freedom result in competing interactions. Due to this, these materials show exotic phases [156–158]. Among strongly correlated materials,

perovskites, Jang et

), carrier concentration

,

interface grown on various substrates (i.e., on GdScO3

). (b) Carrier concentration at room temperature at the LAO-STO interface under various

**Figure 21.** (a) Schematic representation of the distorted rhombohedral crystal structure of LaNiO3 showing highly distorted NiO6 octahedra with lattice parameters of *a* = *b* = 5.4573 Å and *c* = 13.1462 Å. The pseudo-cubic unit cell is ~3.84 Å. (b) Resistivity of bulk polycrystalline LaNiO3 showing it is a paramagnetic metal without any indication of magnetic ordering over the entire temperature range. Reprinted with permission from Refs. [161, 162]. Copyright 2015 Elsevier B. V. Ltd.; Copyright 2014 American Physical Society.

**5. Summary**

ABO3

electronic devices.

**Author details**

**Acknowledgements**

and 2015R1D1A1A02062239).

Abhijit Biswas and Yoon Hee Jeong\*

\*Address all correspondence to: yhj@postech.ac.kr

high temperature superconductor, La1.85Sr0.15CuO4

a conducting oxide interface, LaAlO3

the shape, size, and position of BO6

(3) a colossal magnetoresistive metal, La0.67Sr0.33MnO3

In principle, material functionalities arise from the coupling between spin, lattice, charge, and orbital degrees of freedom. Lattice strain is thus found to be a unique way to engineering the functionalities of many TMOs, which modifies above energy scales. Here, we presented the effect of strain-dependent functionalities of various TMO-based thin films: (1) a

The aforementioned materials all show rich and complex structural, electronic, magnetic and polar phase diagrams that are dependent on epitaxial strain, which is mainly caused by modifications of their crystal structures and the effects of these modification on the coupling of their various degrees of freedoms (relevant energy scales). More specifically, tailoring

 perovskite oxides. Strain-dependent MITs, increase in magnetic transition temperature and ferroelectric polarization can be observed in these materials. Obtaining novel properties by designing artificial oxide heterostructures and the subsequent new physics resulting from the strain effect have always been an interesting topic of research among the thin-film community as cheap and environment friendly oxide thin film-based electronic devices are highly in demand in industry. Although there has been vast progress in the strain-dependent tuning of material properties, there is still long way to go to fully understand the intrinsic mechanisms and theoretical developments behind these strain-dependent phenomena. Nevertheless, strain has provided an avenue to explore materials with novel functionalities. We believe that our experimental investigations along with insightful explanations will provide readers with an easier way to understand the strain effect in epitaxial oxide heterostructures and utilize it to explain the fundamental physics and to commercialize oxide-based

YHJ was supported by the National Research Foundation (NRF) of Korea (SRC-2011-0030786

Department of Physics, Pohang University of Science Technology, Pohang, Republic of Korea


, (2) a highly conductive oxide, SrRuO<sup>3</sup>

Strain Effect in Epitaxial Oxide Heterostructures http://dx.doi.org/10.5772/intechopen.70125

, (4) a multiferroic oxide, BiFeO3

, and (6) a strongly correlated metal, LaNiO3

octahedra by strain give rise to new functionalities in

,

31

.

, (5)

**Figure 22.** (a) Schematic representation of compressive and tensile strain imposed on LaNiO3 by various metal oxide substrates. (b) Low-temperature resistivity of strained LaNiO3 films. With an increase in tensile strain, resistivity at room temperature increases, although the resistivity minima also decrease. (c) The temperature-dependent Hall coefficient (1/*R*H) for strained LaNiO3 films grown on various substrates. With an increase in compressive strain, 1/*R*<sup>H</sup> becomes almost linearly dependent on temperature (1/*R*<sup>H</sup> ∝ *T*), thus bearing a striking resemblance to the behavior of cuprate superconductors. (d) Tensile strain increases rotation of octahedra along the [1 0 0] and [0 1 0], and decreases it along the [0 0 1]. (e) Compressive strain reduces the rotation along the [1 0 0] and [0 1 0], and increases it along the [0 0 1]. Reprinted with permission from Refs [164, 167, 168]. Copyright 2010 American Physical Society; Copyright 2013 American Chemical Society; Copyright 2011 IOP Publishing Ltd and Deutsche Physikalische Gesellschaft.

## **5. Summary**

In principle, material functionalities arise from the coupling between spin, lattice, charge, and orbital degrees of freedom. Lattice strain is thus found to be a unique way to engineering the functionalities of many TMOs, which modifies above energy scales. Here, we presented the effect of strain-dependent functionalities of various TMO-based thin films: (1) a high temperature superconductor, La1.85Sr0.15CuO4 , (2) a highly conductive oxide, SrRuO<sup>3</sup> , (3) a colossal magnetoresistive metal, La0.67Sr0.33MnO3 , (4) a multiferroic oxide, BiFeO3 , (5) a conducting oxide interface, LaAlO3 -SrTiO3 , and (6) a strongly correlated metal, LaNiO3 . The aforementioned materials all show rich and complex structural, electronic, magnetic and polar phase diagrams that are dependent on epitaxial strain, which is mainly caused by modifications of their crystal structures and the effects of these modification on the coupling of their various degrees of freedoms (relevant energy scales). More specifically, tailoring the shape, size, and position of BO6 octahedra by strain give rise to new functionalities in ABO3 perovskite oxides. Strain-dependent MITs, increase in magnetic transition temperature and ferroelectric polarization can be observed in these materials. Obtaining novel properties by designing artificial oxide heterostructures and the subsequent new physics resulting from the strain effect have always been an interesting topic of research among the thin-film community as cheap and environment friendly oxide thin film-based electronic devices are highly in demand in industry. Although there has been vast progress in the strain-dependent tuning of material properties, there is still long way to go to fully understand the intrinsic mechanisms and theoretical developments behind these strain-dependent phenomena. Nevertheless, strain has provided an avenue to explore materials with novel functionalities. We believe that our experimental investigations along with insightful explanations will provide readers with an easier way to understand the strain effect in epitaxial oxide heterostructures and utilize it to explain the fundamental physics and to commercialize oxide-based electronic devices.

## **Acknowledgements**

YHJ was supported by the National Research Foundation (NRF) of Korea (SRC-2011-0030786 and 2015R1D1A1A02062239).

## **Author details**

**Figure 22.** (a) Schematic representation of compressive and tensile strain imposed on LaNiO3

room temperature increases, although the resistivity minima also decrease. (c) The temperature-dependent Hall

becomes almost linearly dependent on temperature (1/*R*<sup>H</sup> ∝ *T*), thus bearing a striking resemblance to the behavior of cuprate superconductors. (d) Tensile strain increases rotation of octahedra along the [1 0 0] and [0 1 0], and decreases it along the [0 0 1]. (e) Compressive strain reduces the rotation along the [1 0 0] and [0 1 0], and increases it along the [0 0 1]. Reprinted with permission from Refs [164, 167, 168]. Copyright 2010 American Physical Society; Copyright 2013

American Chemical Society; Copyright 2011 IOP Publishing Ltd and Deutsche Physikalische Gesellschaft.

substrates. (b) Low-temperature resistivity of strained LaNiO3

coefficient (1/*R*H) for strained LaNiO3

30 Epitaxy

by various metal oxide

films. With an increase in tensile strain, resistivity at

films grown on various substrates. With an increase in compressive strain, 1/*R*<sup>H</sup>

Abhijit Biswas and Yoon Hee Jeong\*

\*Address all correspondence to: yhj@postech.ac.kr

Department of Physics, Pohang University of Science Technology, Pohang, Republic of Korea

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**Chapter 2**

**Provisional chapter**

**Epitaxial Growth of Ge on Si by Magnetron Sputtering**

Epitaxial growth of Ge on Si has received considerable attention for its compatibility with Si process flow and the scarcity of Ge compared with Si. Applications that drive the efforts for integrating Ge with Si include high mobility channel in metal-oxide-semiconductor field-effect transistors, infrared photodetector in Si-based optical devices, and template for III-V growth to fabricate high-efficiency solar cells. Epitaxy Ge on Si can be used as a virtual Ge substrate for fabrication of III-V solar cells, which has advantages of superior mechanical properties and low cost over Ge wafers. This work investigates the epitaxial growth of Ge on Si using magnetron sputtering, which is an environment-friendly, inexpensive, high throughput, and simple deposition technique. The effects of substrate temperature on the properties of Ge are analyzed. A novel method to epitaxially grow Ge on Si by magnetron sputtering at low temperature is developed using one-step aluminumassisted crystallization. By applying an *in-situ* low temperature (50–150°C) heat treatment in between Al and Ge sputter depositions, the epitaxial growth of Ge on Si is achieved. This method significantly lowers the required temperature for and therefore the cost of

**Keywords:** germanium, epitaxy, silicon, magnetron sputtering, substrate temperature,

Epitaxial growth of Ge on Si has received considerable attention for its compatibility with Si process flow and the scarcity of Ge compared with Si. Applications driving the efforts for integrating Ge with Si include: high mobility channel in metal-oxide-semiconductor field-effect transistors [1], infrared photodetector in Si-based optical devices [2], and template for III-V

**Epitaxial Growth of Ge on Si by Magnetron Sputtering**

DOI: 10.5772/intechopen.73554

© 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution,

© 2018 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

and reproduction in any medium, provided the original work is properly cited.

Ziheng Liu, Xiaojing Hao, Anita Ho-Baillie and

Ziheng Liu, Xiaojing Hao, Anita Ho-Baillie and

Additional information is available at the end of the chapter

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/intechopen.73554

epitaxial growth of Ge on Si.

one-step aluminum-assisted crystallization

growth to fabricate high efficiency solar cells [3].

Martin A. Green

**Abstract**

**1. Introduction**

Martin A. Green


**Provisional chapter**

## **Epitaxial Growth of Ge on Si by Magnetron Sputtering Epitaxial Growth of Ge on Si by Magnetron Sputtering**

DOI: 10.5772/intechopen.73554

Ziheng Liu, Xiaojing Hao, Anita Ho-Baillie and Martin A. Green Ziheng Liu, Xiaojing Hao, Anita Ho-Baillie and Martin A. Green

Additional information is available at the end of the chapter Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/intechopen.73554

#### **Abstract**

[160] Sreedhar K, Honig JM, Darwin M, McElfresh M, Shand PM, Xu J, Crooker BC, Spalek

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phases of LaNiO3

44 Epitaxy

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PhysRevB.94.014118

LaNiO3

LaNiO3

Epitaxial growth of Ge on Si has received considerable attention for its compatibility with Si process flow and the scarcity of Ge compared with Si. Applications that drive the efforts for integrating Ge with Si include high mobility channel in metal-oxide-semiconductor field-effect transistors, infrared photodetector in Si-based optical devices, and template for III-V growth to fabricate high-efficiency solar cells. Epitaxy Ge on Si can be used as a virtual Ge substrate for fabrication of III-V solar cells, which has advantages of superior mechanical properties and low cost over Ge wafers. This work investigates the epitaxial growth of Ge on Si using magnetron sputtering, which is an environment-friendly, inexpensive, high throughput, and simple deposition technique. The effects of substrate temperature on the properties of Ge are analyzed. A novel method to epitaxially grow Ge on Si by magnetron sputtering at low temperature is developed using one-step aluminumassisted crystallization. By applying an *in-situ* low temperature (50–150°C) heat treatment in between Al and Ge sputter depositions, the epitaxial growth of Ge on Si is achieved. This method significantly lowers the required temperature for and therefore the cost of epitaxial growth of Ge on Si.

**Keywords:** germanium, epitaxy, silicon, magnetron sputtering, substrate temperature, one-step aluminum-assisted crystallization

#### **1. Introduction**

Epitaxial growth of Ge on Si has received considerable attention for its compatibility with Si process flow and the scarcity of Ge compared with Si. Applications driving the efforts for integrating Ge with Si include: high mobility channel in metal-oxide-semiconductor field-effect transistors [1], infrared photodetector in Si-based optical devices [2], and template for III-V growth to fabricate high efficiency solar cells [3].

© 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. © 2018 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Ge wafers are the commonly used substrates for the fabrication of high efficiency III-V tandem solar cells [4–6]. Though cheaper than III-V materials, Ge wafers are over 100 times more expensive than Si accounting for more than 50% of the cell cost [3]. Compared with Ge wafer, Si wafer is an alternative with low cost, superior mechanical properties, and higher band gap more desirable for the bottom cell in a double or triple stack [7]. However, the lattice constant of Si is too small to match that of the III-V materials as shown in **Figure 1**. The lattice mismatch can induce large densities of defects negating the advantages of Si substrate. Several approaches have been investigated to control the defect density in this mismatched heterostructure including the insertion of various III-V intermediate layers, strained layer super-lattices, and the use of thermal annealing [8]. The obtained material qualities through these methods are not high enough to yield high efficiency III-V cells. A promising alternative is growing a Ge buffer layer to engineer the lattice constant of substrate surface to match that of III-V materials. Ge epitaxial film on Si can be used as a "virtual Ge substrate" for III-V solar cells. The virtual Ge substrate has advantages of superior mechanical properties and low cost over Ge wafer.

supplying epitaxial Ge films on Si, which is potentially capable of large-scale production with good uniformity. This chapter presents the successful epitaxial growth of Ge on Si by magnetron sputtering, investigation on the effects of substrate temperature, and the development of a novel method to grow epitaxial Ge on Si by magnetron sputtering at low temperature

Epitaxial Growth of Ge on Si by Magnetron Sputtering http://dx.doi.org/10.5772/intechopen.73554 47

Three modes are possible in epitaxial growth: Frank-van der Merwe [15], Volmer-Weber [16], and Stranski-Krastanow [17], as shown in **Figure 2**. Frank-van der Merwe and Volmer-Weber modes are pure 2D layer-by-layer growth and 3D island growth, respectively. Stranski-

The interfacial free energy and the lattice mismatch determine which growth mode will be adopted in a given system [18]. In lattice-matched systems, the epitaxial film grows either in layer-by-layer mode or island growth mode depending on the interface energy and surface energy of the epitaxial film. In systems with large lattice mismatch, the growth mode may transit from 2D to island growth (SK mode) to relax strain in the epitaxial film. The early stage of the growth could be layer-by-layer due to the small interface energy. With epitaxial film growing thicker, strain energy is accumulated. The island formation is triggered to lower the

**Figure 2.** Illustrations of three possible epitaxial growth modes: Frank-van der Merwe, Volmer-Weber, and Stranski-

Krastanow (SK mode) is a unique mode of 2D growth plus 3D island formation.

through one-step aluminum-assisted crystallization.

**2. Growth mechanism of Ge epitaxy on Si**

total energy by introducing misfit dislocations.

Krastanow [18].

**2.1. Stranski-Krastanow growth**

This work investigates the epitaxial growth of Ge on Si by magnetron sputtering, which is an environment-friendly, economical, high throughput, and simple deposition technique. Molecular beam epitaxy (MBE) and chemical vapor deposition (CVD) are widely used for Ge epitaxial growth on Si [10–13]. The MBE and CVD systems require higher vacuum (5 × 10−11 and 1.5 × 10−9 mbar, respectively) than magnetron sputtering (5 × 10−7 mbar) used in this work [14]. While MBE is the most expensive of the three and toxic gases such as germane and silane are used in a CVD system, magnetron sputtering offers a lower cost and safer alternative in

**Figure 1.** Lattice/band gap diagram for tetrahedrally coordinated semiconductors and their alloys [9].

supplying epitaxial Ge films on Si, which is potentially capable of large-scale production with good uniformity. This chapter presents the successful epitaxial growth of Ge on Si by magnetron sputtering, investigation on the effects of substrate temperature, and the development of a novel method to grow epitaxial Ge on Si by magnetron sputtering at low temperature through one-step aluminum-assisted crystallization.

## **2. Growth mechanism of Ge epitaxy on Si**

#### **2.1. Stranski-Krastanow growth**

Ge wafers are the commonly used substrates for the fabrication of high efficiency III-V tandem solar cells [4–6]. Though cheaper than III-V materials, Ge wafers are over 100 times more expensive than Si accounting for more than 50% of the cell cost [3]. Compared with Ge wafer, Si wafer is an alternative with low cost, superior mechanical properties, and higher band gap more desirable for the bottom cell in a double or triple stack [7]. However, the lattice constant of Si is too small to match that of the III-V materials as shown in **Figure 1**. The lattice mismatch can induce large densities of defects negating the advantages of Si substrate. Several approaches have been investigated to control the defect density in this mismatched heterostructure including the insertion of various III-V intermediate layers, strained layer super-lattices, and the use of thermal annealing [8]. The obtained material qualities through these methods are not high enough to yield high efficiency III-V cells. A promising alternative is growing a Ge buffer layer to engineer the lattice constant of substrate surface to match that of III-V materials. Ge epitaxial film on Si can be used as a "virtual Ge substrate" for III-V solar cells. The virtual Ge substrate has advantages of superior mechanical properties and

This work investigates the epitaxial growth of Ge on Si by magnetron sputtering, which is an environment-friendly, economical, high throughput, and simple deposition technique. Molecular beam epitaxy (MBE) and chemical vapor deposition (CVD) are widely used for Ge epitaxial growth on Si [10–13]. The MBE and CVD systems require higher vacuum (5 × 10−11 and 1.5 × 10−9 mbar, respectively) than magnetron sputtering (5 × 10−7 mbar) used in this work [14]. While MBE is the most expensive of the three and toxic gases such as germane and silane are used in a CVD system, magnetron sputtering offers a lower cost and safer alternative in

**Figure 1.** Lattice/band gap diagram for tetrahedrally coordinated semiconductors and their alloys [9].

low cost over Ge wafer.

46 Epitaxy

Three modes are possible in epitaxial growth: Frank-van der Merwe [15], Volmer-Weber [16], and Stranski-Krastanow [17], as shown in **Figure 2**. Frank-van der Merwe and Volmer-Weber modes are pure 2D layer-by-layer growth and 3D island growth, respectively. Stranski-Krastanow (SK mode) is a unique mode of 2D growth plus 3D island formation.

The interfacial free energy and the lattice mismatch determine which growth mode will be adopted in a given system [18]. In lattice-matched systems, the epitaxial film grows either in layer-by-layer mode or island growth mode depending on the interface energy and surface energy of the epitaxial film. In systems with large lattice mismatch, the growth mode may transit from 2D to island growth (SK mode) to relax strain in the epitaxial film. The early stage of the growth could be layer-by-layer due to the small interface energy. With epitaxial film growing thicker, strain energy is accumulated. The island formation is triggered to lower the total energy by introducing misfit dislocations.

**Figure 2.** Illustrations of three possible epitaxial growth modes: Frank-van der Merwe, Volmer-Weber, and Stranski-Krastanow [18].

The Ge epitaxial growth on Si can be described as SK growth mode due to the 4.2% lattice mismatch between Si and Ge [19, 20]. In order to be used as a virtual substrate for the III-V deposition, smooth Ge surface is required [21, 22]. The island formation kinetics can be suppressed by shortened atomic surface migration length [23]. The reduced diffusion length can forbid the mass transport over a certain distance, which is required to form islands.

are accelerated toward the source target to sputter neutral atoms of the target. The ejected neutral atoms will travel to the substrate in a straight line unless they have collision with particles such as Ar atoms. The sputtered atoms, which arrive at the substrate may implant, bounce, diffuse, or simply stick onto the substrate, depending on their kinetic energies. As a

Epitaxial Growth of Ge on Si by Magnetron Sputtering http://dx.doi.org/10.5772/intechopen.73554 49

In conventional RF sputtering, most electrons lose their energy in nonionizing collisions are collected by the anode. The efficiency of ionization from energetic collisions between the electrons and gas atoms is low. Magnets are used to increase the percentage of electrons that participate in the ionization process. Large magnets are formed behind the target by applying a magnetic field at right angles to the electric field. The electrons are trapped near the target surface and kept in spiral motion until they collide with gas atoms. The increased probability of ionization significantly improves the efficiency of target materials sputtering and therefore increases the deposition rate at the substrate. Moreover, this allows the use of lower gas pres-

**Figure 3** shows a schematic diagram of the RF magnetron sputtering system employed in this work. Four-inch intrinsic Ge target was used for the depositions of Ge film on Si and 4-inch

zero by tuning the variable capacitors in the impedance matching network. Each target had a shutter to isolate the substrate from the plasma. The tilt angle of the targets and the distance

Gas inlet with mass flow meter was used to supply argon into the main chamber. The vacuum in the main chamber was established by a mechanical rotary pump and a turbo molecular pump. Moreover, a load lock chamber was employed to protect the vacuum condition in the main chamber. Quartz halogen lamps were used to heat the substrate. The deposition rate was controlled by varying the RF power applied on the target and measured by a crystal monitor.

between the targets and the substrate could be adjusted to achieve good uniformity.

The substrate was rotated during deposition to improve uniformity of the films.

**Figure 3.** Schematic diagram of RF magnetron sputtering system used in this work.

target was used for capping layer deposition. The RF powers were supplied to the Ge

targets by two independent RF generators. The RF reverse power was reduced to

result, the substrate will be coated by a thin film composed of target materials.

sure, which may improve the film quality.

SiO2

and SiO2

The diffusion length of Ge atoms could be reduced by using surfactant [24, 25] or low growth temperature [26, 27]. Sb has been used as a surfactant to suppress the Ge island formation. The energy barrier to diffuse is higher on the surfactant-covered surface than that of pure Si surface. In addition, the Ge atoms may be incorporated below the surfactant layer due to the site exchange process and therefore it is difficult for the Ge on top of the surfactant layer to diffuse as a relatively high diffusion barrier that has to be overcome. However, the use of surfactant also induces the incorporation of Sb leading to a n-type doping in the Ge film [28]. The effect of substrate temperature on the Ge surface roughness will be investigated in this work.

#### **2.2. Lattice mismatch**

Due to the 4.2% lattice mismatch between Si and Ge, the Ge epitaxial growth on Si is defectfree only below the critical thickness. The thin wetting layer is compressively strained in plane to adapt its lattice constant to that of the underlying Si substrate. In the meanwhile, a tensile strain is introduced in perpendicular inducing a tetragonal distortion to the Ge lattice. The biaxial strain compensates the lattice mismatch and therefore no defect is formed. The critical thickness for the defect-free growth of strained Ge on Si is in the range of several nanometers, which is also affected by the growth temperature [29].

When Ge growing above the critical thickness, misfit dislocations will nucleate at the interface and thread segments of dislocations run through the layer to the surface as threading dislocations. The misfit dislocations are incorporated to relax the strain arising from the lattice mismatch between Si and Ge by introducing extra half plane of atoms [30]. The misfit dislocations are energetically stable at the Si and Ge interface when Ge layer is above the critical thickness. As byproduct of misfit dislocations, threading dislocations thread either form a dislocation loop or terminate at the film surface. The threading dislocations are detrimental for the electrical devices because they lie cross the whole film reducing the carrier mobility, carrier lifetime, and device reliability [31]. In this work, the epitaxial Ge layer has to be above the critical thickness to achieve a fully relaxed Ge surface matching the lattice of overlying III-V materials. The effect of substrate temperature on the threading dislocation density (TDD) of Ge will be investigated.

## **3. Epitaxial growth of Ge on Si by magnetron sputtering**

#### **3.1. Magnetron sputtering**

Sputtering is a physical vapor deposition method. The target and the substrate are put on the cathode and anode, respectively. An inert gas such as argon (Ar) is introduced to create gaseous plasma by applying a voltage between the cathode and anode. The produced ions (Ar<sup>+</sup> ) are accelerated toward the source target to sputter neutral atoms of the target. The ejected neutral atoms will travel to the substrate in a straight line unless they have collision with particles such as Ar atoms. The sputtered atoms, which arrive at the substrate may implant, bounce, diffuse, or simply stick onto the substrate, depending on their kinetic energies. As a result, the substrate will be coated by a thin film composed of target materials.

The Ge epitaxial growth on Si can be described as SK growth mode due to the 4.2% lattice mismatch between Si and Ge [19, 20]. In order to be used as a virtual substrate for the III-V deposition, smooth Ge surface is required [21, 22]. The island formation kinetics can be suppressed by shortened atomic surface migration length [23]. The reduced diffusion length can

The diffusion length of Ge atoms could be reduced by using surfactant [24, 25] or low growth temperature [26, 27]. Sb has been used as a surfactant to suppress the Ge island formation. The energy barrier to diffuse is higher on the surfactant-covered surface than that of pure Si surface. In addition, the Ge atoms may be incorporated below the surfactant layer due to the site exchange process and therefore it is difficult for the Ge on top of the surfactant layer to diffuse as a relatively high diffusion barrier that has to be overcome. However, the use of surfactant also induces the incorporation of Sb leading to a n-type doping in the Ge film [28]. The effect of substrate temperature on the Ge surface roughness will be investigated in this work.

Due to the 4.2% lattice mismatch between Si and Ge, the Ge epitaxial growth on Si is defectfree only below the critical thickness. The thin wetting layer is compressively strained in plane to adapt its lattice constant to that of the underlying Si substrate. In the meanwhile, a tensile strain is introduced in perpendicular inducing a tetragonal distortion to the Ge lattice. The biaxial strain compensates the lattice mismatch and therefore no defect is formed. The critical thickness for the defect-free growth of strained Ge on Si is in the range of several nanometers,

When Ge growing above the critical thickness, misfit dislocations will nucleate at the interface and thread segments of dislocations run through the layer to the surface as threading dislocations. The misfit dislocations are incorporated to relax the strain arising from the lattice mismatch between Si and Ge by introducing extra half plane of atoms [30]. The misfit dislocations are energetically stable at the Si and Ge interface when Ge layer is above the critical thickness. As byproduct of misfit dislocations, threading dislocations thread either form a dislocation loop or terminate at the film surface. The threading dislocations are detrimental for the electrical devices because they lie cross the whole film reducing the carrier mobility, carrier lifetime, and device reliability [31]. In this work, the epitaxial Ge layer has to be above the critical thickness to achieve a fully relaxed Ge surface matching the lattice of overlying III-V materials. The effect of substrate temperature on the threading dislocation density (TDD) of Ge will be investigated.

Sputtering is a physical vapor deposition method. The target and the substrate are put on the cathode and anode, respectively. An inert gas such as argon (Ar) is introduced to create gaseous plasma by applying a voltage between the cathode and anode. The produced ions (Ar<sup>+</sup>

)

forbid the mass transport over a certain distance, which is required to form islands.

**2.2. Lattice mismatch**

48 Epitaxy

**3.1. Magnetron sputtering**

which is also affected by the growth temperature [29].

**3. Epitaxial growth of Ge on Si by magnetron sputtering**

In conventional RF sputtering, most electrons lose their energy in nonionizing collisions are collected by the anode. The efficiency of ionization from energetic collisions between the electrons and gas atoms is low. Magnets are used to increase the percentage of electrons that participate in the ionization process. Large magnets are formed behind the target by applying a magnetic field at right angles to the electric field. The electrons are trapped near the target surface and kept in spiral motion until they collide with gas atoms. The increased probability of ionization significantly improves the efficiency of target materials sputtering and therefore increases the deposition rate at the substrate. Moreover, this allows the use of lower gas pressure, which may improve the film quality.

**Figure 3** shows a schematic diagram of the RF magnetron sputtering system employed in this work. Four-inch intrinsic Ge target was used for the depositions of Ge film on Si and 4-inch SiO2 target was used for capping layer deposition. The RF powers were supplied to the Ge and SiO2 targets by two independent RF generators. The RF reverse power was reduced to zero by tuning the variable capacitors in the impedance matching network. Each target had a shutter to isolate the substrate from the plasma. The tilt angle of the targets and the distance between the targets and the substrate could be adjusted to achieve good uniformity.

Gas inlet with mass flow meter was used to supply argon into the main chamber. The vacuum in the main chamber was established by a mechanical rotary pump and a turbo molecular pump. Moreover, a load lock chamber was employed to protect the vacuum condition in the main chamber. Quartz halogen lamps were used to heat the substrate. The deposition rate was controlled by varying the RF power applied on the target and measured by a crystal monitor. The substrate was rotated during deposition to improve uniformity of the films.

**Figure 3.** Schematic diagram of RF magnetron sputtering system used in this work.

## **3.2. Experimental details**

In this work, the epitaxial growth of Ge on Si is demonstrated by sputtering Ge target using the AJA ATC-2200 magnetron sputtering system. The base pressure of the chamber was 5 × 10−7 mbar. N-type Si (100) wafers were used as the substrates. The Si substrates were cleaned using RCA solutions [32] followed by a HF dip. The Si substrate was immediately loaded into a load lock chamber after cleaning to minimize the oxidation of the Si surface.

The Ge films were sputter-deposited from a 4-inch intrinsic Ge target (99.999% purity) at a process pressure of 1.5 × 10−3 mbar. Rotation of 30 revolutions per minute was applied to the substrate during deposition to ensure the uniformity of the films. The Ar flow was kept at 15 sccm and the RF power applied to the Ge target was 150 W. The Ge deposition rate was 5 nm/min examined by a quartz crystal deposition rate monitor. 300 nm thick Ge films were sputter-deposited on Si at various substrate temperatures of 300, 400, and 500°C to investigate the effects of substrate temperature. The temperature calibration data was supplied and measured with a Si wafer by the manufacturer of the sputter system.

The surface morphology of Ge films was examined by atomic force microscopy (AFM) with Bruker Icon using the tapping mode. The scan area was 2 × 2 μm. The crystalline quality of the annealed Ge films was analyzed by high resolution X-ray diffraction (XRD), Raman spectroscopy, and transmission electron microscopy (TEM). The XRD measurements were performed with Bruker D8 at a voltage of 45 kV and a current of 100 mA, using Cu *K*α1 radiation (λ = 1.5406 Å). The diffractometer was calibrated by making the Si (400) diffraction peak from the substrate maximized and at its theoretical position. Raman spectra of the Ge films were measured with Renishaw inVia Raman microscope using Ar<sup>+</sup> laser with wavelength of 514 nm as the excitation source. The beam power was limited to 6 mW to prevent the locally induced crystallization of Ge films during the measurement. Static mode with 20 times accumulation was employed to improve the signal to noise ratio. TEM measurements were conducted with Phillips CM200 microscope operating at 200 kV. The TEM samples were prepared by focused ion beam milling using Nova Nanolab 200.

**Figure 4.** (a) XRD 2θ-Ω diffraction patterns of the Ge films deposited on Si at 300°C, 400°C, and 500°C, (b) Si (220) and Ge (220) phi scan patterns collected from the sample deposited at 300°C showing the epitaxial relationship between the

Epitaxial Growth of Ge on Si by Magnetron Sputtering http://dx.doi.org/10.5772/intechopen.73554 51

**Figure 5.** Atomic-resolution cross-sectional TEM image of Ge/Si interface on the sample deposited at 300°C.

Ge film and Si substrate.

#### **3.3. Results and discussions**

XRD 2θ-Ω scans were conducted on the Ge films deposited on Si at 300, 400, and 500°C in the 2θ range between 20 and 75° to examine the crystallinity of the Ge films. As shown in **Figure 4(a)**, apart from the strong Si (400) peak at 69.2° attributed to the substrate, only one peak at around 66° is observed which corresponds to Ge (400). The absence of any other Ge peaks indicates the Ge films might be single-crystalline Ge (100) which requires further examination by XRD Phi scans. **Figure 4(b)** shows Si (220) and Ge (220) Phi scan patterns collected from the sample deposited at 300°C by rotating the specimen with respect to the [110] axis. Only the four (220) reflections are observed in the Ge Phi scan pattern suggesting the film is with fourfold symmetry about an axis normal to the substrate [33]. In addition, the Ge (220) reflections align with the Si substrate (220) reflections indicating the Ge is single-crystalline epitaxy film.

The interface of the Ge film and Si substrate is investigated by high-resolution TEM to confirm the epitaxial growth of Ge on Si. As shown in the atomic-resolution image at the interface in

**3.2. Experimental details**

50 Epitaxy

In this work, the epitaxial growth of Ge on Si is demonstrated by sputtering Ge target using the AJA ATC-2200 magnetron sputtering system. The base pressure of the chamber was 5 × 10−7 mbar. N-type Si (100) wafers were used as the substrates. The Si substrates were cleaned using RCA solutions [32] followed by a HF dip. The Si substrate was immediately loaded into a load lock chamber after cleaning to minimize the oxidation of the Si surface.

The Ge films were sputter-deposited from a 4-inch intrinsic Ge target (99.999% purity) at a process pressure of 1.5 × 10−3 mbar. Rotation of 30 revolutions per minute was applied to the substrate during deposition to ensure the uniformity of the films. The Ar flow was kept at 15 sccm and the RF power applied to the Ge target was 150 W. The Ge deposition rate was 5 nm/min examined by a quartz crystal deposition rate monitor. 300 nm thick Ge films were sputter-deposited on Si at various substrate temperatures of 300, 400, and 500°C to investigate the effects of substrate temperature. The temperature calibration data was supplied and mea-

The surface morphology of Ge films was examined by atomic force microscopy (AFM) with Bruker Icon using the tapping mode. The scan area was 2 × 2 μm. The crystalline quality of the annealed Ge films was analyzed by high resolution X-ray diffraction (XRD), Raman spectroscopy, and transmission electron microscopy (TEM). The XRD measurements were performed with Bruker D8 at a voltage of 45 kV and a current of 100 mA, using Cu *K*α1 radiation (λ = 1.5406 Å). The diffractometer was calibrated by making the Si (400) diffraction peak from the substrate maximized and at its theoretical position. Raman spectra of the Ge films were

as the excitation source. The beam power was limited to 6 mW to prevent the locally induced crystallization of Ge films during the measurement. Static mode with 20 times accumulation was employed to improve the signal to noise ratio. TEM measurements were conducted with Phillips CM200 microscope operating at 200 kV. The TEM samples were prepared by focused

XRD 2θ-Ω scans were conducted on the Ge films deposited on Si at 300, 400, and 500°C in the 2θ range between 20 and 75° to examine the crystallinity of the Ge films. As shown in **Figure 4(a)**, apart from the strong Si (400) peak at 69.2° attributed to the substrate, only one peak at around 66° is observed which corresponds to Ge (400). The absence of any other Ge peaks indicates the Ge films might be single-crystalline Ge (100) which requires further examination by XRD Phi scans. **Figure 4(b)** shows Si (220) and Ge (220) Phi scan patterns collected from the sample deposited at 300°C by rotating the specimen with respect to the [110] axis. Only the four (220) reflections are observed in the Ge Phi scan pattern suggesting the film is with fourfold symmetry about an axis normal to the substrate [33]. In addition, the Ge (220) reflections align with the

The interface of the Ge film and Si substrate is investigated by high-resolution TEM to confirm the epitaxial growth of Ge on Si. As shown in the atomic-resolution image at the interface in

Si substrate (220) reflections indicating the Ge is single-crystalline epitaxy film.

laser with wavelength of 514 nm

sured with a Si wafer by the manufacturer of the sputter system.

measured with Renishaw inVia Raman microscope using Ar<sup>+</sup>

ion beam milling using Nova Nanolab 200.

**3.3. Results and discussions**

**Figure 4.** (a) XRD 2θ-Ω diffraction patterns of the Ge films deposited on Si at 300°C, 400°C, and 500°C, (b) Si (220) and Ge (220) phi scan patterns collected from the sample deposited at 300°C showing the epitaxial relationship between the Ge film and Si substrate.

**Figure 5.** Atomic-resolution cross-sectional TEM image of Ge/Si interface on the sample deposited at 300°C.

**Figure 6.** A schematic phase map of the crystallinity of as-deposited semiconductor films as function of growth rate and temperature [34].

**Figure 5**, the atoms are continuously aligned from the Si substrate to the grown Ge film suggesting successful epitaxy. This results is in good agreement with the XRD measurements.

The crystallinity of the as-deposited film depends on both the substrate temperature and growth rate as indicated in the schematic diagram shown in **Figure 6** [34]. The crystallinity can be improved by increasing the substrate temperature and reducing the growth rate. The XRD and TEM results suggest that substrate temperature of 300°C is enough to obtain single-crystalline Ge epitaxial growth on Si at the growth the rate of 5 nm/min. The effects of substrate temperature on the quality of Ge films are investigated in the following section.

## **4. Effects of substrate temperature**

As reviewed in the previous section, the substrate temperature may play an important role in determining the growth mode. The effects of substrate temperature on the properties of sputter-deposited epitaxial Ge films are discussed in this section. 300 nm thick Ge films were sputter-deposited on Si at various substrate temperatures of 300, 400, and 500°C.

mode when the layer becoming thicker. The thicker layer has large strain energy, which can be lowered by forming isolated thick islands. The island formation can be avoided by reducing the diffusion length of Ge. The reduced diffusion length hinders the mass transport of Ge over large distances which is necessary for the formation of islands [23]. Since the diffusion length of Ge decreases with reducing substrate temperature, the islanding is suppressed at low substrate temperature. As shown in **Figure 7**, layer-by-layer growth can be obtained at low temperature of 300°C to achieve smooth Ge surface, which is favored for the following III-V deposition. However, the low substrate temperature might induce the degradation of crystallinity simulta-

**Figure 7.** 2D and 3D AFM images showing the surface morphology of the Ge films deposited at (a) 300°C, (b) 400°C,

Epitaxial Growth of Ge on Si by Magnetron Sputtering http://dx.doi.org/10.5772/intechopen.73554 53

The XRD reciprocal space mappings (RSM) were conducted to investigate the effect of substrate temperature on the crystallinity of the Ge films. **Figure 8** shows the (004) RSM of the Ge films deposited at (a) 300°C, (b) 400°C, and (c) 500°C. **Figure 8(a)** demonstrates that the Ge

neously which will be investigated by the following XRD and TEM measurements.

and (c) 500°C.

The effect of substrate temperature on surface morphology of the Ge films is investigated using tapping mode AFM. **Figure 7** shows the 2D and 3D AFM images of the Ge films deposited at (a) 300°C, (b) 400°C, and (c) 500°C. It can be seen from the 3D AFM images that the surface morphology varies significantly among the Ge films deposited at different temperatures. The root mean square (RMS) surface roughness of the Ge films increases from 0.49 to 6.87 nm with substrate temperature increasing from 300 to 500°C. The increase in surface roughness with increasing substrate temperature indicates the growth switching from layer-by-layer mode to islanding mode with increasing substrate temperature.

In general, the epitaxial growth of Ge on Si follows the Stranski-Krastanow mode due to the lattice mismatch [18]. The growth initially follows layer-by-layer mode and progresses into island

**Figure 5**, the atoms are continuously aligned from the Si substrate to the grown Ge film suggesting successful epitaxy. This results is in good agreement with the XRD measurements.

**Figure 6.** A schematic phase map of the crystallinity of as-deposited semiconductor films as function of growth rate and

The crystallinity of the as-deposited film depends on both the substrate temperature and growth rate as indicated in the schematic diagram shown in **Figure 6** [34]. The crystallinity can be improved by increasing the substrate temperature and reducing the growth rate. The XRD and TEM results suggest that substrate temperature of 300°C is enough to obtain single-crystalline Ge epitaxial growth on Si at the growth the rate of 5 nm/min. The effects of substrate temperature on the quality of Ge films are investigated in the following section.

As reviewed in the previous section, the substrate temperature may play an important role in determining the growth mode. The effects of substrate temperature on the properties of sputter-deposited epitaxial Ge films are discussed in this section. 300 nm thick Ge films were

The effect of substrate temperature on surface morphology of the Ge films is investigated using tapping mode AFM. **Figure 7** shows the 2D and 3D AFM images of the Ge films deposited at (a) 300°C, (b) 400°C, and (c) 500°C. It can be seen from the 3D AFM images that the surface morphology varies significantly among the Ge films deposited at different temperatures. The root mean square (RMS) surface roughness of the Ge films increases from 0.49 to 6.87 nm with substrate temperature increasing from 300 to 500°C. The increase in surface roughness with increasing substrate temperature indicates the growth switching from layer-by-layer

In general, the epitaxial growth of Ge on Si follows the Stranski-Krastanow mode due to the lattice mismatch [18]. The growth initially follows layer-by-layer mode and progresses into island

sputter-deposited on Si at various substrate temperatures of 300, 400, and 500°C.

mode to islanding mode with increasing substrate temperature.

**4. Effects of substrate temperature**

temperature [34].

52 Epitaxy

**Figure 7.** 2D and 3D AFM images showing the surface morphology of the Ge films deposited at (a) 300°C, (b) 400°C, and (c) 500°C.

mode when the layer becoming thicker. The thicker layer has large strain energy, which can be lowered by forming isolated thick islands. The island formation can be avoided by reducing the diffusion length of Ge. The reduced diffusion length hinders the mass transport of Ge over large distances which is necessary for the formation of islands [23]. Since the diffusion length of Ge decreases with reducing substrate temperature, the islanding is suppressed at low substrate temperature. As shown in **Figure 7**, layer-by-layer growth can be obtained at low temperature of 300°C to achieve smooth Ge surface, which is favored for the following III-V deposition. However, the low substrate temperature might induce the degradation of crystallinity simultaneously which will be investigated by the following XRD and TEM measurements.

The XRD reciprocal space mappings (RSM) were conducted to investigate the effect of substrate temperature on the crystallinity of the Ge films. **Figure 8** shows the (004) RSM of the Ge films deposited at (a) 300°C, (b) 400°C, and (c) 500°C. **Figure 8(a)** demonstrates that the Ge

the Ge layer was limited within the top 20 nanometers by using the wavelength of 514 nm excitation source [36]. As shown in **Figure 9**, the Ge films exhibit peaks centered around 300 cm−1 corresponding to the Ge-Ge optical vibration modes [37]. All the Ge films deposited at various temperatures exhibit peaks positioned at a higher wavenumber than the bulk unstrained Ge, suggesting compressive strains in the films. With increasing substrate temperatures, the peak positions of the Ge films shift to lower wavenumbers toward that of the bulk Ge indicating decreased compressive strain in the films [38], which is in agreement with the XRD results.

Epitaxial Growth of Ge on Si by Magnetron Sputtering http://dx.doi.org/10.5772/intechopen.73554 55

The reduction of compressive strain with increasing substrate temperature might be due to the difference in linear thermal expansion coefficients between Si and Ge. The thermal expansion coefficient of Ge is Δa/a (Ge) = 5.8 × 10−6 ΔT (°C), which is larger than that of Si, Δa/a (Si) = 2.6 × 10−6 ΔT (°C) [39]. The Ge films, which are nearly fully lattice-matched to the Si substrate at the growth temperature experience tensile strain when cooling to room temperature [40]. This is because the perpendicular lattice parameter of the Ge films shrinks more easily during cooling process than the in-plane lattice which is influenced by the underneath Si sub-

**Figure 10** shows the cross-sectional TEM images of Ge samples deposited at 300°C in (a) bright and (b) dark field, deposited at 400°C in (c) bright and (d) dark field, and deposited at 500°C in (e) bright and (f) dark field. As shown in **Figure 10(a)** and **(b)**, the Ge film deposited at 300°C exhibits very high TDD which is estimated to be of the order of 1010 cm−2. The high TDD might be owing to the reduced diffusion length of Ge at low temperature. With increasing substrate temperature, the TDD decreases and some planar defects are observed in the Ge film deposited at 500°C as shown in **Figure 10(c)**–**(f)**. The density of the planar defects is particularly high in the vicinity area of the Ge/Si interface and most of them are restricted to that region and do not extend to the film

strate with lower thermal expansion coefficient.

**Figure 9.** Raman spectra of the Ge films deposited on Si at 300, 400, and 500°C.

**Figure 8.** XRD (004) reciprocal space maps of the Ge films deposited at (a) 300°C, (b) 400°C, and (c) 500°C.

diffraction spots are elongated along the Q<sup>x</sup> direction, which is due to the deteriorated crystal quality [35]. With the substrate temperature increasing from 300 to 500°C, the Ge peak exhibits steeper decay in the Q<sup>x</sup> direction and the Ge peak position shows a slight upwards shift along the Qz direction. These results indicate that the Ge film deposited at higher temperature has lower defect density and reduced compressive strain.

Micro-Raman spectra were used to investigate the structural property of the surface layer in the Ge samples deposited on Si at 300°C, 400°C, and 500°C. The penetration depth of the laser in the Ge layer was limited within the top 20 nanometers by using the wavelength of 514 nm excitation source [36]. As shown in **Figure 9**, the Ge films exhibit peaks centered around 300 cm−1 corresponding to the Ge-Ge optical vibration modes [37]. All the Ge films deposited at various temperatures exhibit peaks positioned at a higher wavenumber than the bulk unstrained Ge, suggesting compressive strains in the films. With increasing substrate temperatures, the peak positions of the Ge films shift to lower wavenumbers toward that of the bulk Ge indicating decreased compressive strain in the films [38], which is in agreement with the XRD results.

The reduction of compressive strain with increasing substrate temperature might be due to the difference in linear thermal expansion coefficients between Si and Ge. The thermal expansion coefficient of Ge is Δa/a (Ge) = 5.8 × 10−6 ΔT (°C), which is larger than that of Si, Δa/a (Si) = 2.6 × 10−6 ΔT (°C) [39]. The Ge films, which are nearly fully lattice-matched to the Si substrate at the growth temperature experience tensile strain when cooling to room temperature [40]. This is because the perpendicular lattice parameter of the Ge films shrinks more easily during cooling process than the in-plane lattice which is influenced by the underneath Si substrate with lower thermal expansion coefficient.

**Figure 10** shows the cross-sectional TEM images of Ge samples deposited at 300°C in (a) bright and (b) dark field, deposited at 400°C in (c) bright and (d) dark field, and deposited at 500°C in (e) bright and (f) dark field. As shown in **Figure 10(a)** and **(b)**, the Ge film deposited at 300°C exhibits very high TDD which is estimated to be of the order of 1010 cm−2. The high TDD might be owing to the reduced diffusion length of Ge at low temperature. With increasing substrate temperature, the TDD decreases and some planar defects are observed in the Ge film deposited at 500°C as shown in **Figure 10(c)**–**(f)**. The density of the planar defects is particularly high in the vicinity area of the Ge/Si interface and most of them are restricted to that region and do not extend to the film

**Figure 9.** Raman spectra of the Ge films deposited on Si at 300, 400, and 500°C.

**Figure 8.** XRD (004) reciprocal space maps of the Ge films deposited at (a) 300°C, (b) 400°C, and (c) 500°C.

quality [35]. With the substrate temperature increasing from 300 to 500°C, the Ge peak exhib-

Micro-Raman spectra were used to investigate the structural property of the surface layer in the Ge samples deposited on Si at 300°C, 400°C, and 500°C. The penetration depth of the laser in

direction. These results indicate that the Ge film deposited at higher temperature

direction, which is due to the deteriorated crystal

direction and the Ge peak position shows a slight upwards shift

diffraction spots are elongated along the Q<sup>x</sup>

has lower defect density and reduced compressive strain.

its steeper decay in the Q<sup>x</sup>

along the Qz

54 Epitaxy

were obtained [46]. The aforementioned conventional AIC includes two steps: (1) depositing a stacked Al and amorphous Ge layer on the Si substrate, (2) postdeposition annealing to induce the layer exchange process. The postdeposition annealing introduces the diffusion

growth of pure Ge on Si through Al at low temperature, one-step aluminum-assisted crystal-

The novelty of one-step aluminum-assisted crystallization of Ge epitaxy on Si lies in the elimination of the postdeposition annealing step [47]. This process simply requires sequential depositions of Al and Ge films via magnetron sputtering in the same chamber without breaking the vacuum. By applying an *in-situ* low temperature (50–150°C) heat treatment in between Al and Ge sputter depositions, the epitaxial growth of Ge on Si is achieved. This low temperature process has a low thermal budget and can fabricate pure Ge layer compared with Si<sup>x</sup>

alloy as obtained in the conventional process. The effects of Al heating temperature on the properties of the epitaxial Ge films are investigated and the mechanism of epitaxial growth of Ge on Si by one-step aluminum-assisted crystallization is discussed based on observations on

The Al films were sputter-deposited onto Si substrates at room temperature using a 2 inch intrinsic Al target (99.999% purity) at a deposition rate of 3 nm/min. The samples then underwent an in-situ heat treatment for 10 minutes prior to the Ge deposition. The Ge films were then sputter-deposited using a 4 inch intrinsic Ge target (99.999% purity) without further intentional substrate heating at 5 nm/min. The Al heating temperatures were varied at 50°C (Sample ID: 60-50-12), 100°C (Sample ID: 60-100-12), and 150°C (Sample ID: 60-150-12) with Al thickness of 60 nm and Ge deposition time of 12 min to investigate the effect of heating temperature. One control sample (Sample ID: 60-NA-12) did not undergo this heat treatment. Shorter Ge deposition of 1 minute (Sample ID: 60-100-1) and 3 minutes (Sample ID: 60-100-3) were experimented on substrates with 60 nm Al deposition and 100°C heat treatment as well with the aim to investigate the mechanism of Ge epitaxial growth on Si by one-step aluminum-assisted crystallization. The Ge samples were analyzed by XRD, TEM and EDS (Phillips CM200 microscope

equipped with an EDAX energy dispersive X-ray spectroscopy system) measurements.

**Figure 11(a)** shows the XRD 2θ-Ω diffraction patterns of samples 60-NA-12, 60-50-12, 60-00- 12 and 60-150-12. For sample 60-NA-12, the XRD pattern shows a peak at 65.2° corresponding to Al (220) and a strong Si (400) peak at 69.2° from the Si substrate. The Ge film on 60-NA-12 is amorphous due to the absence of a Ge peak. For samples 60-50-12, 60-100-12 and 60-150- 12, apart from the Al peak and Si peak, a peak located at 66° is present which corresponds to Ge (400). The absence of any other Ge peaks and the results of X-ray Phi scans indicate the Ge films are single-crystalline Ge (100). **Figure 11(b)** shows the Si (220) and Ge (220) Phi scan patterns collected from sample 60-100-12 by rotating the specimen with respect to the [110] axis. The four (220) reflections are observed in the Ge Phi scan pattern which suggests the film is with fourfold symmetry about an axis normal to the Si substrate [33]. In addition, the Ge (220) reflections align with the Si substrate (220) reflections indicating the Ge is single-

Ge1−x alloy. In order to achieve epitaxial

Epitaxial Growth of Ge on Si by Magnetron Sputtering http://dx.doi.org/10.5772/intechopen.73554

Ge1−x

57

of Si into the Ge layer resulting in formation of Si<sup>x</sup>

samples with various Ge deposition times.

**5.1. Effects of heating temperature**

crystalline epitaxy film.

lization is developed.

**Figure 10.** Cross-sectional TEM images of Ge samples deposited at 300°C in (a) bright and (b) dark field, deposited at 400°C in (c) bright and (d) dark field, and deposited at 500°C in (e) bright and (f) dark field.

surface which is consistent with previous report [41]. The TDD of the Ge film deposited at 500°C is in the order of 109 cm−2, one magnitude order lower than that deposited at 300°C. The improved crystallinity with increasing substrate temperature agrees well with the XRD results.

## **5. Epitaxial growth of Ge on Si at low temperatures by one-step aluminum-assisted crystallization**

The aluminum-induced crystallization (AIC) of Si, Ge and SiGe on foreign substrates has been extensively studied by several groups to obtain polycrystalline material at a low temperature [42–45]. The a-Ge/Al/c-Si structure has been investigated and epitaxial SiGe alloys were obtained [46]. The aforementioned conventional AIC includes two steps: (1) depositing a stacked Al and amorphous Ge layer on the Si substrate, (2) postdeposition annealing to induce the layer exchange process. The postdeposition annealing introduces the diffusion of Si into the Ge layer resulting in formation of Si<sup>x</sup> Ge1−x alloy. In order to achieve epitaxial growth of pure Ge on Si through Al at low temperature, one-step aluminum-assisted crystallization is developed.

The novelty of one-step aluminum-assisted crystallization of Ge epitaxy on Si lies in the elimination of the postdeposition annealing step [47]. This process simply requires sequential depositions of Al and Ge films via magnetron sputtering in the same chamber without breaking the vacuum. By applying an *in-situ* low temperature (50–150°C) heat treatment in between Al and Ge sputter depositions, the epitaxial growth of Ge on Si is achieved. This low temperature process has a low thermal budget and can fabricate pure Ge layer compared with Si<sup>x</sup> Ge1−x alloy as obtained in the conventional process. The effects of Al heating temperature on the properties of the epitaxial Ge films are investigated and the mechanism of epitaxial growth of Ge on Si by one-step aluminum-assisted crystallization is discussed based on observations on samples with various Ge deposition times.

The Al films were sputter-deposited onto Si substrates at room temperature using a 2 inch intrinsic Al target (99.999% purity) at a deposition rate of 3 nm/min. The samples then underwent an in-situ heat treatment for 10 minutes prior to the Ge deposition. The Ge films were then sputter-deposited using a 4 inch intrinsic Ge target (99.999% purity) without further intentional substrate heating at 5 nm/min. The Al heating temperatures were varied at 50°C (Sample ID: 60-50-12), 100°C (Sample ID: 60-100-12), and 150°C (Sample ID: 60-150-12) with Al thickness of 60 nm and Ge deposition time of 12 min to investigate the effect of heating temperature. One control sample (Sample ID: 60-NA-12) did not undergo this heat treatment. Shorter Ge deposition of 1 minute (Sample ID: 60-100-1) and 3 minutes (Sample ID: 60-100-3) were experimented on substrates with 60 nm Al deposition and 100°C heat treatment as well with the aim to investigate the mechanism of Ge epitaxial growth on Si by one-step aluminum-assisted crystallization. The Ge samples were analyzed by XRD, TEM and EDS (Phillips CM200 microscope equipped with an EDAX energy dispersive X-ray spectroscopy system) measurements.

#### **5.1. Effects of heating temperature**

**Figure 10.** Cross-sectional TEM images of Ge samples deposited at 300°C in (a) bright and (b) dark field, deposited at

surface which is consistent with previous report [41]. The TDD of the Ge film deposited at 500°C is in the order of 109 cm−2, one magnitude order lower than that deposited at 300°C. The improved

The aluminum-induced crystallization (AIC) of Si, Ge and SiGe on foreign substrates has been extensively studied by several groups to obtain polycrystalline material at a low temperature [42–45]. The a-Ge/Al/c-Si structure has been investigated and epitaxial SiGe alloys

crystallinity with increasing substrate temperature agrees well with the XRD results.

**5. Epitaxial growth of Ge on Si at low temperatures by one-step** 

400°C in (c) bright and (d) dark field, and deposited at 500°C in (e) bright and (f) dark field.

**aluminum-assisted crystallization**

56 Epitaxy

**Figure 11(a)** shows the XRD 2θ-Ω diffraction patterns of samples 60-NA-12, 60-50-12, 60-00- 12 and 60-150-12. For sample 60-NA-12, the XRD pattern shows a peak at 65.2° corresponding to Al (220) and a strong Si (400) peak at 69.2° from the Si substrate. The Ge film on 60-NA-12 is amorphous due to the absence of a Ge peak. For samples 60-50-12, 60-100-12 and 60-150- 12, apart from the Al peak and Si peak, a peak located at 66° is present which corresponds to Ge (400). The absence of any other Ge peaks and the results of X-ray Phi scans indicate the Ge films are single-crystalline Ge (100). **Figure 11(b)** shows the Si (220) and Ge (220) Phi scan patterns collected from sample 60-100-12 by rotating the specimen with respect to the [110] axis. The four (220) reflections are observed in the Ge Phi scan pattern which suggests the film is with fourfold symmetry about an axis normal to the Si substrate [33]. In addition, the Ge (220) reflections align with the Si substrate (220) reflections indicating the Ge is singlecrystalline epitaxy film.

**Figure 11.** (a) XRD 2θ-Ω diffraction patterns of samples 60-NA-12, 60-50-12, 60-100-12 and 60-150-12, (b) Si (220) and Ge (220) phi scan patterns collected from the sample 60-100-12 showing the epitaxial relationship between the Ge film and Si substrate. (reprinted from Liu et al. [47], with the permission of AIP publishing).

The Ge peak intensity of sample 60-50-12 is lower than that of sample 60-100-12 as shown in **Figure 11(a)** due to incomplete Ge crystallization. The drop in Ge peak intensity for sample 60-150-12 might be due to the lower number of Al grain boundaries compared with that of sample 60-100-12. The Al grain boundaries play an important role in the Al-assisted crystallization process as they supply pathways for the Ge atoms to be epitaxially grown from the Si surface [46]. With increasing heating temperature, Al grain size is enlarged and therefore the density of grain boundaries is reduced [48] verified by the following TEM measurements.

are responsible for supplying pathways for the nucleation of the Ge from the Si substrate [46]. An amorphous Ge layer is shown in **Figure 12(b)** verifying the previous observations that Ge crystallization is in-complete on sample 60-50-12. Although sample 60-50-12 has more nucleation sites, it exhibits more discontinuous Ge layer compared with sample 60-100-12 owing to

**Figure 12.** Cross-sectional TEM images of samples (a) 60-NA-12, (b) 60-50-12, (c) 60-100-12, and (d) 60-150-12. (e) Higher magnification and (f) atomic resolution (with SAED pattern in the insert) images of Ge/Si interface on sample 60-100-12.

Epitaxial Growth of Ge on Si by Magnetron Sputtering http://dx.doi.org/10.5772/intechopen.73554 59

The Ge/Si interface of sample 60-100-12 is magnified and shown in **Figure 12(e)**. The epitaxial growth of the Ge layer on Si is revealed and planar defects are observed at the interface in **Figure 12(e)**. **Figure 12(f)** shows the continuous alignment of the atoms from the Si substrate to the grown Ge film suggesting successful epitaxy. Furthermore, the electron diffraction pattern taken from the Ge layer shown in the insert to **Figure 12(f)** indicates the Ge is single

crystal [49]. This result is in good agreement with the XRD measurements.

the incomplete crystallization.

(reprinted from Liu et al. [47], with the permission of AIP Publishing).

**Figure 12** shows the cross-sectional TEM images of samples 60-NA-12, 60-50-12, 60-100-12, and 60-150-12. **Figure 12(a)** shows the absence of Ge crystallization as the Al and amorphous Ge layers on the Si substrate. **Figure 12(b)**–**(d)** show the Ge epitaxial growth at selected sites on samples 60-50-12, 60-100-12, and 60-150-12. With increasing heating temperature, the crystallization sites decrease probably due to the decrease in density of Al grain boundaries [48], which

**Figure 12.** Cross-sectional TEM images of samples (a) 60-NA-12, (b) 60-50-12, (c) 60-100-12, and (d) 60-150-12. (e) Higher magnification and (f) atomic resolution (with SAED pattern in the insert) images of Ge/Si interface on sample 60-100-12. (reprinted from Liu et al. [47], with the permission of AIP Publishing).

The Ge peak intensity of sample 60-50-12 is lower than that of sample 60-100-12 as shown in **Figure 11(a)** due to incomplete Ge crystallization. The drop in Ge peak intensity for sample 60-150-12 might be due to the lower number of Al grain boundaries compared with that of sample 60-100-12. The Al grain boundaries play an important role in the Al-assisted crystallization process as they supply pathways for the Ge atoms to be epitaxially grown from the Si surface [46]. With increasing heating temperature, Al grain size is enlarged and therefore the density of grain boundaries is reduced [48] verified by the following TEM

**Figure 11.** (a) XRD 2θ-Ω diffraction patterns of samples 60-NA-12, 60-50-12, 60-100-12 and 60-150-12, (b) Si (220) and Ge (220) phi scan patterns collected from the sample 60-100-12 showing the epitaxial relationship between the Ge film and

Si substrate. (reprinted from Liu et al. [47], with the permission of AIP publishing).

**Figure 12** shows the cross-sectional TEM images of samples 60-NA-12, 60-50-12, 60-100-12, and 60-150-12. **Figure 12(a)** shows the absence of Ge crystallization as the Al and amorphous Ge layers on the Si substrate. **Figure 12(b)**–**(d)** show the Ge epitaxial growth at selected sites on samples 60-50-12, 60-100-12, and 60-150-12. With increasing heating temperature, the crystallization sites decrease probably due to the decrease in density of Al grain boundaries [48], which

measurements.

58 Epitaxy

are responsible for supplying pathways for the nucleation of the Ge from the Si substrate [46]. An amorphous Ge layer is shown in **Figure 12(b)** verifying the previous observations that Ge crystallization is in-complete on sample 60-50-12. Although sample 60-50-12 has more nucleation sites, it exhibits more discontinuous Ge layer compared with sample 60-100-12 owing to the incomplete crystallization.

The Ge/Si interface of sample 60-100-12 is magnified and shown in **Figure 12(e)**. The epitaxial growth of the Ge layer on Si is revealed and planar defects are observed at the interface in **Figure 12(e)**. **Figure 12(f)** shows the continuous alignment of the atoms from the Si substrate to the grown Ge film suggesting successful epitaxy. Furthermore, the electron diffraction pattern taken from the Ge layer shown in the insert to **Figure 12(f)** indicates the Ge is single crystal [49]. This result is in good agreement with the XRD measurements.

### **5.2. Mechanism of one-step aluminum-assisted crystallization**

To better understand the mechanism of the epitaxial growth of Ge on Si through one-step aluminum-assisted crystallization, EDS mapping of samples that underwent different Ge deposition times (1 minute, 3 minutes and 12 minutes) were carried out. The cross-sectional TEM images (top row), EDS maps of Ge (middle row) and EDS maps of Al (bottom row) of samples 60-100-1, 60-100-3, and 60-100-12 are shown in **Figure 13(a)**–**(c)**, respectively. They reveal the Ge and Al distributions at different stages of the crystallization process. As shown, the process begins with the Ge nucleating at selected sites at the Si and Al interface. With increasing deposition time, the Ge tends to grow upwards at the initial stage and then grow laterally.

boundary with two interphase boundaries [51]. The diffusion of Ge into the Al grain boundaries forms a pathway to supply the material for crystallization. The crystallization is then driven by the reduction in bulk Gibbs energy when the material changes from amorphous to crystalline [52]. However, this can be counteracted by the increase in interface energy as crystallization proceeds [53]. When a heat treatment is applied, the interface energy at the crystalline-amorphous interface increases, while the interface energy at the crystalline-crystalline decreases [43]. This effectively reduces the energy difference between the crystallineamorphous and the crystalline-crystalline interfaces favoring the crystallization process. This explains the observed Ge crystallization in the heat treated samples. As studied and discussed in previous work [46], the Al/Si is the preferred interface to Ge/Al for nucleation, as observed on sample 60-100-1 in this work. After the nucleation on Si substrate, the epitaxial growth of

Epitaxial Growth of Ge on Si by Magnetron Sputtering http://dx.doi.org/10.5772/intechopen.73554 61

Ge continues with further incorporation of Ge atoms though the Al grain boundaries.

Epitaxial growth of Ge films on Si has been achieved using magnetron sputtering which is low cost, safe and scalable. The effects of substrate temperature on the properties of the Ge films have been investigated. The surface roughness of the Ge films increases with substrate temperature. Smooth surface with RMS roughness of 0.48 nm can be obtained at 300°C owing to the reduced diffusion length of Ge atoms at low temperature. On the other hand, the crystallinity of the Ge films could be improved by increasing substrate temperature as revealed by XRD and TEM measurements. In addition, the compressive strain in the Ge films decreases with increasing substrate temperature owing to the difference in the thermal expansion coef-

Epitaxial growth of Ge films on Si by magnetron sputtering at low temperature has been achieved through one-step aluminum-assisted crystallization. By applying an *in-situ* low temperature (50–150°C) heat treatment in between Al and Ge sputter depositions, the epitaxial growth of Ge on Si can be achieved as verified by high resolution TEM and XRD analyses. The mechanism of epitaxial growth of Ge on Si substrate by one-step aluminum-assisted crystallization is discussed based on observations on samples with various Ge deposition times. This method significantly lowers the required temperature for and therefore the cost of epitaxial

This work has been supported by the Australian Government through the Australian Research Council (ARC, grant number DP160103433, LP110201112) and the Australian Renewable Energy Agency (ARENA) and by Epistar Corporation and Shin Shin Natural Gas Co., Ltd., Taiwan. Responsibility for the views, information or advice expressed herein is not accepted

**6. Conclusions**

ficients between Si and Ge.

growth of Ge on Si.

**Acknowledgements**

by the Australian Government.

The mechanism of the epitaxial growth of Ge on Si by one-step aluminum-assisted crystallization is discussed as follows. The covalent bonds of Ge are weakened at the interface with the Al layer as a consequence of a screening effect of the free electrons in the Al layer [50]. These Ge atoms have relatively high mobility and may provide the agent for initiating the crystallization process. These mobile atoms tend to lower the Gibbs energy of the system by diffusing to sites of low energy such as the Al grain boundaries. This diffusion is sometimes called grain boundary wetting that reduces total interface energy by replacing the grain

**Figure 13.** Cross-sectional TEM images (top), EDS maps of Ge (middle) and al (bottom) of samples (a) 60-100-1, (b) 60-100-3, and (c) 60-100-12. (reprinted from Liu et al. [47], with the permission of AIP publishing.

boundary with two interphase boundaries [51]. The diffusion of Ge into the Al grain boundaries forms a pathway to supply the material for crystallization. The crystallization is then driven by the reduction in bulk Gibbs energy when the material changes from amorphous to crystalline [52]. However, this can be counteracted by the increase in interface energy as crystallization proceeds [53]. When a heat treatment is applied, the interface energy at the crystalline-amorphous interface increases, while the interface energy at the crystalline-crystalline decreases [43]. This effectively reduces the energy difference between the crystallineamorphous and the crystalline-crystalline interfaces favoring the crystallization process. This explains the observed Ge crystallization in the heat treated samples. As studied and discussed in previous work [46], the Al/Si is the preferred interface to Ge/Al for nucleation, as observed on sample 60-100-1 in this work. After the nucleation on Si substrate, the epitaxial growth of Ge continues with further incorporation of Ge atoms though the Al grain boundaries.

## **6. Conclusions**

**5.2. Mechanism of one-step aluminum-assisted crystallization**

60 Epitaxy

To better understand the mechanism of the epitaxial growth of Ge on Si through one-step aluminum-assisted crystallization, EDS mapping of samples that underwent different Ge deposition times (1 minute, 3 minutes and 12 minutes) were carried out. The cross-sectional TEM images (top row), EDS maps of Ge (middle row) and EDS maps of Al (bottom row) of samples 60-100-1, 60-100-3, and 60-100-12 are shown in **Figure 13(a)**–**(c)**, respectively. They reveal the Ge and Al distributions at different stages of the crystallization process. As shown, the process begins with the Ge nucleating at selected sites at the Si and Al interface. With increasing deposition time, the Ge tends to grow upwards at the initial stage and then grow laterally.

The mechanism of the epitaxial growth of Ge on Si by one-step aluminum-assisted crystallization is discussed as follows. The covalent bonds of Ge are weakened at the interface with the Al layer as a consequence of a screening effect of the free electrons in the Al layer [50]. These Ge atoms have relatively high mobility and may provide the agent for initiating the crystallization process. These mobile atoms tend to lower the Gibbs energy of the system by diffusing to sites of low energy such as the Al grain boundaries. This diffusion is sometimes called grain boundary wetting that reduces total interface energy by replacing the grain

**Figure 13.** Cross-sectional TEM images (top), EDS maps of Ge (middle) and al (bottom) of samples (a) 60-100-1, (b)

60-100-3, and (c) 60-100-12. (reprinted from Liu et al. [47], with the permission of AIP publishing.

Epitaxial growth of Ge films on Si has been achieved using magnetron sputtering which is low cost, safe and scalable. The effects of substrate temperature on the properties of the Ge films have been investigated. The surface roughness of the Ge films increases with substrate temperature. Smooth surface with RMS roughness of 0.48 nm can be obtained at 300°C owing to the reduced diffusion length of Ge atoms at low temperature. On the other hand, the crystallinity of the Ge films could be improved by increasing substrate temperature as revealed by XRD and TEM measurements. In addition, the compressive strain in the Ge films decreases with increasing substrate temperature owing to the difference in the thermal expansion coefficients between Si and Ge.

Epitaxial growth of Ge films on Si by magnetron sputtering at low temperature has been achieved through one-step aluminum-assisted crystallization. By applying an *in-situ* low temperature (50–150°C) heat treatment in between Al and Ge sputter depositions, the epitaxial growth of Ge on Si can be achieved as verified by high resolution TEM and XRD analyses. The mechanism of epitaxial growth of Ge on Si substrate by one-step aluminum-assisted crystallization is discussed based on observations on samples with various Ge deposition times. This method significantly lowers the required temperature for and therefore the cost of epitaxial growth of Ge on Si.

## **Acknowledgements**

This work has been supported by the Australian Government through the Australian Research Council (ARC, grant number DP160103433, LP110201112) and the Australian Renewable Energy Agency (ARENA) and by Epistar Corporation and Shin Shin Natural Gas Co., Ltd., Taiwan. Responsibility for the views, information or advice expressed herein is not accepted by the Australian Government.

## **Author details**

Ziheng Liu\*, Xiaojing Hao, Anita Ho-Baillie and Martin A. Green

\*Address all correspondence to: ziheng.liu@unsw.edu.au

School of Photovoltaic and Renewable Energy Engineering, University of New South Wales, Sydney, Australia

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[40] Hartmann JM et al. Reduced pressure–chemical vapor deposition of Ge thick layers on Si(001) for 1.3-1.55-μm photodetection. Journal of Applied Physics. 2004;**95**(10):5905-5913

[41] Ernst F, Pirouz P. Formation of planar defects in the epitaxial growth of GaP on Si substrate by metal organic chemical-vapor deposition. Journal of Applied Physics.

[42] Nast O et al. Aluminum-induced crystallization of amorphous silicon on glass substrates above and below the eutectic temperature. Applied Physics Letters. 1998;**73**(22):3214-3216

[43] Wang ZM et al. Thermodynamics and mechanism of metal-induced crystallization in immiscible alloy systems: Experiments and calculations on Al/a-Ge and Al/a-Si bilayers.

[44] Zhang T-W et al. Diffusion-controlled formation mechanism of dual-phase structure during al induced crystallization of SiGe. Applied Physics Letters. 2012;**100**(7):071908

[45] Gjukic M et al. Aluminum-induced crystallization of amorphous silicon--germanium

grated circuits. Semiconductor Science and Technology. 1996;**11**(2):139

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Physical Review B. 2008;**77**(4):045424

thin films. Applied Physics Letters. 2004;**85**(11):2134-2136

1981


**Chapter 3**

**Provisional chapter**

(PZT) and

O4 (CFO)

**Electrical Properties of Epitaxial Ferroelectric**

**Electrical Properties of Epitaxial Ferroelectric** 

DOI: 10.5772/intechopen.70133

© 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution,

© 2018 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

(BTO) as ferroelectric phase and CoFe2

and reproduction in any medium, provided the original work is properly cited.

In the context of miniaturization of devices, ferroelectric materials are used as multifunctional materials for their well-known intrinsic properties, especially for the switching of polarization in an applied electric field. The high-quality epitaxial thin film structures are used for the possibility to study different effects as low dimensions, interface, strain and strain gradients on ferroelectric materials and other electric characteristics, also representing a possibility to obtain new phenomena and properties that can be used for development of new devices with different functionalities. This chapter is a summary of

 (BTO) obtained by pulsed laser deposition and the correlation with structural quality of the layers and with different electrostatic conditions induced either by electrodes or by the different interlayers. For this purpose in the first part, studies regarding the influence of the substrates and of different top electrodes are performed for Pb(Zr,Ti)

(PZT) 52/48. In the second part, we focused on artificial multiferroic structures from

as magnetic material. We found that interface configuration and strain engineering could control ferroelectric hysteresis, the capacitance or the leakage current magnitude.

**Keywords:** ferroelectric thin films, electrical properties, multilayered structures, electrostatic

the ferroelectric and dielectric behaviour of epitaxial thin films of Pb(Zr,Ti)O<sup>3</sup>

Andra Georgia Boni, Cristina Florentina Chirila,

Raluca Negrea, Corneliu Ghica, Iuliana Pasuk,

Florentina, Raluca Negrea, Corneliu Ghica, Iuliana Pasuk, Ioana Pintilie and Lucian

Additional information is available at the end of the chapter

alternating layers of PZT 20/80 or BaTiO<sup>3</sup>

boundary conditions, interfaces

Additional information is available at the end of the chapter

Ioana Pintilie and Lucian Pintilie

Andra Georgia Boni, Cristina Chirila

http://dx.doi.org/10.5772/intechopen.70133

**Abstract**

BaTiO<sup>3</sup>

O3

**Heterostructures**

**Heterostructures**

Pintilie

**Provisional chapter**

## **Electrical Properties of Epitaxial Ferroelectric Electrical Properties of Epitaxial Ferroelectric**

DOI: 10.5772/intechopen.70133

#### **Heterostructures Heterostructures**

Andra Georgia Boni, Cristina Florentina Chirila,

Andra Georgia Boni, Cristina Chirila

Raluca Negrea, Corneliu Ghica, Iuliana Pasuk, Florentina, Raluca Negrea, Corneliu Ghica,

Ioana Pintilie and Lucian Pintilie Iuliana Pasuk, Ioana Pintilie and Lucian Pintilie

Additional information is available at the end of the chapter Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/intechopen.70133

#### **Abstract**

In the context of miniaturization of devices, ferroelectric materials are used as multifunctional materials for their well-known intrinsic properties, especially for the switching of polarization in an applied electric field. The high-quality epitaxial thin film structures are used for the possibility to study different effects as low dimensions, interface, strain and strain gradients on ferroelectric materials and other electric characteristics, also representing a possibility to obtain new phenomena and properties that can be used for development of new devices with different functionalities. This chapter is a summary of the ferroelectric and dielectric behaviour of epitaxial thin films of Pb(Zr,Ti)O<sup>3</sup> (PZT) and BaTiO<sup>3</sup> (BTO) obtained by pulsed laser deposition and the correlation with structural quality of the layers and with different electrostatic conditions induced either by electrodes or by the different interlayers. For this purpose in the first part, studies regarding the influence of the substrates and of different top electrodes are performed for Pb(Zr,Ti) O3 (PZT) 52/48. In the second part, we focused on artificial multiferroic structures from alternating layers of PZT 20/80 or BaTiO<sup>3</sup> (BTO) as ferroelectric phase and CoFe2 O4 (CFO) as magnetic material. We found that interface configuration and strain engineering could control ferroelectric hysteresis, the capacitance or the leakage current magnitude.

**Keywords:** ferroelectric thin films, electrical properties, multilayered structures, electrostatic boundary conditions, interfaces

and reproduction in any medium, provided the original work is properly cited.

© 2018 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

© 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution,

## **1. Introduction**

Ferroelectrics are multifunctional materials possessing special properties derived from the presence of the spontaneous polarization in the absence of an applied electric field. Ferroelectricity is electrical analogue of ferromagnetism, the distinguishing property of ferroelectricity being the possibility of reversing the spontaneous polarization when an external electric field is applied in the opposite direction. As a consequence, the polarization describes a hysteresis loop as magnetization does in ferromagnetic materials. Ferroelectric materials also possess piezoelectric and pyroelectric properties which are used in many electronic applications, such as tunable capacitors, ferroelectric nonvolatile memories, ultrasound sensors or generators and infrared sensors [1–4]. Another interesting topic is related to multiferroic materials—single phase or heterostructures—which possess more than one order parameter (usually magnetic and ferroelectric ordering) and which can lead to new applications if there is a coupling between the order parameters [5–9].

voltage axis, modification of remnant polarization and occurrence of diode-like current char-

As complex equivalent circuits are used for many applications involving ferroelectric materials, it ensures that good knowledge of the electric properties of these materials is a very important topic besides the deposition method and the structural quality. The ferroelectric materials/thin films should be integrated in a capacitor-like structure for the study of the electrical properties. Therefore, a common way to build such a structure is to deposit a continuous conductor thin film as bottom electrode, on which ferroelectric thin film is further deposited. On top of this structure, the top electrode is deposited using a shadow mask, which delimitates the active area of the capacitor. The specific measurements can be realized by connecting

The most used characterization techniques for investigation of ferroelectric properties are hysteresis loops of polarization versus the applied electric field, small signal capacitance measurements (as dependence of capacitance on voltage, frequency or temperature) and leakage current. These characteristics offer information about the ferroelectric character of the structure (e.g. the measurement of a rectangular hysteresis loop or a butterfly shape of the capacitance-voltage characteristics) or the values for different parameters of interest (dielec-

One of the most studied classes of ferroelectric materials is oxide ferroelectrics, especially

the most investigated materials from this category from the point of view of applications. In this chapter, we will present the electrical and ferroelectric properties for this type of epitaxial ferroelectric thin films, obtained by pulsed laser deposition (PLD), and their dependence on the type of the substrate used for deposition or on the material used for the top electrode. Further on, we will show that, by constructing artificially layered structures from thin films of ferroelectric materials and materials having different electric/dielectric properties, the ferroelectric/electric properties can be modified and engineered to obtain enhanced or even new properties. For example, due to either electromechanical or electrostatic interactions, a tuning of capacitance, switching behaviour or leakage current magnitude can be

The term epitaxy refers to a film growth on a substrate with crystallographic structure close to that of the deposited layer. Epitaxial growth is one of the most important techniques in the present microelectronic industry, allowing a better correlation between structure and the macroscopic properties of thin films. Important problems can be studied in this way, related to physics of surfaces, interfaces and strain engineering. There are a wide variety of growth techniques that can be used to obtain epitaxial thin films including sputtering, metal-organic chemical vapour deposition, pulsed laser deposition, molecular beam epitaxy, physical vapour deposition, etc. In this chapter, we will discuss the heteroepitaxial growth, by pulsed

and Pb(Zr,Ti)O<sup>3</sup>

Electrical Properties of Epitaxial Ferroelectric Heterostructures

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69

(PZT) are

tric constant, coercive field, magnitude of polarization and transition temperature).

acteristics with dependence on polarization direction [20–22].

the measurement circuit on the upper and bottom electrodes.

the subclass of the materials with perovskite structure. BaTiO<sup>3</sup>

realized.

**2. Epitaxy**

For many applications, the ferroelectrics are used either as bulk ceramics/single crystals or as thin films with different structural qualities, from polycrystalline to epitaxial. The necessary electrical properties for different applications of ferroelectric materials are strongly influenced by the structural quality. For instance, the existence of the grains and grain boundaries in nanostructured thin films/polycrystalline thin films can induce modification on the magnitude of polarization, dielectric constant and so forth. As for the standard semiconductors, the studies of intrinsic electrical properties should be performed on high-quality single-crystal samples. One method to obtain such samples is to deposit thin films of epitaxial quality. The obtaining of epitaxy for ferroelectric materials often involves the deposition of the ferroelectric thin films on single-crystal substrates, with different buffer or electrode layers, resulting in a heteroepitaxial growth of the film. Therefore, the use of materials with different values for the lattice parameters can generate mechanical tensions/deformations and strain in the lattice of the ferroelectric film [10–13].

It is known that, by changing the pressure on ferroelectric bulk ceramics or single crystals, the transition temperature, piezoelectric and dielectric constants can be modified. In the case of thin films, applying significant hydrostatic pressure to induce modification of ferroelectric properties leads to physical cracks of the samples. Thus, the epitaxy offers the possibility to induce strain and strain-polarization coupling for the enhancement of ferroelectric properties. Examples of the influence of the strain in epitaxial heterostructures are enhancement of polarization in BaTiO<sup>3</sup> (BTO) [14–16], the shift of the transition temperature for PbTiO<sup>3</sup> and BaTiO<sup>3</sup> films towards higher values [17], room temperature-induced ferroelectricity in SrTiO<sup>3</sup> thin films [14–16] and in un-doped HfO2 layers [18] or in artificial superlattices [19] formed from non-ferroelectric materials, etc. These phenomena are specific for fully coherent thin films with low density of dislocations. Nevertheless, by growing the thickness of the deposited ferroelectric layer, many dislocations and other defects appear in order to minimize the free energy of the systems. Different lattice relaxation processes could generate strain gradients in the films, which could imply a flexoelectric field. The effects of these supplementary fields lead to different behaviours in polarization switching, shift of the hysteresis loop along voltage axis, modification of remnant polarization and occurrence of diode-like current characteristics with dependence on polarization direction [20–22].

As complex equivalent circuits are used for many applications involving ferroelectric materials, it ensures that good knowledge of the electric properties of these materials is a very important topic besides the deposition method and the structural quality. The ferroelectric materials/thin films should be integrated in a capacitor-like structure for the study of the electrical properties. Therefore, a common way to build such a structure is to deposit a continuous conductor thin film as bottom electrode, on which ferroelectric thin film is further deposited. On top of this structure, the top electrode is deposited using a shadow mask, which delimitates the active area of the capacitor. The specific measurements can be realized by connecting the measurement circuit on the upper and bottom electrodes.

The most used characterization techniques for investigation of ferroelectric properties are hysteresis loops of polarization versus the applied electric field, small signal capacitance measurements (as dependence of capacitance on voltage, frequency or temperature) and leakage current. These characteristics offer information about the ferroelectric character of the structure (e.g. the measurement of a rectangular hysteresis loop or a butterfly shape of the capacitance-voltage characteristics) or the values for different parameters of interest (dielectric constant, coercive field, magnitude of polarization and transition temperature).

One of the most studied classes of ferroelectric materials is oxide ferroelectrics, especially the subclass of the materials with perovskite structure. BaTiO<sup>3</sup> and Pb(Zr,Ti)O<sup>3</sup> (PZT) are the most investigated materials from this category from the point of view of applications. In this chapter, we will present the electrical and ferroelectric properties for this type of epitaxial ferroelectric thin films, obtained by pulsed laser deposition (PLD), and their dependence on the type of the substrate used for deposition or on the material used for the top electrode. Further on, we will show that, by constructing artificially layered structures from thin films of ferroelectric materials and materials having different electric/dielectric properties, the ferroelectric/electric properties can be modified and engineered to obtain enhanced or even new properties. For example, due to either electromechanical or electrostatic interactions, a tuning of capacitance, switching behaviour or leakage current magnitude can be realized.

## **2. Epitaxy**

**1. Introduction**

68 Epitaxy

is a coupling between the order parameters [5–9].

of the ferroelectric film [10–13].

polarization in BaTiO<sup>3</sup>

thin films [14–16] and in un-doped HfO2

BaTiO<sup>3</sup>

Ferroelectrics are multifunctional materials possessing special properties derived from the presence of the spontaneous polarization in the absence of an applied electric field. Ferroelectricity is electrical analogue of ferromagnetism, the distinguishing property of ferroelectricity being the possibility of reversing the spontaneous polarization when an external electric field is applied in the opposite direction. As a consequence, the polarization describes a hysteresis loop as magnetization does in ferromagnetic materials. Ferroelectric materials also possess piezoelectric and pyroelectric properties which are used in many electronic applications, such as tunable capacitors, ferroelectric nonvolatile memories, ultrasound sensors or generators and infrared sensors [1–4]. Another interesting topic is related to multiferroic materials—single phase or heterostructures—which possess more than one order parameter (usually magnetic and ferroelectric ordering) and which can lead to new applications if there

For many applications, the ferroelectrics are used either as bulk ceramics/single crystals or as thin films with different structural qualities, from polycrystalline to epitaxial. The necessary electrical properties for different applications of ferroelectric materials are strongly influenced by the structural quality. For instance, the existence of the grains and grain boundaries in nanostructured thin films/polycrystalline thin films can induce modification on the magnitude of polarization, dielectric constant and so forth. As for the standard semiconductors, the studies of intrinsic electrical properties should be performed on high-quality single-crystal samples. One method to obtain such samples is to deposit thin films of epitaxial quality. The obtaining of epitaxy for ferroelectric materials often involves the deposition of the ferroelectric thin films on single-crystal substrates, with different buffer or electrode layers, resulting in a heteroepitaxial growth of the film. Therefore, the use of materials with different values for the lattice parameters can generate mechanical tensions/deformations and strain in the lattice

It is known that, by changing the pressure on ferroelectric bulk ceramics or single crystals, the transition temperature, piezoelectric and dielectric constants can be modified. In the case of thin films, applying significant hydrostatic pressure to induce modification of ferroelectric properties leads to physical cracks of the samples. Thus, the epitaxy offers the possibility to induce strain and strain-polarization coupling for the enhancement of ferroelectric properties. Examples of the influence of the strain in epitaxial heterostructures are enhancement of

(BTO) [14–16], the shift of the transition temperature for PbTiO<sup>3</sup>

layers [18] or in artificial superlattices [19] formed

films towards higher values [17], room temperature-induced ferroelectricity in SrTiO<sup>3</sup>

from non-ferroelectric materials, etc. These phenomena are specific for fully coherent thin films with low density of dislocations. Nevertheless, by growing the thickness of the deposited ferroelectric layer, many dislocations and other defects appear in order to minimize the free energy of the systems. Different lattice relaxation processes could generate strain gradients in the films, which could imply a flexoelectric field. The effects of these supplementary fields lead to different behaviours in polarization switching, shift of the hysteresis loop along

and

The term epitaxy refers to a film growth on a substrate with crystallographic structure close to that of the deposited layer. Epitaxial growth is one of the most important techniques in the present microelectronic industry, allowing a better correlation between structure and the macroscopic properties of thin films. Important problems can be studied in this way, related to physics of surfaces, interfaces and strain engineering. There are a wide variety of growth techniques that can be used to obtain epitaxial thin films including sputtering, metal-organic chemical vapour deposition, pulsed laser deposition, molecular beam epitaxy, physical vapour deposition, etc. In this chapter, we will discuss the heteroepitaxial growth, by pulsed laser deposition, of oxide thin films with ferroelectric/multiferroic properties. There are three known growth modes: (1) Frank-Van der Merwe, layer-by-layer growth; (2) Volmer-Weber, island growth and (3) Stranski-Krastanov, a combination of layer-by-layer and island growth. Thermodynamic approach was used in order to explain these growth modes in close to equilibrium conditions [23]. The balance between free energies from the film surface (γF ), the substrate surface (γ<sup>S</sup> ) and the interface between them (γ<sup>I</sup> ) is the key factor that determines the thin film morphology in this approach. Frank-Van der Merwe growth mode is characterized by the fact that the deposited atoms or molecules are more strongly bonded to the substrate than in between them, thus forming a continuous layer on the substrate. In the case of the Volmer-Weber growth mode, the atoms and molecules are more strongly bonded in between them, forming island on the substrate, thus the wetting of the substrate is poor. Stranski-Krastanov mode is characterized by the fact that, at the beginning of the growth, the atoms and molecules form complete monolayers on the substrate (layer-by-layer growth, usually 1–5 monolayers), and then islands start to develop (growth mode changes to island formation). The transition from monolayers to islands is caused by increased tensions (strain) from increasing the layer thickness. Experimentally, the growing of thin films is not an equilibrium process; therefore kinetic effects have to be taken into account, leading to the occurrence of different growth modes. The above-mentioned growth modes and their schematic representations are shown in **Figure 1**.

**3. Growth method**

physical aspects as follows:

deposited on the substrate.

epitaxial growth of the thin films.

**3.1. Experimental setup**

that the substrate is, usually, heated.

Pulsed laser deposition, as the name suggests, is a technique, which uses pulses of laser radiation to remove material from the surface of a solid target. The technique involves complex

**Figure 2.** Atomic force microscopy images obtained on STO substrate after each processing step: upper image, fresh

Electrical Properties of Epitaxial Ferroelectric Heterostructures

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71

substrate; middle image, substrate after etching; and lower image, substrate after thermal annealing.

**1.** Interaction between the laser radiation and the target material—high temperature is achieved over a small area (the area of the laser spot) due to the high power of the laser beam in the short period of the laser pulse; this leads to a number of processes occurring at the target surface, such as material decomposition, ionization and evaporation. One has to mention that the target has the same chemical composition as the film intended to be

**2.** Transfer of the ablated material: the evaporated material from the step 1 forms a plasma

**3.** Deposition of the ablated material on the substrate—this step consists in the adsorption/ chemisorption of the ablated material on the surface of the substrate. One has to mention

**4.** Nucleation and growth of the film on the surface of the substrate—the main condition for this process to occur is represented by the balance between free energies from the film

Each step involved in the pulsed laser deposition process is crucial for obtaining the hetero-

The experimental setup is designed for the deposition of thin films and multilayers from oxide materials and consists of an excimer laser source (KrF, λ = 248 nm) with a pulse duration of

plume over the substrate on which the film has to be deposited.

surface, the substrate surface and the interface between them.

A preliminary substrate preparation has to be achieved in order to obtain heteroepitaxial thin films on single-crystal SrTiO<sup>3</sup> (STO) substrates. The substrate preparation consists in transforming an optically polished surface into a step-and-terrace surface that is well ordered even on an atomic scale. For this purpose, the SrTiO<sup>3</sup> substrates are etched in NH4 -HF solution to remove Sr residue and to obtain a purely Ti-terminated surface and to get a highquality step-and-terrace structure on the surface. All step edges should have equal height (single unit cell ~ 0.4 nm), and the steps should be approximately parallel and equidistant. This can be obtained after an annealing process, at elevated temperatures, of the etched substrates. The substrate transformation after each processing step is investigated by atomic force microscopy, and the results are presented in **Figure 2**.

**Figure 1.** Growth modes for epitaxial thin films: (a) Frank-Van der Merwe, (b) Stranski-Krastanov and (c) Volmer-Weber.

**Figure 2.** Atomic force microscopy images obtained on STO substrate after each processing step: upper image, fresh substrate; middle image, substrate after etching; and lower image, substrate after thermal annealing.

## **3. Growth method**

laser deposition, of oxide thin films with ferroelectric/multiferroic properties. There are three known growth modes: (1) Frank-Van der Merwe, layer-by-layer growth; (2) Volmer-Weber, island growth and (3) Stranski-Krastanov, a combination of layer-by-layer and island growth. Thermodynamic approach was used in order to explain these growth modes in close to equi-

film morphology in this approach. Frank-Van der Merwe growth mode is characterized by the fact that the deposited atoms or molecules are more strongly bonded to the substrate than in between them, thus forming a continuous layer on the substrate. In the case of the Volmer-Weber growth mode, the atoms and molecules are more strongly bonded in between them, forming island on the substrate, thus the wetting of the substrate is poor. Stranski-Krastanov mode is characterized by the fact that, at the beginning of the growth, the atoms and molecules form complete monolayers on the substrate (layer-by-layer growth, usually 1–5 monolayers), and then islands start to develop (growth mode changes to island formation). The transition from monolayers to islands is caused by increased tensions (strain) from increasing the layer thickness. Experimentally, the growing of thin films is not an equilibrium process; therefore kinetic effects have to be taken into account, leading to the occurrence of different growth modes. The above-mentioned growth modes and their schematic representations are

A preliminary substrate preparation has to be achieved in order to obtain heteroepitaxial

transforming an optically polished surface into a step-and-terrace surface that is well ordered

tion to remove Sr residue and to obtain a purely Ti-terminated surface and to get a highquality step-and-terrace structure on the surface. All step edges should have equal height (single unit cell ~ 0.4 nm), and the steps should be approximately parallel and equidistant. This can be obtained after an annealing process, at elevated temperatures, of the etched substrates. The substrate transformation after each processing step is investigated by atomic

**Figure 1.** Growth modes for epitaxial thin films: (a) Frank-Van der Merwe, (b) Stranski-Krastanov and (c) Volmer-Weber.

), the sub-


) is the key factor that determines the thin

(STO) substrates. The substrate preparation consists in

substrates are etched in NH4

librium conditions [23]. The balance between free energies from the film surface (γF

) and the interface between them (γ<sup>I</sup>

strate surface (γ<sup>S</sup>

70 Epitaxy

shown in **Figure 1**.

thin films on single-crystal SrTiO<sup>3</sup>

even on an atomic scale. For this purpose, the SrTiO<sup>3</sup>

force microscopy, and the results are presented in **Figure 2**.

Pulsed laser deposition, as the name suggests, is a technique, which uses pulses of laser radiation to remove material from the surface of a solid target. The technique involves complex physical aspects as follows:


Each step involved in the pulsed laser deposition process is crucial for obtaining the heteroepitaxial growth of the thin films.

#### **3.1. Experimental setup**

The experimental setup is designed for the deposition of thin films and multilayers from oxide materials and consists of an excimer laser source (KrF, λ = 248 nm) with a pulse duration of 20 ns; a target carrousel with four targets of 2″ diameter, allowing permanent rotation of each target; a substrate holder with controlled motion on five axes and possibility to heat the substrate up to 1000°C; a deposition chamber allowing base vacuum down to 10−7 mbar; and high-pressure reflection high-energy electron diffraction (RHEED) system for in situ characterization. The entire system is controlled by PC and is presented in **Figure 3**.

ferroelectric, pyroelectric and piezoelectric properties depend on temperature, strain and Zr/ Ti ratio. Around Zr/Ti ratio of 52/48 this material presents a morphotropic phase boundary, and this composition is often preferred due to enhanced dielectric constant and/or piezoelectric

In the last years, great efforts have been dedicated to the epitaxial growth of ferroelectric thin films with the purpose of obtaining enhanced properties compared to that of the polycrystalline ones. There are many reports on obtaining high-quality epitaxial PZT thin films, deposited by various

is an increased need to obtain the same material performances on substrates (Si) allowing rapid integration of ferroelectric materials in the existing complementary metal–oxide–semiconductor (C-MOS) technology. First attempts to deposit PZT layers on Si were realized in the context of constructing metal-ferroelectric-semiconductor field-effect transistors, and it was found out that silicates or other parasitic phases are formed at the PZT-Si interface [28]. To overcome these problems, insulating buffer layers were used as barriers to avoid diffusion of Pb atoms towards Si interface, but this method leads to high depolarization fields. As a consequence, the polarization

In this context, our first results presented in this section consist in evidencing epitaxial deposition by PLD of PZT on Si (001) using as interlayer a MBE-deposited thin film of STO which acts as a barrier for Pb diffusion and as a template for the growth of the subsequent layers. A

the PZT film was grown. Even if an epitaxial structure is obtained using this configuration of deposited layers, many structural and electrical differences are observed compared to the

XRD 2θ−ω diagrams are presented in **Figure 4** for both types of samples, PZT/SRO/STO/Si and PZT/SRO/STO, showing only (00l) (l = 1,2,3,4) maximas for PZT, SRO and STO layers, indicating an out-of-plane-oriented pseudocubic structure for both cases. Around SRO and STO peaks, the layered fringes evidenced in the inset figures are specific for epitaxial thin films and indicate very smooth and parallel interfaces. The PZT out-of-plane lattice parameter is calculated from this data, and a significantly larger value is obtained in the case of the single-crystal STO substrate (cPZT = 4.113 Å) compared to the case of Si substrate with STO buffer layer (cPZT = 4.055 Å). In addition, the rocking curves recorded around 002 lines suggest a better alignment of the crystal planes for PZT films deposited on STO substrate, with a full width at half maximum of 0.2°, compared to 0.6° in the case of the PZT films deposited on STO-buffered Si substrate. Phi scans were performed on tilted crystalline planes to evidence the cube-on-cube growing relation between PZT, SRO and STO and to determine the (001) orientation relation between the planes of the Si substrate and those of the oxide layers (see **Figure 4**). The epitaxial growth is confirmed by obtaining the four peaks, related to the fourfold rotation axis of the pseudocubic symmetry. The in-plane orientation relations are such that PZT[100]//SRO[100]//STO[100]//Si[110] and are schematically represented in inset figures

Transmission electron microscopy (TEM) investigations are performed for both structures for a complete structural characterization. It can be easily observed in both cases that the

same ferroelectric capacitor structure deposited on single-crystal STO substrate [33].

(SRO) has been deposited by PLD to serve as bottom electrode, and then

(STO), but there

73

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methods on single-crystal substrates with perovskite structures such as SrTiO<sup>3</sup>

magnitude decreases, and the retention properties are deteriorated [29–32].

coefficient [24–27].

20 nm film of SrRuO<sup>3</sup>

of Phi scans.

The energy density of the laser pulse (fluence) can reach 5 J/cm2 , and the repetition rate is in the 1–10 Hz range. The laser beam is delivered on the target surface at an angle 45° to the normal. The pressure inside the chamber can be varied during the deposition by changing the flow rate of deposition gas (O2 or Ar) using mass flow controllers. The substrate temperature is controlled with a proportional–integral–derivative controller (PID controller) temperature controller from room temperature (RT) up to 1000°C. The distance between target and substrate can be adjusted from 40 to 80 mm. All these parameters have to be optimized for each material in order to get the desired heteroepitaxial thin films.

**Figure 3.** Schematic view of the pulsed laser deposition system.

## **4. Epitaxial ferroelectric thin films: structural and electrical properties**

One representative and widely studied material of the class of perovskite ferroelectrics is lead titanate-zirconate Pb(Zr,Ti)O<sup>3</sup> (PZT). Its phase diagram is quite complex, and its structural, ferroelectric, pyroelectric and piezoelectric properties depend on temperature, strain and Zr/ Ti ratio. Around Zr/Ti ratio of 52/48 this material presents a morphotropic phase boundary, and this composition is often preferred due to enhanced dielectric constant and/or piezoelectric coefficient [24–27].

20 ns; a target carrousel with four targets of 2″ diameter, allowing permanent rotation of each target; a substrate holder with controlled motion on five axes and possibility to heat the substrate up to 1000°C; a deposition chamber allowing base vacuum down to 10−7 mbar; and high-pressure reflection high-energy electron diffraction (RHEED) system for in situ charac-

in the 1–10 Hz range. The laser beam is delivered on the target surface at an angle 45° to the normal. The pressure inside the chamber can be varied during the deposition by changing the

is controlled with a proportional–integral–derivative controller (PID controller) temperature controller from room temperature (RT) up to 1000°C. The distance between target and substrate can be adjusted from 40 to 80 mm. All these parameters have to be optimized for each

**4. Epitaxial ferroelectric thin films: structural and electrical properties**

One representative and widely studied material of the class of perovskite ferroelectrics is lead

(PZT). Its phase diagram is quite complex, and its structural,

or Ar) using mass flow controllers. The substrate temperature

, and the repetition rate is

terization. The entire system is controlled by PC and is presented in **Figure 3**.

The energy density of the laser pulse (fluence) can reach 5 J/cm2

material in order to get the desired heteroepitaxial thin films.

flow rate of deposition gas (O2

72 Epitaxy

titanate-zirconate Pb(Zr,Ti)O<sup>3</sup>

**Figure 3.** Schematic view of the pulsed laser deposition system.

In the last years, great efforts have been dedicated to the epitaxial growth of ferroelectric thin films with the purpose of obtaining enhanced properties compared to that of the polycrystalline ones. There are many reports on obtaining high-quality epitaxial PZT thin films, deposited by various methods on single-crystal substrates with perovskite structures such as SrTiO<sup>3</sup> (STO), but there is an increased need to obtain the same material performances on substrates (Si) allowing rapid integration of ferroelectric materials in the existing complementary metal–oxide–semiconductor (C-MOS) technology. First attempts to deposit PZT layers on Si were realized in the context of constructing metal-ferroelectric-semiconductor field-effect transistors, and it was found out that silicates or other parasitic phases are formed at the PZT-Si interface [28]. To overcome these problems, insulating buffer layers were used as barriers to avoid diffusion of Pb atoms towards Si interface, but this method leads to high depolarization fields. As a consequence, the polarization magnitude decreases, and the retention properties are deteriorated [29–32].

In this context, our first results presented in this section consist in evidencing epitaxial deposition by PLD of PZT on Si (001) using as interlayer a MBE-deposited thin film of STO which acts as a barrier for Pb diffusion and as a template for the growth of the subsequent layers. A 20 nm film of SrRuO<sup>3</sup> (SRO) has been deposited by PLD to serve as bottom electrode, and then the PZT film was grown. Even if an epitaxial structure is obtained using this configuration of deposited layers, many structural and electrical differences are observed compared to the same ferroelectric capacitor structure deposited on single-crystal STO substrate [33].

XRD 2θ−ω diagrams are presented in **Figure 4** for both types of samples, PZT/SRO/STO/Si and PZT/SRO/STO, showing only (00l) (l = 1,2,3,4) maximas for PZT, SRO and STO layers, indicating an out-of-plane-oriented pseudocubic structure for both cases. Around SRO and STO peaks, the layered fringes evidenced in the inset figures are specific for epitaxial thin films and indicate very smooth and parallel interfaces. The PZT out-of-plane lattice parameter is calculated from this data, and a significantly larger value is obtained in the case of the single-crystal STO substrate (cPZT = 4.113 Å) compared to the case of Si substrate with STO buffer layer (cPZT = 4.055 Å). In addition, the rocking curves recorded around 002 lines suggest a better alignment of the crystal planes for PZT films deposited on STO substrate, with a full width at half maximum of 0.2°, compared to 0.6° in the case of the PZT films deposited on STO-buffered Si substrate. Phi scans were performed on tilted crystalline planes to evidence the cube-on-cube growing relation between PZT, SRO and STO and to determine the (001) orientation relation between the planes of the Si substrate and those of the oxide layers (see **Figure 4**). The epitaxial growth is confirmed by obtaining the four peaks, related to the fourfold rotation axis of the pseudocubic symmetry. The in-plane orientation relations are such that PZT[100]//SRO[100]//STO[100]//Si[110] and are schematically represented in inset figures of Phi scans.

Transmission electron microscopy (TEM) investigations are performed for both structures for a complete structural characterization. It can be easily observed in both cases that the

**Figure 4.** (a) XRD 2Theta-Omega scans (the insets are details around the 001 lines, showing the layer fringes of SRO, or of both SRO and STO thin films, respectively), (b) rocking curves taken at PZT 002, STO 002 and Si 004 lines and (c) phi scans obtained in asymmetric geometry by locating the {103} planes of STO and PZT and the {113} planes of Si (insets, sketches of the in-plane relationships deduced from the phi scans).

SRO and PZT layer thickness is of about 100 and 20 nm, respectively. In the case of the structure deposited on Si substrate, a bright thin layer with thickness of 4 nm is detected at the interface between Si and STO layers, and it is attributed to a native layer of SiO2 . Epitaxial relation between the constituent layers and the orientation relationship between crystallographic planes are revealed from the selected area electron diffraction patterns (SAED). The results obtained for the lattice constant of PZT from SAED images are in accordance with those obtained by XRD, again indicating a more relaxed PZT in the case of Si substrate compared to a more elongated unit cell in the case of PZT deposited on STO substrate. High-resolution TEM (HRTEM) images are acquired in order to observe the quality of the interfaces between the constituent layers. A strain contrast is revealed in the PZT layer in the case of the sample deposited on Si substrate, with a distorted region at the interface with the bottom SRO electrode, region-containing clusters of dislocations (**Figures 5** and **6**).

All the differences observed in the structural quality of the deposited layers and interfaces are having a significant impact on the macroscopic electrical properties of the two structures, as will be presented further on.

The presence of the hysteresis loop, describing the change in spontaneous polarization when an external electric field is applied on the ferroelectric capacitor, is the most important property of a ferroelectric material. The defining parameters of the hysteresis loop are saturated polarization (maximum value of polarization), remnant polarization (the value of polarization

**Figure 6.** (a) HRTEM image at low magnification of PZT/SRO/STO/Si heterostructures, (b) SAED pattern corresponding


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to TEM image (a), (c) HRTEM image of the Si-SiO2

HRTEM image of the SRO-PZT interface.

**Figure 5.** (a) TEM image at low magnification of PZT/SRO/STO heterostructure, (b) SAED pattern corresponding to TEM

image (a), (c) HRTEM image of the STO-SRO interface and (d) HRTEM image of the SRO-PZT interface.

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**Figure 5.** (a) TEM image at low magnification of PZT/SRO/STO heterostructure, (b) SAED pattern corresponding to TEM image (a), (c) HRTEM image of the STO-SRO interface and (d) HRTEM image of the SRO-PZT interface.

SRO and PZT layer thickness is of about 100 and 20 nm, respectively. In the case of the structure deposited on Si substrate, a bright thin layer with thickness of 4 nm is detected at the interface between Si and STO layers, and it is attributed to a native layer of SiO2

sketches of the in-plane relationships deduced from the phi scans).

**Figure 4.** (a) XRD 2Theta-Omega scans (the insets are details around the 001 lines, showing the layer fringes of SRO, or of both SRO and STO thin films, respectively), (b) rocking curves taken at PZT 002, STO 002 and Si 004 lines and (c) phi scans obtained in asymmetric geometry by locating the {103} planes of STO and PZT and the {113} planes of Si (insets,

Epitaxial relation between the constituent layers and the orientation relationship between crystallographic planes are revealed from the selected area electron diffraction patterns (SAED). The results obtained for the lattice constant of PZT from SAED images are in accordance with those obtained by XRD, again indicating a more relaxed PZT in the case of Si substrate compared to a more elongated unit cell in the case of PZT deposited on STO substrate. High-resolution TEM (HRTEM) images are acquired in order to observe the quality of the interfaces between the constituent layers. A strain contrast is revealed in the PZT layer in the case of the sample deposited on Si substrate, with a distorted region at the interface with the bottom SRO electrode, region-containing clusters of dislocations

All the differences observed in the structural quality of the deposited layers and interfaces are having a significant impact on the macroscopic electrical properties of the two structures, as

(**Figures 5** and **6**).

74 Epitaxy

will be presented further on.

.

**Figure 6.** (a) HRTEM image at low magnification of PZT/SRO/STO/Si heterostructures, (b) SAED pattern corresponding to TEM image (a), (c) HRTEM image of the Si-SiO2 -STO interfaces, (d) HRTEM image of the STO-SRO interface and (e) HRTEM image of the SRO-PZT interface.

The presence of the hysteresis loop, describing the change in spontaneous polarization when an external electric field is applied on the ferroelectric capacitor, is the most important property of a ferroelectric material. The defining parameters of the hysteresis loop are saturated polarization (maximum value of polarization), remnant polarization (the value of polarization at zero applied field) and coercive field (the required electric field to have zero polarization). The classic circuit to record a hysteresis loop is based on the Sawyer-Tower experiment [34]. A similar principle used nowadays, computer controlled equipment, is able to record at the same time both current and charge (polarization) hystereses. The current loop recorded for a ferroelectric capacitor should present the two peaks, one for each polarity of the applied voltage. The peaks are attributed to polarization switching from one direction to the other. The polarization-voltage loop is obtained by integration of the current loop.

are also presented in **Figure 7**. It can be observed that the structures present different shapes of the characteristic and that the values for capacitance and coercive voltages are dependent on the used substrate. In the case of the PZT film deposited on the Si substrate, the value of the dielectric constant at 0 V is 650, much higher than the value of 240 obtained for the PZT film grown on STO substrate. Furthermore, an asymmetry can be observed in the case of PZT/SRO/ STO structure. The two capacitance peaks have different values for positive and negative volt-

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The differences observed between the two structures, and mentioned above, are related to the previously described differences in the structural quality of the ferroelectric films deposited on different substrates. The higher polarization value obtained for the PZT film deposited on the STO substrate is correlated to a higher strain in this case, while the lower value for the film deposited on Si substrate is explained by the increased density of defects in the ferroelectric layer. These defects may suppress the switching of ferroelectric domains, determining a lower polarization value and a slower reversal of polarization, with a larger width of the switching

An imprint voltage around 1 V is observed in the hysteresis loop of the structure deposited on the STO substrate, suggesting the presence of an internal electric field oriented towards the top electrode. This internal field cannot be assigned to different work functions of the bottom SRO electrode (4.6–4.9 eV) [35] and top Pt electrode (5.65 eV) [36] as the same electrodes are used for the PZT film deposited on Si substrate. However, the imprint is very much reduced in this case, leading to a more symmetric hysteresis loop, as shown in **Figure 7 (d)**. This is an indication that the internal electric field has a different origin, such as a gradient of the strain

distribution or non-homogenous spatial distribution of defects like oxygen vacancies.

tion, SRO) on PZT layer deposited on Si substrate with STO buffer layer.

has the highest value around 20 μC/cm2

Despite these differences, the values of the most important parameters, such as remnant polarization and dielectric constant, belong to the same order of magnitude. This proves that high-quality epitaxial PZT films can be grown by PLD on Si substrates with STO buffer layer, allowing their rapid integration with semiconductor technology. The electric properties can be further tuned by changing the electrode material of the ferroelectric capacitor [37, 38]. The influence of the electrode-ferroelectric interface on the macroscopic electrical properties of epitaxial PZT films has been previously studied [39] for films with tetragonal structure deposited on single-crystal STO substrate, but it was less studied for epitaxial PZT films deposited on Si substrate and with composition near the morphotropic phase boundary [38]. Therefore, different materials were used as top electrodes (Pt, Ir, Ru and an oxide with metallic conduc-

The hysteresis loops and C-V characteristics obtained at room temperature for all four types of electrodes are presented in **Figure 8**. A first observation is that the shape of the hysteresis loops and the values of the remnant polarizations and coercive fields depend on the material used for the top electrode. For example, in the case of SRO top electrode, the remnant polarization

both hysteresis and C-V loop are almost symmetric, which is expected due to symmetry of the electrode configuration for this structure (both top and bottom electrodes are SRO). The small shift of the hysteresis, of 0.2 V towards positive voltages, observed in this case can be explained

and the highest coercive voltage of 3.7 V. Moreover,

age polarities, with a shaper maxima and higher value for positive voltages.

current peaks.

The ferroelectric character is checked for the two structures by recording the hysteresis loops, and the obtained results are presented in **Figure 7**. Even if both samples present an epitaxial relation between deposited layers and ferroelectricity is evidenced in both cases by the presence of the switching peaks in the current hysteresis, many relevant properties and values are different. For instance, in the case of the structure deposited on STO substrate, the switching peaks are sharper, and the polarization loop is more rectangular than the case of the structure deposited on Si substrate. In addition, the values of the remnant polarization are different: 26 μC/cm2 for PZT on Si compared to 48 μC/cm2 for PZT on STO substrate. The coercive voltage is lower in the case of PZT deposited on Si, 1.3 V compared to 2.5 V for the other structure.

The presence of ferroelectricity is also revealed by the butterfly shape of the capacitance-voltage (C-V) characteristics, which is also related to the switching phenomena by the relation*<sup>ε</sup>* <sup>=</sup> \_\_1 *ε*0 \_\_\_ ∂*E* <sup>∂</sup>*<sup>P</sup>*. The differences between the C-V measurement and the previously described P-V measurement consist in the fact that the former is performed by superimposing a small amplitude AC voltage (to measure the capacitance) over a DC voltage (setting the polarization value), while the latter is performed by applying a variable voltage (sin or triangle waveform) on the sample. Therefore, the C-V measurement is quasi-static, while P-V is dynamic. The C-V characteristics

**Figure 7.** (a and d) Polarization hysteresis loop for PZT deposited on Si substrate and STO substrate, respectively; (b and e) current hysteresis loops; and (c and f) capacitance-voltage characteristics.

are also presented in **Figure 7**. It can be observed that the structures present different shapes of the characteristic and that the values for capacitance and coercive voltages are dependent on the used substrate. In the case of the PZT film deposited on the Si substrate, the value of the dielectric constant at 0 V is 650, much higher than the value of 240 obtained for the PZT film grown on STO substrate. Furthermore, an asymmetry can be observed in the case of PZT/SRO/ STO structure. The two capacitance peaks have different values for positive and negative voltage polarities, with a shaper maxima and higher value for positive voltages.

at zero applied field) and coercive field (the required electric field to have zero polarization). The classic circuit to record a hysteresis loop is based on the Sawyer-Tower experiment [34]. A similar principle used nowadays, computer controlled equipment, is able to record at the same time both current and charge (polarization) hystereses. The current loop recorded for a ferroelectric capacitor should present the two peaks, one for each polarity of the applied voltage. The peaks are attributed to polarization switching from one direction to the other. The

The ferroelectric character is checked for the two structures by recording the hysteresis loops, and the obtained results are presented in **Figure 7**. Even if both samples present an epitaxial relation between deposited layers and ferroelectricity is evidenced in both cases by the presence of the switching peaks in the current hysteresis, many relevant properties and values are different. For instance, in the case of the structure deposited on STO substrate, the switching peaks are sharper, and the polarization loop is more rectangular than the case of the structure deposited on Si substrate. In addition, the values of the remnant polarization are different: 26 μC/cm2

The presence of ferroelectricity is also revealed by the butterfly shape of the capacitance-voltage (C-V) characteristics, which is also related to the switching phenomena by the relation*<sup>ε</sup>* <sup>=</sup> \_\_1

The differences between the C-V measurement and the previously described P-V measurement consist in the fact that the former is performed by superimposing a small amplitude AC voltage (to measure the capacitance) over a DC voltage (setting the polarization value), while the latter is performed by applying a variable voltage (sin or triangle waveform) on the sample. Therefore, the C-V measurement is quasi-static, while P-V is dynamic. The C-V characteristics

**Figure 7.** (a and d) Polarization hysteresis loop for PZT deposited on Si substrate and STO substrate, respectively; (b and

e) current hysteresis loops; and (c and f) capacitance-voltage characteristics.

for PZT on STO substrate. The coercive voltage is lower in the

for

*ε*0 \_\_\_ ∂*E* <sup>∂</sup>*<sup>P</sup>*.

polarization-voltage loop is obtained by integration of the current loop.

case of PZT deposited on Si, 1.3 V compared to 2.5 V for the other structure.

PZT on Si compared to 48 μC/cm2

76 Epitaxy

The differences observed between the two structures, and mentioned above, are related to the previously described differences in the structural quality of the ferroelectric films deposited on different substrates. The higher polarization value obtained for the PZT film deposited on the STO substrate is correlated to a higher strain in this case, while the lower value for the film deposited on Si substrate is explained by the increased density of defects in the ferroelectric layer. These defects may suppress the switching of ferroelectric domains, determining a lower polarization value and a slower reversal of polarization, with a larger width of the switching current peaks.

An imprint voltage around 1 V is observed in the hysteresis loop of the structure deposited on the STO substrate, suggesting the presence of an internal electric field oriented towards the top electrode. This internal field cannot be assigned to different work functions of the bottom SRO electrode (4.6–4.9 eV) [35] and top Pt electrode (5.65 eV) [36] as the same electrodes are used for the PZT film deposited on Si substrate. However, the imprint is very much reduced in this case, leading to a more symmetric hysteresis loop, as shown in **Figure 7 (d)**. This is an indication that the internal electric field has a different origin, such as a gradient of the strain distribution or non-homogenous spatial distribution of defects like oxygen vacancies.

Despite these differences, the values of the most important parameters, such as remnant polarization and dielectric constant, belong to the same order of magnitude. This proves that high-quality epitaxial PZT films can be grown by PLD on Si substrates with STO buffer layer, allowing their rapid integration with semiconductor technology. The electric properties can be further tuned by changing the electrode material of the ferroelectric capacitor [37, 38]. The influence of the electrode-ferroelectric interface on the macroscopic electrical properties of epitaxial PZT films has been previously studied [39] for films with tetragonal structure deposited on single-crystal STO substrate, but it was less studied for epitaxial PZT films deposited on Si substrate and with composition near the morphotropic phase boundary [38]. Therefore, different materials were used as top electrodes (Pt, Ir, Ru and an oxide with metallic conduction, SRO) on PZT layer deposited on Si substrate with STO buffer layer.

The hysteresis loops and C-V characteristics obtained at room temperature for all four types of electrodes are presented in **Figure 8**. A first observation is that the shape of the hysteresis loops and the values of the remnant polarizations and coercive fields depend on the material used for the top electrode. For example, in the case of SRO top electrode, the remnant polarization has the highest value around 20 μC/cm2 and the highest coercive voltage of 3.7 V. Moreover, both hysteresis and C-V loop are almost symmetric, which is expected due to symmetry of the electrode configuration for this structure (both top and bottom electrodes are SRO). The small shift of the hysteresis, of 0.2 V towards positive voltages, observed in this case can be explained

The structures with Pt and Ir top electrodes have similar characteristics. This is an expected result considering that Pt and Ir are in the same group of precious metals, with the same structure of the electron shells (same period of the Mendeleev's table). For these two struc-

towards positive voltages is expected in the case of Pt, due to the higher work function for Pt than SRO bottom electrode, but the magnitude of the internal field is much lower than the difference between work functions. In addition, in the case of Ir, there is no shift of the hysteresis loop, even if the difference between work functions is almost 1 eV. These results confirm again that the origin of imprints is related to the different defect distributions at the top and bottom electrode interfaces and not related to the differences between the work functions of the top

The polarization and coercive voltage have much lower values in the case of Ru top elec-

ages. The significant differences obtained in the case of Ru top electrode can be assigned to

increased density of oxygen vacancy (which acts as a donor-type defect) at the top interface

The dielectric constant obtained from C-V measurements at maximum applied voltage, where contribution from polarization switching is reduced, is dependent on the material used as top electrode: 392, 523, 443 and 309 for SRO, Pt, Ir and Ru, respectively. One can observe from **Figure 8** that the value of measured capacitance is dependent on the value of the applied voltage. The explanation for this behaviour is that the ferroelectric-electrode interface behaves like a Schottky contact, with an associated Schottky capacitance dependent on interface properties

when the material for the top electrode is changed, affecting in this manner the capacitance of the entire metal-ferroelectric-metal structure and leading to different capacitance values for negative and positive voltages as observed in the C-V characteristics presented in **Figure 8**.

One way to obtain new electrical properties/new phenomena, of interest for new applications, is to deposit multilayered structures by combining ferroelectric thin films with thin films from materials having different properties, for example, ferroelectric/paraelectric, ferroelectric/ dielectric and ferroelectric/ferromagnetic, or by introducing composition gradients. Examples of new phenomena experimentally evidenced in multilayered heterostructures are negative capacitance in ferroelectric superlattices, enhancement of the electro-resistance or multiple ferroelectric states. One of the most known categories of multilayered structures is the one

of artificial multiferroics, obtained by combining ferroelectric thin films (PZT, BaTiO<sup>3</sup>

O4


Sr1−x MnO<sup>3</sup>

with thin films having magnetic properties (CoFe2

and, in consequence, to an electric field oriented towards the bottom contact.

*q ε*<sup>0</sup> *εst N* \_eff

2(*V* + *V*bi)

**5. Ferroelectric multilayered thin films: structural and electrical** 

and 1.2 V, respectively—with an imprint of 0.6 V towards negative volt-

, and the coercive voltage is 2.5 V. A shift of the hysteresis loop

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, which also has a high conductivity. This process leads to an

[40]. Therefore, the values of *Neff* and *Vbi* can change



tures, polarization is 12 μC/cm2

and bottom electrodes.

a Ru oxidation, forming RuO2

as in the following equation: *<sup>C</sup>* <sup>=</sup> √

trode—8 μC/cm2

**properties**

**Figure 8.** Hysteresis loops and capacitance-voltage characteristics obtained for different top electrodes: (a,b) for SRO, (c,d) for Pt, (e,f) for Ir and (g,h) for Ru, respectively.

by different deposition sequences (PZT deposited on SRO at bottom interface compared to SRO deposited on PZT at top interface), leading to small differences in the electronic properties of the two PZT/SRO interfaces.

The structures with Pt and Ir top electrodes have similar characteristics. This is an expected result considering that Pt and Ir are in the same group of precious metals, with the same structure of the electron shells (same period of the Mendeleev's table). For these two structures, polarization is 12 μC/cm2 , and the coercive voltage is 2.5 V. A shift of the hysteresis loop towards positive voltages is expected in the case of Pt, due to the higher work function for Pt than SRO bottom electrode, but the magnitude of the internal field is much lower than the difference between work functions. In addition, in the case of Ir, there is no shift of the hysteresis loop, even if the difference between work functions is almost 1 eV. These results confirm again that the origin of imprints is related to the different defect distributions at the top and bottom electrode interfaces and not related to the differences between the work functions of the top and bottom electrodes.

The polarization and coercive voltage have much lower values in the case of Ru top electrode—8 μC/cm2 and 1.2 V, respectively—with an imprint of 0.6 V towards negative voltages. The significant differences obtained in the case of Ru top electrode can be assigned to a Ru oxidation, forming RuO2 , which also has a high conductivity. This process leads to an increased density of oxygen vacancy (which acts as a donor-type defect) at the top interface and, in consequence, to an electric field oriented towards the bottom contact.

The dielectric constant obtained from C-V measurements at maximum applied voltage, where contribution from polarization switching is reduced, is dependent on the material used as top electrode: 392, 523, 443 and 309 for SRO, Pt, Ir and Ru, respectively. One can observe from **Figure 8** that the value of measured capacitance is dependent on the value of the applied voltage. The explanation for this behaviour is that the ferroelectric-electrode interface behaves like a Schottky contact, with an associated Schottky capacitance dependent on interface properties as in the following equation: *<sup>C</sup>* <sup>=</sup> √ *q ε*<sup>0</sup> *εst N* \_eff 2(*V* + *V*bi) [40]. Therefore, the values of *Neff* and *Vbi* can change when the material for the top electrode is changed, affecting in this manner the capacitance of the entire metal-ferroelectric-metal structure and leading to different capacitance values for negative and positive voltages as observed in the C-V characteristics presented in **Figure 8**.

## **5. Ferroelectric multilayered thin films: structural and electrical properties**

by different deposition sequences (PZT deposited on SRO at bottom interface compared to SRO deposited on PZT at top interface), leading to small differences in the electronic proper-

**Figure 8.** Hysteresis loops and capacitance-voltage characteristics obtained for different top electrodes: (a,b) for SRO,

ties of the two PZT/SRO interfaces.

78 Epitaxy

(c,d) for Pt, (e,f) for Ir and (g,h) for Ru, respectively.

One way to obtain new electrical properties/new phenomena, of interest for new applications, is to deposit multilayered structures by combining ferroelectric thin films with thin films from materials having different properties, for example, ferroelectric/paraelectric, ferroelectric/ dielectric and ferroelectric/ferromagnetic, or by introducing composition gradients. Examples of new phenomena experimentally evidenced in multilayered heterostructures are negative capacitance in ferroelectric superlattices, enhancement of the electro-resistance or multiple ferroelectric states. One of the most known categories of multilayered structures is the one of artificial multiferroics, obtained by combining ferroelectric thin films (PZT, BaTiO<sup>3</sup> -(BTO)) with thin films having magnetic properties (CoFe2 O4 -CFO, La<sup>x</sup> Sr1−x MnO<sup>3</sup> -LSMO). Besides at least two order parameters (ferroelectric polarization and magnetization), these materials also can present magneto-electric coupling mediated by interfacial strain or charge, making them very suitable for future applications and devices.

The electrical and ferroelectric characteristics of multiferroic heterostructures will be presented in this section. The structures were obtained by combining PZT or BTO ferroelectric thin films with CFO layers. The first part of the study consists in analysing the influence of the PZT (20/80)-CFO or BTO-CFO interfaces on the structural, ferroelectric and dielectric properties of the multilayer. Two different configurations, symmetrical (PZT-CFO-PZT or BTO-CFO-BTO) and asymmetrical (PZT-CFO or BTO-CFO), have been selected and deposited on (100) STO single crystal with SRO bottom electrode [41].

The XRD 2θ−ω scans reveal pseudocubic structures of the deposited layers for all cases of symmetric and asymmetric structures and for both ferroelectric layers: the full scan from 10 to 110° presents only 00l peaks for constituent layers: SRO, PZT or BTO and CFO. To prove the epitaxial relation between the deposited layers, azimuth phi scan is performed on {103} skew planes for STO, SRO and PZT and on {115} planes of CFO. The results are shown in **Figure 9** for PZT-based structures which mention that the same results are obtained for BTO-based structures. These results indicate a cube-on-cube epitaxial relation for all four structures, and the in-plane orientation is CFO[100]||PZT[100]||SRO[100]||STO[100].

**Figures 10** and **11** present TEM images obtained for multilayered structures. The TEM images at low magnifications reveal the constituent layers as well as their thickness. It can be noticed that the CFO layer has a pyramidal growth with a roughness surface, determined by a Volmer-Weber growth mechanisms determined by the lattice mismatch between PZT and CFO. The first layer of ferroelectric materials (PZT or BTO) is of high quality, as is it expected due to small lattice mismatch between ferroelectric layers and SRO bottom electrode and substrate. The second layer of PZT or BTO in symmetric structures presents an increased density of defects induced by the CFO layers, although the hetero-epitaxy is preserved.

In the experimental study of the multilayered structures, it is very important to decide if their electrical properties are a simple superposition of the bulk properties of the constituent materials or are a result of interface phenomena. For example, when a ferroelectric layer is combined with a paraelectric layer, two competing phenomena are determined by the presence of the interface:

strain fields or strain gradients coming from lattice mismatch between the layers and the associated lattice relaxation mechanisms to reduce the total free energy and depolarization fields with origin in the discontinuity of the polarization charges which will determine different ways of response of the ferroelectric layer such as formation of polydomain structure or transition to a

**Figure 11.** (a)TEM image at low magnification of BTO-CFO heterostructure, (b) HRTEM images of the STO-SRO and SRO-BTO interfaces, (c) TEM image at low magnification of BTO-CFO-BTO heterostructure and (d) HRTEM images of

**Figure 10.** TEM image at low magnification of PZT-CFO and PZT-CFO-PZT heterostructure (first line) and HRTEM

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images of the STO-SRO, SRO-PZT and PZT-CFO-PZT interfaces (second line).

paraelectric state.

the BTO-CFO-BTO interfaces.

**Figure 9.** (a) XRD 2θ−ω scans zoomed near STO 004 for PZT-based multilayers structures, (b) XRD 2θ−ω scans zoomed near STO 004 for BTO-based multilayers structures and (c) Phi scans obtained in asymmetric geometry by location the {103} planes of STO and PZT and the {115} planes of CFO.

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least two order parameters (ferroelectric polarization and magnetization), these materials also can present magneto-electric coupling mediated by interfacial strain or charge, making them

The electrical and ferroelectric characteristics of multiferroic heterostructures will be presented in this section. The structures were obtained by combining PZT or BTO ferroelectric thin films with CFO layers. The first part of the study consists in analysing the influence of the PZT (20/80)-CFO or BTO-CFO interfaces on the structural, ferroelectric and dielectric properties of the multilayer. Two different configurations, symmetrical (PZT-CFO-PZT or BTO-CFO-BTO) and asymmetrical (PZT-CFO or BTO-CFO), have been selected and deposited on

The XRD 2θ−ω scans reveal pseudocubic structures of the deposited layers for all cases of symmetric and asymmetric structures and for both ferroelectric layers: the full scan from 10 to 110° presents only 00l peaks for constituent layers: SRO, PZT or BTO and CFO. To prove the epitaxial relation between the deposited layers, azimuth phi scan is performed on {103} skew planes for STO, SRO and PZT and on {115} planes of CFO. The results are shown in **Figure 9** for PZT-based structures which mention that the same results are obtained for BTO-based structures. These results indicate a cube-on-cube epitaxial relation for all four structures, and

**Figures 10** and **11** present TEM images obtained for multilayered structures. The TEM images at low magnifications reveal the constituent layers as well as their thickness. It can be noticed that the CFO layer has a pyramidal growth with a roughness surface, determined by a Volmer-Weber growth mechanisms determined by the lattice mismatch between PZT and CFO. The first layer of ferroelectric materials (PZT or BTO) is of high quality, as is it expected due to small lattice mismatch between ferroelectric layers and SRO bottom electrode and substrate. The second layer of PZT or BTO in symmetric structures presents an increased density

In the experimental study of the multilayered structures, it is very important to decide if their electrical properties are a simple superposition of the bulk properties of the constituent materials or are a result of interface phenomena. For example, when a ferroelectric layer is combined with a paraelectric layer, two competing phenomena are determined by the presence of the interface:

**Figure 9.** (a) XRD 2θ−ω scans zoomed near STO 004 for PZT-based multilayers structures, (b) XRD 2θ−ω scans zoomed near STO 004 for BTO-based multilayers structures and (c) Phi scans obtained in asymmetric geometry by location the

{103} planes of STO and PZT and the {115} planes of CFO.

very suitable for future applications and devices.

80 Epitaxy

(100) STO single crystal with SRO bottom electrode [41].

the in-plane orientation is CFO[100]||PZT[100]||SRO[100]||STO[100].

of defects induced by the CFO layers, although the hetero-epitaxy is preserved.

**Figure 10.** TEM image at low magnification of PZT-CFO and PZT-CFO-PZT heterostructure (first line) and HRTEM images of the STO-SRO, SRO-PZT and PZT-CFO-PZT interfaces (second line).

**Figure 11.** (a)TEM image at low magnification of BTO-CFO heterostructure, (b) HRTEM images of the STO-SRO and SRO-BTO interfaces, (c) TEM image at low magnification of BTO-CFO-BTO heterostructure and (d) HRTEM images of the BTO-CFO-BTO interfaces.

strain fields or strain gradients coming from lattice mismatch between the layers and the associated lattice relaxation mechanisms to reduce the total free energy and depolarization fields with origin in the discontinuity of the polarization charges which will determine different ways of response of the ferroelectric layer such as formation of polydomain structure or transition to a paraelectric state.

The following results show how different electrostatic boundary conditions modify ferroelectric and dielectric properties of multilayered structures. Typical hysteresis loops obtained for epitaxial PZT 20/80 and BTO layers grown on STO substrate with SRO top and bottom electrodes are presented in **Figure 12 (a, d)**. The PZT20/80-based capacitor presents a rectangular shape of the polarization loop, with two sharp current peaks associated to polarization switching from one direction to the other. The remnant and saturated polarization have similar values, around 85 μC/cm2 ,, and the coercive field is around 100 kV/cm2 . For the BTO-based capacitor, the remnant polarization is around 15 μC/cm2 , the saturated polarization around 25 μC/cm2 and the coercive field around 50 kV/cm2 . The polarization hysteresis loop is elongated, and the switching current peaks are broader compared to the PZT case. Those are typical characteristics for these two ferroelectric materials and are further used as references to be compared with the ferroelectric hysteresis loops obtained for asymmetric and symmetric multilayered structures mentioned above.

ferroelectric layers, the hysteresis characteristics are approximately symmetric: similar coercive voltages and polarization values for both voltage polarities, with similar ampli-

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The ferroelectric characteristics of symmetric PZT-CFO-PZT and BTO-CFO-BTO structures become similar with the ones of simple metal-ferroelectric-metal structures, with similar values for the polarization and coercive field. The presence of the CFO layer between the ferroelectric films induces a higher leakage current in the case of PZT-based multilayered structure. In the case of BTO-based structure, the effect is opposite, the presence of the CFO layer leading to a lower leakage current and lower back-switching effects, determining in this

The capacitance-voltage measurements performed at 100 kHz frequency, for the two multilayered structures based on PZT, are depicted in **Figure 13**. The ferroelectric behaviour is also confirmed, for both types of structures, by the butterfly shape of the characteristics. In the case of the asymmetric structure, the capacitance is much lower than in the case of the symmetric structure even if the thickness is lower. Furthermore, the tunability is much lower; the variation of the capacitance value between the peak and the maximum applied voltage is 6 pF, compared to 20 pF in the case of the symmetric structure. In addition, the asymmetry between the values of the capacitance maxima, in the case of the asymmetric structure, can be explained by the presence of asymmetric electrode interfaces, leading to different values of the associated capacitances (different interface properties). The dielectric behaviour is further examined by measuring the dependence on frequency of the capacitance and dielectric losses for the two types of the structures. The results are compared with those obtained on metal-ferroelectric-metal capacitors and on metal-CFO-metal structures. As regards the SRO-PZT-SRO structure, the dielectric behaviour is typical for a ferroelectric/isolator material: there is a small decrease of the capacitance with increasing the frequency, with low values of the dielectric losses. Also, the results obtained on SRO-CFO-SRO structure, presented in **Figure 14 (c–d)** are specific for ferrite-based capacitors [42]:

**Figure 13.** Capacitance voltage characteristics for PZT-based multilayered structures for (a) asymmetric configuration

way a more rectangular shape of the polarization hysteresis loop.

tude of the switching currents.

and (b) symmetric configuration.

In what concerns the asymmetric structures, as PZT-CFO or BTO-CFO, the modifications of the hysteresis characteristics are similar for both cases, meaning decrease of the remnant polarization and increase of the coercive field, increase in the width of the switching current peaks and increase of the polarization back switching. These changes are due to imperfect screening of polarization charges at the top interfaces, due to the presence of less conductive CFO layer compared with metallic SRO electrodes. The high depolarization field existing in the system is compensated on the expense of polarization value, which decreases due to the electrostatic coupling between the component layers. Another interesting observation is that, even if the structures are totally asymmetric, with completely different electrostatic boundary conditions at the top and bottom interfaces of the

**Figure 12.** Hysteresis loop for (a) PZT20/80-based capacitor, (b) PZT-CFO asymmetric structure, (c) PZT-CFO-PZT symmetric structure, (d) BTO-based capacitor, (e) BTO-CFO asymmetric structure and (f) BTO-CFO-BTO symmetric structure.

ferroelectric layers, the hysteresis characteristics are approximately symmetric: similar coercive voltages and polarization values for both voltage polarities, with similar amplitude of the switching currents.

The following results show how different electrostatic boundary conditions modify ferroelectric and dielectric properties of multilayered structures. Typical hysteresis loops obtained for epitaxial PZT 20/80 and BTO layers grown on STO substrate with SRO top and bottom electrodes are presented in **Figure 12 (a, d)**. The PZT20/80-based capacitor presents a rectangular shape of the polarization loop, with two sharp current peaks associated to polarization switching from one direction to the other. The remnant and saturated polarization have simi-

gated, and the switching current peaks are broader compared to the PZT case. Those are typical characteristics for these two ferroelectric materials and are further used as references to be compared with the ferroelectric hysteresis loops obtained for asymmetric and symmetric

In what concerns the asymmetric structures, as PZT-CFO or BTO-CFO, the modifications of the hysteresis characteristics are similar for both cases, meaning decrease of the remnant polarization and increase of the coercive field, increase in the width of the switching current peaks and increase of the polarization back switching. These changes are due to imperfect screening of polarization charges at the top interfaces, due to the presence of less conductive CFO layer compared with metallic SRO electrodes. The high depolarization field existing in the system is compensated on the expense of polarization value, which decreases due to the electrostatic coupling between the component layers. Another interesting observation is that, even if the structures are totally asymmetric, with completely different electrostatic boundary conditions at the top and bottom interfaces of the

**Figure 12.** Hysteresis loop for (a) PZT20/80-based capacitor, (b) PZT-CFO asymmetric structure, (c) PZT-CFO-PZT symmetric structure, (d) BTO-based capacitor, (e) BTO-CFO asymmetric structure and (f) BTO-CFO-BTO symmetric

,, and the coercive field is around 100 kV/cm2

. For the BTO-based

, the saturated polarization around

. The polarization hysteresis loop is elon-

lar values, around 85 μC/cm2

multilayered structures mentioned above.

25 μC/cm2

82 Epitaxy

structure.

capacitor, the remnant polarization is around 15 μC/cm2

and the coercive field around 50 kV/cm2

The ferroelectric characteristics of symmetric PZT-CFO-PZT and BTO-CFO-BTO structures become similar with the ones of simple metal-ferroelectric-metal structures, with similar values for the polarization and coercive field. The presence of the CFO layer between the ferroelectric films induces a higher leakage current in the case of PZT-based multilayered structure. In the case of BTO-based structure, the effect is opposite, the presence of the CFO layer leading to a lower leakage current and lower back-switching effects, determining in this way a more rectangular shape of the polarization hysteresis loop.

The capacitance-voltage measurements performed at 100 kHz frequency, for the two multilayered structures based on PZT, are depicted in **Figure 13**. The ferroelectric behaviour is also confirmed, for both types of structures, by the butterfly shape of the characteristics. In the case of the asymmetric structure, the capacitance is much lower than in the case of the symmetric structure even if the thickness is lower. Furthermore, the tunability is much lower; the variation of the capacitance value between the peak and the maximum applied voltage is 6 pF, compared to 20 pF in the case of the symmetric structure. In addition, the asymmetry between the values of the capacitance maxima, in the case of the asymmetric structure, can be explained by the presence of asymmetric electrode interfaces, leading to different values of the associated capacitances (different interface properties). The dielectric behaviour is further examined by measuring the dependence on frequency of the capacitance and dielectric losses for the two types of the structures. The results are compared with those obtained on metal-ferroelectric-metal capacitors and on metal-CFO-metal structures. As regards the SRO-PZT-SRO structure, the dielectric behaviour is typical for a ferroelectric/isolator material: there is a small decrease of the capacitance with increasing the frequency, with low values of the dielectric losses. Also, the results obtained on SRO-CFO-SRO structure, presented in **Figure 14 (c–d)** are specific for ferrite-based capacitors [42]:

**Figure 13.** Capacitance voltage characteristics for PZT-based multilayered structures for (a) asymmetric configuration and (b) symmetric configuration.

structure deposited on SRO bottom electrode presents different characteristics: evident splitting of the PZT lines, associated with two nodes in RSM map, having different in-plane and out-of-plane lattice parameters. These values are associated to the two different PZT layers: one

fully strained, with in-plane parameter close to STO lattice constant (most probably bottom PZT layer), and one almost fully relaxed, with similar parameters as for the PZT film in structure

**Figure 15.** TEM image at low magnification of PZT-CFO-PZT deposited on SRO bottom electrode (left) and of PZT-CFO-

The ferroelectric behaviour, for both structures, is comparatively presented in **Figure 16** through polarization hysteresis loops and capacitance-voltage characteristics. Both structures present rectangular hysteresis loops and well-evidenced butterfly shape of C-V characteris-

for structure with LSMO bottom electrode)

• Much higher shift of the hysteresis loop towards positive voltages for the structure depos-

**Figure 16.** (a) The polarization hysteresis loops; (b) capacitance-voltage characteristics for PZT-CFO-PZT symmetric structure deposited on SRO bottom electrode and LSMO bottom electrode and (c) the dependence of current density on

voltage for the two studied structures and compared with a simple thin layer of PZT-based capacitor.

for structure with SRO bottom elec-

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deposited on LSMO electrode (**Figure 15**).

PZT deposited on LSMO bottom electrode (right).

trode and 60 μC/cm2

ited on SRO

tics. However, a series of differences are easily observed: • Different values of remnant polarization (90 μC/cm2

**Figure 14.** (a) XRD diagrams zoomed near the 004 line of STO and (b) RSM images for PZT-CFO-PZT deposited on SRO bottom electrode (left) and of PZT-CFO-PZT deposited on LSMO bottom electrode (right).

the values of the capacitance present a steplike decrease with frequency, with one order of magnitude difference between low and high frequencies; dielectric losses present a fast decreasing up to 1 kHz, followed by a peak in the frequency range where the capacitance decreases.

The dielectric behaviour for the two types of multilayered structures is different, compared to the behaviour of the single-phase PZT or CFO-based capacitors, and is strongly dependent on the symmetry of the structure. Even if the multilayered structures display steplike decrease of the capacitance with the increase of frequency and peaks in dielectric losses, the values for capacitance and dielectric losses are lower than the case of the simple CFO capacitors. The dependence of the capacitance and dielectric losses on frequency for multilayered structures are determined especially by an additional interface polarization/charge, due to the presence of interfaces between layers of materials with different permittivity and resistivity values. At high frequencies, the value of the capacitance for multilayered structures is closer to that estimated from the serial connection of the capacitors associated to component layers (PZT or CFO). For lower frequencies, the capacitance value is significantly dependent on the number of interfaces, increasing as the number of interfaces in the structure increases. In addition, the position and magnitude of the relaxation peak are strongly related to the configurations of the multilayer structure. Further results will show how different strains and strain gradients influence the ferroelectric and dielectric properties. As an example, we consider two symmetric structures of PZT/CFO/PZT, with thinner PZT layer (50 nm) than previous examples, deposited on two different bottom electrodes SRO and LSMO.

The results of XRD investigations performed on these two symmetric structures, deposited on two different bottom electrodes, are presented in **Figure 14 (a)** for 2θ−ω around 004 line of PZT and in **Figure 14 (b)** for reciprocal space mapping (RSM). The structure deposited on LSMO electrode presents only a peak for PZT in XRD pattern, corresponding to a bulk out of plane lattice parameter, and only one node in RSM map is attributed to a fully relaxed PZT. The structure deposited on SRO bottom electrode presents different characteristics: evident splitting of the PZT lines, associated with two nodes in RSM map, having different in-plane and out-of-plane lattice parameters. These values are associated to the two different PZT layers: one

**Figure 15.** TEM image at low magnification of PZT-CFO-PZT deposited on SRO bottom electrode (left) and of PZT-CFO-PZT deposited on LSMO bottom electrode (right).

the values of the capacitance present a steplike decrease with frequency, with one order of magnitude difference between low and high frequencies; dielectric losses present a fast decreasing up to 1 kHz, followed by a peak in the frequency range where the capacitance

**Figure 14.** (a) XRD diagrams zoomed near the 004 line of STO and (b) RSM images for PZT-CFO-PZT deposited on SRO

bottom electrode (left) and of PZT-CFO-PZT deposited on LSMO bottom electrode (right).

The dielectric behaviour for the two types of multilayered structures is different, compared to the behaviour of the single-phase PZT or CFO-based capacitors, and is strongly dependent on the symmetry of the structure. Even if the multilayered structures display steplike decrease of the capacitance with the increase of frequency and peaks in dielectric losses, the values for capacitance and dielectric losses are lower than the case of the simple CFO capacitors. The dependence of the capacitance and dielectric losses on frequency for multilayered structures are determined especially by an additional interface polarization/charge, due to the presence of interfaces between layers of materials with different permittivity and resistivity values. At high frequencies, the value of the capacitance for multilayered structures is closer to that estimated from the serial connection of the capacitors associated to component layers (PZT or CFO). For lower frequencies, the capacitance value is significantly dependent on the number of interfaces, increasing as the number of interfaces in the structure increases. In addition, the position and magnitude of the relaxation peak are strongly related to the configurations of the multilayer structure. Further results will show how different strains and strain gradients influence the ferroelectric and dielectric properties. As an example, we consider two symmetric structures of PZT/CFO/PZT, with thinner PZT layer (50 nm) than previous examples, deposited on two different bottom electrodes

The results of XRD investigations performed on these two symmetric structures, deposited on two different bottom electrodes, are presented in **Figure 14 (a)** for 2θ−ω around 004 line of PZT and in **Figure 14 (b)** for reciprocal space mapping (RSM). The structure deposited on LSMO electrode presents only a peak for PZT in XRD pattern, corresponding to a bulk out of plane lattice parameter, and only one node in RSM map is attributed to a fully relaxed PZT. The

decreases.

84 Epitaxy

SRO and LSMO.

fully strained, with in-plane parameter close to STO lattice constant (most probably bottom PZT layer), and one almost fully relaxed, with similar parameters as for the PZT film in structure deposited on LSMO electrode (**Figure 15**).

The ferroelectric behaviour, for both structures, is comparatively presented in **Figure 16** through polarization hysteresis loops and capacitance-voltage characteristics. Both structures present rectangular hysteresis loops and well-evidenced butterfly shape of C-V characteristics. However, a series of differences are easily observed:


**Figure 16.** (a) The polarization hysteresis loops; (b) capacitance-voltage characteristics for PZT-CFO-PZT symmetric structure deposited on SRO bottom electrode and LSMO bottom electrode and (c) the dependence of current density on voltage for the two studied structures and compared with a simple thin layer of PZT-based capacitor.


These differences could be correlated with different structural characteristics determined by XRD and TEM investigations. A totally relaxed structure in the case of the LSMO bottom electrode implies a lower tetragonality and explains lower polarization values. The structural defects, observed in TEM imagines for both PZT layers of this structure, could act as polarization domain pinning centres which determines a slower reversal of polarization from one direction towards the other. The structure deposited on SRO presents two PZT layers with different structural properties. As a consequence, we assume that there is a strain gradient that could be correlated with the existence of an internal electric field pointing towards the top interface that explains the shift observed in the P-V loop of this structure.

A less discussed topic in this chapter, but very important for the operation of ferroelectric devices, is the leakage current. A higher leakage current is detrimental for long-term operation of ferroelectric-based devices. Thus, a significant research effort is dedicated to the identification of the conduction mechanisms, which control the leakage current in ferroelectric thin films and to find a solution to decrease the value of the leakage current. The dependence of the leakage current on voltage (I-V characteristics) is presented in **Figure 17 (c)** for the cases of the two PZT-CFO-PZT structures deposited in SRO and LSMO electrodes. The results are compared with those obtained for a simple PZT capacitor with similar thickness. It is clear that, even if these structures operate at higher voltages, the leakage current is much lower than for a simple PZT layer, the differences being around two orders of magnitude for the structure deposited on SRO.

It was shown in the previous section that the number of interfaces in this multilayered heterostructures determines the dielectric behaviour. Further, **Figure 17** presents the results of the measurements regarding the dependence of the capacitance and dielectric losses, on frequency and temperature, for these two symmetrical structures, with different strain conditions and structural quality of the ferroelectric layers. The values of capacitance and dielectric losses at temperatures below 250 K are similar to those obtained for single-phase PZT capacitor presented in **Figure 18**. This behaviour is modified towards a Maxwell-Wagner mechanism with an increase in temperature, specific for multilayered structures with interfaces between materials with different electric properties. The transition between low-temperature and high-temperature dielectric behaviour can be correlated with a strong variation of the resistivity of the CFO layer with temperature as is exemplified in **Figure 17 (f)**. Therefore, the difference in resistivity between PZT and CFO layers will increase with temperature, favouring in this way Maxwell-Wagner polarization mechanism. The capacitance at lower frequencies and the relaxation marked by the peak in dielectric losses are strongly dependent on the structure and on the temperature. It can be observed that for the structure deposited on LSMO electrode, the values of the capacitance at lower frequencies are higher, and the frequency where the maximum in dielectric losses occurs is higher than for the structure deposited on SRO, at the same temperature.

**Figure 18.** (a) The dependence of capacitance on frequency, (b) the dependence of the dielectric loses on frequency comparatively presented for PZT-based structures and (c) the dependence of capacitance and dielectric losses on

**Figure 17.** (a and b) The dependence of capacitance and dielectric losses, respectively, on frequency and for different temperatures for LSMO bottom electrode case; (c and d) the dependence of capacitance and dielectric losses, respectively, on frequency and for different temperatures for SRO bottom electrode case; (e) the Arrhenius plot of the maximum dielectric losses frequencies and (f) the variation of impedance of a thin layer CFO-based capacitor on temperature.

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frequency for a thin layer of CFO-based capacitor.

Electrical Properties of Epitaxial Ferroelectric Heterostructures http://dx.doi.org/10.5772/intechopen.70133 87

• Higher tunability in the case of LSMO bottom electrode

structure.

86 Epitaxy

structure deposited on SRO.

SRO, at the same temperature.

• A small asymmetry between capacitance maxima in the case of SRO bottom electrode

These differences could be correlated with different structural characteristics determined by XRD and TEM investigations. A totally relaxed structure in the case of the LSMO bottom electrode implies a lower tetragonality and explains lower polarization values. The structural defects, observed in TEM imagines for both PZT layers of this structure, could act as polarization domain pinning centres which determines a slower reversal of polarization from one direction towards the other. The structure deposited on SRO presents two PZT layers with different structural properties. As a consequence, we assume that there is a strain gradient that could be correlated with the existence of an internal electric field pointing towards the top interface that explains the shift observed in the P-V loop of this

A less discussed topic in this chapter, but very important for the operation of ferroelectric devices, is the leakage current. A higher leakage current is detrimental for long-term operation of ferroelectric-based devices. Thus, a significant research effort is dedicated to the identification of the conduction mechanisms, which control the leakage current in ferroelectric thin films and to find a solution to decrease the value of the leakage current. The dependence of the leakage current on voltage (I-V characteristics) is presented in **Figure 17 (c)** for the cases of the two PZT-CFO-PZT structures deposited in SRO and LSMO electrodes. The results are compared with those obtained for a simple PZT capacitor with similar thickness. It is clear that, even if these structures operate at higher voltages, the leakage current is much lower than for a simple PZT layer, the differences being around two orders of magnitude for the

It was shown in the previous section that the number of interfaces in this multilayered heterostructures determines the dielectric behaviour. Further, **Figure 17** presents the results of the measurements regarding the dependence of the capacitance and dielectric losses, on frequency and temperature, for these two symmetrical structures, with different strain conditions and structural quality of the ferroelectric layers. The values of capacitance and dielectric losses at temperatures below 250 K are similar to those obtained for single-phase PZT capacitor presented in **Figure 18**. This behaviour is modified towards a Maxwell-Wagner mechanism with an increase in temperature, specific for multilayered structures with interfaces between materials with different electric properties. The transition between low-temperature and high-temperature dielectric behaviour can be correlated with a strong variation of the resistivity of the CFO layer with temperature as is exemplified in **Figure 17 (f)**. Therefore, the difference in resistivity between PZT and CFO layers will increase with temperature, favouring in this way Maxwell-Wagner polarization mechanism. The capacitance at lower frequencies and the relaxation marked by the peak in dielectric losses are strongly dependent on the structure and on the temperature. It can be observed that for the structure deposited on LSMO electrode, the values of the capacitance at lower frequencies are higher, and the frequency where the maximum in dielectric losses occurs is higher than for the structure deposited on

**Figure 17.** (a and b) The dependence of capacitance and dielectric losses, respectively, on frequency and for different temperatures for LSMO bottom electrode case; (c and d) the dependence of capacitance and dielectric losses, respectively, on frequency and for different temperatures for SRO bottom electrode case; (e) the Arrhenius plot of the maximum dielectric losses frequencies and (f) the variation of impedance of a thin layer CFO-based capacitor on temperature.

**Figure 18.** (a) The dependence of capacitance on frequency, (b) the dependence of the dielectric loses on frequency comparatively presented for PZT-based structures and (c) the dependence of capacitance and dielectric losses on frequency for a thin layer of CFO-based capacitor.

## **6. Conclusions**

This chapter presents the electrical properties of epitaxial ferroelectric thin films and multilayers. A short description of the deposition/growing steps used to obtain high-quality epitaxial ferroelectric structures, with sharp interfaces, is presented at the beginning. The main experimental results show how ferroelectric and dielectric properties depend on the structural quality of the ferroelectric layer and on the electrostatic boundary conditions.

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## **Acknowledgements**

The authors acknowledge the financial support of the Romanian Ministry of Education-Executive Unit for Funding High Education, Research, Development and Innovation (MEN-UEFISCDI) through the Nucleus Program PN16-4801; the Idea-Complex Research Grant PN-II-ID-PCCE-2011-2-0006 (Contract No. 3/2012); the IFA-CEA (Contract No. C503/2016); and the CNCS-UEFISCDI Project of PN-II-PT-PCCA-2013-4-0470 (Contract No. 238/2014).

## **Author details**

Andra Georgia Boni\*, Cristina Florentina Chirila, Raluca Negrea, Corneliu Ghica, Iuliana Pasuk, Ioana Pintilie and Lucian Pintilie

\*Address all correspondence to: andra.boni@infim.ro

National Institute of Materials Physics, Bucharest-Magurele, Romania

## **References**


**6. Conclusions**

88 Epitaxy

**Acknowledgements**

**Author details**

**References**

Iuliana Pasuk, Ioana Pintilie and Lucian Pintilie

\*Address all correspondence to: andra.boni@infim.ro

This chapter presents the electrical properties of epitaxial ferroelectric thin films and multilayers. A short description of the deposition/growing steps used to obtain high-quality epitaxial ferroelectric structures, with sharp interfaces, is presented at the beginning. The main experimental results show how ferroelectric and dielectric properties depend on the structural qual-

The authors acknowledge the financial support of the Romanian Ministry of Education-Executive Unit for Funding High Education, Research, Development and Innovation (MEN-UEFISCDI) through the Nucleus Program PN16-4801; the Idea-Complex Research Grant PN-II-ID-PCCE-2011-2-0006 (Contract No. 3/2012); the IFA-CEA (Contract No. C503/2016); and the CNCS-UEFISCDI Project of PN-II-PT-PCCA-2013-4-0470 (Contract No. 238/2014).

Andra Georgia Boni\*, Cristina Florentina Chirila, Raluca Negrea, Corneliu Ghica,

[1] Scott JF. Applications of modern ferroelectrics. Science. 2007 Feb 16;**315**(5814):954-959

[2] Lallart M, editor. Ferroelectrics - Applications [Internet]. InTech; 2011. Available from:

[3] Okuyama M, Ishibashi Y, editors. Ferroelectric Thin Films [Internet]. Berlin, Heidelberg: Springer Berlin Heidelberg; 2005. (Ascheron CE, Kölsch HJ, Skolaut W, editors. Topics in Applied Physics; vol. 98). Available from: http://link.springer.com/10.1007/b99517

[4] Scott JF. Ferroelectric Memories [Internet]. Berlin, Heidelberg: Springer Berlin Heidelberg; 2000. (Itoh K, Sakurai T, editors. Springer Series in Advanced Microelectronics; vol. 3).

[5] Eerenstein W, Mathur ND, Scott JF. Multiferroic and magnetoelectric materials. Nature. 2006;**442**:759-765. doi: 10.1038/nature05023. Available from: http://www.nature.com/

National Institute of Materials Physics, Bucharest-Magurele, Romania

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Available from: http://link.springer.com/10.1007/978-3-662-04307-3

nature/journal/v442/n7104/full/nature05023.html

ity of the ferroelectric layer and on the electrostatic boundary conditions.


[22] Zhang J, Xu R, Damodaran AR, Chen Z-H, Martin LW. Understanding order in compositionally graded ferroelectrics: Flexoelectricity, gradient, and depolarization field effects. Physical Review B. 2014 Jun 13;**89**(22):224101

[35] Hartmann AJ, Neilson M, Lamb RN, Watanabe K, Scott JF. Ruthenium oxide and strontium ruthenate electrodes for ferroelectric thin-films capacitors. Applied Physics A. 2000

[36] Schaeffer JK, Fonseca LRC, Samavedam SB, Liang Y, Tobin PJ, White BE. Contributions to the effective work function of platinum on hafnium dioxide. Applied Physics Letters [Internet]. 2004 Sep 6;**85**(10). Available from: http://www.osti.gov/scitech/biblio/20632781

[37] Pintilie L, Alexe M. Metal-ferroelectric-metal heterostructures with Schottky contacts. I. Influence of the ferroelectric properties. Journal of Applied Physics. 2005 Dec

[38] Boni AG, Chirila C, Pasuk I, Negrea R, Trupina L, Le Rhun G, et al. Electrode interface

[39] Pintilie I, Teodorescu CM, Ghica C, Chirila C, Boni AG, Hrib L, et al. Polarization-control of the potential barrier at the electrode interfaces in epitaxial ferroelectric thin films. ACS

[40] Sze SM. Physics of Semiconductor Devices [Internet]. 2nd ed. John Wiley & Sons;

[41] Chirila C, Ibanescu G, Hrib L, Negrea R, Pasuk I, Kuncser V, et al. Structural, electric and

–CoFe2 O4

[42] Gutiérrez D, Foerster M, Fina I, Fontcuberta J, Fritsch D, Ederer C. Dielectric response of

Available from: https://archive.org/details/PhysicsOfSemiconductorDevices

buffer layer. Thin Solid Films. 2015;**593**:124-130

films grown on Si substrates

Electrical Properties of Epitaxial Ferroelectric Heterostructures

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heterostructures. Thin Solid Films. 2013

spinel thin films. Physical Review B. 2012 Sep 10;**86**(12):125309

controlled electrical properties in epitaxial Pb(Zr0.52Ti0.48)O<sup>3</sup>

Applied Material Interfaces. 2014 Feb 26;**6**(4):2929-2939

O4

magnetic properties of Pb(Zr0.2Ti0.8)O<sup>3</sup>

Feb;**70**(2):239-242

15;**98**(12):124103

with SrTiO<sup>3</sup>

Oct 31;**545**:2-7

epitaxially strained CoFe2


[35] Hartmann AJ, Neilson M, Lamb RN, Watanabe K, Scott JF. Ruthenium oxide and strontium ruthenate electrodes for ferroelectric thin-films capacitors. Applied Physics A. 2000 Feb;**70**(2):239-242

[22] Zhang J, Xu R, Damodaran AR, Chen Z-H, Martin LW. Understanding order in compositionally graded ferroelectrics: Flexoelectricity, gradient, and depolarization field effects.

[23] Crystal Growth Beginners - AbeBooks [Internet]. Available from: https://www.abebooks.

[24] Jaffe B, Cook WR, Jaffe H. In: Cook BJR, Jaffe H, editors. Piezoelectric Ceramics [Internet]. Academic Press; 1971. p. v. Available from: http://www.sciencedirect.com/science/

[25] Kim DM, Eom CB, Nagarajan V, Ouyang J, Ramesh R, Vaithyanathan V, et al. Thickness dependence of structural and piezoelectric properties of epitaxial Pb(Zr0.52,Ti0.48)O<sup>3</sup>

[26] Uchino Kenji. Piezoelectric Actuators and Ultrasonic Motors [Internet]. Springer; 1997.

[27] Noheda B, Gonzalo JA, Cross LE, Guo R, Park S-E, Cox DE, et al. Tetragonal-tomonoclinic phase transition in a ferroelectric perovskite: The structure of PbZr0.52Ti0.48O<sup>3</sup>

[28] Zhu Y, Yan P, Yi T, Cao L, Li L. Interface diffusion and chemical reaction on the interface

[29] Lin A, Hong X, Wood V, Verevkin AA, Ahn CH, McKee RA, et al. Epitaxial growth of

buffered oxidized Si substrates and its application to ferroelectric nonvolatile memory

on Si and its nanoscale piezoelectric properties. Applied Physics Letters.


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of a PZT film/Si(III) sample during annealing treatment in N2

[30] Basit NA, Kim HK, Blachere J. Growth of highly oriented Pb(Zr, Ti)O<sup>3</sup>

field-effect transistors. Applied Physics Letters. 1998 Dec 28;**73**(26):3941-3943

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[32] Wen-Chieh Shih, Pi-Chun Juan, and Joseph Ya-min Lee. Fabrication and characteriza-

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STO (100) substrates. Journal of Material Science. 2015 Mar 14;**50**(11):3883-3894

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article/pii/B9780123795502500041

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Pb(Zr0.2Ti0.8)O<sup>3</sup>

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the ferroelectric/electric properties of the PbZr0.52Ti0.48O<sup>3</sup>


**Chapter 4**

**Provisional chapter**

**Tm on W(110): A Growth Study by Scanning Tunneling**

Exploring bottom-up procedures to achieve island and particles with a defined size can open opportunities in many applications. This contribution focuses on the growth of epitaxial Tm islands, below the monolayer range, on the W(110) surface by studying in situ the diffusion process at high temperature, between 700 and 1200 K, by means of scanning tunnel microscopy (STM) to determine the topography of the Tm deposits as a function of the coverage and thermal treatments of an initial room temperature deposit. Samples subject to a prolonged heating process, spending several hours at temperatures below 700 K, show that the average Tm islands size remains constant at higher temperatures, in contrast with samples subject to a faster heating. It is observed that the presence of carbon strongly limits the diffusion of Tm, thus leading to the formation of pseudomorphic

**Keywords:** surface diffusion, scanning tunneling microscopy, rare earth nanostructures,

Growing rare earth (RE) on the (110) surface of bcc metals (Mo, W, or Nb) has been widely used to obtain layers with the basal plane of the rare earth on this film plane [1–5]. Although the (110)bcc and (0001)hcp surfaces do not match with each other and therefore, the concept of epitaxial growth is not applicable; it has proven to still be possible to prepare quite perfect superlattices and films. Historically, the preparation of rare earth artificial superlattices dates from 1985 [1], with the Gd-Y system showing a novel magnetic behavior that has been

**Tm on W(110): A Growth Study by Scanning Tunneling** 

DOI: 10.5772/intechopen.70218

© 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution,

© 2018 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

and reproduction in any medium, provided the original work is properly cited.

David Coffey, José I. Arnaudas, David Serrate and

David Coffey, José I. Arnaudas, David Serrate

Additional information is available at the end of the chapter

nanometric islands instead of a full monolayer.

nucleation, self-organization

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/intechopen.70218

**Microscopy**

and Miguel Ciria

**Abstract**

**1. Introduction**

**Microscopy**

Miguel Ciria

#### **Tm on W(110): A Growth Study by Scanning Tunneling Microscopy Tm on W(110): A Growth Study by Scanning Tunneling Microscopy**

DOI: 10.5772/intechopen.70218

David Coffey, José I. Arnaudas, David Serrate and Miguel Ciria David Coffey, José I. Arnaudas, David Serrate and Miguel Ciria

Additional information is available at the end of the chapter Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/intechopen.70218

#### **Abstract**

Exploring bottom-up procedures to achieve island and particles with a defined size can open opportunities in many applications. This contribution focuses on the growth of epitaxial Tm islands, below the monolayer range, on the W(110) surface by studying in situ the diffusion process at high temperature, between 700 and 1200 K, by means of scanning tunnel microscopy (STM) to determine the topography of the Tm deposits as a function of the coverage and thermal treatments of an initial room temperature deposit. Samples subject to a prolonged heating process, spending several hours at temperatures below 700 K, show that the average Tm islands size remains constant at higher temperatures, in contrast with samples subject to a faster heating. It is observed that the presence of carbon strongly limits the diffusion of Tm, thus leading to the formation of pseudomorphic nanometric islands instead of a full monolayer.

**Keywords:** surface diffusion, scanning tunneling microscopy, rare earth nanostructures, nucleation, self-organization

## **1. Introduction**

Growing rare earth (RE) on the (110) surface of bcc metals (Mo, W, or Nb) has been widely used to obtain layers with the basal plane of the rare earth on this film plane [1–5]. Although the (110)bcc and (0001)hcp surfaces do not match with each other and therefore, the concept of epitaxial growth is not applicable; it has proven to still be possible to prepare quite perfect superlattices and films. Historically, the preparation of rare earth artificial superlattices dates from 1985 [1], with the Gd-Y system showing a novel magnetic behavior that has been

and reproduction in any medium, provided the original work is properly cited.

© 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, © 2018 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

relevant in the history of nanostructured magnetic materials, as it was the first observation of antiferromagnetic coupling between ferromagnetic blocks occurring through a nonmagnetic spacer [4].

full monolayer is first formed on which subsequent pyramidal multilayer islands are able to grow. The study presented here is focused on the sub-monolayer regime and its evolution with temperature treatments. It is shown that the size of the islands can be controlled by the density of impurities on the W(110) surface, which diffuses from the bulk to the surface over

Tm on W(110): A Growth Study by Scanning Tunneling Microscopy

http://dx.doi.org/10.5772/intechopen.70218

95

The scanning tunneling microscope (STM) is a lensless microscope, able to bypass the diffraction limits imposed by the finite numerical aperture and wavelength, where the image is reconstructed by measuring a pointwise matrix of the interaction between the sample and a probe; the probe consists of a very sharp wire, which, when brought close enough to a metallic surface, conducts via quantum tunneling [14, 15]. By moving this probe along the surface, the variation of the tunnel current provides information of the local density of states (LDOS) at the surface of the sample, therefore making STM strictly a surface technique. Due to the exponential dependence of quantum tunneling with the width of the barrier, STM is extremely sensitive to features at the atomic scale, which goes hand in hand with the weakness of being very vulnerable to contamination at said scale. To reduce the exposure of samples to unwanted molecules, experiments are typically performed in ultra high vacuum conditions (UHV, *P* ≤ 10−10 mbar), maintaining vacuum unbroken along the whole experimental process, from sample preparation to STM measurements.

The STM used in this work is a SPECS Aarhus HT-STM [16], which can operate over a wide range of temperatures, 90–1300 K. A large copper block surrounds the sample acting as both temperature reservoir and damping mass to reduce vibrations. High temperatures are obtained by thermal radiation from a W filament that can be approached to the back of the sample. The STM systems are equipped with a Nanonis SPM control system for data acquisition and interfacing with the microscopes. Data treatment and analysis are performed using

STM tips are prepared by electrochemically etching a W wire in a NaOH solution. The wire is positioned through a small flat ring where a drip of the solution is placed, forming a thin layer by surface tension, minimizing the length of the wire exposed to etching which provides

The preparation of a clean W(110) surface is procedurally less complicated than other surfaces, but more demanding in the design of the heating stage and sample holder, as they involve materials such as W or Mo which are difficult to machine, but able to withstand tem-

time at high temperatures.

**2. Experimental details**

**2.1. Scanning tunneling microscopy**

WSxM [17] and Gwyddion [18].

**2.2. Preparation of Tm/W(110)**

*2.2.1. Cleaning and carbon contamination of the W(110)*

for a more robust tip.

peratures above 2300 K.

The (110) surface of W offers the opportunity of studying the magnetic behavior of ordered RE overlayers on top of a conductive but nonmagnetic substrate. In general, the body-centered cubic crystals of refractory metals such as W and Mo promote the two-dimensional layer growth of RE with no intermixing [6–8] with the (110) surface, yielding morphologies with low corrugation.

Thulium represents an interesting case, since it is the only heavy RE which orders magnetically along the *c* axis of the bulk hcp crystal structure. Between the Néel temperature, *T*N = 58, and 40 K, the magnetic moments are ferromagnetically ordered within the hcp basal-plane layers and have an incommensurate sinusoidal modulation along the *c* axis. The easy axis is parallel to the *c* axis, owing to the strong crystal-field anisotropy. Upon decreasing the temperature, the propagation wave number along the *c* axis increases, and below ~30 K, a ferrimagnetic structure with a sevenlayer repeat distance develops: the magnetic moments point up along the *c* axis in three layers and down in the consecutive four layers [9, 10]. As the reduction of thickness along the *c* axis could drastically influence the magnetic behavior of Tm, it is interesting to investigate the limit case of one atomic layer. Thulium grows heteroepitaxially on the W(110) surface, with the [1010] direction of the Tm layer along the [110] direction of the (110) substrate, similar to the Nishiyama-Wasserman orientation (see **Figure 1**) observed in other RE/W(110) systems [11, 12].

In nanostructured systems, there exists a strong relation between the magnetic properties of the nanostructure and its crystalline configuration and size, both being controllable by the preparation procedure. Tm on W(110) presents a large variety of morphologies depending on the coverage and thermal treatment after deposition, ranging from single atoms and clusters, to nanowires, to crystalline hexagonal monolayer islands for coverages below the monolayer and a hexagonal pyramidal Stranski-Krastanov growth for a multilayer coverage, where a

**Figure 1.** Nishiyama-Waserman orientation relationship for a closed-packed fcc or hcp overlayer (right) on a bcc (110) surface (left). The Miller indices of the directions in the overlayer are those appropriate for an fcc structure. Adapted from [13].

full monolayer is first formed on which subsequent pyramidal multilayer islands are able to grow. The study presented here is focused on the sub-monolayer regime and its evolution with temperature treatments. It is shown that the size of the islands can be controlled by the density of impurities on the W(110) surface, which diffuses from the bulk to the surface over time at high temperatures.

## **2. Experimental details**

relevant in the history of nanostructured magnetic materials, as it was the first observation of antiferromagnetic coupling between ferromagnetic blocks occurring through a nonmagnetic

The (110) surface of W offers the opportunity of studying the magnetic behavior of ordered RE overlayers on top of a conductive but nonmagnetic substrate. In general, the body-centered cubic crystals of refractory metals such as W and Mo promote the two-dimensional layer growth of RE with no intermixing [6–8] with the (110) surface, yielding morphologies with low corrugation. Thulium represents an interesting case, since it is the only heavy RE which orders magnetically along the *c* axis of the bulk hcp crystal structure. Between the Néel temperature, *T*N = 58, and 40 K, the magnetic moments are ferromagnetically ordered within the hcp basal-plane layers and have an incommensurate sinusoidal modulation along the *c* axis. The easy axis is parallel to the *c* axis, owing to the strong crystal-field anisotropy. Upon decreasing the temperature, the propagation wave number along the *c* axis increases, and below ~30 K, a ferrimagnetic structure with a sevenlayer repeat distance develops: the magnetic moments point up along the *c* axis in three layers and down in the consecutive four layers [9, 10]. As the reduction of thickness along the *c* axis could drastically influence the magnetic behavior of Tm, it is interesting to investigate the limit case of one atomic layer. Thulium grows heteroepitaxially on the W(110) surface, with the [1010] direction of the Tm layer along the [110] direction of the (110) substrate, similar to the Nishiyama-

Wasserman orientation (see **Figure 1**) observed in other RE/W(110) systems [11, 12].

In nanostructured systems, there exists a strong relation between the magnetic properties of the nanostructure and its crystalline configuration and size, both being controllable by the preparation procedure. Tm on W(110) presents a large variety of morphologies depending on the coverage and thermal treatment after deposition, ranging from single atoms and clusters, to nanowires, to crystalline hexagonal monolayer islands for coverages below the monolayer and a hexagonal pyramidal Stranski-Krastanov growth for a multilayer coverage, where a

**Figure 1.** Nishiyama-Waserman orientation relationship for a closed-packed fcc or hcp overlayer (right) on a bcc (110) surface (left). The Miller indices of the directions in the overlayer are those appropriate for an fcc structure. Adapted

spacer [4].

94 Epitaxy

from [13].

#### **2.1. Scanning tunneling microscopy**

The scanning tunneling microscope (STM) is a lensless microscope, able to bypass the diffraction limits imposed by the finite numerical aperture and wavelength, where the image is reconstructed by measuring a pointwise matrix of the interaction between the sample and a probe; the probe consists of a very sharp wire, which, when brought close enough to a metallic surface, conducts via quantum tunneling [14, 15]. By moving this probe along the surface, the variation of the tunnel current provides information of the local density of states (LDOS) at the surface of the sample, therefore making STM strictly a surface technique. Due to the exponential dependence of quantum tunneling with the width of the barrier, STM is extremely sensitive to features at the atomic scale, which goes hand in hand with the weakness of being very vulnerable to contamination at said scale. To reduce the exposure of samples to unwanted molecules, experiments are typically performed in ultra high vacuum conditions (UHV, *P* ≤ 10−10 mbar), maintaining vacuum unbroken along the whole experimental process, from sample preparation to STM measurements.

The STM used in this work is a SPECS Aarhus HT-STM [16], which can operate over a wide range of temperatures, 90–1300 K. A large copper block surrounds the sample acting as both temperature reservoir and damping mass to reduce vibrations. High temperatures are obtained by thermal radiation from a W filament that can be approached to the back of the sample. The STM systems are equipped with a Nanonis SPM control system for data acquisition and interfacing with the microscopes. Data treatment and analysis are performed using WSxM [17] and Gwyddion [18].

STM tips are prepared by electrochemically etching a W wire in a NaOH solution. The wire is positioned through a small flat ring where a drip of the solution is placed, forming a thin layer by surface tension, minimizing the length of the wire exposed to etching which provides for a more robust tip.

## **2.2. Preparation of Tm/W(110)**

#### *2.2.1. Cleaning and carbon contamination of the W(110)*

The preparation of a clean W(110) surface is procedurally less complicated than other surfaces, but more demanding in the design of the heating stage and sample holder, as they involve materials such as W or Mo which are difficult to machine, but able to withstand temperatures above 2300 K.

The main contaminant in a tungsten single crystal is carbon, which is dissolved in the bulk and diffuses to the surface over time. The procedure to remove said C, described in [19], consists in annealing cycles in an oxygen-rich atmosphere (*T* ~ 1500 K, *P*02 ~ 5 × 10−7 to 1 × 10−8 mbar) which causes the C adsorbates to react with the oxygen, forming CO molecules that can desorb from the surface. The second step in the procedure is to perform a short, high temperature flash of the sample (*T* > 2300 K) which removes atomic oxygen adsorbates and other remaining impurities from the sample. By performing several annealing-flash cycles, until the flashes do not produce a significant pressure spike (*P*Flash ≤ 1 × 10−10 mbar), a high quality clean surface is obtained. An STM image of a clean W(110) surface is shown in **Figure 2a**, with 34 adsorbates in a 40 × 40 nm2 area, a ~0.3% of a monolayer. Carbon adsorbates appear as depressions on the surface, as they present a lower LDOS. To the right, **Figure 2b**, the LEED pattern corresponding to the clean surface is shown, where the rectangular lattice of the W(110) surface results in clear and well-defined spots; the [110] and [001] directions are indicated by lines.

As with any diffusion process, the rate at which C reaches the surface is strongly related to the temperature of the crystal, which during the experiments performed in this chapter is in the 700 to 1200 K range for hours at a time, strongly enhancing the C segregation. This produces a change in the quality of the surface over time, affecting the growth of Tm structures. Understanding how the surface evolves as C contamination grows is therefore important for high temperature experiments. Locally, carbon reconstruction patches will start to form where the adsorbate density is high enough; over time, the carbon reconstruction will cover the whole surface. An STM image of said reconstruction is shown in **Figure 3** accompanied by the corresponding LEED pattern showing the 15 × 3 relation [20].

capabilities of this and other area analysis techniques (such as Auger), and STM characterization is required to ensure an adequate surface for experiments sensitive to even low densities

= 1 nA. (b) Corresponding

Tm on W(110): A Growth Study by Scanning Tunneling Microscopy

http://dx.doi.org/10.5772/intechopen.70218

97

**Figure 3.** (a) STM image of the Carbon reconstruction on W(110) taken at *V*Bias = 100 mV, *I*<sup>t</sup>

Evaporation of Tm has been performed by using an electron beam evaporator. The e-beam heats a molybdenum crucible where the evaporant material is located in the form of flakes, obtaining a rate near 1 ML/min, as measured by a fluxmeter at the exit of the evaporator, where the current is proportional to the number of ions crossing the fluxmeter section per

**Figure 4a** presents an STM image, taken at 4.2 K in a low temperature instrument, of the Tm ML along with the corresponding LEED pattern in **Figure 4d**, illustrating the situation. The STM image on the left, **Figure 4a**, shows a quasi-hexagonal symmetry on the Tm layer which should be noted is not atomic resolution, but rather a Moiré pattern caused by the overlap of the triangular Tm lattice and the rectangular W(110) surface, shown in greater detail in **Figure 4b**; the actual atomic resolution of the Tm layer can be seen in **Figure 4c**. The LEED pattern in **Figure 4d** presents the spots due the W(110) seen in **Figure 2b** and an added quasihexagonal structure corresponding to the Tm layer; satellite points forming an hexagon sur-

The lattice parameter measured along [001] is 4.08 Å, while the two other sides of the isosceles triangle measure 3.92 Å. This means that the Tm ML displays a fairly distorted hexagonal structure, forming in fact a rhombic or isosceles triangular lattice. Thus, the lattice mismatch between Tm and W is large enough to produce in the first monolayer of thulium, an asymmetric distortion of the hcp structure that, with respect to the bulk lattice parameters, is compressed along the [110] W by 1% and expanded along [001] W by about 15%; the W lattice

of impurities.

unit of time.

*2.2.2. Evaporation of Tm*

LEED pattern illustrating the 15 × 3 reconstruction.

**2.3. Tm monolayer: structural characterization**

rounding the Tm spots are due to the Moiré pattern.

While LEED measurements are able to distinguish between the two situations presented in **Figures 2** and **3**, quantifying the non-reconstructed adsorbate density is beyond the

**Figure 2.** (a) STM image of a clean W(110) surface taken at *V*Bias = 100 mV, *I*<sup>t</sup> = 1 nA. Carbon adsorbates appear as dark spots around and serve as scatter centers for the surface state, which is clearly visible around them. (b) LEED pattern corresponding to the clean W(110) surface, with the [110] and [001] directions indicated by lines.

**Figure 3.** (a) STM image of the Carbon reconstruction on W(110) taken at *V*Bias = 100 mV, *I*<sup>t</sup> = 1 nA. (b) Corresponding LEED pattern illustrating the 15 × 3 reconstruction.

capabilities of this and other area analysis techniques (such as Auger), and STM characterization is required to ensure an adequate surface for experiments sensitive to even low densities of impurities.

#### *2.2.2. Evaporation of Tm*

The main contaminant in a tungsten single crystal is carbon, which is dissolved in the bulk and diffuses to the surface over time. The procedure to remove said C, described in [19], consists in annealing cycles in an oxygen-rich atmosphere (*T* ~ 1500 K, *P*02 ~ 5 × 10−7 to 1 × 10−8 mbar) which causes the C adsorbates to react with the oxygen, forming CO molecules that can desorb from the surface. The second step in the procedure is to perform a short, high temperature flash of the sample (*T* > 2300 K) which removes atomic oxygen adsorbates and other remaining impurities from the sample. By performing several annealing-flash cycles, until the flashes do not produce a significant pressure spike (*P*Flash ≤ 1 × 10−10 mbar), a high quality clean surface is obtained. An STM image of a clean W(110) surface is shown in **Figure 2a**, with 34 adsorbates

surface, as they present a lower LDOS. To the right, **Figure 2b**, the LEED pattern corresponding to the clean surface is shown, where the rectangular lattice of the W(110) surface results in

As with any diffusion process, the rate at which C reaches the surface is strongly related to the temperature of the crystal, which during the experiments performed in this chapter is in the 700 to 1200 K range for hours at a time, strongly enhancing the C segregation. This produces a change in the quality of the surface over time, affecting the growth of Tm structures. Understanding how the surface evolves as C contamination grows is therefore important for high temperature experiments. Locally, carbon reconstruction patches will start to form where the adsorbate density is high enough; over time, the carbon reconstruction will cover the whole surface. An STM image of said reconstruction is shown in **Figure 3** accompanied by

While LEED measurements are able to distinguish between the two situations presented in **Figures 2** and **3**, quantifying the non-reconstructed adsorbate density is beyond the

spots around and serve as scatter centers for the surface state, which is clearly visible around them. (b) LEED pattern

= 1 nA. Carbon adsorbates appear as dark

clear and well-defined spots; the [110] and [001] directions are indicated by lines.

the corresponding LEED pattern showing the 15 × 3 relation [20].

**Figure 2.** (a) STM image of a clean W(110) surface taken at *V*Bias = 100 mV, *I*<sup>t</sup>

corresponding to the clean W(110) surface, with the [110] and [001] directions indicated by lines.

area, a ~0.3% of a monolayer. Carbon adsorbates appear as depressions on the

in a 40 × 40 nm2

96 Epitaxy

Evaporation of Tm has been performed by using an electron beam evaporator. The e-beam heats a molybdenum crucible where the evaporant material is located in the form of flakes, obtaining a rate near 1 ML/min, as measured by a fluxmeter at the exit of the evaporator, where the current is proportional to the number of ions crossing the fluxmeter section per unit of time.

#### **2.3. Tm monolayer: structural characterization**

**Figure 4a** presents an STM image, taken at 4.2 K in a low temperature instrument, of the Tm ML along with the corresponding LEED pattern in **Figure 4d**, illustrating the situation. The STM image on the left, **Figure 4a**, shows a quasi-hexagonal symmetry on the Tm layer which should be noted is not atomic resolution, but rather a Moiré pattern caused by the overlap of the triangular Tm lattice and the rectangular W(110) surface, shown in greater detail in **Figure 4b**; the actual atomic resolution of the Tm layer can be seen in **Figure 4c**. The LEED pattern in **Figure 4d** presents the spots due the W(110) seen in **Figure 2b** and an added quasihexagonal structure corresponding to the Tm layer; satellite points forming an hexagon surrounding the Tm spots are due to the Moiré pattern.

The lattice parameter measured along [001] is 4.08 Å, while the two other sides of the isosceles triangle measure 3.92 Å. This means that the Tm ML displays a fairly distorted hexagonal structure, forming in fact a rhombic or isosceles triangular lattice. Thus, the lattice mismatch between Tm and W is large enough to produce in the first monolayer of thulium, an asymmetric distortion of the hcp structure that, with respect to the bulk lattice parameters, is compressed along the [110] W by 1% and expanded along [001] W by about 15%; the W lattice

Increasing the temperature of the sample to *T* = 700 K facilitates diffusion, resulting in migration of Tm to the step edges, as well as aggregation into small islands (**Figure 5b**). It should be noted that changes in the configuration of the sample occur in a time window smaller than the thermalization time required by the system, as no strong evolution is observed at this

temperature *T*). Increasing the temperature above 900 K produces a notable change in the configuration, as Tm structures acquire visible hexagonal characteristics. **Figure 5c** shows the resulting sample at this temperature, where all Tm have migrated to the step edges forming a

In contrast to the previous example, a strikingly different behavior is observed for a similar starting coverage if the heating process is altered. **Figure 6a** shows the sample as deposited at room temperature, and while the coverage is roughly 1.5–2.0 times that of **Figure 5a**, it is still

In order to try and capture the diffusion process, longer time periods are spent measuring this sample at lower temperatures (600, 650, and 700 K), without observing any significant change at any given temperature, pointing to an equilibrium for the island size that is reached in the first few minutes after increasing the temperature, before the drift is low enough to allow STM measurements. Increasing the time spent at lower temperatures, however, does have a significant effect regarding the presence of C on the surface, which is much more evident in **Figure 6b** than for an equivalent temperature (730 K) reached in a shorter time, as in **Figure 5b**; the other difference between the two images is that in this case, Tm does not migrate to the step edge or form larger islands, as the diffusion process is inhibited by the

The difference in behavior is stronger as the temperature is increased as the large, regular islands with hexagonal characteristics, where all the Tm accumulates leaving free the majority of the tungsten surface are nowhere to be seen; instead, small irregular islands are distributed

**Figure 6.** Tm/W(110) sample with a low Tm coverage (a) at RT, as deposited, (b) at 730 K after 4 h in the 600 to 730 K range, causing a high density of C adsorbates on the tungsten surface and (c) at 1100 K, after 3 h in the 750–1100 K range,

T is the time *t* that the sample has been at a given

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<sup>700</sup> K = 10 to 30 min (where *t*

presence of a large quantity of carbon adsorbates.

showing the surface covered in carbon reconstruction patches.

wire along the edge that expands into islands with sharp hexagonal angles.

low enough for it to consist in small clusters as well as some atom-like objects.

temperature from *t*

**Figure 4.** (a) STM image of a Tm/W(110) sample showing the Tm monolayer on W(110); the clean W surface can be seen to the sides of the Tm layer. (b) Detail of the Moiré pattern of the Tm monolayer and (c) detail of the underlying atomic resolution. (d) LEED pattern corresponding to the Tm monolayer on W(110) showing the spots corresponding to the crystalline structure surrounded by satellites corresponding to the Moiré pattern.

parameter is slightly enlarged respect to the bulk, with *a*W = 3.173 Å. This results in a Tm: W coincidence match of 2:3 and 7:9 along the [110] and [001] W directions, respectively.

## **3. Experimental results**

#### **3.1. Low coverage: single atoms and clusters**

One of the peculiarities of this system is that for low coverages, even at room temperature, single atoms and small clusters present a very low diffusion and do not aggregate into larger objects until higher temperatures, as illustrated by **Figure 5a**.

**Figure 5.** Tm/W(110) sample with a low Tm coverage (a) at RT, as deposited, (b) at 700 K after 4 h in the 550–700 K range, causing a high density of C adsorbates on the tungsten surface and (c) at 900 K, after 3 additional hours in the 700–900 K range, showing the surface covered in carbon reconstruction patches.

Increasing the temperature of the sample to *T* = 700 K facilitates diffusion, resulting in migration of Tm to the step edges, as well as aggregation into small islands (**Figure 5b**). It should be noted that changes in the configuration of the sample occur in a time window smaller than the thermalization time required by the system, as no strong evolution is observed at this temperature from *t* <sup>700</sup> K = 10 to 30 min (where *t* T is the time *t* that the sample has been at a given temperature *T*). Increasing the temperature above 900 K produces a notable change in the configuration, as Tm structures acquire visible hexagonal characteristics. **Figure 5c** shows the resulting sample at this temperature, where all Tm have migrated to the step edges forming a wire along the edge that expands into islands with sharp hexagonal angles.

In contrast to the previous example, a strikingly different behavior is observed for a similar starting coverage if the heating process is altered. **Figure 6a** shows the sample as deposited at room temperature, and while the coverage is roughly 1.5–2.0 times that of **Figure 5a**, it is still low enough for it to consist in small clusters as well as some atom-like objects.

In order to try and capture the diffusion process, longer time periods are spent measuring this sample at lower temperatures (600, 650, and 700 K), without observing any significant change at any given temperature, pointing to an equilibrium for the island size that is reached in the first few minutes after increasing the temperature, before the drift is low enough to allow STM measurements. Increasing the time spent at lower temperatures, however, does have a significant effect regarding the presence of C on the surface, which is much more evident in **Figure 6b** than for an equivalent temperature (730 K) reached in a shorter time, as in **Figure 5b**; the other difference between the two images is that in this case, Tm does not migrate to the step edge or form larger islands, as the diffusion process is inhibited by the presence of a large quantity of carbon adsorbates.

parameter is slightly enlarged respect to the bulk, with *a*W = 3.173 Å. This results in a Tm: W

**Figure 4.** (a) STM image of a Tm/W(110) sample showing the Tm monolayer on W(110); the clean W surface can be seen to the sides of the Tm layer. (b) Detail of the Moiré pattern of the Tm monolayer and (c) detail of the underlying atomic resolution. (d) LEED pattern corresponding to the Tm monolayer on W(110) showing the spots corresponding to the

One of the peculiarities of this system is that for low coverages, even at room temperature, single atoms and small clusters present a very low diffusion and do not aggregate into larger

**Figure 5.** Tm/W(110) sample with a low Tm coverage (a) at RT, as deposited, (b) at 700 K after 4 h in the 550–700 K range, causing a high density of C adsorbates on the tungsten surface and (c) at 900 K, after 3 additional hours in the 700–900 K

coincidence match of 2:3 and 7:9 along the [110] and [001] W directions, respectively.

**3. Experimental results**

98 Epitaxy

**3.1. Low coverage: single atoms and clusters**

objects until higher temperatures, as illustrated by **Figure 5a**.

crystalline structure surrounded by satellites corresponding to the Moiré pattern.

range, showing the surface covered in carbon reconstruction patches.

The difference in behavior is stronger as the temperature is increased as the large, regular islands with hexagonal characteristics, where all the Tm accumulates leaving free the majority of the tungsten surface are nowhere to be seen; instead, small irregular islands are distributed

**Figure 6.** Tm/W(110) sample with a low Tm coverage (a) at RT, as deposited, (b) at 730 K after 4 h in the 600 to 730 K range, causing a high density of C adsorbates on the tungsten surface and (c) at 1100 K, after 3 h in the 750–1100 K range, showing the surface covered in carbon reconstruction patches.

along the surface with multiple carbon reconstruction patches covering the rest of the tungsten. **Figure 6c** shows this behavior, including double-layer islands due to the constraints imposed by the growing carbon reconstruction, even after increasing the temperature up to 1100 K.

#### **3.2. Mid coverage: 0.5 monolayers**

At higher coverages, Tm still does not tend to aggregate into a single continuous layer but rather tends to form small objects a few nanometers wide (**Figure 7a**) which, when annealed at temperatures around 600 K, evolve into small flat islands (**Figure 7b**). Following a slow heating process, as done for lower coverages, produces a similar behavior: the segregation of carbon is strongly enhanced which favors the formation of large patches of carbon reconstruction, inhibiting the diffusion of Tm and thus limiting the size of the islands; with the island size constrained by carbon, increasing the temperature up to 950 K induces a structural change where the islands become regular in shape, with hexagonal features, but without merging into large patches, but rather staying mainly as 10–15 nm wide individual islands.

It is not until the coverage is near the full monolayer that Tm does, in fact, aggregate rather than forming smaller individual objects. In this state, Tm presents a high corrugation and an irregular appearance, as seen in **Figure 8a**. Increasing the temperature to 780 K favors the mobility of Tm, allowing for the formation of a smoother but still irregular layer with a more compact structure, as shown by the fact that the tungsten surface is clearly visible in **Figure 8b** and that maintaining the sample at this temperature does not increase the proportion of visible tungsten, therefore discarding reevaporation of Tm as the cause of the observed decrease in coverage. As for the case of low coverage shown in **Figure 5**, at temperatures around 950 K, the Tm layer forms a hexagonal structure a single atomic layer in height, although in the form of large patches in this case (pictured in **Figure 8c**), as performing a faster annealing process conserves a surface clean enough for the Tm to diffuse all along the step edges, leaving the rest of the W step free of smaller Tm objects.

The evolution of the system as seen in **Figure 8** can actually be monitored by STM, as it changes in a scale of minutes. **Figure 9** shows the same area of the course of 30 min at *T* = 780 K, showing a dynamic behavior. The evolution pictured occurs 40 min after setting the temperature

set point; some self-assembled nanowires can be seen in the first images, although the overwhelming majority of Tm is forming irregular-shaped islands. Over time, the islands expand, approaching the full monolayer and covering the wire structures. As no new material is added during this time, the increase in surface covered by the Tm islands is due to the system evolving to a new, less compact configuration. At higher temperatures, this is then followed by a

**Figure 9.** From left to right, top to bottom: Evolution over 30 min of the sample at 750 K. Thulium islands expand,

covering the whole surface.

**Figure 8.** Tm/W(110) sample with a coverage around 0.5 ML coverage (a) as deposited at RT (b) at 750 K and (c) at 950 K. Islands change from irregular and rough in (b) to the crystalline with a Moiré pattern (c) for higher temperatures.

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structural change into a more compact hexagonal lattice, as seen from **Figure 8b** and **c**.

**Figure 7.** Tm/W(110) sample with coverage near 0.5 ML (a) at RT, as deposited, in the form of irregular islands (b) at 750 K showing flatter, but still irregular islands and (c) at 950 K, where the diffusion is limited by the presence of C reconstruction patches and Tm takes the form small islands with hexagonal features.

along the surface with multiple carbon reconstruction patches covering the rest of the tungsten. **Figure 6c** shows this behavior, including double-layer islands due to the constraints imposed by the growing carbon reconstruction, even after increasing the temperature up to 1100 K.

At higher coverages, Tm still does not tend to aggregate into a single continuous layer but rather tends to form small objects a few nanometers wide (**Figure 7a**) which, when annealed at temperatures around 600 K, evolve into small flat islands (**Figure 7b**). Following a slow heating process, as done for lower coverages, produces a similar behavior: the segregation of carbon is strongly enhanced which favors the formation of large patches of carbon reconstruction, inhibiting the diffusion of Tm and thus limiting the size of the islands; with the island size constrained by carbon, increasing the temperature up to 950 K induces a structural change where the islands become regular in shape, with hexagonal features, but without merging into large patches, but rather staying mainly as 10–15 nm wide individual islands. It is not until the coverage is near the full monolayer that Tm does, in fact, aggregate rather than forming smaller individual objects. In this state, Tm presents a high corrugation and an irregular appearance, as seen in **Figure 8a**. Increasing the temperature to 780 K favors the mobility of Tm, allowing for the formation of a smoother but still irregular layer with a more compact structure, as shown by the fact that the tungsten surface is clearly visible in **Figure 8b** and that maintaining the sample at this temperature does not increase the proportion of visible tungsten, therefore discarding reevaporation of Tm as the cause of the observed decrease in coverage. As for the case of low coverage shown in **Figure 5**, at temperatures around 950 K, the Tm layer forms a hexagonal structure a single atomic layer in height, although in the form of large patches in this case (pictured in **Figure 8c**), as performing a faster annealing process conserves a surface clean enough for the Tm to diffuse all along the step edges, leaving the rest of the W step free of smaller Tm objects. The evolution of the system as seen in **Figure 8** can actually be monitored by STM, as it changes in a scale of minutes. **Figure 9** shows the same area of the course of 30 min at *T* = 780 K, showing a dynamic behavior. The evolution pictured occurs 40 min after setting the temperature

**Figure 7.** Tm/W(110) sample with coverage near 0.5 ML (a) at RT, as deposited, in the form of irregular islands (b) at 750 K showing flatter, but still irregular islands and (c) at 950 K, where the diffusion is limited by the presence of C

reconstruction patches and Tm takes the form small islands with hexagonal features.

**3.2. Mid coverage: 0.5 monolayers**

100 Epitaxy

**Figure 8.** Tm/W(110) sample with a coverage around 0.5 ML coverage (a) as deposited at RT (b) at 750 K and (c) at 950 K. Islands change from irregular and rough in (b) to the crystalline with a Moiré pattern (c) for higher temperatures.

**Figure 9.** From left to right, top to bottom: Evolution over 30 min of the sample at 750 K. Thulium islands expand, covering the whole surface.

set point; some self-assembled nanowires can be seen in the first images, although the overwhelming majority of Tm is forming irregular-shaped islands. Over time, the islands expand, approaching the full monolayer and covering the wire structures. As no new material is added during this time, the increase in surface covered by the Tm islands is due to the system evolving to a new, less compact configuration. At higher temperatures, this is then followed by a structural change into a more compact hexagonal lattice, as seen from **Figure 8b** and **c**.

#### **3.3. High coverage: above 1 monolayer**

For higher initial coverages, above the monolayer, the Stranski-Krastanov growth mode is evident, with Tm forming multiple-layer high hexagonal pyramids in **Figure 10a**. Annealing this sample illustrates the origin of this growth mode: the W-Tm interface is energetically more favorable than the Tm-Tm interface; therefore, completion of the initial wetting layer takes priority over subsequent layers, as illustrated by the fact that the said higher Tm layers are reevaporated at lower temperatures than the wetting layer. Thus, annealing at high temperature, a multilayer sample, such as **Figure 10a**, leads to a similar result as for submonolayer samples, with the already discussed heteroepitaxial monolayer with a Moiré pattern, pictured in **Figure 10b**.

At high temperatures, carbon segregation to the surface is fast enough to observe its effect over consecutive scans. **Figure 11** shows the same area of the Tm monolayer at 1000 K over the course of 5 min. The small dark patch in **Figure 11a** is an area with carbon reconstruction which grows over time, while other small patch appears (**Figure 11b**), eventually merging with each other, forming a larger area of carbon reconstruction along the step edge. The growth of the carbon reconstruction patches displaces Tm from the layer, rather than growing below it, as it can be seen in **Figure 11b** and **c**: small areas on the Tm layer with a greyer color appear to have carbon beneath, while a darker area, similar in hue to the reconstruction along the step edge, seems to have displaced the Tm layer.

This effect is also seen on other samples, as shown in **Figure 12**, while the time evolution is not captured, it can be seen that Tm is displaced by the carbon reconstruction onto the second layer in **Figure 12a**, and 30 min later in **Figure 12b**, the Tm layer is flat once again, with Tm organized along to the step edge and carbon adsorbates and reconstruction patches on the outer side of the step. As the coverage is lower than the initial, it suggests a reevaporation at this temperature of the material that moves onto the second layer.

In this case, the carbon reconstruction patches within the layer have grown to the point where it is favorable for Tm to move to the second layer. Over time, this Tm is reevaporated reducing the total coverage, while the remaining material reorganizes forming a continuous layer with the carbon reconstruction patches along the step edges.

**Figure 10.** (a) Multilayer Thulium sample as deposited at room temperature showing hexagonal pyramidal islands. (b) After annealing at 1100 K, leaving only monolayer Tm islands on the W(110) surface; carbon reconstruction patches can also be seen.

**4. Analysis**

step edge.

**4.1. Size distribution of Tm islands**

To study the effect of carbon adsorbates on the diffusion of Tm on the W(110) surface and thus on the resulting island size, it is interesting to first introduce the basic ideas involved in

**Figure 12.** (a) Tm being displaced by carbon reconstruction patches at 1050 K. (b) The same sample 30 min later while keeping the temperature at 1050 K, showing that Tm has compensated for the displaced material by migrating to the

**Figure 11.** Evolution over 5 min of the sample at 1000 K, showing the growth of a carbon reconstruction patch, displacing

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the Tm layer: (a) At eh beginning, (b) the time between and (c) at the end of the sequence.

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**Figure 11.** Evolution over 5 min of the sample at 1000 K, showing the growth of a carbon reconstruction patch, displacing the Tm layer: (a) At eh beginning, (b) the time between and (c) at the end of the sequence.

**Figure 12.** (a) Tm being displaced by carbon reconstruction patches at 1050 K. (b) The same sample 30 min later while keeping the temperature at 1050 K, showing that Tm has compensated for the displaced material by migrating to the step edge.

## **4. Analysis**

**3.3. High coverage: above 1 monolayer**

102 Epitaxy

the step edge, seems to have displaced the Tm layer.

this temperature of the material that moves onto the second layer.

the carbon reconstruction patches along the step edges.

also be seen.

For higher initial coverages, above the monolayer, the Stranski-Krastanov growth mode is evident, with Tm forming multiple-layer high hexagonal pyramids in **Figure 10a**. Annealing this sample illustrates the origin of this growth mode: the W-Tm interface is energetically more favorable than the Tm-Tm interface; therefore, completion of the initial wetting layer takes priority over subsequent layers, as illustrated by the fact that the said higher Tm layers are reevaporated at lower temperatures than the wetting layer. Thus, annealing at high temperature, a multilayer sample, such as **Figure 10a**, leads to a similar result as for submonolayer samples, with the already discussed heteroepitaxial monolayer with a Moiré pattern, pictured in **Figure 10b**.

At high temperatures, carbon segregation to the surface is fast enough to observe its effect over consecutive scans. **Figure 11** shows the same area of the Tm monolayer at 1000 K over the course of 5 min. The small dark patch in **Figure 11a** is an area with carbon reconstruction which grows over time, while other small patch appears (**Figure 11b**), eventually merging with each other, forming a larger area of carbon reconstruction along the step edge. The growth of the carbon reconstruction patches displaces Tm from the layer, rather than growing below it, as it can be seen in **Figure 11b** and **c**: small areas on the Tm layer with a greyer color appear to have carbon beneath, while a darker area, similar in hue to the reconstruction along

This effect is also seen on other samples, as shown in **Figure 12**, while the time evolution is not captured, it can be seen that Tm is displaced by the carbon reconstruction onto the second layer in **Figure 12a**, and 30 min later in **Figure 12b**, the Tm layer is flat once again, with Tm organized along to the step edge and carbon adsorbates and reconstruction patches on the outer side of the step. As the coverage is lower than the initial, it suggests a reevaporation at

In this case, the carbon reconstruction patches within the layer have grown to the point where it is favorable for Tm to move to the second layer. Over time, this Tm is reevaporated reducing the total coverage, while the remaining material reorganizes forming a continuous layer with

**Figure 10.** (a) Multilayer Thulium sample as deposited at room temperature showing hexagonal pyramidal islands. (b) After annealing at 1100 K, leaving only monolayer Tm islands on the W(110) surface; carbon reconstruction patches can

#### **4.1. Size distribution of Tm islands**

To study the effect of carbon adsorbates on the diffusion of Tm on the W(110) surface and thus on the resulting island size, it is interesting to first introduce the basic ideas involved in the description of nucleation on ideal surfaces, omitting the effect of impurities, anisotropies, steps, and other deviations from a perfect surface.

when *T* increases, and other factors as the crystal symmetry of the substrate and the structure

The mean-field nucleation theory has been used to obtain a simple expression for the concen-

*<sup>E</sup>* \_\_\_\_\_\_\_ *<sup>i</sup>*

is its bonding energy. A stable cluster means that it grows more rap-

(*<sup>i</sup>* <sup>+</sup> 2) *kB <sup>T</sup>*] (2)

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of 2-D islands of size *i* for the case of complete condensation [21, 22, 25]:

idly than it decays, for instance by a dissociation process, during the course of deposition.

While the discussion above pertains to the case of clusters with a small number of atoms, the dependence of the equilibrium island size with temperature is a general conclusion. **Figure 13** shows the island size evolution with temperature of a sample, where little carbon has segregated over the whole sequence, leading to a final island size that is actually limited by the step size, as seen in the lower section of **Figure 13**, illustrating the sample at different stages.

**Figure 13.** (a) Island size evolution with temperature. Below, from left to right, the evolution of the island size on the same sample at (b) room temperature, (c) 730 K and (d) 950 K. Note that the island size at high *T* is limited by the step

\_\_ *D <sup>F</sup>*) −*χ* exp[

of a film, either amorphous or crystalline.

*nx* ∝ (

**4.2. Influence of carbon adsorbates in island size**

*4.1.2. Mean field calculation*

where *χ = i*/(*i+2*), and *Ei*

tration *nx*

size.

Once an atom or molecule is absorbed onto a surface, it can be reevaporated or diffused along the surface. Adatoms diffusing on the surface can encounter each other leading to the formation of dimers, clusters, and larger two-dimensional islands. These islands, as a whole, are stable and do not diffuse further; their shape and size, however, can change by dissociation and diffusion of the adatoms on the edges.

Island nucleation and growth (precoalescence stage) continues until islands grow to the point of merging with each other. At this point, continued growth of the layer consists in the filling of the remaining holes (post-coalescence stage). Thus, at constant temperature, the number of islands increases over time until coalescence between them begins, reducing the total number of individual islands. For the case of three dimensional islands, if no additional material is deposited on top of the island, but rather there is a transference between layers, overcoming the Ehrlich-Schwoebel energy barrier associated with the interlayer jumping is required.

The behavior of single-component metallic systems is well understood, based on scaling properties of measured island densities and shapes as a function or temperature and covering. Several reviews present a thorough presentation of the state of the art [21, 22]. Usually, the diffusion process is presented in the context of a clean surface: only the adatoms and the surface are considered to obtain the relevant parameters [23]. In some cases of practical interest, the diffusion happens on surfaces partly covered by other impurities, and the diffusion is modified with respect to that observed in a clean surface, e.g., adsorbed hydrogen atoms enhances the self-diffusion of Pt by two orders of magnitude [24].

#### *4.1.1. Island density*

Two factors influence the nucleation and growth of islands: Deposition of atoms onto the surface with a flux *F* and thermally activated diffusion of adatoms along the surface with a diffusion coefficient *D*:

*D* = *D*<sup>0</sup> exp(-*U*/ *kB T*) (1)

where *U* is the diffusion barrier and *kB* the Boltzmann constant. For atomic systems, *D0 = νa<sup>2</sup>* , where *ν* is an attempt frequency, and *a* is the lattice constant of the substrate. Thus, with the definitions of *F* and *D*, the mean time for a unit cell to be hit by an atom is *1*/*Fa2* , and the mean time after which the atom leaves the cell by diffusion is *a2* /*D*. Some conclusions can be obtained observing Eq. (1): adatom diffusion is thermally activated, thus increasing temperature produces an increment of *D,* and adatoms can diffuse over longer distances. As a result, the density *N* of stable islands becomes smaller with increasing *T*, and the number of atoms forming the island increases.

In order to describe and quantify the structures observed by STM or AFM as function of coverage *Θ* or temperature, a complete set of equations has been obtained in the literature [21]. A fundamental concept is the critical island size or critical nucleus *i*. This variable denotes the critical cluster size, which becomes stable on adding an atom. Clusters with *i+1* atoms are more likely to grow than to dissociate. *i* depends on the substrate temperature, increasing when *T* increases, and other factors as the crystal symmetry of the substrate and the structure of a film, either amorphous or crystalline.

#### *4.1.2. Mean field calculation*

the description of nucleation on ideal surfaces, omitting the effect of impurities, anisotropies,

Once an atom or molecule is absorbed onto a surface, it can be reevaporated or diffused along the surface. Adatoms diffusing on the surface can encounter each other leading to the formation of dimers, clusters, and larger two-dimensional islands. These islands, as a whole, are stable and do not diffuse further; their shape and size, however, can change by dissociation

Island nucleation and growth (precoalescence stage) continues until islands grow to the point of merging with each other. At this point, continued growth of the layer consists in the filling of the remaining holes (post-coalescence stage). Thus, at constant temperature, the number of islands increases over time until coalescence between them begins, reducing the total number of individual islands. For the case of three dimensional islands, if no additional material is deposited on top of the island, but rather there is a transference between layers, overcoming the Ehrlich-Schwoebel energy barrier associated with the interlayer jumping is required.

The behavior of single-component metallic systems is well understood, based on scaling properties of measured island densities and shapes as a function or temperature and covering. Several reviews present a thorough presentation of the state of the art [21, 22]. Usually, the diffusion process is presented in the context of a clean surface: only the adatoms and the surface are considered to obtain the relevant parameters [23]. In some cases of practical interest, the diffusion happens on surfaces partly covered by other impurities, and the diffusion is modified with respect to that observed in a clean surface, e.g., adsorbed hydrogen atoms

Two factors influence the nucleation and growth of islands: Deposition of atoms onto the surface with a flux *F* and thermally activated diffusion of adatoms along the surface with a

*D* = *D*<sup>0</sup> exp(-*U*/ *kB T*) (1)

where *U* is the diffusion barrier and *kB* the Boltzmann constant. For atomic systems, *D0 = νa<sup>2</sup>*

where *ν* is an attempt frequency, and *a* is the lattice constant of the substrate. Thus, with the defi-

ing Eq. (1): adatom diffusion is thermally activated, thus increasing temperature produces an increment of *D,* and adatoms can diffuse over longer distances. As a result, the density *N* of stable islands becomes smaller with increasing *T*, and the number of atoms forming the island increases. In order to describe and quantify the structures observed by STM or AFM as function of coverage *Θ* or temperature, a complete set of equations has been obtained in the literature [21]. A fundamental concept is the critical island size or critical nucleus *i*. This variable denotes the critical cluster size, which becomes stable on adding an atom. Clusters with *i+1* atoms are more likely to grow than to dissociate. *i* depends on the substrate temperature, increasing

nitions of *F* and *D*, the mean time for a unit cell to be hit by an atom is *1*/*Fa2*

after which the atom leaves the cell by diffusion is *a2*

,

, and the mean time

/*D*. Some conclusions can be obtained observ-

enhances the self-diffusion of Pt by two orders of magnitude [24].

steps, and other deviations from a perfect surface.

and diffusion of the adatoms on the edges.

*4.1.1. Island density*

104 Epitaxy

diffusion coefficient *D*:

The mean-field nucleation theory has been used to obtain a simple expression for the concentration *nx* of 2-D islands of size *i* for the case of complete condensation [21, 22, 25]:

$$n\_x \propto \left(\frac{D}{F}\right)^{-\chi} \exp\left[\frac{E\_i}{(i+2)k\_yT}\right] \tag{2}$$

where *χ = i*/(*i+2*), and *Ei* is its bonding energy. A stable cluster means that it grows more rapidly than it decays, for instance by a dissociation process, during the course of deposition.

#### **4.2. Influence of carbon adsorbates in island size**

While the discussion above pertains to the case of clusters with a small number of atoms, the dependence of the equilibrium island size with temperature is a general conclusion. **Figure 13** shows the island size evolution with temperature of a sample, where little carbon has segregated over the whole sequence, leading to a final island size that is actually limited by the step size, as seen in the lower section of **Figure 13**, illustrating the sample at different stages.

**Figure 13.** (a) Island size evolution with temperature. Below, from left to right, the evolution of the island size on the same sample at (b) room temperature, (c) 730 K and (d) 950 K. Note that the island size at high *T* is limited by the step size.

This is in stark contrast with the behavior described for samples, where the annealing process is performed over a longer time, allowing for a greater density of carbon adsorbates on the surface, as seen previously in **Figures 6** and **7**. Plotting the island size as a function of temperature for several samples illustrates how different the behavior is between a clean surface and one saturated with the 15 × 3 carbon reconstruction.

**5. Conclusion**

to create self-ensembled nanosystems.

José Luis Diez-Ferrer for providing the images of **Figure 3**.

\*Address all correspondence to: miguel.ciria@csic.es

Universidad de Zaragoza, Zaragoza, Spain

David Coffey1,2,3, José I. Arnaudas2,3, David Serrate2,3 and Miguel Ciria1,3\*

1 Instituto de Ciencia de Materiales de Aragón, Consejo Superior de Investigaciones

2 Laboratorio de Microscopías Avanzadas, Fundación Instituto de Nanociencia de Aragón,

3 Departamento de Física de la Materia Condensada, Universidad de Zaragoza, Zaragoza,

**Acknowledgements**

**Author details**

Spain

Científicas, Zaragoza, Spain

In this chapter, the preparation of single atomic layer Tm films on a W(110) substrate is explored. Sub-monoloyer Tm deposits can present a varied morphology depending on initial coverage, substrate temperature and adsorbate density. The key to achieving highquality pseudomorphic Tm films resides in an annealing process after evaporation, which motivates the study presented here, where STM experiments are performed at high temperature to observe in situ the evolution of the Tm film. Measurements over time evidence the diffusion of carbon adsorbates from the bulk of the W crystal onto the surface. The effect of carbon impurity density on the diffusion process of Tm atoms is studied by observing the evolution of multiple samples at different initial coverages following different thermal processes, with longer times leading to a higher adsorbate density. It is observed that the presence of carbon strongly limits the diffusion of Tm, thus leading to the formation of pseudomorphic nanometric islands instead of the full monolayer. The ultimate result of the procedure described in this chapter indicates that with careful control of the impurity density, structures with mean Tm island size down to 5 nm in diameter can be obtained, an interesting achievement considering that the magnetic anisotropy of Tm foresees perpendicular magnetization in these islands. This work highlights the role of surface adsorbates on the diffusion process of single atoms, and how it governs the nucleation of islands; experimental evidence is presented of control over the mean island size by means of inducing a change in the diffusion parameters on the surface in a controlled fashion by using impurities existing in the substrate, a procedure that could be extrapolated to other magnetic materials

Tm on W(110): A Growth Study by Scanning Tunneling Microscopy

http://dx.doi.org/10.5772/intechopen.70218

107

This work was supported by the Spanish MICINN (Grants MAT2015-66726-R and MAT2013- 46593-C6-3-P), Gobierno de Aragón (Grant E81), and Fondo Social Europeo. We thank Dr.

It is not trivial to quantify the number of impurities, especially with experiments at high temperature where resolution might be compromised to avoid risking tip crash, further complicated by drift issues. **Figure 14** shows the island size evolution for several sets of samples, divided roughly in three categories depending on the carbon density on the surface: Low Carbon (blue hues in the graph), where the sample remains reasonably clean after the annealing process and island size is limited mainly by the size of the steps and the amount of Tm available; Mid Carbon, where carbon reconstruction patches and a high density of carbon adsorbates strongly limit the mean island size; High Carbon, with carbon reconstruction patches covering the whole surface.

A careful control over the carbon density on the W(110) surface can thus provide a reliable method for obtaining self-assembled islands with a definite size, ranging from being limited by the atomic step size to islands under 5 nm in diameter.

**Figure 14.** (a) Island size evolution with temperature for a set of samples. Below, representative final states for different samples, corresponding to the curves marked as (b) sample 030 at a final temperature of 950 K, with low carbon presence resulting in large islands; (c) sample 031 at 950 K, with a strong presence of carbon reconstruction, but segregated after the islands already increased in size; and (d) sample 040 at 1050 K, where very small regular islands can be observed all over the surface, due to the inhibited diffusion due to the high density of carbon on the surface.

## **5. Conclusion**

This is in stark contrast with the behavior described for samples, where the annealing process is performed over a longer time, allowing for a greater density of carbon adsorbates on the surface, as seen previously in **Figures 6** and **7**. Plotting the island size as a function of temperature for several samples illustrates how different the behavior is between a clean surface and

It is not trivial to quantify the number of impurities, especially with experiments at high temperature where resolution might be compromised to avoid risking tip crash, further complicated by drift issues. **Figure 14** shows the island size evolution for several sets of samples, divided roughly in three categories depending on the carbon density on the surface: Low Carbon (blue hues in the graph), where the sample remains reasonably clean after the annealing process and island size is limited mainly by the size of the steps and the amount of Tm available; Mid Carbon, where carbon reconstruction patches and a high density of carbon adsorbates strongly limit the mean island size; High Carbon, with carbon reconstruction patches covering the whole surface. A careful control over the carbon density on the W(110) surface can thus provide a reliable method for obtaining self-assembled islands with a definite size, ranging from being limited

**Figure 14.** (a) Island size evolution with temperature for a set of samples. Below, representative final states for different samples, corresponding to the curves marked as (b) sample 030 at a final temperature of 950 K, with low carbon presence resulting in large islands; (c) sample 031 at 950 K, with a strong presence of carbon reconstruction, but segregated after the islands already increased in size; and (d) sample 040 at 1050 K, where very small regular islands can be observed all

over the surface, due to the inhibited diffusion due to the high density of carbon on the surface.

one saturated with the 15 × 3 carbon reconstruction.

106 Epitaxy

by the atomic step size to islands under 5 nm in diameter.

In this chapter, the preparation of single atomic layer Tm films on a W(110) substrate is explored. Sub-monoloyer Tm deposits can present a varied morphology depending on initial coverage, substrate temperature and adsorbate density. The key to achieving highquality pseudomorphic Tm films resides in an annealing process after evaporation, which motivates the study presented here, where STM experiments are performed at high temperature to observe in situ the evolution of the Tm film. Measurements over time evidence the diffusion of carbon adsorbates from the bulk of the W crystal onto the surface. The effect of carbon impurity density on the diffusion process of Tm atoms is studied by observing the evolution of multiple samples at different initial coverages following different thermal processes, with longer times leading to a higher adsorbate density. It is observed that the presence of carbon strongly limits the diffusion of Tm, thus leading to the formation of pseudomorphic nanometric islands instead of the full monolayer. The ultimate result of the procedure described in this chapter indicates that with careful control of the impurity density, structures with mean Tm island size down to 5 nm in diameter can be obtained, an interesting achievement considering that the magnetic anisotropy of Tm foresees perpendicular magnetization in these islands. This work highlights the role of surface adsorbates on the diffusion process of single atoms, and how it governs the nucleation of islands; experimental evidence is presented of control over the mean island size by means of inducing a change in the diffusion parameters on the surface in a controlled fashion by using impurities existing in the substrate, a procedure that could be extrapolated to other magnetic materials to create self-ensembled nanosystems.

## **Acknowledgements**

This work was supported by the Spanish MICINN (Grants MAT2015-66726-R and MAT2013- 46593-C6-3-P), Gobierno de Aragón (Grant E81), and Fondo Social Europeo. We thank Dr. José Luis Diez-Ferrer for providing the images of **Figure 3**.

## **Author details**

David Coffey1,2,3, José I. Arnaudas2,3, David Serrate2,3 and Miguel Ciria1,3\*

\*Address all correspondence to: miguel.ciria@csic.es

1 Instituto de Ciencia de Materiales de Aragón, Consejo Superior de Investigaciones Científicas, Zaragoza, Spain

2 Laboratorio de Microscopías Avanzadas, Fundación Instituto de Nanociencia de Aragón, Universidad de Zaragoza, Zaragoza, Spain

3 Departamento de Física de la Materia Condensada, Universidad de Zaragoza, Zaragoza, Spain

## **References**

[1] Kwo J, Gyorgy EM, McWhan DB, et al. Magnetic and structural properties of singlecrystal rare-earth Gd-Y superlattices. Physical Review Letters. 1985;**55**:1402-1405

[17] Horcas I, Fernández R, Gómez-Rodríguez JM, et al. WSXM: A software for scanning probe microscopy and a tool for nanotechnology. Review of Scientific Instruments.

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[18] Nečas D, Klapetek P. Gwyddion: An open-source software for SPM data analysis.

[19] Bode M, Krause S, Berbil-Bautista L, et al. On the preparation and electronic properties

[20] Bode M, Pascal R, Wiesendanger R. STM study of carbon-induced reconstructions on W(110): Strong evidence for a surface lattice deformation. Surface Science.

[21] Brune H. Microscopic view of epitaxial metal growth: Nucleation and aggregation.

[22] Einax M, Dieterich W, Maass P. *Colloquium* : Cluster growth on surfaces: Densities, size distributions, and morphologies. Reviews of Modern Physics. 2013;**85**:921-939

[23] Brune H, Bales GS, Jacobsen J, et al. Measuring surface diffusion from nucleation island

[24] Horch S, Lorensen HT. Enhancement of surface self-diffusion of platinum atoms by

[25] Venables JA. Nucleation calculations in a pair-binding model. Physical Review B.

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[1] Kwo J, Gyorgy EM, McWhan DB, et al. Magnetic and structural properties of singlecrystal rare-earth Gd-Y superlattices. Physical Review Letters. 1985;**55**:1402-1405

[2] Weller D, Alvarado SF, Gudat W, et al. Observation of surface-enhanced magnetic order and magnetic surface reconstruction on Gd(0001). Physical Review Letters. 1985;

[3] Kwo J, Hong M, Nakahara S. Growth of rare-earth single crystals by molecular beam epitaxy: The epitaxial relationship between hcp rare earth and bcc niobium. Applied

[4] Majkrzak CF, Cable JW, Kwo J, et al. Observation of a magnetic antiphase domain structure with long-range order in a synthetic Gd-Y superlattice. Physical Review Letters.

[5] Salamon MB, Sinha S, Rhyne JJ, et al. Long-range incommensurate magnetic order in a

[6] Kolaczkiewicz J, Bauer E. The adsorption of Eu, Gd and Tb on the W(110) surface.

[7] Nicklin CL, Binns C, Norris C, et al. Valence state of low-dimensional thulium structures

[8] Bodenbach M, Höhr A, Laubschat C, et al. Surface electronic structure of Tm(0001) and

[9] Koehler WC, Cable JW, Wollan EO, et al. Magnetic structures of thulium. Physical

[10] Brun TO, Sinha SK, Wakabayashi N, et al. Temperature dependence of the periodicity of the magnetic structure of thulium metal. Physical Review B. 1970;**1**:1251-1253

[11] Li H, Tian D, Quinn J, et al. Structural and electronic properties of ultrathin films of Gd,

[12] Tober ED, Ynzunza RX, Westphal C, et al. Relationship between morphology and magnetic behavior for Gd thin films on W(110). Physical Review B. 1996;**53**:5444-5448 [13] Barret S, Dhesi S. The Structure of Rare-Earth Metal Surfaces. London: Imperial C; 2001 [14] Binnig G, Rohrer H, Gerber C, et al. Surface studies by scanning tunneling microscopy.

[15] Binnig G, Rohrer H. Scanning tunneling microscopy. Helvetica Physica Acta. 1982;**55**:726 [16] Petersen L, Schunack M, Schaefer B, et al. A fast-scanning, low- and variable-temperature scanning tunneling microscope. Review of Scientific Instruments. 2001;**72**:1438

Dy-Y multilayer. Physical Review Letters. 1986;**56**:259-262

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**Section 2**

**Epitaxy Monte Carlo Simulation and Reactor**

**Design**

**Epitaxy Monte Carlo Simulation and Reactor Design**

**Chapter 5**

**Provisional chapter**

**Monte Carlo Simulation of Epitaxial Growth**

**Monte Carlo Simulation of Epitaxial Growth**

DOI: 10.5772/intechopen.70220

A numerical Monte Carlo (MC) model is described in detail to simulate epitaxial growth. This model allows the formation of structural defects, like substitutional defects and vacancies, and desorption of adsorbed atoms on the surface. The latter feature supports the study of epitaxial growth at very high kinetic regime. The model proposed here is applied to simulate the homoepitaxial growth of Si. The results obtained fit well to the experimental reports on (0 0 1) silicon homoepitaxy. The easy implementation of a large number of microscopic processes and the three-dimensional spatial information during the film growth suggests that the model can be applied to simulate the growth of binary, ternary, or more compounds and even the growth of superlattices and heterostructures.

**Keywords:** Monte Carlo simulation, molecular beam epitaxy, epitaxial growth,

Computer simulation has been successfully applied to the study of surface growth by molecular beam epitaxy (MBE) [1]. These simulation results play a key role in understanding and elucidating various aspects of MBE growth. These simulations provide an atomistic interpretation of the changes in characteristic reflection high energy electron diffraction (RHEED) patterns, observed in real-time, that are related to the different growth modes, i.e., from island nucleation to layer-by-layer growth mode. Additionally, by simulation, the dependency of substrate temperature and the growth rate in the vacancy formation and structural defects can be evaluated [2–6]. However, the majority of these computational models for simulating

> © 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution,

© 2018 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

and reproduction in any medium, provided the original work is properly cited.

Celso I. Fornari, Gabriel Fornari,

Celso I. Fornari, Gabriel Fornari,

http://dx.doi.org/10.5772/intechopen.70220

lattice-matched substrates

Jerônimo dos S. Travelho

**Abstract**

**1. Introduction**

Jerônimo dos S. Travelho

Paulo H. de O. Rappl, Eduardo Abramof and

Paulo H. de O. Rappl, Eduardo Abramof and

Additional information is available at the end of the chapter

Additional information is available at the end of the chapter

#### **Monte Carlo Simulation of Epitaxial Growth Monte Carlo Simulation of Epitaxial Growth**

DOI: 10.5772/intechopen.70220

Celso I. Fornari, Gabriel Fornari, Paulo H. de O. Rappl, Eduardo Abramof and Jerônimo dos S. Travelho Celso I. Fornari, Gabriel Fornari, Paulo H. de O. Rappl, Eduardo Abramof and Jerônimo dos S. Travelho

Additional information is available at the end of the chapter Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/intechopen.70220

#### **Abstract**

A numerical Monte Carlo (MC) model is described in detail to simulate epitaxial growth. This model allows the formation of structural defects, like substitutional defects and vacancies, and desorption of adsorbed atoms on the surface. The latter feature supports the study of epitaxial growth at very high kinetic regime. The model proposed here is applied to simulate the homoepitaxial growth of Si. The results obtained fit well to the experimental reports on (0 0 1) silicon homoepitaxy. The easy implementation of a large number of microscopic processes and the three-dimensional spatial information during the film growth suggests that the model can be applied to simulate the growth of binary, ternary, or more compounds and even the growth of superlattices and heterostructures.

**Keywords:** Monte Carlo simulation, molecular beam epitaxy, epitaxial growth, lattice-matched substrates

### **1. Introduction**

Computer simulation has been successfully applied to the study of surface growth by molecular beam epitaxy (MBE) [1]. These simulation results play a key role in understanding and elucidating various aspects of MBE growth. These simulations provide an atomistic interpretation of the changes in characteristic reflection high energy electron diffraction (RHEED) patterns, observed in real-time, that are related to the different growth modes, i.e., from island nucleation to layer-by-layer growth mode. Additionally, by simulation, the dependency of substrate temperature and the growth rate in the vacancy formation and structural defects can be evaluated [2–6]. However, the majority of these computational models for simulating

and reproduction in any medium, provided the original work is properly cited.

© 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, © 2018 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

neglects desorption effect and, consequently, do not explain growth at high substrate temperatures, where the growth rate is decreased due to desorption of atoms adsorbed on the surface. Besides, the models often use structural approximations, in which the formation of defects is not allowed. In this work, a numerical Monte Carlo (MC) model is presented, in which desorption processes and structural defects are allowed, being possible to study limit cases, i.e., low kinetic energy regime, where structural defects are more likely, and high kinetic energy regime, where the desorption rate competes with the deposition rate.

In the past decades, the interest in MBE was promoted mainly by the exciting properties of semiconductor structures due to two characteristics: high control in the atomic level and reproducibility. Nowadays, after the theoretical prediction of the topological phase of the matter, the MBE technique has shown to be a promising way to obtain high-quality samples, without using counter doping to suppress free carriers due to the structural defects [9].

Monte Carlo Simulation of Epitaxial Growth http://dx.doi.org/10.5772/intechopen.70220 115

Growth of MBE can take place on a substrate composed of the same material, e.g., silicon epitaxy on Si substrates [10], or on different materials, e.g., Ge epitaxy on Si [11]. The first is called homoepitaxy and the second is called heteroepitaxy. These growth conditions may lead to different growth mechanisms, due to the differences in the lattice parameters. Basically, there are three different modes of growth: Volmer-Weber, Stranski-Krastanov, and Frankvan der Merwe, which will occur depending on the experimental parameters and the lattice

In Volmer-Weber's mode, the interaction of the adsorbed atoms is much stronger among them than with the substrate surface, which leads to the formation of clusters or three dimensional islands. As growth proceeds, these islands expand, widening their volumes, whose height greatly exceeds the thickness of a monolayer (ML), leading to the simultaneous growth of

In Frank-van der Merwe's mode, the atoms adsorbed on the surface have a stronger interaction with the surface, leading to the formation of a complete ML before another starts to grow. This layer-by-layer growth mode is often referred as a bi-dimensional growth and is shown

The last mode of growth, called Stranski-Krastanov, is characterized by mixing both previously mentioned. In this mode, the adsorbed atoms begin to grow layer-by-layer. When the critical layer thickness is reached, which value depends on the specific physical properties of each compound, the elastic energy accumulated in the growth relaxes, resulting in the forma-

Of course, all these growth modes are important, since each has a particular application. For the growth of topological insulators, such as bismuth chalcogenide compounds, the Frankvan der Merwe mode is necessary, because the aim here is to minimize structural defects during the formation of the epitaxial layers [12]. However, to manufacture low-dimensional

tion of clusters or islands. This mode of growth is shown in **Figure 1(c)** [8].

**Figure 1.** Modes of growth: (a) Volmer-Weber; (b) Frank-van der Merwe; and (c) Stranski-Krastanov.

atomic layers with rough surface, as shown in **Figure 1(a)** [8].

**2.1. Growth mechanisms**

mismatches.

in **Figure 1(b)** [8].

This chapter is organized as follows: Section 2 presents a review on molecular beam epitaxy, focusing on the growth modes and the most common experimental techniques used to characterize thin epitaxial films. Section 3 presents a brief review of computational models of epitaxial growth simulation, and the model developed in this work. Section 4 presents the simulation results of silicon (Si) homoepitaxial growth on Si (0 0 1). Finally, Section 5 presents the main conclusions and new applications of the proposed model.

## **2. Molecular beam epitaxy**

Molecular beam epitaxy (MBE) is a state-of-the-art ultra-high vacuum (UHV) thin film growth technique. The materials that will compose the films are sublimated from highly stable effusion cells, forming the molecular beam, which is deposited on an independently heated substrate. The substrate is a monocrystalline material and the impinging atoms, from the solid source, follow the substrate crystalline orientation. The physicochemical interaction mechanisms between two phases, in this case, vapor solid, with the growing solid, is called epitaxy, which has a Greek root: *epi* means "above" and *taxis* means "an ordered manner" [7].

Since the system operates in a UHV environment, the mean free path of the vapor species is much larger than the distance between the solid sources and the substrate. The interactions of the molecular beam, before colliding with the substrate surface, can be neglected. The substrate temperature is controlled independently of the effusion cells and is kept low relative to the temperatures of the cells. Therefore, the growth far from the thermodynamic equilibrium makes it possible to compensate distinct thermodynamic properties of the different materials, besides allowing the growth of high-quality monocrystalline films.

The UHV conditions in the MBE growth chamber result in an extremely low background impurity level, which allows the growth of samples with high doping control. Besides, several materials can be sublimated simultaneously and, by means of independent shutter control, multi-layer systems, with very sharp interfaces, can be obtained. Among that, a wide range of alloy composition and different doping levels can be achieved. The growth conditions are reproducible, highly stable and can vary over a wide range, which is crucial for optimizing the growth for specific materials. Additionally, compatibility with *in situ* analysis tools provides insights into the microscopic processes involved in the growth. The reflection highenergy electron diffraction (RHEED), for example, probes the film surface and, due to the small angle of the incident electron beam, provides information on surface morphology, in real time, during the growth [8].

In the past decades, the interest in MBE was promoted mainly by the exciting properties of semiconductor structures due to two characteristics: high control in the atomic level and reproducibility. Nowadays, after the theoretical prediction of the topological phase of the matter, the MBE technique has shown to be a promising way to obtain high-quality samples, without using counter doping to suppress free carriers due to the structural defects [9].

#### **2.1. Growth mechanisms**

neglects desorption effect and, consequently, do not explain growth at high substrate temperatures, where the growth rate is decreased due to desorption of atoms adsorbed on the surface. Besides, the models often use structural approximations, in which the formation of defects is not allowed. In this work, a numerical Monte Carlo (MC) model is presented, in which desorption processes and structural defects are allowed, being possible to study limit cases, i.e., low kinetic energy regime, where structural defects are more likely, and high

This chapter is organized as follows: Section 2 presents a review on molecular beam epitaxy, focusing on the growth modes and the most common experimental techniques used to characterize thin epitaxial films. Section 3 presents a brief review of computational models of epitaxial growth simulation, and the model developed in this work. Section 4 presents the simulation results of silicon (Si) homoepitaxial growth on Si (0 0 1). Finally, Section 5 presents

Molecular beam epitaxy (MBE) is a state-of-the-art ultra-high vacuum (UHV) thin film growth technique. The materials that will compose the films are sublimated from highly stable effusion cells, forming the molecular beam, which is deposited on an independently heated substrate. The substrate is a monocrystalline material and the impinging atoms, from the solid source, follow the substrate crystalline orientation. The physicochemical interaction mechanisms between two phases, in this case, vapor solid, with the growing solid, is called epitaxy,

Since the system operates in a UHV environment, the mean free path of the vapor species is much larger than the distance between the solid sources and the substrate. The interactions of the molecular beam, before colliding with the substrate surface, can be neglected. The substrate temperature is controlled independently of the effusion cells and is kept low relative to the temperatures of the cells. Therefore, the growth far from the thermodynamic equilibrium makes it possible to compensate distinct thermodynamic properties of the different materials,

The UHV conditions in the MBE growth chamber result in an extremely low background impurity level, which allows the growth of samples with high doping control. Besides, several materials can be sublimated simultaneously and, by means of independent shutter control, multi-layer systems, with very sharp interfaces, can be obtained. Among that, a wide range of alloy composition and different doping levels can be achieved. The growth conditions are reproducible, highly stable and can vary over a wide range, which is crucial for optimizing the growth for specific materials. Additionally, compatibility with *in situ* analysis tools provides insights into the microscopic processes involved in the growth. The reflection highenergy electron diffraction (RHEED), for example, probes the film surface and, due to the small angle of the incident electron beam, provides information on surface morphology, in

which has a Greek root: *epi* means "above" and *taxis* means "an ordered manner" [7].

kinetic energy regime, where the desorption rate competes with the deposition rate.

the main conclusions and new applications of the proposed model.

besides allowing the growth of high-quality monocrystalline films.

**2. Molecular beam epitaxy**

114 Epitaxy

real time, during the growth [8].

Growth of MBE can take place on a substrate composed of the same material, e.g., silicon epitaxy on Si substrates [10], or on different materials, e.g., Ge epitaxy on Si [11]. The first is called homoepitaxy and the second is called heteroepitaxy. These growth conditions may lead to different growth mechanisms, due to the differences in the lattice parameters. Basically, there are three different modes of growth: Volmer-Weber, Stranski-Krastanov, and Frankvan der Merwe, which will occur depending on the experimental parameters and the lattice mismatches.

In Volmer-Weber's mode, the interaction of the adsorbed atoms is much stronger among them than with the substrate surface, which leads to the formation of clusters or three dimensional islands. As growth proceeds, these islands expand, widening their volumes, whose height greatly exceeds the thickness of a monolayer (ML), leading to the simultaneous growth of atomic layers with rough surface, as shown in **Figure 1(a)** [8].

In Frank-van der Merwe's mode, the atoms adsorbed on the surface have a stronger interaction with the surface, leading to the formation of a complete ML before another starts to grow. This layer-by-layer growth mode is often referred as a bi-dimensional growth and is shown in **Figure 1(b)** [8].

The last mode of growth, called Stranski-Krastanov, is characterized by mixing both previously mentioned. In this mode, the adsorbed atoms begin to grow layer-by-layer. When the critical layer thickness is reached, which value depends on the specific physical properties of each compound, the elastic energy accumulated in the growth relaxes, resulting in the formation of clusters or islands. This mode of growth is shown in **Figure 1(c)** [8].

Of course, all these growth modes are important, since each has a particular application. For the growth of topological insulators, such as bismuth chalcogenide compounds, the Frankvan der Merwe mode is necessary, because the aim here is to minimize structural defects during the formation of the epitaxial layers [12]. However, to manufacture low-dimensional

**Figure 1.** Modes of growth: (a) Volmer-Weber; (b) Frank-van der Merwe; and (c) Stranski-Krastanov.

structures, such as quantum dots, when island morphology is required, the growth parameters of the Volmer-Weber mode are determined to control the density, size, and distribution of the islands.

SOS model, the growth quality can only be evaluated by the growing surface. This approach has been widely used in growth simulations of MBE due to the successful interpretations of

This MC computational growth model was implemented using the nearest-neighbor and lattice-gas approximation. The first approximation, as mentioned, considers the interaction only with the in-plane nearest neighbor. **Figure 2(a)** shows an example for a cubic lattice structure, which has a maximum of four in-plane neighbors. Therefore, the potential energy of each lattice point is determined by analyzing the number of bonds between the closest atoms. This approximation has been widely used in MBE simulations [21]. The second approximation considers a fixed crystalline structure, with sites at which the atoms from the solid source can be accommodated. In this case, the possible crystalline positions can be either occupied or empty. Once a fixed crystalline structure is considered, no strain is accounted in this model. **Figure 2(b)** illustrates the lattice gas approximation. It is good to emphasize that these approximations do not allow studying surface reconstruction, since the atomic positions are predetermined and the atoms can fill or not each one. Besides, these approximations allow only the study of homoepitaxy or, in some cases, heteroepitaxy of lattice-matched substrates, e.g.,

[12]. In similar cases, the lattice gas approximation can be employed in the numerical models. The processes considered, in the model presented in this chapter, are shown in **Figure 3**. After deposition (a), surface atoms are allowed either to migrate to another position (b–e) or to desorb (g), and structural defects can be formed (f). The surface is defined as an occupied lattice position with dangling bonds. This statement is also valid for atoms near a hole, since these atoms have one or more dangling bonds due to the presence of the hole itself. This means that the neighboring atoms can migrate and fill the hole, turning on the bulk diffusion process. Models in which bulk defects are considered allow for the study of structural defect formation at low kinetic energy regimes, e.g., growth by MBE at low substrate temperatures. In addition,

**Figure 2.** (a) Determination of the number of nearest neighbor to a chosen position of a cubic lattice. In this example, the atom has three in-plane bonds and one out-of-plane bond. (b) The lattice gas approximation considers a fixed empty crystalline structure, in which the atoms from the solid source are accommodated, initiating epitaxial growth.

(1 1 1), where the lattice mismatch is of only 0.04%

Monte Carlo Simulation of Epitaxial Growth http://dx.doi.org/10.5772/intechopen.70220 117

RHEED intensity oscillations and the surface atomistic processes.

**3.2. The Monte Carlo epitaxial model**

the growth of bismuth telluride on BaF2

### **2.2. Characterization techniques**

RHEED and atomic force microscope (AFM) are the most common experimental techniques applied to characterize the surface of epitaxial films. The first, as mentioned, provides information *in situ* and in real time on surface reconstruction, growth rate, and growth mode. The second allows probing the surface morphology of the film.

The RHEED equipment, basically, consists of an electron gun, in the energy range of 10–50 keV, and a phosphorescent screen. The electron beam is directed to the sample surface, at low angle (<5°). The de Broglie wavelength of electrons for this energy range is 0.17–0.06 Å, which corresponds to the interatomic distances in the crystalline lattice. Therefore, whenever the difference between the incident beam and the diffracted one is equal to a vector of the reciprocal lattice, there will be a maximum of diffraction.

The AFM technique provides high-resolution images of the surface morphology. A piezoelectric is used to scan the sample surface, and a very sharp tip is used to probe the surface. The tip deflection is measured at each point, providing spatial information in the real space of the surface. This information can be directly compared to the simulation results, in order to validate the growth models.

## **3. Molecular beam epitaxial models**

#### **3.1. Epitaxial growth models**

The most common nucleation models used in the simulation of growth by MBE are either completely deterministic or totally stochastic. The deterministic models are based on the temporal evolution of differential equations and study microscopic parameters or stability properties of the growing surface. The deterministic models do not contain explicit spatial information of the growing surface [13–15].

Alternatively, to the analytic simulations, there are models that consider the stochastic nature of the microscopic processes. These stochastic calculations are typically implemented in the form of molecular dynamics (MD) or kinetic Monte Carlo (MC) simulations [16–18]. The MC simulation allows the easy implementation of a large number of microscopic processes. The rate of each microscopic process is obtained from first principle calculations or from experiments. These models are often in agreement with experimental works and provide spatial information of the growing surface [19].

The solid-on-solid (SOS) approach is very common in Monte Carlo simulation models [20]. In this approximation, one atom can only be accommodated on another atom, and therefore, structural defects, such as vacancies, are not allowed. Since bulk defects are not allowed in the SOS model, the growth quality can only be evaluated by the growing surface. This approach has been widely used in growth simulations of MBE due to the successful interpretations of RHEED intensity oscillations and the surface atomistic processes.

#### **3.2. The Monte Carlo epitaxial model**

structures, such as quantum dots, when island morphology is required, the growth parameters of the Volmer-Weber mode are determined to control the density, size, and distribution

RHEED and atomic force microscope (AFM) are the most common experimental techniques applied to characterize the surface of epitaxial films. The first, as mentioned, provides information *in situ* and in real time on surface reconstruction, growth rate, and growth mode. The

The RHEED equipment, basically, consists of an electron gun, in the energy range of 10–50 keV, and a phosphorescent screen. The electron beam is directed to the sample surface, at low angle (<5°). The de Broglie wavelength of electrons for this energy range is 0.17–0.06 Å, which corresponds to the interatomic distances in the crystalline lattice. Therefore, whenever the difference between the incident beam and the diffracted one is equal to a vector of the reciprocal lattice,

The AFM technique provides high-resolution images of the surface morphology. A piezoelectric is used to scan the sample surface, and a very sharp tip is used to probe the surface. The tip deflection is measured at each point, providing spatial information in the real space of the surface. This information can be directly compared to the simulation results, in order

The most common nucleation models used in the simulation of growth by MBE are either completely deterministic or totally stochastic. The deterministic models are based on the temporal evolution of differential equations and study microscopic parameters or stability properties of the growing surface. The deterministic models do not contain explicit spatial

Alternatively, to the analytic simulations, there are models that consider the stochastic nature of the microscopic processes. These stochastic calculations are typically implemented in the form of molecular dynamics (MD) or kinetic Monte Carlo (MC) simulations [16–18]. The MC simulation allows the easy implementation of a large number of microscopic processes. The rate of each microscopic process is obtained from first principle calculations or from experiments. These models are often in agreement with experimental works and provide spatial

The solid-on-solid (SOS) approach is very common in Monte Carlo simulation models [20]. In this approximation, one atom can only be accommodated on another atom, and therefore, structural defects, such as vacancies, are not allowed. Since bulk defects are not allowed in the

of the islands.

116 Epitaxy

**2.2. Characterization techniques**

there will be a maximum of diffraction.

**3. Molecular beam epitaxial models**

information of the growing surface [13–15].

information of the growing surface [19].

to validate the growth models.

**3.1. Epitaxial growth models**

second allows probing the surface morphology of the film.

This MC computational growth model was implemented using the nearest-neighbor and lattice-gas approximation. The first approximation, as mentioned, considers the interaction only with the in-plane nearest neighbor. **Figure 2(a)** shows an example for a cubic lattice structure, which has a maximum of four in-plane neighbors. Therefore, the potential energy of each lattice point is determined by analyzing the number of bonds between the closest atoms. This approximation has been widely used in MBE simulations [21]. The second approximation considers a fixed crystalline structure, with sites at which the atoms from the solid source can be accommodated. In this case, the possible crystalline positions can be either occupied or empty. Once a fixed crystalline structure is considered, no strain is accounted in this model. **Figure 2(b)** illustrates the lattice gas approximation. It is good to emphasize that these approximations do not allow studying surface reconstruction, since the atomic positions are predetermined and the atoms can fill or not each one. Besides, these approximations allow only the study of homoepitaxy or, in some cases, heteroepitaxy of lattice-matched substrates, e.g., the growth of bismuth telluride on BaF2 (1 1 1), where the lattice mismatch is of only 0.04% [12]. In similar cases, the lattice gas approximation can be employed in the numerical models.

The processes considered, in the model presented in this chapter, are shown in **Figure 3**. After deposition (a), surface atoms are allowed either to migrate to another position (b–e) or to desorb (g), and structural defects can be formed (f). The surface is defined as an occupied lattice position with dangling bonds. This statement is also valid for atoms near a hole, since these atoms have one or more dangling bonds due to the presence of the hole itself. This means that the neighboring atoms can migrate and fill the hole, turning on the bulk diffusion process.

Models in which bulk defects are considered allow for the study of structural defect formation at low kinetic energy regimes, e.g., growth by MBE at low substrate temperatures. In addition,

**Figure 2.** (a) Determination of the number of nearest neighbor to a chosen position of a cubic lattice. In this example, the atom has three in-plane bonds and one out-of-plane bond. (b) The lattice gas approximation considers a fixed empty crystalline structure, in which the atoms from the solid source are accommodated, initiating epitaxial growth.

**Figure 3.** Allowed processes during MC simulation of thin film growth by MBE: (a) deposition of atoms, arriving from the solid sources, on the surface of a growing film; (b) surface diffusion to a more stable position; (c) atom in an unstable position, without lateral bonds, which can either desorb to the vacuum volume or diffuse to a more stable position; (d) surface diffusion or migration to a higher kink lattice; (e) possible surface diffusion forming overhang; (f) hole formed in the structure volume; and (g) desorption.

In the model, a certain amount of atoms is deposited on the first step of each round of the

**Figure 4.** Flow chart showing the two-step model. During one time unit, a number of atoms are randomly deposited on the growing surface. After deposition, all surface sites are randomly analyzed. Surface diffusion or desorption can occur during this process. The deposition time is increased by one unit, and the process is repeated until the total growth time

Monte Carlo Simulation of Epitaxial Growth http://dx.doi.org/10.5772/intechopen.70220 119

*NX* = *L*<sup>2</sup> . *D* (1)

In this equation, *NX* is the number of atoms from specie *X* that will be deposited per second, and *L* is the lateral dimension of the substrate (the size of one side of the square matrix). The constant *D* is the reciprocal of the experimental deposition rate, given in seconds per mono layers (s/ML), i.e., *D* = 1/*GR*, where *GR* is the experimental growth rate in ML/s. In this model, it is possible to simulate the growth of materials composed by one or more atomic species. In that case, the first step of the model will be repeated *Ntot* times, with *Ntot* = *NX* + *NY* + …, where *X*, *Y* indicate each atomic species. To fit the simulation to the experimental data, *D* must be

In the second step, each position of the surface is analyzed randomly. The surface control is managed by a linear dynamic data structure (implemented through a linked list), containing

In a certain drawn position, the probability of surface diffusion or desorption is calculated. These probabilities are given as the product of an observation time, *τ*, and a hopping rate, *RD*, *<sup>E</sup>*,

*PD*, *<sup>E</sup>* = *τ* . *RD*, *<sup>E</sup>* (2)

Theoretically, the observation time should be as low as possible, *τ* → 0. However, a very low observation time leads to a high computational time, since the second step is repeated until the integrated observation time is equal to one unit, as shown in Eq. (3). In practice, a good

value is *τ* ≈ 0.01, which means that the second step of the model is repeated 100 times,

simulation. This amount depends directly on the substrate area, as given by Eq. (1),

carefully determined for each atomic species in the model.

all spatial coordinates and the atomic species.

for diffusion (*D*) or desorption (*E*), as shown in Eq. (2),

*3.2.2. Surface analysis*

is achieved.

the desorption process of atoms at the surface is critical for investigating high-energy growth regimes, since desorption of adsorbed atoms (adatoms) significantly affects the growth rate and morphology of films at very high substrate temperatures.

The implementation of this model can be divided into two steps: deposition and surface analysis. The first step is responsible for the seating of the atoms on the growing surface, which, in a computational view, can be seen as a square matrix being filled with numbers. In sequence, the second step starts, and each position of the matrix is analyzed. At this point, for each matrix position, a calculation is made and, depending on the result, one of the possibilities described in **Figure 3** can occur, except for the process shown in **Figure 3(a)**.

These steps are repeated until a certain growth time, as shown in **Figure 4**. For each loop interaction, a time unit is added to the deposition time. By using deposition rates equivalent to the experimental ones and increasing the number of site-analysis during the second step, i.e., the number of times each position is analyzed, it is possible to use an approximately equivalent experimental time unit.

#### *3.2.1. Deposition rate*

Depending on the temperature of the effusion cells, different growth rates are achieved. These rates can be experimentally determined, *in situ*, by measuring RHEED intensity oscillations or using a quartz crystal microbalance. In addition, these rates can be determined by directly measuring the film thickness after growth.

**Figure 4.** Flow chart showing the two-step model. During one time unit, a number of atoms are randomly deposited on the growing surface. After deposition, all surface sites are randomly analyzed. Surface diffusion or desorption can occur during this process. The deposition time is increased by one unit, and the process is repeated until the total growth time is achieved.

In the model, a certain amount of atoms is deposited on the first step of each round of the simulation. This amount depends directly on the substrate area, as given by Eq. (1),

$$N\_{\chi} = L^2 \cdot D \tag{1}$$

In this equation, *NX* is the number of atoms from specie *X* that will be deposited per second, and *L* is the lateral dimension of the substrate (the size of one side of the square matrix). The constant *D* is the reciprocal of the experimental deposition rate, given in seconds per mono layers (s/ML), i.e., *D* = 1/*GR*, where *GR* is the experimental growth rate in ML/s. In this model, it is possible to simulate the growth of materials composed by one or more atomic species. In that case, the first step of the model will be repeated *Ntot* times, with *Ntot* = *NX* + *NY* + …, where *X*, *Y* indicate each atomic species. To fit the simulation to the experimental data, *D* must be carefully determined for each atomic species in the model.

#### *3.2.2. Surface analysis*

the desorption process of atoms at the surface is critical for investigating high-energy growth regimes, since desorption of adsorbed atoms (adatoms) significantly affects the growth rate

**Figure 3.** Allowed processes during MC simulation of thin film growth by MBE: (a) deposition of atoms, arriving from the solid sources, on the surface of a growing film; (b) surface diffusion to a more stable position; (c) atom in an unstable position, without lateral bonds, which can either desorb to the vacuum volume or diffuse to a more stable position; (d) surface diffusion or migration to a higher kink lattice; (e) possible surface diffusion forming overhang; (f) hole formed

The implementation of this model can be divided into two steps: deposition and surface analysis. The first step is responsible for the seating of the atoms on the growing surface, which, in a computational view, can be seen as a square matrix being filled with numbers. In sequence, the second step starts, and each position of the matrix is analyzed. At this point, for each matrix position, a calculation is made and, depending on the result, one of the possibilities

These steps are repeated until a certain growth time, as shown in **Figure 4**. For each loop interaction, a time unit is added to the deposition time. By using deposition rates equivalent to the experimental ones and increasing the number of site-analysis during the second step, i.e., the number of times each position is analyzed, it is possible to use an approximately equivalent

Depending on the temperature of the effusion cells, different growth rates are achieved. These rates can be experimentally determined, *in situ*, by measuring RHEED intensity oscillations or using a quartz crystal microbalance. In addition, these rates can be determined by directly

and morphology of films at very high substrate temperatures.

experimental time unit.

in the structure volume; and (g) desorption.

118 Epitaxy

measuring the film thickness after growth.

*3.2.1. Deposition rate*

described in **Figure 3** can occur, except for the process shown in **Figure 3(a)**.

In the second step, each position of the surface is analyzed randomly. The surface control is managed by a linear dynamic data structure (implemented through a linked list), containing all spatial coordinates and the atomic species.

In a certain drawn position, the probability of surface diffusion or desorption is calculated. These probabilities are given as the product of an observation time, *τ*, and a hopping rate, *RD*, *<sup>E</sup>*, for diffusion (*D*) or desorption (*E*), as shown in Eq. (2),

$$\mathcal{P}\_{\mathcal{D},\mathcal{E}} = \{ \boldsymbol{\tau} \dots \boldsymbol{\mathcal{R}}\_{\mathcal{D},\mathcal{E}} \} \tag{2}$$

Theoretically, the observation time should be as low as possible, *τ* → 0. However, a very low observation time leads to a high computational time, since the second step is repeated until the integrated observation time is equal to one unit, as shown in Eq. (3). In practice, a good value is *τ* ≈ 0.01, which means that the second step of the model is repeated 100 times,

$$
\sum \pi\_i = 1.\tag{3}
$$

shows a draw number, where none of the events was reached, and **Figure 5(b)** shows the

When a diffusion event is reached, the atom will migrate to any random neighboring position in the lattice. For a desorption event, the atom is simply removed from the surface. Since the MBE equipment operates under UHV conditions, the mean free path inside the growth chamber is very high, and these atoms can stick to the MBE wall chamber without interacting

For very high substrate temperatures, some lattice positions can be considered unstable, since the probability of diffusion and/or desorption can surpass one unit. Whenever the sum of the

*PD* + *PE* > 1 . (7)

This situation tries to describe limiting conditions, where the growing rate is overlapped by the desorption rate. Since this event occurs at high substrate temperatures, the adatoms have a very high surface mobility. To accomplish this condition, each time a "right event" is reached all available surface positions are analyzed. If one or more of these positions offers enough bonds to avoid another "right event," the atom migrates randomly to one of these positions. Otherwise, if none of the surface positions is stable enough, i.e., if Eq. (6) is true, the

To avoid border effects, a periodic boundary condition was implemented. Atoms located at the borders of the substrate have only two or three in-plane bonds. By increasing the substrate temperature, these positions can become more unstable. The toroid considers a closed substrate, such as: *x*(1) ↔ *x*(*L*) and *y*(1) ↔ *y*(*L*). In this sense, if an equivalent position is occupied,

To obtain the stochastic nature of the microscopic processes, the Mersenne Twister random number generator was employed, which is a 623 dimensionally equidistributed uniform

Surface roughness is estimated based on the exposed surface, without computing any struc-

thickness of the entire film. The equation for roughness estimation resembles the *Rsq* coefficient, obtained experimentally from atomic force microscopy (AFM), scanning tunneling

\_\_\_\_\_\_\_\_\_\_ (*h*(*x*,*y*) <sup>−</sup> ¯ *h*)

represents the highest position occupied by an atom, and ¯¯*h* is the average

2. (8)

Monte Carlo Simulation of Epitaxial Growth http://dx.doi.org/10.5772/intechopen.70220 121

*<sup>L</sup>*<sup>2</sup> <sup>∑</sup> *x*=0 *L* ∑ *y*=0 *L* 2 √

pseudorandom number generator with an accuracy of up to 32 bits [22].

tural defects. The simulated film roughness is calculated by:

*σ* = \_\_1

probabilities surpasses one unit, as shown in Eq. (7), a "right event" is achieved,

activation of a surface diffusion event.

with the molecular beam.

atom desorbs to the vacuum.

*3.2.4. Random numbers*

*3.2.5. Quantifying results*

The term *h*(*x*,*y*)

*x*(1) ↔ *x*(*L*), the atom located at *x*(1) gets a bond.

The hopping rate is determined by an Arrhenius equation, as shown in Eq. (4),

$$\mathcal{R}\_{\mathcal{D},E} = \mathcal{R}\_0 \cdot e^{-\frac{\mathcal{L}\_{\rm tot}}{\mathcal{L}\_I T}} \tag{4}$$

In this equation, *ED*,*E* is the energy for diffusion (*D*) or desorption (*E*), *kB* is the Boltzmann constant, and *T* is the substrate temperature. The typical vibration frequency of the atom,*R*<sup>0</sup> , is function of Planck constant, *h*, and is given by Eq. (5), typically around 1013 Hz,

$$R\_0 = \frac{2\,k\_g\,T}{h}.\tag{5}$$

The energies for diffusion or desorption can be obtained from *ab initio* calculations or by experimental results. These values can be fitted to the experimental data to reproduce the experimental results.

The energy depends on the number of bonds that each atom possesses. Equation (6) presents the energy required for an atom to diffuse (*ED*) or desorb (*EE*),

$$E\_{\rm D,E} = m E\_{\rm D0,E0} + m E\_{\rm D1,E1'} \tag{6}$$

where *m* is the number of out-of-plane bonds, *n* is the number of in-plane bonds (see **Figure 2(a)**), and the sub-indices *D*0 and *E*0 indicate the energy required to diffuse or desorb, respectively, for one out-of-plane bond.

The sub-indices *DL* and *EL* indicate the energy required to diffuse or desorb, respectively, for one in-plane bond. In practice, in a cubic lattice, *m* = 0 or 1 and *n* = 0, 1, 2, 3 or 4. When an atom is located on a vacancy, which is an unoccupied site in the lattice, *m* = 0.

#### *3.2.3. Probabilities*

At each round, in the second step, all surface positions are analyzed once. For each position, the number of in-plane and out-of-plane bonds is computed, and then, the probabilities for diffusion and desorption are calculated. A random number is generated, and if it reaches one of these events, the atom will migrate to another available position or desorb. **Figure 5(a)**

**Figure 5.** (a) Example of a draw number where none of the events is reached and (b) when a surface diffusion event is achieved.

shows a draw number, where none of the events was reached, and **Figure 5(b)** shows the activation of a surface diffusion event.

When a diffusion event is reached, the atom will migrate to any random neighboring position in the lattice. For a desorption event, the atom is simply removed from the surface. Since the MBE equipment operates under UHV conditions, the mean free path inside the growth chamber is very high, and these atoms can stick to the MBE wall chamber without interacting with the molecular beam.

For very high substrate temperatures, some lattice positions can be considered unstable, since the probability of diffusion and/or desorption can surpass one unit. Whenever the sum of the probabilities surpasses one unit, as shown in Eq. (7), a "right event" is achieved,

$$P\_D + P\_\mathbb{E} > 1\,\,.\tag{7}$$

This situation tries to describe limiting conditions, where the growing rate is overlapped by the desorption rate. Since this event occurs at high substrate temperatures, the adatoms have a very high surface mobility. To accomplish this condition, each time a "right event" is reached all available surface positions are analyzed. If one or more of these positions offers enough bonds to avoid another "right event," the atom migrates randomly to one of these positions. Otherwise, if none of the surface positions is stable enough, i.e., if Eq. (6) is true, the atom desorbs to the vacuum.

To avoid border effects, a periodic boundary condition was implemented. Atoms located at the borders of the substrate have only two or three in-plane bonds. By increasing the substrate temperature, these positions can become more unstable. The toroid considers a closed substrate, such as: *x*(1) ↔ *x*(*L*) and *y*(1) ↔ *y*(*L*). In this sense, if an equivalent position is occupied, *x*(1) ↔ *x*(*L*), the atom located at *x*(1) gets a bond.

#### *3.2.4. Random numbers*

∑

*RD*,*<sup>E</sup>* = *R*<sup>0</sup> . *e* <sup>−</sup>

*<sup>R</sup>*<sup>0</sup> <sup>=</sup> <sup>2</sup> *kB <sup>T</sup>* \_\_\_\_

respectively, for one out-of-plane bond.

experimental results.

120 Epitaxy

*3.2.3. Probabilities*

achieved.

*i*=1

In this equation, *ED*,*E* is the energy for diffusion (*D*) or desorption (*E*), *kB* is the Boltzmann constant, and *T* is the substrate temperature. The typical vibration frequency of the atom,*R*<sup>0</sup>

The energies for diffusion or desorption can be obtained from *ab initio* calculations or by experimental results. These values can be fitted to the experimental data to reproduce the

The energy depends on the number of bonds that each atom possesses. Equation (6) pres-

*ED*,*<sup>E</sup>* = *mED*0,*E*<sup>0</sup> + *nEDL*,*EL* , (6)

where *m* is the number of out-of-plane bonds, *n* is the number of in-plane bonds (see **Figure 2(a)**), and the sub-indices *D*0 and *E*0 indicate the energy required to diffuse or desorb,

The sub-indices *DL* and *EL* indicate the energy required to diffuse or desorb, respectively, for one in-plane bond. In practice, in a cubic lattice, *m* = 0 or 1 and *n* = 0, 1, 2, 3 or 4. When an atom

At each round, in the second step, all surface positions are analyzed once. For each position, the number of in-plane and out-of-plane bonds is computed, and then, the probabilities for diffusion and desorption are calculated. A random number is generated, and if it reaches one of these events, the atom will migrate to another available position or desorb. **Figure 5(a)**

**Figure 5.** (a) Example of a draw number where none of the events is reached and (b) when a surface diffusion event is

*E* \_\_\_\_ *D*,*E*

The hopping rate is determined by an Arrhenius equation, as shown in Eq. (4),

function of Planck constant, *h*, and is given by Eq. (5), typically around 1013 Hz,

ents the energy required for an atom to diffuse (*ED*) or desorb (*EE*),

is located on a vacancy, which is an unoccupied site in the lattice, *m* = 0.

*τ<sup>i</sup>* = 1. (3)

*kBT* (4)

*<sup>h</sup>* . (5)

, is

To obtain the stochastic nature of the microscopic processes, the Mersenne Twister random number generator was employed, which is a 623 dimensionally equidistributed uniform pseudorandom number generator with an accuracy of up to 32 bits [22].

#### *3.2.5. Quantifying results*

Surface roughness is estimated based on the exposed surface, without computing any structural defects. The simulated film roughness is calculated by:

$$
\sigma = \frac{1}{L^2} \sum\_{x=0}^{L} \sum\_{y=0}^{L} \sqrt[2]{\left(h\_{\{x,y\}} - \overline{h}\right)^2}. \tag{8}
$$

The term *h*(*x*,*y*) represents the highest position occupied by an atom, and ¯¯*h* is the average thickness of the entire film. The equation for roughness estimation resembles the *Rsq* coefficient, obtained experimentally from atomic force microscopy (AFM), scanning tunneling microscopy (STM), or X-ray reflectivity measurements, which allows a direct comparison between simulation and experimental results reported in the literature (Section 2.2).

RHEED patterns are very sensitive to the surface roughness and morphology of the outer layers. The growth rate can be estimated *in situ* during MBE growth through the RHEED intensity oscillations, which is dynamically calculated by:

$$I(t) = \left(\sum \left(-1\right)^{n} . . \mathcal{S}\_{n}(t)\right)^{2}.\tag{9}$$

This condition is evidenced by very clear oscillations on the surface roughness profile, with a period of approximately 100 s. The oscillation ends in a minimum, indicating that the 10th layer is practically completed. Increasing the substrate temperature to 1200 K, the surface roughness is raised to a value around 1 ML, which is a consequence of film thickness inhomo-

**Figure 6.** Surface roughness profiles for films grown on different substrate temperatures (*T*SUB). Due to limited surface diffusion for films grown at room temperature, high roughness is obtained. Raising the substrate temperature, a high surface mobility is achieved, leading to a step-by-step growth mode at 800 K. For even higher substrate temperatures, atoms are allowed to diffuse with elevated rate and the reevaporation becomes significant, enhancing surface roughness.

Monte Carlo Simulation of Epitaxial Growth http://dx.doi.org/10.5772/intechopen.70220 123

The results of RHEED intensity oscillations dynamically calculated for a set of growth conditions are displayed in **Figure 7**. At room temperature, the calculated intensity does not exhibit any oscillations, which indicates that the intensity of the interference pattern is suppressed by the rough surface. The growth at *T*SUB between 600 and 800 K exhibits well-defined intensity oscillations with a period around 100 s, indicating a growth rate of 1 ML/s. At 600 K, the oscillations are less intense and less symmetric than at 800 K, indicating the growth of more than one layer at the same time. For substrate temperatures around 800 K a layer-by-layer growth mode is achieved, evidenced by the symmetric RHEED intensity oscillation and confirmed by the calculated surface roughness (**Figure 6**). At 1200 K, the intensity oscillations disappear again. The layer-by-layer mode is lost due to higher surface atoms mobility, which leads to rougher surfaces. These results agree very well to experimental work of (0 0 1) Si homoepitaxy [24]. In this report, the RHEED intensity oscillations are weak and vanish after 2 min of deposition at room temperature and at 1270 K, whereas they are intense, well defined, and longstanding for substrate temperatures between 600 K and 900 K. Surface coverage of the first 10 layers was calculated and is presented in **Figure 8(a)** as a function of substrate temperature. At lower temperatures, more than one atomic layer is filled at the same time, due to low surface diffusion. This is evidenced in the lower panel of **Figure 8**, where the 10th layer starts to be filled around 400 s, whereas the other 9 layers are still been filled. At *T*SUB = 600 K, the coverage

geneity, due to high surface diffusion rates.

where the term *Sn* (*t*) is the exposed cover of the *n*th layer at time *t*. This equation is slightly different from the equations used in the SOS models, since it calculates the reflected intensity using only surface atoms exposed to the beam [23].

## **4. Simulation results**

#### **4.1. Silicon (0 0 1)**

For the simulation of a (0 0 1) Si homoepitaxy, the energy value for diffusion to out-of-plane bond is *ED*<sup>0</sup> = 1 eV and the in-plane energy is *EDL* = 0.5 eV. The energy barrier for the evaporation process was determined by fitting the growth rate curves as a function of substrate temperature with the calculated growth rates. The curves were calculated using the vapor pressure of silicon as a function of temperature and the Knudsen equation [8]. The out-of-plane energy barrier found for evaporation is *EE*<sup>0</sup> = 3.8 eV and the in-plane energy is *EEL* = 0.3 eV. The out-ofplane barrier energy determines the inflection point of the growth rate curve, and the in-plane energy determines directly the derivative of the curve, which is the rate of change as a function of substrate temperature.

During growth simulation, the exposed surface, surface roughness, RHEED intensity, structural defects density, growth rate, and the partial structure, containing all atoms coordinates, were continuously recorded as a function of time. The substrate temperature was investigated in a range varying from room temperature up to the silicon melting point. The external parameters of the simulation are substrate temperature, deposition rate, lattice size, and deposition time.

**Figure 6** presents surface roughness in monolayers (ML) for four different substrate temperatures (*T*SUB). The deposition rate was kept constant at 0.01 ML/s during 1000 s of deposition, which results in films thicknesses with approximately 10 ML. At room temperature (300 K), the atoms on surface do not have sufficient energy to migrate leading to a limited surface diffusion, which favors the formation of structural defects, like vacancies and overhangs. As the substrate temperature increases to 600 K, the diffusion hopping rate raises and atoms situated on unstable positions, with a few bonds, may migrate to more stable positions on the lattice. This process decreases the surface roughness, as observed in **Figure 6**, since the innermost layers tend to be fulfilled. The growing surface at this condition is dominated by coalescence of small clusters. For substrate temperature of 800 K, a layer-by-layer growth mode is reached.

microscopy (STM), or X-ray reflectivity measurements, which allows a direct comparison

RHEED patterns are very sensitive to the surface roughness and morphology of the outer layers. The growth rate can be estimated *in situ* during MBE growth through the RHEED

*<sup>n</sup>* (−1)

different from the equations used in the SOS models, since it calculates the reflected intensity

For the simulation of a (0 0 1) Si homoepitaxy, the energy value for diffusion to out-of-plane bond is *ED*<sup>0</sup> = 1 eV and the in-plane energy is *EDL* = 0.5 eV. The energy barrier for the evaporation process was determined by fitting the growth rate curves as a function of substrate temperature with the calculated growth rates. The curves were calculated using the vapor pressure of silicon as a function of temperature and the Knudsen equation [8]. The out-of-plane energy barrier found for evaporation is *EE*<sup>0</sup> = 3.8 eV and the in-plane energy is *EEL* = 0.3 eV. The out-ofplane barrier energy determines the inflection point of the growth rate curve, and the in-plane energy determines directly the derivative of the curve, which is the rate of change as a function

During growth simulation, the exposed surface, surface roughness, RHEED intensity, structural defects density, growth rate, and the partial structure, containing all atoms coordinates, were continuously recorded as a function of time. The substrate temperature was investigated in a range varying from room temperature up to the silicon melting point. The external parameters of the simulation are substrate temperature, deposition rate, lattice size, and

**Figure 6** presents surface roughness in monolayers (ML) for four different substrate temperatures (*T*SUB). The deposition rate was kept constant at 0.01 ML/s during 1000 s of deposition, which results in films thicknesses with approximately 10 ML. At room temperature (300 K), the atoms on surface do not have sufficient energy to migrate leading to a limited surface diffusion, which favors the formation of structural defects, like vacancies and overhangs. As the substrate temperature increases to 600 K, the diffusion hopping rate raises and atoms situated on unstable positions, with a few bonds, may migrate to more stable positions on the lattice. This process decreases the surface roughness, as observed in **Figure 6**, since the innermost layers tend to be fulfilled. The growing surface at this condition is dominated by coalescence of small clusters. For substrate temperature of 800 K, a layer-by-layer growth mode is reached.

*<sup>n</sup>* . *Sn* (*t*) ) 2

(*t*) is the exposed cover of the *n*th layer at time *t*. This equation is slightly

. (9)

between simulation and experimental results reported in the literature (Section 2.2).

intensity oscillations, which is dynamically calculated by:

*I*(*t*) = (∑

using only surface atoms exposed to the beam [23].

where the term *Sn*

122 Epitaxy

**4.1. Silicon (0 0 1)**

**4. Simulation results**

of substrate temperature.

deposition time.

**Figure 6.** Surface roughness profiles for films grown on different substrate temperatures (*T*SUB). Due to limited surface diffusion for films grown at room temperature, high roughness is obtained. Raising the substrate temperature, a high surface mobility is achieved, leading to a step-by-step growth mode at 800 K. For even higher substrate temperatures, atoms are allowed to diffuse with elevated rate and the reevaporation becomes significant, enhancing surface roughness.

This condition is evidenced by very clear oscillations on the surface roughness profile, with a period of approximately 100 s. The oscillation ends in a minimum, indicating that the 10th layer is practically completed. Increasing the substrate temperature to 1200 K, the surface roughness is raised to a value around 1 ML, which is a consequence of film thickness inhomogeneity, due to high surface diffusion rates.

The results of RHEED intensity oscillations dynamically calculated for a set of growth conditions are displayed in **Figure 7**. At room temperature, the calculated intensity does not exhibit any oscillations, which indicates that the intensity of the interference pattern is suppressed by the rough surface. The growth at *T*SUB between 600 and 800 K exhibits well-defined intensity oscillations with a period around 100 s, indicating a growth rate of 1 ML/s. At 600 K, the oscillations are less intense and less symmetric than at 800 K, indicating the growth of more than one layer at the same time. For substrate temperatures around 800 K a layer-by-layer growth mode is achieved, evidenced by the symmetric RHEED intensity oscillation and confirmed by the calculated surface roughness (**Figure 6**). At 1200 K, the intensity oscillations disappear again. The layer-by-layer mode is lost due to higher surface atoms mobility, which leads to rougher surfaces. These results agree very well to experimental work of (0 0 1) Si homoepitaxy [24]. In this report, the RHEED intensity oscillations are weak and vanish after 2 min of deposition at room temperature and at 1270 K, whereas they are intense, well defined, and longstanding for substrate temperatures between 600 K and 900 K. Surface coverage of the first 10 layers was calculated and is presented in **Figure 8(a)** as a function of substrate temperature.

At lower temperatures, more than one atomic layer is filled at the same time, due to low surface diffusion. This is evidenced in the lower panel of **Figure 8**, where the 10th layer starts to be filled around 400 s, whereas the other 9 layers are still been filled. At *T*SUB = 600 K, the coverage

**Figure 7.** Normalized RHEED intensity oscillations dynamically calculated for several growth substrate temperatures (*T*SUB). The intensity oscillations are suppressed at room temperature and at 1200 K, indicating rough surfaces at these conditions. For intermediated substrate temperatures, from 600 to 800 K, clearly defined oscillations are observed.

chart shows that simultaneous growth occurs for a maximum of two layers, whereas, at 800 K, the chart evidences the growth of only one layer per time period. Raising *T*SUB to 1200 K, the high diffusion hopping rate recovers simultaneous layer growth and generates noisy lines on the surface coverage profile. Besides that reevaporation process becomes significant, contributing to an increase of spiked profile due to an abrupt change on the atomic layers coverage.

The exposed surface is presented in **Figure 8(b)** for growth temperatures between 300 K and 800 K.

The dependence of the defects density formed during film growth as a function of the substrate temperature is presented in **Figure 9** for different deposition rates. This graph shows that, for each deposition rate, there is a threshold temperature where the defect density starts to decay exponentially. This temperature is higher for higher deposition rates. As the deposition rate increases, higher diffusion rates, i.e., higher temperatures are needed to accommodate the impinging atoms without the formation of holes. The local minima observed in the curves of **Figure 9** correspond to the variation of the diffusion rate due to the average number

from 300 to 700 K). At *T*SUB = 800 K, a transition from cluster to layer-by-layer growth is achieved.

**Figure 8.** (a) Surface coverage as a function of deposition time of the first ten atomic layers for substrate temperatures from 300 K to 1200 K. (b) Exposed surface for a *L* = 100 lattice positions and four substrate temperatures. Increasing substrate temperature enhances atoms mobility, lowering surface roughness by widening terraces on the surface (*T*SUB

Monte Carlo Simulation of Epitaxial Growth http://dx.doi.org/10.5772/intechopen.70220 125

At lower substrate temperatures regimes, the hopping rate is decreased, inhibiting the atoms mobility. These growth conditions are favorable to structural defects, which leads to rough

of bonds of the surface atoms.

From room temperature to *T*SUB = 500 K, the images present a rough surface with cluster of Si atoms close to each other. At 700 K, the surface becomes much more flat, exhibiting large terraces with monolayer islands and a few void lakes. This growth condition is mostly controlled by islands coalescence and is on transition to the layer-by-layer growth regime. Raising the substrate temperature to 800 K, a plain layer-by-layer growth mode is observed, where the lowermost atomic layers are completely fulfilled by a step-flow mechanism before a new layer start to be formed. These results are in agreement with experimental STM images captured in an ultra-high vacuum MBE system right after the (0 0 1) Si homoepitaxy growth [25].

**Figure 8.** (a) Surface coverage as a function of deposition time of the first ten atomic layers for substrate temperatures from 300 K to 1200 K. (b) Exposed surface for a *L* = 100 lattice positions and four substrate temperatures. Increasing substrate temperature enhances atoms mobility, lowering surface roughness by widening terraces on the surface (*T*SUB from 300 to 700 K). At *T*SUB = 800 K, a transition from cluster to layer-by-layer growth is achieved.

chart shows that simultaneous growth occurs for a maximum of two layers, whereas, at 800 K, the chart evidences the growth of only one layer per time period. Raising *T*SUB to 1200 K, the high diffusion hopping rate recovers simultaneous layer growth and generates noisy lines on the surface coverage profile. Besides that reevaporation process becomes significant, contributing to an increase of spiked profile due to an abrupt change on the atomic layers coverage. The exposed surface is presented in **Figure 8(b)** for growth temperatures between 300 K and

**Figure 7.** Normalized RHEED intensity oscillations dynamically calculated for several growth substrate temperatures (*T*SUB). The intensity oscillations are suppressed at room temperature and at 1200 K, indicating rough surfaces at these conditions. For intermediated substrate temperatures, from 600 to 800 K, clearly defined oscillations are observed.

From room temperature to *T*SUB = 500 K, the images present a rough surface with cluster of Si atoms close to each other. At 700 K, the surface becomes much more flat, exhibiting large terraces with monolayer islands and a few void lakes. This growth condition is mostly controlled by islands coalescence and is on transition to the layer-by-layer growth regime. Raising the substrate temperature to 800 K, a plain layer-by-layer growth mode is observed, where the lowermost atomic layers are completely fulfilled by a step-flow mechanism before a new layer start to be formed. These results are in agreement with experimental STM images captured in

an ultra-high vacuum MBE system right after the (0 0 1) Si homoepitaxy growth [25].

800 K.

124 Epitaxy

The dependence of the defects density formed during film growth as a function of the substrate temperature is presented in **Figure 9** for different deposition rates. This graph shows that, for each deposition rate, there is a threshold temperature where the defect density starts to decay exponentially. This temperature is higher for higher deposition rates. As the deposition rate increases, higher diffusion rates, i.e., higher temperatures are needed to accommodate the impinging atoms without the formation of holes. The local minima observed in the curves of **Figure 9** correspond to the variation of the diffusion rate due to the average number of bonds of the surface atoms.

At lower substrate temperatures regimes, the hopping rate is decreased, inhibiting the atoms mobility. These growth conditions are favorable to structural defects, which leads to rough

the bulk. The model presented here can be applied to understand the growth dynamics of these

This chapter presented firstly a brief description of the molecular beam epitaxy and the main growth modes achieved using this technique as well as of the most common experimental tools to probe thin film surfaces. The second part described a numerical model based on

The model proposed here is applied to simulate the molecular beam epitaxial growth of Si on (0 0 1) Si substrate. The results obtained fit well to the experimental reports on (0 0 1) silicon homoepitaxy. At low substrate temperatures, films exhibit a high density of structural defects and a very rough surface. On the other hand, for high temperatures, large surface terraces are achieved with a low density of bulk defects. At even higher substrate temperatures, the surface roughness increases due to the high mobility of the atoms at the surface, which could lead to non-homogeneity of the film thickness. By further increasing the substrate temperature, the atoms have sufficient energy to desorb, resulting in a reduction of the growth rate. The large number of microscopic processes and the three-dimensional spatial information during the film growth allow the model to simulate the growth of binary, ternary, or more compounds and even the growth of superlattices and heterostructures. In addition, the model allows an easy implementation to study thermal treatments in crystalline structures and sur-

, Paulo H. de O. Rappl<sup>1</sup>

1 Laboratório Associado de Sensores e Materiais—LAS, National Institute for Space Research,

2 Laboratório Associado de Computação e Matemática Aplicada—LAC, National Institute for

[1] Madhukar A, Ghaisas SV. The nature of molecular beam epitaxial growth examined via computer simulations. Critical Reviews in Solid State and Materials Sciences. 1988;**14**:1-

, Eduardo Abramof1

and

Monte Carlo Simulation of Epitaxial Growth http://dx.doi.org/10.5772/intechopen.70220 127

compounds, elucidating the mechanisms of structural defect formation.

Monte Carlo method to simulate epitaxial growth.

\*, Gabriel Fornari2

\*Address all correspondence to: celso@las.inpe.br

Space Research, São José dos Campos, SP, Brazil

130. DOI: 10.1080/01611598808241266

**5. Conclusion**

face sputtering processes.

Jerônimo dos S. Travelho2

São José dos Campos, SP, Brazil

**Author details**

Celso I. Fornari1

**References**

**Figure 9.** Density of holes formed in the simulated films as a function of substrate temperature for deposition rate varying from 0.01 ML/s up to 2.56 ML/s.

surfaces. For higher temperatures, in an energetically unstable condition with many dangling bonds, the hopping rate for diffusion raises. This condition favors atoms located in unstable positions to search other points in the lattice with lower energy, decreasing the number of structural defects and the surface roughness. With higher substrate temperatures, the atoms located in the surface are allowed to migrate in a short period of time. This condition allows atoms to migrate to a more stable position, like on kinks, giving rise to a step-flow growth mode with flatter surfaces and less structural defects. For even higher substrate temperatures, the hopping rate for diffusion is very high, even for positions with many bonds. In this situation, several diffusion movements are allowed, producing inhomogeneous thicknesses with rougher surfaces. The hopping rate for reevaporation begins to be significant, lowering the growth rate. If substrate temperature continues to increase, the reevaporation rate becomes more and more significant, until growth rate vanishes.

#### **4.2. Applications**

This model can be applied to study low and high kinetic growth regimes, since this numerical model of MBE growth considers bulk defects and desorption process and the growth of multiple elements, such as binary and ternary alloys. Besides, it is possible to study thermal treatment effects on crystalline structures, sputtering processes of surfaces, and even the growth on substrates with cleavage steps.

One topic example, which has attracted a lot of attention from experimental scientists, is topological insulator materials. The most common archetypes of this new electronic state of matter are the bismuth chalcogenides compounds, such as Bi2 Te<sup>3</sup> and Bi2 Se<sup>3</sup> . This class of matter has a nontrivial topological order, resulting in a metallic behavior attributed to the surface states but insulating behavior in the bulk. However, the presence of spontaneous structural defects in these compounds leads to electric conduction in the bulk, which overlaps with surface states. Of course, in order to achieve practical applications, it is fundamental to have insulating samples in the bulk. The model presented here can be applied to understand the growth dynamics of these compounds, elucidating the mechanisms of structural defect formation.

## **5. Conclusion**

This chapter presented firstly a brief description of the molecular beam epitaxy and the main growth modes achieved using this technique as well as of the most common experimental tools to probe thin film surfaces. The second part described a numerical model based on Monte Carlo method to simulate epitaxial growth.

The model proposed here is applied to simulate the molecular beam epitaxial growth of Si on (0 0 1) Si substrate. The results obtained fit well to the experimental reports on (0 0 1) silicon homoepitaxy. At low substrate temperatures, films exhibit a high density of structural defects and a very rough surface. On the other hand, for high temperatures, large surface terraces are achieved with a low density of bulk defects. At even higher substrate temperatures, the surface roughness increases due to the high mobility of the atoms at the surface, which could lead to non-homogeneity of the film thickness. By further increasing the substrate temperature, the atoms have sufficient energy to desorb, resulting in a reduction of the growth rate.

The large number of microscopic processes and the three-dimensional spatial information during the film growth allow the model to simulate the growth of binary, ternary, or more compounds and even the growth of superlattices and heterostructures. In addition, the model allows an easy implementation to study thermal treatments in crystalline structures and surface sputtering processes.

## **Author details**

surfaces. For higher temperatures, in an energetically unstable condition with many dangling bonds, the hopping rate for diffusion raises. This condition favors atoms located in unstable positions to search other points in the lattice with lower energy, decreasing the number of structural defects and the surface roughness. With higher substrate temperatures, the atoms located in the surface are allowed to migrate in a short period of time. This condition allows atoms to migrate to a more stable position, like on kinks, giving rise to a step-flow growth mode with flatter surfaces and less structural defects. For even higher substrate temperatures, the hopping rate for diffusion is very high, even for positions with many bonds. In this situation, several diffusion movements are allowed, producing inhomogeneous thicknesses with rougher surfaces. The hopping rate for reevaporation begins to be significant, lowering the growth rate. If substrate temperature continues to increase, the reevaporation rate becomes

**Figure 9.** Density of holes formed in the simulated films as a function of substrate temperature for deposition rate

This model can be applied to study low and high kinetic growth regimes, since this numerical model of MBE growth considers bulk defects and desorption process and the growth of multiple elements, such as binary and ternary alloys. Besides, it is possible to study thermal treatment effects on crystalline structures, sputtering processes of surfaces, and even the growth

One topic example, which has attracted a lot of attention from experimental scientists, is topological insulator materials. The most common archetypes of this new electronic state of matter

a nontrivial topological order, resulting in a metallic behavior attributed to the surface states but insulating behavior in the bulk. However, the presence of spontaneous structural defects in these compounds leads to electric conduction in the bulk, which overlaps with surface states. Of course, in order to achieve practical applications, it is fundamental to have insulating samples in

Te<sup>3</sup>

and Bi2

Se<sup>3</sup>

. This class of matter has

more and more significant, until growth rate vanishes.

are the bismuth chalcogenides compounds, such as Bi2

**4.2. Applications**

on substrates with cleavage steps.

varying from 0.01 ML/s up to 2.56 ML/s.

126 Epitaxy

Celso I. Fornari1 \*, Gabriel Fornari2 , Paulo H. de O. Rappl<sup>1</sup> , Eduardo Abramof1 and Jerônimo dos S. Travelho2

\*Address all correspondence to: celso@las.inpe.br

1 Laboratório Associado de Sensores e Materiais—LAS, National Institute for Space Research, São José dos Campos, SP, Brazil

2 Laboratório Associado de Computação e Matemática Aplicada—LAC, National Institute for Space Research, São José dos Campos, SP, Brazil

## **References**

[1] Madhukar A, Ghaisas SV. The nature of molecular beam epitaxial growth examined via computer simulations. Critical Reviews in Solid State and Materials Sciences. 1988;**14**:1- 130. DOI: 10.1080/01611598808241266

[2] Family F, Lam PM. Renormalization-group analysis and simulational studies of groove instabilitiy in surface growth. Physica A: Statistical, Mechanics and Its Applications. 1994;**205**:272-283. DOI: 10.1016/0378-4371(94)90504-5

[17] Günther V, Mauß F, Klauer C, Schlawitschek C. Kinetic Monte Carlo simulation of the epitaxial growth of Si(1 0 0). Physica Status Solidi (c). 2012;**9**:1955-1962. DOI: 10.1002/

Monte Carlo Simulation of Epitaxial Growth http://dx.doi.org/10.5772/intechopen.70220 129

[18] Günther V, Mauß F. Si(100)2×1 epitaxy: A kinetic Monte Carlo simulation of the surface

[19] Stumpf R, Scheffler M. Ab initio calculations of energies and self-diffusion on flat and stepped surfaces of Al and their implications on crystal growth. Physical Review B,

[20] Weeks JD, Gilmer GH, Jackson KA. Analytical theory of crystal growth. The Journal of

[21] Marmorkos IK, Das Sarma S. Kinetic simulation of molecular beam epitaxial growth dynamics. Surface Science. 1990;**237**:L411-L416. DOI: 10.1016/0039-6028(90)90511-6 [22] Matsumoto M, Nishimura T. Mersenne twister: A 623-dimensionally equidistributed uniform pseudo-random number generator. ACM Transactionson Modeling and

[23] Marmorkos IK, Das Sarma S. Atomistic numerical study of molecular-beam-epitaxial growth kinetics. Physical Review B. 1992;**45**:11262-11272. DOI: 10.1103/PhysRevB.45.11262

[24] Sakamoto T, Kawai NJ, Nakagawa T, Ohta K, Kojima T, Hashiguchi G. Rheed intensity oscillations during silicon MBE growth. Surface Science. 1986;**174**:651-657. DOI:10.

[25] Jernigan GG, Thompson PE. Temperature dependence of atomic scale morphology in Si homoepitaxy between 350 and 800 °C on Si (100) by molecular beam epitaxy. Journal of Vacuum Science & Technology A: Vacuum, Surfaces, and Films. 2001;**19**:2307-2311. DOI:

growth. Physics Procedia. 2013;**40**:56-64. DOI: 10.1016/j.phpro.2012.12.008

Condensed Matter. 1996;**53**:4958-4973. DOI: 10.1103/PhysRevB.53.4958

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[17] Günther V, Mauß F, Klauer C, Schlawitschek C. Kinetic Monte Carlo simulation of the epitaxial growth of Si(1 0 0). Physica Status Solidi (c). 2012;**9**:1955-1962. DOI: 10.1002/ pssc.201200340

[2] Family F, Lam PM. Renormalization-group analysis and simulational studies of groove instabilitiy in surface growth. Physica A: Statistical, Mechanics and Its Applications.

[3] Levi AC, Kotrla M. Theory and simulation of crystal growth. Journal of Physics:

[4] Das Sarma S, Tamborenea P. A new universality class for kinetic growth: Onedimensional molecular-beam epitaxy. Physical Review Letters. 1991;**66**:325-328. DOI:

[5] Das Sarma S, Lanczycki C, Kotlyar R, Ghaisas S. Scale invariance and dynamical correlations in growth models of molecular beam epitaxy. Physical Review E. 1996;**53**:359-388.

[6] Landau DP, Pal S. Monte Carlo simulation of simple models for thin film growth by

[7] Bauer G, Springholz G. Molecular beam epitaxy—Aspects and applications. Vacuum.

[8] Herman MA, Sitter H. Molecular Beam Epitaxy: Fundamentas and Current Status. 2nd

[9] Ando Y. Topological insulator materials. Journal of the Physical Society of Japan.

[10] Schelling C, Springholz G, Schäffler F. New kinetic growth instabilities in Si(001) homoepitaxy. Thin Solid Films. 2000;**369**:1-4. DOI: 10.1016/S0040-6090(00)00823-3

[11] Eaglesham DJ, Cerullo M. Low-temperature growth of Ge on Si(100). Applied Physics

Te<sup>3</sup> topo-

substrates.

[12] Fornari CI, Rappl PHO, Morelhão SL, Abramof E. Structural properties of Bi<sup>2</sup>

logical insulator thin films grown by molecular beam epitaxy on (111) BaF<sup>2</sup>

Journal of Applied Physics. 2016;**119**:156303-1-156303-9. DOI: 10.1063/1.4947266

[13] Ratsch C, Venables JA. Nucleation theory and the early stages of thin film growth. Journal of Vacuum Science & Technology A: Vacuum, Surfaces, and Films. 2003;**21**:s96-

[14] Kariotis R, Lagally MG. Rate equation modelling of epitaxial growth. Surface Science.

[15] Aumann CE, Kariotis R, Lagally MG. Rate equation modeling of interface width. Journal of Vacuum Science & Technology A: Vacuum, Surfaces, and Films. 1989;**7**:2180-2185.

[16] Liang YY, Yoon SF, Fitzgerald EA. Kinetic Monte Carlo simulation of quantum dot growth on stepped substrates. Journal of Physics D: Applied Physics. 2013;**46**:495102.

MBE. Thin Solid Films. 1996;**272**:184-194. DOI: 10.1016/0040-6090(95)06945-3

1994;**205**:272-283. DOI: 10.1016/0378-4371(94)90504-5

1992;**43**:357-365. DOI: 10.1016/0042-207X(92)90038-X

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DOI: 10.1103/PhysRevE.53.359

Condensed Matter. 1997;**9**:299-344. DOI: 10.1088/0953-8984/9/2/001


**Chapter 6**

Provisional chapter

**Silicon Epitaxial Reactor for Minimal Fab**

Silicon Epitaxial Reactor for Minimal Fab

Cost-effective and mass production of size-controlled wafers becomes one of the future trends for electronic devices. Herein, we design a Minimal Fab system for the growth of half-inch-diameter silicon wafer devices. Different from the conventional chemical vapour deposition (CVD) systems, a new-type of CVD reactor was designed and developed for the Minimal Fab. The minimal CVD reactor has a small reaction chamber for rapid growth processes. It employed (i) a vertical gas flow, (ii) heating modules using concentrated infrared light, (iii) chlorine trifluoride gas for quick reactor cleaning and (iv) optimized epitaxial growth conditions so that the reactor cleaning is not necessary. Reducing the total gas flow rate is an effective way to increase the wafer temperature. The heating process was further assisted by the absorption of infrared light by the precursor trichlorosilane. The slimly designed reflector could help in improving the

DOI: 10.5772/intechopen.69986

Keywords: chemical vapour deposition, infrared light heating, reflectors, cleaning

The electronic device fabrication follows the two major trends, that is, the larger silicon wafer diameter and smaller design rule [1], mainly for economic reasons. A huge number of the device chips are produced in this manufacturing system. These trends require a huge invest-

However, we have the other technical trend [2] that the highly integrated device chips are customized and applied to various fields including the information technologies. For this purpose, a small amount of various chips are flexibly produced. Here, the Minimal Fab [3–6] is expected to flexibly produce just the right number of electronic device chips, from one to

> © The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and eproduction in any medium, provided the original work is properly cited.

© 2018 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Ning Li, Hitoshi Habuka, Yuuki Ishida,

Ning Li, Hitoshi Habuka, Yuuki Ishida,

Additional information is available at the end of the chapter

Additional information is available at the end of the chapter

Shin-ichi Ikeda and Shiro Hara

Shin-ichi Ikeda and Shiro Hara

Abstract

heating speed.

process

1. Introduction

ment for developing and preparing the plant.

http://dx.doi.org/10.5772/intechopen.69986

#### **Chapter 6** Provisional chapter

## **Silicon Epitaxial Reactor for Minimal Fab** Silicon Epitaxial Reactor for Minimal Fab

DOI: 10.5772/intechopen.69986

Ning Li, Hitoshi Habuka, Yuuki Ishida, Shin-ichi Ikeda and Shiro Hara Ning Li, Hitoshi Habuka, Yuuki Ishida,

Additional information is available at the end of the chapter Shin-ichi Ikeda and Shiro Hara

http://dx.doi.org/10.5772/intechopen.69986 Additional information is available at the end of the chapter

Abstract

Cost-effective and mass production of size-controlled wafers becomes one of the future trends for electronic devices. Herein, we design a Minimal Fab system for the growth of half-inch-diameter silicon wafer devices. Different from the conventional chemical vapour deposition (CVD) systems, a new-type of CVD reactor was designed and developed for the Minimal Fab. The minimal CVD reactor has a small reaction chamber for rapid growth processes. It employed (i) a vertical gas flow, (ii) heating modules using concentrated infrared light, (iii) chlorine trifluoride gas for quick reactor cleaning and (iv) optimized epitaxial growth conditions so that the reactor cleaning is not necessary. Reducing the total gas flow rate is an effective way to increase the wafer temperature. The heating process was further assisted by the absorption of infrared light by the precursor trichlorosilane. The slimly designed reflector could help in improving the heating speed.

Keywords: chemical vapour deposition, infrared light heating, reflectors, cleaning process

## 1. Introduction

The electronic device fabrication follows the two major trends, that is, the larger silicon wafer diameter and smaller design rule [1], mainly for economic reasons. A huge number of the device chips are produced in this manufacturing system. These trends require a huge investment for developing and preparing the plant.

However, we have the other technical trend [2] that the highly integrated device chips are customized and applied to various fields including the information technologies. For this purpose, a small amount of various chips are flexibly produced. Here, the Minimal Fab [3–6] is expected to flexibly produce just the right number of electronic device chips, from one to

© The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and eproduction in any medium, provided the original work is properly cited.

million, on-demand and on-time, consuming less material and power. For this concept, a small silicon wafer having 12.5 mm diameter allows the great flexibility. It enables the very quick processes of the lithography, thin film formation, annealing and others. The instruments have a very small footprint. The chemical vapour deposition (CVD) process and its reactor should be developed as the key technology.

SiHCl3 ! �

simply depends on the wafer temperature.

employing the cold wall environment.

2.2. Thermal condition

wafer becomes high.

written as follows:

SiCl2 þ HCl↑ ð

SiCl2 þ H2 ! �

�

Assuming the Eley-Rideal model, the growth rate is expressed as follows:

significantly larger than k<sup>r</sup> [H2], the epitaxial growth rate becomes as follows:

�

Similar to the ordinary silicon epitaxial growth, trichlorosilane (SiHCl3) is used in a hydrogen ambient. Firstly, trichlorosilane is chemisorbed at the surface to form the intermediate species, \*SiCl2. Next, it reacts with hydrogen to form silicon. Thus, the overall chemical reaction is

Growth rate <sup>¼</sup> <sup>k</sup>Adkr½SiHCl3�½H2�

Where kAd and k<sup>r</sup> are the rate constant for Eqs. (1) and (2), respectively. When kAd [SiHCl3] is

Because the hydrogen concentration in the reactor is nearly constant, the epitaxial growth rate

Generally, the epitaxial growth rate at 1100�C is about 1–4 μm/min by the ordinary horizontal

In order to avoid the formation of surface defects, such as light point defects, the gas phase chemical reaction is suppressed by maintaining the gas phase temperature low, that is, by

Figure 1 shows the heat transport for the silicon wafer in the minimal CVD reactor. The half-inch silicon wafer is heated by the infrared flux, QIR, emitted from the halogen lamps. The heat is emitted from the half-inch silicon wafer, QEm, as radiation heat. The gas flow containing the

By concentrating the infrared flux, QIR effectively reaches and locally heats the substrate with minimizing the heat loss. The distance between the silicon wafer and the gas nozzle can be changed by finely adjusting QFlow. In order to effectively heat the half-inch wafer, the half-inch wafer is placed below the reflector, as shown in Figure 2(a). The half-inch silicon wafer is heated

By employing this geometry, QEm is high, because the emission of radiation heat is not disturbed. Although the QEm value decreases the wafer temperature, the increasing rate of the wafer temperature is high because of the high QIR value. Additionally, the cooling rate of the

cold wall reactor and is about 8 μm/min by the high-speed rotation vertical reactor.

precursor gas from the gas nozzle takes the heat away from the wafer, QFlow.

using the infrared flux coming from the upper outside.

kAd½SiHCl3� þ kr½H2�

: Chemisorbed at surfaceÞ (1)

Silicon Epitaxial Reactor for Minimal Fab http://dx.doi.org/10.5772/intechopen.69986 133

Si þ 2HCl↑ (2)

; (4)

SiHCl3 þ H2 ! Si þ 3HCl↑ (3)

Growth rate ¼ kr½H2� (5)

Ordinary CVD reactors used for epitaxial growth of large-diameter wafers consume a large amount of gases and heating power. For fast growth of small-scale devices, such as 12.5-mm wafer, Minimal Fab is designed better because a slow gas flow rate and slim heating modules are used. In addition, the environment inside the growth chamber is easily maintained and therefore the regular chamber cleaning for ordinary CVD reactors becomes less necessary for Minimal Fab. However, some parameters that are ignored in ordinary CVD systems may become effective in Minimal Fab. Special care should be paid to finely tune those important parameters.

To fabricate reactors for small substrates, the thermal condition becomes different when compared to that for the large substrates [7]. The concentrated infrared flux effectively heats the small substrate; the thermal process becomes very rapid. In addition to the heating system, the highly reactive gas of chlorine trifluoride (ClF3) [8] is chosen for the reactor cleaning because it can easily remove the silicon film, unnecessarily formed in the CVD reactor, at various temperatures even at room temperature.

In Section 2 [9], a small footprint CVD reactor for producing silicon thin films is explained. This employs the technical issues of (i) vertical gas flow, (ii) a concentrated infrared flux and (iii) in situ reactor cleaning using chlorine trifluoride gas. Steps (i) and (ii) achieve a less heating energy and a rapid cooling. The cleaning process is rapid by (iii). The heating step is not necessary because the chlorine trifluoride gas is reactive even at room temperature. Section 3 explains the practical thermal condition [10, 11]. For achieving the rapid process, the infrared light absorption by the precursor gas is useful. Simultaneously, the cleaning-free process becomes possible. In Section 4, the heat transport near the wafer is evaluated [12]. The thin plates are recognized to be the suitable reflector material. For the quick temperature up and down, the reactor parts set near the wafer should be small, slim and thin. The wafer rotation and the highly heat-conductive susceptor help in achieving the symmetrical and uniform profile of silicon epitaxial film thickness.

## 2. Silicon chemical vapour deposition process for minimal fab

In this section, the CVD reactor was designed and developed, taking into account the thermal process using the reflector, which concentrates infrared flux. The reactor cleaning process using the highly reactive chlorine trifluoride gas is also employed.

#### 2.1. Chemical reaction for silicon epitaxy

The chemical reactions at silicon substrate surfaces [13] are briefly shown as follows:

$$\text{'SiHCl}\_3 \rightarrow \text{'SiCl}\_2 + \text{HCl} \uparrow \quad (\text{':Chernisorbed at surface}) \tag{1}$$

$$\rm{^\*SiCl}\_2 + H\_2 \to \rm{^\*Si} + 2HCl \uparrow \tag{2}$$

Similar to the ordinary silicon epitaxial growth, trichlorosilane (SiHCl3) is used in a hydrogen ambient. Firstly, trichlorosilane is chemisorbed at the surface to form the intermediate species, \*SiCl2. Next, it reacts with hydrogen to form silicon. Thus, the overall chemical reaction is written as follows:

$$\text{SiHCl}\_3 + \text{H}\_2 \rightarrow \text{Si} + \text{3HCl} \uparrow \tag{3}$$

Assuming the Eley-Rideal model, the growth rate is expressed as follows:

$$\text{Growth rate} = \frac{k\_{\text{Ad}}k\_r[\text{SiHCl}\_3][\text{H}\_2]}{k\_{\text{Ad}}[\text{SiHCl}\_3] + k\_r[\text{H}\_2]},\tag{4}$$

Where kAd and k<sup>r</sup> are the rate constant for Eqs. (1) and (2), respectively. When kAd [SiHCl3] is significantly larger than k<sup>r</sup> [H2], the epitaxial growth rate becomes as follows:

$$\text{Growth rate} = k\_r[\text{H}\_2] \tag{5}$$

Because the hydrogen concentration in the reactor is nearly constant, the epitaxial growth rate simply depends on the wafer temperature.

Generally, the epitaxial growth rate at 1100�C is about 1–4 μm/min by the ordinary horizontal cold wall reactor and is about 8 μm/min by the high-speed rotation vertical reactor.

In order to avoid the formation of surface defects, such as light point defects, the gas phase chemical reaction is suppressed by maintaining the gas phase temperature low, that is, by employing the cold wall environment.

#### 2.2. Thermal condition

million, on-demand and on-time, consuming less material and power. For this concept, a small silicon wafer having 12.5 mm diameter allows the great flexibility. It enables the very quick processes of the lithography, thin film formation, annealing and others. The instruments have a very small footprint. The chemical vapour deposition (CVD) process and its reactor should be

Ordinary CVD reactors used for epitaxial growth of large-diameter wafers consume a large amount of gases and heating power. For fast growth of small-scale devices, such as 12.5-mm wafer, Minimal Fab is designed better because a slow gas flow rate and slim heating modules are used. In addition, the environment inside the growth chamber is easily maintained and therefore the regular chamber cleaning for ordinary CVD reactors becomes less necessary for Minimal Fab. However, some parameters that are ignored in ordinary CVD systems may become effective in Minimal Fab. Special care should be paid to finely tune those important

To fabricate reactors for small substrates, the thermal condition becomes different when compared to that for the large substrates [7]. The concentrated infrared flux effectively heats the small substrate; the thermal process becomes very rapid. In addition to the heating system, the highly reactive gas of chlorine trifluoride (ClF3) [8] is chosen for the reactor cleaning because it can easily remove the silicon film, unnecessarily formed in the CVD reactor, at various tem-

In Section 2 [9], a small footprint CVD reactor for producing silicon thin films is explained. This employs the technical issues of (i) vertical gas flow, (ii) a concentrated infrared flux and (iii) in situ reactor cleaning using chlorine trifluoride gas. Steps (i) and (ii) achieve a less heating energy and a rapid cooling. The cleaning process is rapid by (iii). The heating step is not necessary because the chlorine trifluoride gas is reactive even at room temperature. Section 3 explains the practical thermal condition [10, 11]. For achieving the rapid process, the infrared light absorption by the precursor gas is useful. Simultaneously, the cleaning-free process becomes possible. In Section 4, the heat transport near the wafer is evaluated [12]. The thin plates are recognized to be the suitable reflector material. For the quick temperature up and down, the reactor parts set near the wafer should be small, slim and thin. The wafer rotation and the highly heat-conductive susceptor help in achieving the symmetrical and uniform

2. Silicon chemical vapour deposition process for minimal fab

The chemical reactions at silicon substrate surfaces [13] are briefly shown as follows:

using the highly reactive chlorine trifluoride gas is also employed.

In this section, the CVD reactor was designed and developed, taking into account the thermal process using the reflector, which concentrates infrared flux. The reactor cleaning process

developed as the key technology.

peratures even at room temperature.

profile of silicon epitaxial film thickness.

2.1. Chemical reaction for silicon epitaxy

parameters.

132 Epitaxy

Figure 1 shows the heat transport for the silicon wafer in the minimal CVD reactor. The half-inch silicon wafer is heated by the infrared flux, QIR, emitted from the halogen lamps. The heat is emitted from the half-inch silicon wafer, QEm, as radiation heat. The gas flow containing the precursor gas from the gas nozzle takes the heat away from the wafer, QFlow.

By concentrating the infrared flux, QIR effectively reaches and locally heats the substrate with minimizing the heat loss. The distance between the silicon wafer and the gas nozzle can be changed by finely adjusting QFlow. In order to effectively heat the half-inch wafer, the half-inch wafer is placed below the reflector, as shown in Figure 2(a). The half-inch silicon wafer is heated using the infrared flux coming from the upper outside.

By employing this geometry, QEm is high, because the emission of radiation heat is not disturbed. Although the QEm value decreases the wafer temperature, the increasing rate of the wafer temperature is high because of the high QIR value. Additionally, the cooling rate of the wafer becomes high.

2.4. Reactor

2.5. Process

explained in detail in Section 2.6.

Figure 2(a) shows the reactor, which consists of a quartz tube (inner diameter of 24 mm), a quartz wafer holder, gas inlets, three halogen lamps, and a reflector. A half-inch silicon wafer is set on the quartz wafer holder. The inner zone and the outer zone gas inlets have diameters of 7 and 24 mm, respectively. A half of the total gas was introduced to each of the inlets. The distance between the silicon wafer and the bottom of the inner zone gas inlet was 3 cm, in this section. Figure 2(c) shows a photograph which depicts the half-inch silicon wafer heated by the infrared flux.

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Figure 2(b) shows the CVD reactor having an ordinary type reflector. The half-inch silicon wafer is enclosed in the reflector. The infrared flux approaches via the various paths experiencing multiple reflections by the reflector. Comparing this with the minimal CVD reactor, the half-inch wafer cooling rate is shown to be influenced by the reflector geometry. This will be

The wafer temperature is measured in ambient nitrogen by an R-type thermocouple, directly attached to the backside of the half-inch silicon wafer. During the silicon film deposition in ambient hydrogen, the thermocouple is placed in the quartz wafer holder, as shown in Figure 2(a).

For the silicon film formation, the carrier gas and precursor gas are vertically introduced to the silicon wafer. The carrier gas is hydrogen (H2) and the precursor gas is trichlorosilane. The cleaning gas is chlorine trifluoride diluted to 5% in ambient nitrogen at atmospheric pressure. The total gas flow rate is 0.2–1.2 slm. The half-inch silicon wafer is heated to 800–1100C.

The silicon CVD process is shown in Figure 3. After the silicon wafer is heated, the trichlorosilane gas is introduced for the silicon deposition. After terminating the trichlorosilane gas supply, the wafer is cooled down and unloaded from the reactor. The chlorine trifluoride gas is introduced into the reactor at atmospheric pressure and at room temperature for

Figure 3. Silicon chemical vapour deposition process for the Minimal Fab.

Figure 1. Heat transport for the silicon wafer in the minimal CVD reactor.

Figure 2. The minimal CVD reactor, (a) using the reflector concentrating the infrared flux to the silicon wafer, (b) using the ordinary type reflector, in which the silicon wafer is enclosed and (c) photograph of the minimal reactor.

#### 2.3. Cleaning process

The reactor cleaning is necessary for removing the film produced around the substrate, such as at the wafer holder and the quartz tube. The typical silicon CVD process [14] utilizes hydrogen chloride gas near 1200�C. Such high-temperature process requires a long period for increasing and decreasing the temperature. By contrast, the chlorine trifluoride gas is useful, because the following chemical reaction occurs at any temperatures, even at room temperature [8],

$$\text{\textbullet 3Si} + \text{4Cl} \text{F}\_3 \rightarrow \text{\textbullet SiF}\_4 \uparrow + \text{2Cl}\_2 \uparrow \tag{6}$$

#### 2.4. Reactor

Figure 2(a) shows the reactor, which consists of a quartz tube (inner diameter of 24 mm), a quartz wafer holder, gas inlets, three halogen lamps, and a reflector. A half-inch silicon wafer is set on the quartz wafer holder. The inner zone and the outer zone gas inlets have diameters of 7 and 24 mm, respectively. A half of the total gas was introduced to each of the inlets. The distance between the silicon wafer and the bottom of the inner zone gas inlet was 3 cm, in this section. Figure 2(c) shows a photograph which depicts the half-inch silicon wafer heated by the infrared flux.

Figure 2(b) shows the CVD reactor having an ordinary type reflector. The half-inch silicon wafer is enclosed in the reflector. The infrared flux approaches via the various paths experiencing multiple reflections by the reflector. Comparing this with the minimal CVD reactor, the half-inch wafer cooling rate is shown to be influenced by the reflector geometry. This will be explained in detail in Section 2.6.

The wafer temperature is measured in ambient nitrogen by an R-type thermocouple, directly attached to the backside of the half-inch silicon wafer. During the silicon film deposition in ambient hydrogen, the thermocouple is placed in the quartz wafer holder, as shown in Figure 2(a).

#### 2.5. Process

2.3. Cleaning process

134 Epitaxy

The reactor cleaning is necessary for removing the film produced around the substrate, such as at the wafer holder and the quartz tube. The typical silicon CVD process [14] utilizes hydrogen chloride gas near 1200�C. Such high-temperature process requires a long period for increasing and decreasing the temperature. By contrast, the chlorine trifluoride gas is useful, because the

Figure 2. The minimal CVD reactor, (a) using the reflector concentrating the infrared flux to the silicon wafer, (b) using

the ordinary type reflector, in which the silicon wafer is enclosed and (c) photograph of the minimal reactor.

3Si þ 4ClF3 ! 3SiF4↑ þ 2Cl2↑ (6)

following chemical reaction occurs at any temperatures, even at room temperature [8],

Figure 1. Heat transport for the silicon wafer in the minimal CVD reactor.

For the silicon film formation, the carrier gas and precursor gas are vertically introduced to the silicon wafer. The carrier gas is hydrogen (H2) and the precursor gas is trichlorosilane. The cleaning gas is chlorine trifluoride diluted to 5% in ambient nitrogen at atmospheric pressure. The total gas flow rate is 0.2–1.2 slm. The half-inch silicon wafer is heated to 800–1100C.

The silicon CVD process is shown in Figure 3. After the silicon wafer is heated, the trichlorosilane gas is introduced for the silicon deposition. After terminating the trichlorosilane gas supply, the wafer is cooled down and unloaded from the reactor. The chlorine trifluoride gas is introduced into the reactor at atmospheric pressure and at room temperature for

Figure 3. Silicon chemical vapour deposition process for the Minimal Fab.

removing the silicon film formed on various places in the reactor. The flow rate of nitrogen and chlorine trifluoride gas is 1 and 0.05 slm, respectively.

The TWafer value increases by the increasing V value and decreases by the increasing FTotalGas value and CTCS value. Particularly, the increase in FTotalGas of 10 sccm and that of CTCS of 0.25%

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Following Eq. (7), the half-inch wafer temperature is estimated as a function of the lamp voltage and the total gas flow rate at the trichlorosilane concentration fixed to be 3.5%, as shown in Figure 5. Eq (7) shows that the lamp voltage becomes 10–20 V lower by decreasing

As shown in Figure 6(a), a polysilicon film is formed on the wafer holder and on the inner wall of the quartz tube during the film deposition. The thick silicon film is formed at a height near that of the half-inch silicon wafer, because the reactor inner wall near the substrate is high.

Because the film on the quartz wall might produce particles to cause surface defects, it must be removed. Thus, chlorine trifluoride gas [2] at 5% is introduced into the reactor at room temperature in the ambient nitrogen. Figure 6(b) shows a reactor before introducing the chlorine trifluoride gas. Figure 6(c) shows that the silicon film on the right half of the reactor wall was removed after 1 min. The right half of the wafer holder is clearly observed. Although

As shown in Figure 6(d), only a small amount of the polysilicon film remains after 2 min on the left position of the reactor wall. After 3 min, the polysilicon film is perfectly removed, as shown in Figure 6(e) which clearly gives an image of the entire wafer holder. The polysilicon film formed on the inner wall of the quartz tube is quickly and perfectly removed at room

the silicon film on the left half of the reactor wall reduces, a thick film still remains.

Figure 5. Wafer temperature changing with the lamp voltage and the total gas flow rate.

induces a 1C decrease in TWafer.

the total gas flow rate.

2.8. Reactor cleaning

temperature.

#### 2.6. Cooling rate

The capability of the reflector is first evaluated by the cooling rate of the half-inch silicon wafer. Figure 4 shows the cooling rate of the minimal CVD reactor at the nitrogen flow rate of 1 slm, using the reflectors of minimal and ordinary type, shown in Figure 2(a) and (b), respectively. Figure 4 shows the decreasing temperatures of the half-inch wafer. The cooling rate of the minimal CVD reactor is �22 K/s, which is 20% greater than that using the ordinary-type reflector.

#### 2.7. Heat balance

The electric power for heating the silicon wafer is evaluated with adjusting the gas flow rate and the trichlorosilane gas concentration. The half-inch wafer temperature is obtained following the relationship between the temperatures on the backside of the half-inch wafer and the temperature below the quartz wafer holder measured by thermocouple. Additionally, based on the silicon film growth rate saturation [13] at temperatures lower than 1000�C and at the high trichlorosilane gas concentrations, the half-inch wafer temperature is obtained.

The half-inch wafer temperature in a steady state is influenced by various conditions, such as the lamp voltage, V (V), the total gas flow rate, FTotalGas (sccm) and the trichlorosilane gas concentration, CTCS (%). Using a least-squares approximation, the half-inch wafer temperature, TWafer ( �C), is obtained, assuming that each parameter linearly influences the TWafer value.

$$T\_{\text{wafer}}(^{\circ}\text{C}) = 90\sqrt{V(V)} - 0.13F\_{\text{TotalGas}}(\text{sccm}) - 4.3C\_{\text{TCS}}(^{\circ}\text{\textdegree}) + 310(^{\circ}\text{C})\tag{7}$$

Figure 4. Cooling rate of half-inch silicon wafer in the minimal CVD reactor and the reactor using the ordinary type reflector. (In ambient nitrogen: 1 slm and atmospheric pressure.).

The TWafer value increases by the increasing V value and decreases by the increasing FTotalGas value and CTCS value. Particularly, the increase in FTotalGas of 10 sccm and that of CTCS of 0.25% induces a 1C decrease in TWafer.

Following Eq. (7), the half-inch wafer temperature is estimated as a function of the lamp voltage and the total gas flow rate at the trichlorosilane concentration fixed to be 3.5%, as shown in Figure 5. Eq (7) shows that the lamp voltage becomes 10–20 V lower by decreasing the total gas flow rate.

#### 2.8. Reactor cleaning

removing the silicon film formed on various places in the reactor. The flow rate of nitrogen and

The capability of the reflector is first evaluated by the cooling rate of the half-inch silicon wafer. Figure 4 shows the cooling rate of the minimal CVD reactor at the nitrogen flow rate of 1 slm, using the reflectors of minimal and ordinary type, shown in Figure 2(a) and (b), respectively. Figure 4 shows the decreasing temperatures of the half-inch wafer. The cooling rate of the minimal

The electric power for heating the silicon wafer is evaluated with adjusting the gas flow rate and the trichlorosilane gas concentration. The half-inch wafer temperature is obtained following the relationship between the temperatures on the backside of the half-inch wafer and the temperature below the quartz wafer holder measured by thermocouple. Additionally, based on the silicon film growth rate saturation [13] at temperatures lower than 1000�C and at the

The half-inch wafer temperature in a steady state is influenced by various conditions, such as the lamp voltage, V (V), the total gas flow rate, FTotalGas (sccm) and the trichlorosilane gas concentration, CTCS (%). Using a least-squares approximation, the half-inch wafer temperature,

�C), is obtained, assuming that each parameter linearly influences the TWafer value.

Figure 4. Cooling rate of half-inch silicon wafer in the minimal CVD reactor and the reactor using the ordinary type

<sup>V</sup>ðV<sup>Þ</sup> <sup>p</sup> � <sup>0</sup>:13FTotalGasðsccmÞ � <sup>4</sup>:3CTCSð%Þ þ <sup>310</sup><sup>ð</sup>

�

CÞ (7)

CVD reactor is �22 K/s, which is 20% greater than that using the ordinary-type reflector.

high trichlorosilane gas concentrations, the half-inch wafer temperature is obtained.

chlorine trifluoride gas is 1 and 0.05 slm, respectively.

2.6. Cooling rate

136 Epitaxy

2.7. Heat balance

TWafer (

Twaferð �

<sup>C</sup>Þ ¼ <sup>90</sup> ffiffiffiffiffiffiffiffiffiffiffi

reflector. (In ambient nitrogen: 1 slm and atmospheric pressure.).

As shown in Figure 6(a), a polysilicon film is formed on the wafer holder and on the inner wall of the quartz tube during the film deposition. The thick silicon film is formed at a height near that of the half-inch silicon wafer, because the reactor inner wall near the substrate is high.

Because the film on the quartz wall might produce particles to cause surface defects, it must be removed. Thus, chlorine trifluoride gas [2] at 5% is introduced into the reactor at room temperature in the ambient nitrogen. Figure 6(b) shows a reactor before introducing the chlorine trifluoride gas. Figure 6(c) shows that the silicon film on the right half of the reactor wall was removed after 1 min. The right half of the wafer holder is clearly observed. Although the silicon film on the left half of the reactor wall reduces, a thick film still remains.

As shown in Figure 6(d), only a small amount of the polysilicon film remains after 2 min on the left position of the reactor wall. After 3 min, the polysilicon film is perfectly removed, as shown in Figure 6(e) which clearly gives an image of the entire wafer holder. The polysilicon film formed on the inner wall of the quartz tube is quickly and perfectly removed at room temperature.

Figure 5. Wafer temperature changing with the lamp voltage and the total gas flow rate.

Figure 6. Reactor appearance along the reactor cleaning at room temperature. (a) After the film deposition; (b–e): the decrease of poly Si film.

## 3. Thermal condition

The wafer temperature is influenced by many parameters [9] of lamp voltage, total gas flow rate and trichlorosilane gas concentration. The details of these thermal influences are evaluated. Particularly, the light absorption and the heat transport by the gases are the major issues. Table 1 shows the experimental conditions.

3.2. Influence of total gas flow rate

Figure 7. Temperature shift cause by SiHCl3 supply for 4 min (at 64 V).

Table 1. Silicon CVD conditions.

decreasing total gas flow rate.

Figure 8 shows the wafer holder temperature during the silicon deposition. Dark squares are the temperatures at the hydrogen and trichlorosilane flow rate of 220 and 12 sccm, respectively. The wafer holder temperature increases from 8 min; the temperature increase becomes faster after the addition of trichlorosilane at 10 min. The wafer holder temperature reaches 588C. The temperatures at the hydrogen and trichlorosilane flow rate of 165 and 9 sccm, respectively, are shown by white squares. The wafer holder temperature reaches 626C which is higher than that at the higher gas flow rate. The wafer holder temperature increases with the

Although Figure 7 might show that the decrease in the trichlorosilane gas flow rate induces the temperature decrease by means of less infrared absorption, the wafer holder temperature is

actually increased. It is due to the heat transport by the gas flow [9].

Parameters Value

Electric power 55–100 V

Substrate temperature 800–1000C

Pressure Atmospheric pressure Hydrogen gas flow rate 100–1000 sccm Trichlorosilane gas flow rate 2–60 sccm Chlorine trifluoride gas flow rate 50 sccm

Substrate 12.5 mm diameter silicon wafer

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Deposition time 1 min n times or n minutes once

#### 3.1. Temperature change caused by trichlorosilane

Figure 7 shows the quartz wafer holder temperature. The hydrogen and trichlorosilane flow rate are 220 and 12 sccm, respectively. The wafer holder temperature slowly becomes 568C in the ambient consisting of only hydrogen, as shown using dark squares. When the trichlorosilane gas is added from 9 to 13 min, the wafer holder temperature increases, as shown using white squares, and reaches 609C. Empirically, the wafer surface temperature increase by the trichlorosilane gas is c.a. 80 K.

Trichlorosilane has the infrared light absorption [15] at 3.3 and 2.2 μm. The halogen lamp emits the light near 1 μm, the wavelength of which widely distributes [16] to that longer than 2 μm. Thus, the trichlorosilane considerably absorbs the infrared light from the halogen lamps; it increases the temperature of the gas phase.


Table 1. Silicon CVD conditions.

3. Thermal condition

decrease of poly Si film.

138 Epitaxy

Table 1 shows the experimental conditions.

increase by the trichlorosilane gas is c.a. 80 K.

increases the temperature of the gas phase.

3.1. Temperature change caused by trichlorosilane

The wafer temperature is influenced by many parameters [9] of lamp voltage, total gas flow rate and trichlorosilane gas concentration. The details of these thermal influences are evaluated. Particularly, the light absorption and the heat transport by the gases are the major issues.

Figure 6. Reactor appearance along the reactor cleaning at room temperature. (a) After the film deposition; (b–e): the

Figure 7 shows the quartz wafer holder temperature. The hydrogen and trichlorosilane flow rate are 220 and 12 sccm, respectively. The wafer holder temperature slowly becomes 568C in the ambient consisting of only hydrogen, as shown using dark squares. When the trichlorosilane gas is added from 9 to 13 min, the wafer holder temperature increases, as shown using white squares, and reaches 609C. Empirically, the wafer surface temperature

Trichlorosilane has the infrared light absorption [15] at 3.3 and 2.2 μm. The halogen lamp emits the light near 1 μm, the wavelength of which widely distributes [16] to that longer than 2 μm. Thus, the trichlorosilane considerably absorbs the infrared light from the halogen lamps; it

Figure 7. Temperature shift cause by SiHCl3 supply for 4 min (at 64 V).

#### 3.2. Influence of total gas flow rate

Figure 8 shows the wafer holder temperature during the silicon deposition. Dark squares are the temperatures at the hydrogen and trichlorosilane flow rate of 220 and 12 sccm, respectively. The wafer holder temperature increases from 8 min; the temperature increase becomes faster after the addition of trichlorosilane at 10 min. The wafer holder temperature reaches 588C. The temperatures at the hydrogen and trichlorosilane flow rate of 165 and 9 sccm, respectively, are shown by white squares. The wafer holder temperature reaches 626C which is higher than that at the higher gas flow rate. The wafer holder temperature increases with the decreasing total gas flow rate.

Although Figure 7 might show that the decrease in the trichlorosilane gas flow rate induces the temperature decrease by means of less infrared absorption, the wafer holder temperature is actually increased. It is due to the heat transport by the gas flow [9].

not only concentrates the infrared rays to the wafer surface but also absorbs the heat coming from the lamps. Then, the reflector becomes high temperature. Through the reflector, various parts and the gas phase, the heat absorbed by the reflector is slowly conducted to the wafer. The temperature of reflector surface and wafer gradually increases during reaching the thermal steady state. Particularly, the massive metallic parts require long time for reaching a thermal steady state. In this case, the heating process requires more electric power and finer heat distribution control. In order to design a quick heat transport through the reflector maintaining low electric power, a thin and slim reflector is expected. The reflector geometry

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Infrared rays tend to converge to generate a hot spot [7]. For broadening the locally formed heat profile, a silicon carbide susceptor having high heat conductivity is convenient. Additionally, the wafer rotation is popular and effective for averaging the temperature distribution and

In this section for achieving a quick thermal process, the heating behaviour is evaluated using two types of reflectors, that is, the Type-I reflector made of thick mirror plates used in the previous sections and the Type-II reflector made of thin plates. Additionally, the roles of the wafer rotation and the silicon carbide susceptor are explained for preparing a uniformly thick

Figure 10 shows the detail of minimal CVD reactor. Similar to the previous sections, the reactor has the inner and the outer inlet. The distance between the wafer and the inner inlet is 51–56 mm. In this section for improving the heat conduction, the silicon carbide plates are

Figure 11 shows the Type-I and Type-II reflectors covered with an electroplated gold film. Three reflectors are horizontally arranged around the quartz tube, as shown in Figure 10. Figure 11(a) shows the Type-I reflector, which is evaluated in the previous sections. The main body of the Type-I reflector is a 50-mm-thick mirror plate. Its thick body maintains the temperature stable during the long process, because it is not sensitive to fluctuations in the temperature around the reactor. However, it may result in slow heat conduction through it.

As shown in Figure 12(a) and (b), through the Type-I reflector and the Type-II reflector, respectively, the heat from the halogen lamps is transported to the silicon wafer. The solid lines indicate the heat conduction from the lamp to the reflector plate. This heat conduction also heats the wafer, with the radiation heat indicated by the dotted lines. Because the heat conduction requires long period to reach long distance, the large and thick Type-I reflector slowly

The Type-II reflector is shown in Figure 11(b). This reflector consists of a 5-mm-thick plate which is significantly thinner than that of the Type-I reflector. This thin plate makes the heat transport through itself quicker than that of the Type-I reflector. Particularly, the temperature difference between the inside and outside of the reflector plate is reduced. The thermal process

achieves the steady state and makes the thermal process slow and long.

by the Type-II reflector can be quicker than that of the Type-I reflector.

should be optimized for the minimal CVD reactor.

the film growth rate [17].

silicon epitaxial film.

4.1. Reactor and reflector design

inserted beneath the wafer.

Figure 8. Temperature increase by the decreasing H2 flow rate (at 65 V).


Figure 9. Film growth and wall deposition.

#### 3.3. Temperature and obtained film surface

Figure 9 shows the relationship between the wafer temperature, the film surface and the quartz wall deposition. At a very high temperature, the silicon film deposition occurs at the silicon wafer surface and the quartz tube inner wall surface. The optimum temperatures produce the specular silicon epitaxial film without the tube wall deposition.

## 4. Reflector influence on rapid heating

In order to achieve the uniform-thick epitaxial film, the thermal conditions are important. The important issues are the infrared ray reflection design [7] and the heat transport through the reflectors set around the wafer. The CVD reactor for the large-diameter wafer has the large infrared lamp module consisting of large and thick reflector plates [9–11]. The reflector surface not only concentrates the infrared rays to the wafer surface but also absorbs the heat coming from the lamps. Then, the reflector becomes high temperature. Through the reflector, various parts and the gas phase, the heat absorbed by the reflector is slowly conducted to the wafer. The temperature of reflector surface and wafer gradually increases during reaching the thermal steady state. Particularly, the massive metallic parts require long time for reaching a thermal steady state. In this case, the heating process requires more electric power and finer heat distribution control. In order to design a quick heat transport through the reflector maintaining low electric power, a thin and slim reflector is expected. The reflector geometry should be optimized for the minimal CVD reactor.

Infrared rays tend to converge to generate a hot spot [7]. For broadening the locally formed heat profile, a silicon carbide susceptor having high heat conductivity is convenient. Additionally, the wafer rotation is popular and effective for averaging the temperature distribution and the film growth rate [17].

In this section for achieving a quick thermal process, the heating behaviour is evaluated using two types of reflectors, that is, the Type-I reflector made of thick mirror plates used in the previous sections and the Type-II reflector made of thin plates. Additionally, the roles of the wafer rotation and the silicon carbide susceptor are explained for preparing a uniformly thick silicon epitaxial film.

#### 4.1. Reactor and reflector design

3.3. Temperature and obtained film surface

Figure 9. Film growth and wall deposition.

140 Epitaxy

Figure 8. Temperature increase by the decreasing H2 flow rate (at 65 V).

4. Reflector influence on rapid heating

Figure 9 shows the relationship between the wafer temperature, the film surface and the quartz wall deposition. At a very high temperature, the silicon film deposition occurs at the silicon wafer surface and the quartz tube inner wall surface. The optimum temperatures

In order to achieve the uniform-thick epitaxial film, the thermal conditions are important. The important issues are the infrared ray reflection design [7] and the heat transport through the reflectors set around the wafer. The CVD reactor for the large-diameter wafer has the large infrared lamp module consisting of large and thick reflector plates [9–11]. The reflector surface

produce the specular silicon epitaxial film without the tube wall deposition.

Figure 10 shows the detail of minimal CVD reactor. Similar to the previous sections, the reactor has the inner and the outer inlet. The distance between the wafer and the inner inlet is 51–56 mm. In this section for improving the heat conduction, the silicon carbide plates are inserted beneath the wafer.

Figure 11 shows the Type-I and Type-II reflectors covered with an electroplated gold film. Three reflectors are horizontally arranged around the quartz tube, as shown in Figure 10. Figure 11(a) shows the Type-I reflector, which is evaluated in the previous sections. The main body of the Type-I reflector is a 50-mm-thick mirror plate. Its thick body maintains the temperature stable during the long process, because it is not sensitive to fluctuations in the temperature around the reactor. However, it may result in slow heat conduction through it.

As shown in Figure 12(a) and (b), through the Type-I reflector and the Type-II reflector, respectively, the heat from the halogen lamps is transported to the silicon wafer. The solid lines indicate the heat conduction from the lamp to the reflector plate. This heat conduction also heats the wafer, with the radiation heat indicated by the dotted lines. Because the heat conduction requires long period to reach long distance, the large and thick Type-I reflector slowly achieves the steady state and makes the thermal process slow and long.

The Type-II reflector is shown in Figure 11(b). This reflector consists of a 5-mm-thick plate which is significantly thinner than that of the Type-I reflector. This thin plate makes the heat transport through itself quicker than that of the Type-I reflector. Particularly, the temperature difference between the inside and outside of the reflector plate is reduced. The thermal process by the Type-II reflector can be quicker than that of the Type-I reflector.

Figure 10. Half-inch silicon CVD reactor for the Minimal Fab.

adjusted to 700–1000C for Step B, forming the silicon epitaxial film for several minutes by the

Figure 12. Heat transport from halogen lamp to silicon wafer through (a) Type-I and (b) Type-II reflectors. Dotted lines:

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The process shown in Figure 13(a) has the stand-by step, Step C, between Step A and Step B. Step C, waiting for Step B after Step A, realizes the parallel process. The two virtual reactors, the A and B Reactors, are arranged for Steps A and B, respectively. Step C transports the wafer from the A Reactor to the B Reactor at low temperatures. Although the additional period is necessary for increasing and decreasing the temperature, Steps A and B can be simultaneously performed. The parallel process of Steps A and B is expected to become quicker. Thus, in the first part, Step C is intentionally performed using the Type-I and -II reflectors, in order to

Figure 13. Process of silicon epitaxial growth by (a) Steps A–C and by (b) Steps A and B. Step A removes native oxide

film, Step B forms silicon epitaxial film and Step C is for stand-by. Dotted lines show virtual reactor process.

chemical reaction [13] following Eq. (3).

heat transport by radiation; solid lines: heat transport by conduction and gas flow.

Figure 11. Two reflectors of (a) Type-I and (b) Type-II.

#### 4.2. Process

The gas mixture of hydrogen (H2) and trichlorosilane (SiHCl3, TCS) is vertically introduced to the silicon wafer in ambient hydrogen at atmospheric pressure, as shown in Figure 10. The gas flow rates of the H2 and TCS are 215 and 9 sccm, respectively. The electric power of 55–65 V is supplied to the halogen lamps. The total electric power is less than 1500 W.

Typically, the epitaxial film formation process has two major steps. Step A removes the native oxide film on the silicon wafer surface at 1100C for 1 min. Next, the wafer temperature is

Figure 12. Heat transport from halogen lamp to silicon wafer through (a) Type-I and (b) Type-II reflectors. Dotted lines: heat transport by radiation; solid lines: heat transport by conduction and gas flow.

adjusted to 700–1000C for Step B, forming the silicon epitaxial film for several minutes by the chemical reaction [13] following Eq. (3).

The process shown in Figure 13(a) has the stand-by step, Step C, between Step A and Step B. Step C, waiting for Step B after Step A, realizes the parallel process. The two virtual reactors, the A and B Reactors, are arranged for Steps A and B, respectively. Step C transports the wafer from the A Reactor to the B Reactor at low temperatures. Although the additional period is necessary for increasing and decreasing the temperature, Steps A and B can be simultaneously performed. The parallel process of Steps A and B is expected to become quicker. Thus, in the first part, Step C is intentionally performed using the Type-I and -II reflectors, in order to

4.2. Process

142 Epitaxy

The gas mixture of hydrogen (H2) and trichlorosilane (SiHCl3, TCS) is vertically introduced to the silicon wafer in ambient hydrogen at atmospheric pressure, as shown in Figure 10. The gas flow rates of the H2 and TCS are 215 and 9 sccm, respectively. The electric power of 55–65 V is

Typically, the epitaxial film formation process has two major steps. Step A removes the native oxide film on the silicon wafer surface at 1100C for 1 min. Next, the wafer temperature is

supplied to the halogen lamps. The total electric power is less than 1500 W.

Figure 10. Half-inch silicon CVD reactor for the Minimal Fab.

Figure 11. Two reflectors of (a) Type-I and (b) Type-II.

Figure 13. Process of silicon epitaxial growth by (a) Steps A–C and by (b) Steps A and B. Step A removes native oxide film, Step B forms silicon epitaxial film and Step C is for stand-by. Dotted lines show virtual reactor process.

compare their thermal behaviours through exactly the same process. In the second part, the effect of Step C was evaluated.

When the wafer holder temperature, TWH, is 650C, the silicon epitaxial film growth rate was

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The silicon epitaxial film is formed by the two types of reflectors, as shown in Figure 15. The gas flow rates of the TCS and the H2 were 9 and 215 sccm, respectively. Step C is intentionally introduced for cooling the reflector and for comparing the two types of reflector through the same process. In Figure 15, the dotted line and the solid line show the wafer holder temperatures during Step B immediately after Step C, by the Type-I and -II reflectors, respectively.

For the Type-I reflector, the TCS gas is introduced between 0 and 5 min. The wafer holder temperature finally becomes 573C at 5 min at the halogen lamp voltage of 63 V. The solid line shows the temperature change using the Type-II reflector. The wafer holder temperature reaches 621C at 4 min at the halogen lamp voltage of 62 V. The Type-II reflector can achieve

The wafer holder temperature using the Type-I reflector still increases at 5 min as shown in Figure 15. As shown by the dotted line in Figure 16, the wafer holder temperature using the Type-I reflector at the halogen lamp voltage of 62 V can reach 553C at 10 min. This is 70C lower than that by the Type-II reflector. Additionally, the temperature using the Type-I reflector is entirely lower than that of Type-II through Steps A–C. Thus, the Type-II reflector

In Figures 15 and 16, the wafer holder temperature increases after introducing the TCS gas at Step B. Because TCS gas absorbs the infrared light [15, 16], the gas phase temperature increases

Figure 15. Temperature of wafer holder during Step B immediately after Step C. Dotted line: Type-I reflector at 63 V for 5

about 1.2 μm/min, corresponding to the T<sup>W</sup> value near 960C.

the wafer temperature higher and faster than the Type-I reflector do.

achieves a quicker heating process.

and finally the wafer temperature increases.

min and solid line: Type-II reflector at 62 V for 4 min.

#### 4.3. Wafer rotation and susceptor

For obtaining the uniform-thick epitaxial film by the classical ways [18], the wafer rotation and the silicon carbide susceptor are employed, as shown in Figure 14. Because even the slow wafer rotation has the effect of averaging the film growth rate along the concentric circle [17], the epitaxial film thickness is expected to become flat over the wafer. Silicon carbide has a high thermal conductivity [19] for decreasing the temperature difference over the wafer. The diameter and the thickness of the silicon carbide plate are 16 and 0.58 mm, respectively. Three silicon carbide plates are stacked beneath the silicon wafer.

#### 4.4. Wafer temperature evaluation

The wafer holder temperature, TWH, is measured and evaluated. The silicon wafer temperature, TW, is obtained from the silicon epitaxial growth rate. At the wafer temperature lower than 1000�C and at the TCS gas concentration higher than 1%, the silicon epitaxial growth rate is governed by the surface chemical reaction. The epitaxial growth rate is expressed using the wafer temperature, TW, [13]

$$\text{Growth rate} \left(\upmu\text{m/min}\right) = 1.95 \times 109 \,\text{e}^{\left(-26100/T\_W\right)} \qquad \left(T\_W < 1000^{\circ}\text{C}\right) . \tag{8}$$

Figure 14. Half-inch wafer and silicon carbide susceptor on rotating wafer holder.

When the wafer holder temperature, TWH, is 650C, the silicon epitaxial film growth rate was about 1.2 μm/min, corresponding to the T<sup>W</sup> value near 960C.

compare their thermal behaviours through exactly the same process. In the second part, the

For obtaining the uniform-thick epitaxial film by the classical ways [18], the wafer rotation and the silicon carbide susceptor are employed, as shown in Figure 14. Because even the slow wafer rotation has the effect of averaging the film growth rate along the concentric circle [17], the epitaxial film thickness is expected to become flat over the wafer. Silicon carbide has a high thermal conductivity [19] for decreasing the temperature difference over the wafer. The diameter and the thickness of the silicon carbide plate are 16 and 0.58 mm, respectively. Three

The wafer holder temperature, TWH, is measured and evaluated. The silicon wafer temperature, TW, is obtained from the silicon epitaxial growth rate. At the wafer temperature lower than 1000�C and at the TCS gas concentration higher than 1%, the silicon epitaxial growth rate is governed by the surface chemical reaction. The epitaxial growth rate is expressed using the

ð�26100=TW <sup>Þ</sup> <sup>ð</sup>TW <sup>&</sup>lt; <sup>1000</sup>�

CÞ: (8)

effect of Step C was evaluated.

144 Epitaxy

4.3. Wafer rotation and susceptor

4.4. Wafer temperature evaluation

wafer temperature, TW, [13]

silicon carbide plates are stacked beneath the silicon wafer.

Growth rate ðμm=minÞ ¼ 1:95 � 109 e

Figure 14. Half-inch wafer and silicon carbide susceptor on rotating wafer holder.

The silicon epitaxial film is formed by the two types of reflectors, as shown in Figure 15. The gas flow rates of the TCS and the H2 were 9 and 215 sccm, respectively. Step C is intentionally introduced for cooling the reflector and for comparing the two types of reflector through the same process. In Figure 15, the dotted line and the solid line show the wafer holder temperatures during Step B immediately after Step C, by the Type-I and -II reflectors, respectively.

For the Type-I reflector, the TCS gas is introduced between 0 and 5 min. The wafer holder temperature finally becomes 573C at 5 min at the halogen lamp voltage of 63 V. The solid line shows the temperature change using the Type-II reflector. The wafer holder temperature reaches 621C at 4 min at the halogen lamp voltage of 62 V. The Type-II reflector can achieve the wafer temperature higher and faster than the Type-I reflector do.

The wafer holder temperature using the Type-I reflector still increases at 5 min as shown in Figure 15. As shown by the dotted line in Figure 16, the wafer holder temperature using the Type-I reflector at the halogen lamp voltage of 62 V can reach 553C at 10 min. This is 70C lower than that by the Type-II reflector. Additionally, the temperature using the Type-I reflector is entirely lower than that of Type-II through Steps A–C. Thus, the Type-II reflector achieves a quicker heating process.

In Figures 15 and 16, the wafer holder temperature increases after introducing the TCS gas at Step B. Because TCS gas absorbs the infrared light [15, 16], the gas phase temperature increases and finally the wafer temperature increases.

Figure 15. Temperature of wafer holder during Step B immediately after Step C. Dotted line: Type-I reflector at 63 V for 5 min and solid line: Type-II reflector at 62 V for 4 min.

Figure 16. Temperature of wafer holder during Step B after Step C. Dotted line by Type-I reflector at 62 V for 10 min. Solid line by Type-II reflector at 62 V for 4 min.

For the thermal process optimization, the influence of Step C on the wafer temperature is evaluated using the Type-II reflector. Figure 17 shows the wafer holder temperature with and without Step C at the halogen lamp voltage of 62 V. The flow rates of H2 gas and TCS gas are 215 and 9 sccm, respectively.

The halogen lamp voltage at Step B is 60 V. The film thickness distribution is evaluated at five points along the longitudinal and transverse lines, using the dotted line and the solid line, respectively, as shown in Figure 18. Figure 18(a) shows the thickness profile of the epitaxial film which is formed without using the wafer rotation and without using the silicon carbide susceptor. The epitaxial film thickness along the x-axis is from 1.5 to 3.5 μm. By contrast, the epitaxial film thickness along the y-axis is very flat. In this figure, the film thickness shows a decrease from right to left. The epitaxial growth rate is near 0.5 μm/min, which corresponds to the wafer temperature of 950C following Eq. (4). The epitaxial growth rate in Figure 18 is governed by the rate of surface chemical reaction [13]. By the relationship, obtained in Section 2 [9], the introduced gas reaches the wafer surface and decreases its temperature. As shown in Figure 19(a), by the asymmetric gas flow direction, the surface temperature is low in the left region. Corresponding to this temperature trend, the epitaxial film in the left region is thinner than that in the right region. Additionally, when the wafer is directly loaded on the quartz wafer holder, an adiabaticlike environment is formed. It produces a locally high-temperature region and the non-uniform

Figure 17. Wafer holder temperature using Type-II reflector. Dotted line: along Steps A, C and B and solid line: along

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Steps A and B without Step C.

The wafer rotation is used for adjusting the asymmetric condition. Figure 18(b) shows the epitaxial film thickness profile, when the wafer rotates. The epitaxial film thickness shows a hill and a valley along the x- and y-axes. Although the thickness profile is averaged along the concentric circle of the rotating wafer, rather the complicated thickness profile appears. The

thick film, because the infrared rays are easily concentrated to a local spot [20].

The dotted line shows the wafer holder temperature through Steps A, C and B. In Step A, the wafer holder temperature reaches 650C. During Step C, the wafer holder temperature is cooled to about 250C, by decreasing the halogen lamp voltage to 30 from 80 V. The wafer holder temperature is then increased in Step B. At the halogen lamp voltage of 62 V, the wafer holder temperature becomes 621C at 14 min. However, the wafer holder temperature still increases even at 14 min.

The solid line shows the wafer holder temperature during Steps A and B without Step C. The temperature during Step A is the same as the dotted line. After Step A, the halogen lamp voltage is increased to 62 V. The wafer holder temperature reaches 618C at 6 min in a steady state. Thus, the process deleting Step C can be quick and stable.

#### 4.5. Wafer rotation and susceptor

Using the Type-II reflector, the silicon epitaxial film is formed on the half-inch silicon wafer surface, by Steps A and B. The TCS and H2 flow rates are 9 and 215 sccm, respectively, for 4 min.

Figure 17. Wafer holder temperature using Type-II reflector. Dotted line: along Steps A, C and B and solid line: along Steps A and B without Step C.

For the thermal process optimization, the influence of Step C on the wafer temperature is evaluated using the Type-II reflector. Figure 17 shows the wafer holder temperature with and without Step C at the halogen lamp voltage of 62 V. The flow rates of H2 gas and TCS gas are

Figure 16. Temperature of wafer holder during Step B after Step C. Dotted line by Type-I reflector at 62 V for 10 min.

The dotted line shows the wafer holder temperature through Steps A, C and B. In Step A, the wafer holder temperature reaches 650C. During Step C, the wafer holder temperature is cooled to about 250C, by decreasing the halogen lamp voltage to 30 from 80 V. The wafer holder temperature is then increased in Step B. At the halogen lamp voltage of 62 V, the wafer holder temperature becomes 621C at 14 min. However, the wafer holder temperature still

The solid line shows the wafer holder temperature during Steps A and B without Step C. The temperature during Step A is the same as the dotted line. After Step A, the halogen lamp voltage is increased to 62 V. The wafer holder temperature reaches 618C at 6 min in a steady

Using the Type-II reflector, the silicon epitaxial film is formed on the half-inch silicon wafer surface, by Steps A and B. The TCS and H2 flow rates are 9 and 215 sccm, respectively, for 4 min.

state. Thus, the process deleting Step C can be quick and stable.

215 and 9 sccm, respectively.

146 Epitaxy

Solid line by Type-II reflector at 62 V for 4 min.

increases even at 14 min.

4.5. Wafer rotation and susceptor

The halogen lamp voltage at Step B is 60 V. The film thickness distribution is evaluated at five points along the longitudinal and transverse lines, using the dotted line and the solid line, respectively, as shown in Figure 18. Figure 18(a) shows the thickness profile of the epitaxial film which is formed without using the wafer rotation and without using the silicon carbide susceptor. The epitaxial film thickness along the x-axis is from 1.5 to 3.5 μm. By contrast, the epitaxial film thickness along the y-axis is very flat. In this figure, the film thickness shows a decrease from right to left. The epitaxial growth rate is near 0.5 μm/min, which corresponds to the wafer temperature of 950C following Eq. (4). The epitaxial growth rate in Figure 18 is governed by the rate of surface chemical reaction [13]. By the relationship, obtained in Section 2 [9], the introduced gas reaches the wafer surface and decreases its temperature. As shown in Figure 19(a), by the asymmetric gas flow direction, the surface temperature is low in the left region. Corresponding to this temperature trend, the epitaxial film in the left region is thinner than that in the right region. Additionally, when the wafer is directly loaded on the quartz wafer holder, an adiabaticlike environment is formed. It produces a locally high-temperature region and the non-uniform thick film, because the infrared rays are easily concentrated to a local spot [20].

The wafer rotation is used for adjusting the asymmetric condition. Figure 18(b) shows the epitaxial film thickness profile, when the wafer rotates. The epitaxial film thickness shows a hill and a valley along the x- and y-axes. Although the thickness profile is averaged along the concentric circle of the rotating wafer, rather the complicated thickness profile appears. The

local low- or high-temperature spot, denoted by the letter L, still remains. An additional method

Silicon Epitaxial Reactor for Minimal Fab http://dx.doi.org/10.5772/intechopen.69986 149

The locally high and low temperatures over the wafer surface may be produced due to the quartz material having a low thermal conductivity [20]. The heat transport in the horizontal direction is enhanced by the silicon carbide susceptor. Figure 19(c) shows that the local nonuniformity of the wafer temperature remaining even using the wafer rotation is reduced by the high heat transport through the silicon carbide susceptor. As shown in Figure 18(c), the

By using the small, thin and simple geometry of the reactor parts, the quick and flat epitaxial film production is possible. This concept is valid not only for the minimal CVD reactor.

A chemical vapour deposition reactor for the growth of half-inch silicon wafers is designed by employing (i) a vertical gas flow, (ii) rapid thermal operation using concentrated infrared light and (iii) a quick reactor cleaning process. For the rapid heating process, absorption of infrared light and heat transport by the flowing gases are active parameters. Under the optimized conditions, the cleaning-free process is possible. The reactor parts placed near the wafer must be small, slim and thin for quickly heating the wafer. The wafer rotation and the heatconductive susceptor help to fabricate uniform silicon epitaxial films. Overall, important parameters are listed in Table 2. This table includes several parameters which are active and

is necessary for obtaining the flat silicon film.

5. Summary

useful for the small-sized reactor.

Parameters Value

Trichlorosilane gas flow rate 20 sccm

Deposition time 1–8 min Substrate temperature 800–1000C Substrate rotation 4 rpm

Substrate 12.5 mm diameter silicon wafer Gas flow Vertical (from top to bottom) Pressure Atmospheric pressure Precursor Trichlorosilane (SiHCl3) Hydrogen gas flow rate Less than 200 sccm

Chlorine trifluoride gas flow rate (Reactor cleaning) 50 sccm in 1000 sccm in N2

Electric power 55–65 V, less than 1500 W Substrate surface cleaning Near 1000C in H2 within 1 min

Heating module Concentrated infrared light (Three halogen lamps) Slim

and thin reflector

epitaxial film thickness becomes very flat along the x- and y-axes.

Figure 18. Thickness profile of obtained silicon epitaxial film: (a) without wafer rotation and without silicon carbide susceptor, (b) with wafer rotation and without silicon carbide susceptor and (c) with wafer rotation and with three silicon carbide susceptors.

Figure 19. Influence of gas flow from the inlet, wafer rotation and silicon carbide susceptor on the epitaxial film thickness (a) with no wafer rotation and no silicon carbide susceptor, (b) with wafer rotation and no silicon carbide susceptor and (c) with wafer rotation and three silicon carbide susceptors.

local low- or high-temperature spot, denoted by the letter L, still remains. An additional method is necessary for obtaining the flat silicon film.

The locally high and low temperatures over the wafer surface may be produced due to the quartz material having a low thermal conductivity [20]. The heat transport in the horizontal direction is enhanced by the silicon carbide susceptor. Figure 19(c) shows that the local nonuniformity of the wafer temperature remaining even using the wafer rotation is reduced by the high heat transport through the silicon carbide susceptor. As shown in Figure 18(c), the epitaxial film thickness becomes very flat along the x- and y-axes.

By using the small, thin and simple geometry of the reactor parts, the quick and flat epitaxial film production is possible. This concept is valid not only for the minimal CVD reactor.

## 5. Summary

Figure 18. Thickness profile of obtained silicon epitaxial film: (a) without wafer rotation and without silicon carbide susceptor, (b) with wafer rotation and without silicon carbide susceptor and (c) with wafer rotation and with three silicon

Figure 19. Influence of gas flow from the inlet, wafer rotation and silicon carbide susceptor on the epitaxial film thickness (a) with no wafer rotation and no silicon carbide susceptor, (b) with wafer rotation and no silicon carbide susceptor and (c)

with wafer rotation and three silicon carbide susceptors.

carbide susceptors.

148 Epitaxy

A chemical vapour deposition reactor for the growth of half-inch silicon wafers is designed by employing (i) a vertical gas flow, (ii) rapid thermal operation using concentrated infrared light and (iii) a quick reactor cleaning process. For the rapid heating process, absorption of infrared light and heat transport by the flowing gases are active parameters. Under the optimized conditions, the cleaning-free process is possible. The reactor parts placed near the wafer must be small, slim and thin for quickly heating the wafer. The wafer rotation and the heatconductive susceptor help to fabricate uniform silicon epitaxial films. Overall, important parameters are listed in Table 2. This table includes several parameters which are active and useful for the small-sized reactor.



References

230-238

[1] http://www.itrs.net/

[2] Thean A. Silicon & beyond CMOS: The path of advanced electronic structure engineering

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[4] Khumpuang S, Hara S. A MOSFET fabrication using a maskless lithography system in clean-localized environment of Minimal Fab. IEEE Transactions on Semiconductor

[5] Khumpuang S, Imura F, Hara S. Analyses on cleanroom-free performance and transistor manufacturing cycle time of Minimal Fab. IEEE Transactions on Semiconductor

[6] Khumpuang S, Maekawa S, Hara S. Photolithography for Minimal Fab system. IEEJ

[7] Habuka H, Otsuka T, Mayusumi M, Shimada M, Okuyama K. A direct approach to evaluate the thermal condition of a silicon substrate under infrared rays and specular

[8] Habuka H, Sukenobu T, Koda H, Takeuchi T, Aihara M. Silicon etch rate using chlorine

[9] Li N, Habuka H, Ikeda S, Hara S. Silicon chemical vapor deposition process using a halfinch silicon wafer for minimal manufacturing system. Physics Procedia. 2013;46C:

[10] Li N, Habuka H, Ikeda S, Ishida Y, Hara S. Practical thermal condition of silicon CVD reactor for minimal manufacturing. In: Industrial Engineering, Machine Design and Automation (IEMDA 2014) & Computer Science and Application (CCSA 2014). pp. 393-400. 2014 International Conference on Materials Science and Energy Engineering (CMSEE

[11] Li N, Habuka H, Ikeda S, Ishida Y, Hara S. Practical thermal condition of silicon CVD reactor for minimal manufacturing. In: Proceedings of the Forum on the Science and Technology of Silicon Materials; 19–22 Oct. 2014; Hamamatsu, Japan. pp. 219-221.The

[12] Li N, Habuka H, Ishida Y, Ikeda S-i, Hara S. Reflector influence on rapid heating of minimal manufacturing chemical vapor deposition reactor. ECS Journal of Solid State

[13] Habuka H, Nagoya T, Mayusumi M, Katayama M, Shimada M, Okuyama K. Model on transport phenomena and epitaxial growth of silicon thin film in SiHCl3-H2 system under

Science and Technology. 2016;5(5):P280-P284. DOI: 10.1149/2.0251605jss

atmospheric pressure. Journal of Crystal Growth. 1996;169:61-72

for low-voltage transistors. Solid State Phenomena. 2013;195:3

Transactions on Sensors and Micromachines. 2013;133:272-277

reflectors. Journal of Electrochemical Society. 1999;146(2):713-718

trifluoride. Journal of Electrochemical Society. 2004;151:G783

2014). December 12-14, 2014, Sanya, Hainan, China

Japan Society for the Promotion of Science (2014)

[3] http://unit.aist.go.jp/neri/mini-sys/fabsystem/index.html

Manufacturing. 2015;28(3):393-398

Manufacturing. 2015;28(4):551-556

Table 2. List of parameters: silicon epitaxial growth for Minimal Fab.


Table 3. Comparison between minimal and ordinary CVD reactor.

The differences of the reactor design between the Minimal Fab and the ordinary CVD are listed in Table 3. The film growth on a small wafer using small gas flow rates significantly reduces system cost.

## Author details

Ning Li<sup>1</sup> , Hitoshi Habuka<sup>1</sup> \*, Yuuki Ishida2,3, Shin-ichi Ikeda2,3 and Shiro Hara2,3

\*Address all correspondence to: habuka1@ynu.ac.jp

1 Department of Chemical and Energy Engineering, Yokohama National University, Yokohama, Japan

2 National Institutes of Advanced Science and Technology, AIST Tsukuba Central 2, Tsukuba, Japan

3 Minimal Fab Development Association, AIST Tsukuba Central 2, Tsukuba, Japan

## References

The differences of the reactor design between the Minimal Fab and the ordinary CVD are listed in Table 3. The film growth on a small wafer using small gas flow rates significantly reduces

1 Department of Chemical and Energy Engineering, Yokohama National University,

3 Minimal Fab Development Association, AIST Tsukuba Central 2, Tsukuba, Japan

2 National Institutes of Advanced Science and Technology, AIST Tsukuba Central 2, Tsukuba,

\*, Yuuki Ishida2,3, Shin-ichi Ikeda2,3 and Shiro Hara2,3

pancake, and so on

Forced flow, Vertical (downward), horizontal, cylinder,

system cost.

150 Epitaxy

Ning Li<sup>1</sup>

Japan

Author details

Yokohama, Japan

, Hitoshi Habuka<sup>1</sup>

\*Address all correspondence to: habuka1@ynu.ac.jp

Parameters Value

Footprint 30 45 cm

Table 2. List of parameters: silicon epitaxial growth for Minimal Fab.

Total gas flow rate <0.2 slm >100 slm Growth rate Near 1 μm/min 1–8 μm/min

Gas flow Natural convection, Vertical (downward)

Pressure 1 atm (or reduced pressure) 1 atm or reduced pressure Precursor SiHCl3 SiHCl3, SiH2Cl2, SiH4, and so on

Heating method Concentrated light by lamp heating Lamp, resistant and inductive heating

Reactor cleaning ClF3 gas at higher than RT HCl gas near 1200C

Footprint 0.3 0.45 m2 Several Several m<sup>2</sup> Throughput Several tens wafers/min (Target) Several wafers/min Reactor price > \$30,000 (Target) > \$3,000,000

Electric power <1500 W >100,000 W

Table 3. Comparison between minimal and ordinary CVD reactor.

Susceptor Silicon carbide plate

Minimal CVD reactor Ordinary CVD reactor

Wafer diameter 12.5 mm, single wafer 150, 200, 300 and 450 mm, multi-(batch) and single wafer


[14] Morishita J, Wu S, Ishihara Y, Kimijima T. Observation of purifier performance to reduce moisture in hydrogen chloride by near infrared laser absorption spectrometry. Journal of Applied Physics. 1997;36:L1706

**Section 3**

**III-V Epitaxy**


**Section 3**
