**Germanium-on-Silicon for Integrated Silicon Photonics**

Xiaochen Sun *Massachusetts Institute of Technology USA*

## **1. Introduction**

To meet the unprecedented demands for data transmission speed and bandwidth silicon integrated photonics that can generate, modulate, process and detect light signals is being developed. Integrated silicon photonics that can be built using existing CMOS fabrication facilities offers the tantalizing prospect of a scalable and cost-efficient solution to replace electrical interconnects. Silicon, together with commonly used dielectric materials in CMOS processes such as silicon dioxide, is a great material system for optical confinement and wave transmission in near infrared range. However, silicon is not a good choice for active photonic devices due to its transparency in such wavelength range. Germanium and GeSi alloy, the materials that have long been adopted to improve the performance of silicon transistors in many ways, have been showing their potential as the building blocks of such active integrated optical devices. This chapter discusses the research of using germanium and GeSi for silicon-integrated photodetection and light source in the contexts of material physics and growth, device design and fabrication.

This introduction section briefly introduces the background of integrated silicon photonics and some germanium properties which are important for photonic applications. Next section focuses on waveguide-integrated germanium photodetectors which can readily be integrated with silicon waveguide on mature silicon or silicon-on-insulator (SOI) platform. The physics and design considerations of these devices are presented with details. The fabrication processes of these devices are also discussed with some extent. Next section includes a newly developed field that using germanium for light sources in silicon photonics applications such as light-emitting-diodes (LEDs) and lasers. There has been a few breakthroughs in this topic including the author's work of epitaxial germanium LEDs and optically pumped lasers operating at room temperature. The physics of this unusual concept of using indirect band gap material for light emission is discussed in details and some important results are presented.

#### **1.1 Integrated silicon photonics**

Silicon integrated circuits (ICs) had been developed in an extraordinary pace for almost four decades before 2005. It is known as Moore's law that the number of transistors in an integrated circuit doubles roughly every eighteen months (Moore, 1965). The scalability is the main reason of the tremendous success of many silicon IC based technologies (Haensch et al., 2006), such as silicon complimentary metal oxide semiconductor (Si-CMOS) technology.

Silicon Photonics 3

Germanium-on-Silicon for Integrated Silicon Photonics 5

grown on silicon since late 1970s after the invention of molecular beam epitaxy (MBE) (Bean

Despite the importance of the studies of germanium epitaxy by MBE, it is recognized by many researchers that MBE is not likely to be a good choice for massive device manufacturing. The complexity of MBE equipment and the low yield of single wafer MBE process eventually gave way to chemical vapor deposition (CVD) for growing germanium and GeSi films on silicon substrate. A variety of CVD growth techniques have been developed for germanium and GeSi epitaxy since 1980s and the crystalline quality is equal to, if not better than, what can be

The development of germanium and GeSi CVD epitaxy followed the work of CVD silicon epitaxy demanded by advanced metal-oxide-semiconductor field-effect transistor (MOSFET) devices. Like silicon epitaxy, early GeSi epitaxy in CVD systems was performed at atmospheric pressure. This type of growth usually requires a hydrogen prebake with an option of hydrochloride (HCl) vapor etch at very high temperature (>1100◦C) to volatilize or dissolve native SiO2 or carbon on the silicon surface (Raider et al., 1975; Vossen et al., 1984). The growth temperature is carefully chosen (e.g. around 800◦C) to balance between a reasonable germanium growth rate and the prevention of relaxation of metastable strained layer. A typical CVD reactor of such kind used by some researchers for GeSi growth (Kamins & Meyer, 1991) is made by ASM International. Atmospheric pressure CVD has insurmountable shortcomings which make it less popular in growing high quality silicon and germanium epitaxial films nowadays. The atmospheric pressure chamber condition can not avoid impurities contaminations from ambient and the need for very high temperature bake and growth causes autodoping issue, a phenomenon where doped regions existent in a

To overcome these shortcomings, ultra-high vacuum chemical vapor deposition (UHVCVD) was introduced by Meyerson and co-workers at IBM T. J. Watson Research Center in 1986 (Meyerson, 1986). In a UHVCVD system, the base pressure of the chamber is usually in the range of 10−<sup>8</sup> <sup>∼</sup> <sup>10</sup>−<sup>9</sup> torr when idling and 10−<sup>3</sup> torr during growth. At this ultra high vacuum environment, the contamination can be well controlled at a very low level. For example, the system induced background partial pressure of contaminants such as water vapor, oxygen, and hydrocarbons is limited to values in the range of 10−<sup>11</sup> torr (Meyerson, 1992). As a result of the superior condition of ambient and substrate surface, the germanium and GeSi epitaxial growth is performed at relatively low temperatures (400∼700◦C) without requiring extensive high temperature hydrogen pre-bake. UHVCVD technique is suitable for manufacturing owing to its high throughput multiple-wafer growth process. The early work of GeSi UHVCVD epitaxy focused on high silicon content GeSi alloy films driven by the demands for mobility enhancement by strained GeSi in CMOS transistors (Meyerson, 1990). There are numerous work on this type of GeSi epitaxy, however it is not our primary interest in the photonic applications described in this chapter. There was some UHVCVD germanium epitaxy reports in the early 1990s (Kobayashi et al., 1990), while the extensive development of pure germanium epitaxy by UHVCVD began in the early to late 1990s (Currie et al., 1998;

On the other hand, germanium can also be grown with very high carrier (mainly hydrogen gas) flow rate at relaxed chamber base pressure. Rapid growth rate and surface passivation as a result of high carrier flow rate reduces of the chance of impurities contamination. The base pressure during growth e.g. tens of Torrs, is much higher than that in the UHVCVD case while lower than atmospheric pressure thereby this approach is called reduced pressure

et al., 1984; Garozzo et al., 1982; Kasper & Herzog, 1977; Tsaur et al., 1981).

substrate transfer substantial amounts of dopant into the epitaxial layer.

Luan et al., 1999) as a result of the booming photonics research.

achieved in MBE process.

The scalability of Si-CMOS technology is not only about the shrinkage of the dimensions of the devices, but also a number of other factors for maintaining the power density while boosting the performance. However, many issues against further scaling have been found including applied voltage barrier (threshold voltage) and passive component heating due to sub-threshold leakage current. In 2005, "for the first time in thirty five years, the clock speed of the fastest commercial computer chips has not increased" (Muller, 2005) because of the above reasons.

In order to solve these problems in data transmission speed scaling and passive component heat dissipation, optical interconnects relying on silicon photonics are proposed as a promising solution. Silicon photonics offers a platform for the monolithic integration of optics and microelectronics on the same silicon chips (Lipson, 2004), aiming for many applications including the optical interconnects (Haurylau et al., 2006). At present, electrical circuit speed or propagation delay is limited by interconnect RC delay which increases with the scaling of device dimensions. Optical interconnects which use phonon as information carrier are not subject to the RC delay in the first place. The weak electrical interaction between photons and guiding media inherently minimize heat generation in propagation. The interaction among photons is also weak at lower optical power so that multiple transmission using different wavelengths can co-exist in the same propagation channel. This wavelength multiplexing (WDM) technique dramatically increase the aggregated bandwidth of the transmission system. To achieve such optical interconnects using compatible silicon processing techniques is the major task of monolithic integrated silicon photonics (Aicher & Haberger, 1999; OConnor et al., 2007; O'Connor et al., 2006). The compatibility with ´ silicon enables a cost-effective, scalable and manufacturable solution for implementing silicon photonics. To address its importance and rapid growth, a roadmap of silicon photonics has been developed by academic and industrial professionals and released on a yearly basis (Kirchain & Kimerling, 2007).

#### **1.2 Germanium epitaxy on silicon**

The world's first transistor is made from Germanium by John Bardeen, Walter Brattain and William Shockley at Bell Labs in December, 1947. Beginning with this invention, a revolution of semiconductor electronics quickly started and have profoundly changed our life in many ways. But germanium, the first used semiconductor material, soon gave its crown to another semiconductor in the same elementary group - silicon - in this great revolution. Silicon has superior properties than germanium in many ways: chemical and mechanical stability, stable oxides and etc. Based on silicon, integrated circuit (IC) was realized and appeared in numerous electronic devices that we use and carry everyday.

Silicon was so successful that germanium was forgotten by most researchers for decades soon after the first silicon transistor was invented and commercialized from Texas Instrument in 1952. However, germanium has its own advantages, e.g. higher carrier mobility than silicon, thereby some researchers investigated ways to integrate germanium on silicon substrates. As semiconductor devices generally require single crystalline germanium thin films, the attempts of heterogeneous epitaxy of germanium on silicon emerged. People soon found a great difficulty of growing germanium thicker than its critical thickness because there is 4% mismatch between the lattice constants of germanium and silicon. Although the earliest work of the epitaxy of germanium-silicon (GeSi) alloy on silicon dates back to 1962 (Miller & Grieco, 1962), good quality pure germanium films or high germanium content GeSi films have been 2 Will-be-set-by-IN-TECH

The scalability of Si-CMOS technology is not only about the shrinkage of the dimensions of the devices, but also a number of other factors for maintaining the power density while boosting the performance. However, many issues against further scaling have been found including applied voltage barrier (threshold voltage) and passive component heating due to sub-threshold leakage current. In 2005, "for the first time in thirty five years, the clock speed of the fastest commercial computer chips has not increased" (Muller, 2005) because of the above

In order to solve these problems in data transmission speed scaling and passive component heat dissipation, optical interconnects relying on silicon photonics are proposed as a promising solution. Silicon photonics offers a platform for the monolithic integration of optics and microelectronics on the same silicon chips (Lipson, 2004), aiming for many applications including the optical interconnects (Haurylau et al., 2006). At present, electrical circuit speed or propagation delay is limited by interconnect RC delay which increases with the scaling of device dimensions. Optical interconnects which use phonon as information carrier are not subject to the RC delay in the first place. The weak electrical interaction between photons and guiding media inherently minimize heat generation in propagation. The interaction among photons is also weak at lower optical power so that multiple transmission using different wavelengths can co-exist in the same propagation channel. This wavelength multiplexing (WDM) technique dramatically increase the aggregated bandwidth of the transmission system. To achieve such optical interconnects using compatible silicon processing techniques is the major task of monolithic integrated silicon photonics (Aicher & Haberger, 1999; OConnor et al., 2007; O'Connor et al., 2006). The compatibility with ´ silicon enables a cost-effective, scalable and manufacturable solution for implementing silicon photonics. To address its importance and rapid growth, a roadmap of silicon photonics has been developed by academic and industrial professionals and released on a yearly basis

The world's first transistor is made from Germanium by John Bardeen, Walter Brattain and William Shockley at Bell Labs in December, 1947. Beginning with this invention, a revolution of semiconductor electronics quickly started and have profoundly changed our life in many ways. But germanium, the first used semiconductor material, soon gave its crown to another semiconductor in the same elementary group - silicon - in this great revolution. Silicon has superior properties than germanium in many ways: chemical and mechanical stability, stable oxides and etc. Based on silicon, integrated circuit (IC) was realized and appeared in

Silicon was so successful that germanium was forgotten by most researchers for decades soon after the first silicon transistor was invented and commercialized from Texas Instrument in 1952. However, germanium has its own advantages, e.g. higher carrier mobility than silicon, thereby some researchers investigated ways to integrate germanium on silicon substrates. As semiconductor devices generally require single crystalline germanium thin films, the attempts of heterogeneous epitaxy of germanium on silicon emerged. People soon found a great difficulty of growing germanium thicker than its critical thickness because there is 4% mismatch between the lattice constants of germanium and silicon. Although the earliest work of the epitaxy of germanium-silicon (GeSi) alloy on silicon dates back to 1962 (Miller & Grieco, 1962), good quality pure germanium films or high germanium content GeSi films have been

reasons.

(Kirchain & Kimerling, 2007).

**1.2 Germanium epitaxy on silicon**

numerous electronic devices that we use and carry everyday.

grown on silicon since late 1970s after the invention of molecular beam epitaxy (MBE) (Bean et al., 1984; Garozzo et al., 1982; Kasper & Herzog, 1977; Tsaur et al., 1981).

Despite the importance of the studies of germanium epitaxy by MBE, it is recognized by many researchers that MBE is not likely to be a good choice for massive device manufacturing. The complexity of MBE equipment and the low yield of single wafer MBE process eventually gave way to chemical vapor deposition (CVD) for growing germanium and GeSi films on silicon substrate. A variety of CVD growth techniques have been developed for germanium and GeSi epitaxy since 1980s and the crystalline quality is equal to, if not better than, what can be achieved in MBE process.

The development of germanium and GeSi CVD epitaxy followed the work of CVD silicon epitaxy demanded by advanced metal-oxide-semiconductor field-effect transistor (MOSFET) devices. Like silicon epitaxy, early GeSi epitaxy in CVD systems was performed at atmospheric pressure. This type of growth usually requires a hydrogen prebake with an option of hydrochloride (HCl) vapor etch at very high temperature (>1100◦C) to volatilize or dissolve native SiO2 or carbon on the silicon surface (Raider et al., 1975; Vossen et al., 1984). The growth temperature is carefully chosen (e.g. around 800◦C) to balance between a reasonable germanium growth rate and the prevention of relaxation of metastable strained layer. A typical CVD reactor of such kind used by some researchers for GeSi growth (Kamins & Meyer, 1991) is made by ASM International. Atmospheric pressure CVD has insurmountable shortcomings which make it less popular in growing high quality silicon and germanium epitaxial films nowadays. The atmospheric pressure chamber condition can not avoid impurities contaminations from ambient and the need for very high temperature bake and growth causes autodoping issue, a phenomenon where doped regions existent in a substrate transfer substantial amounts of dopant into the epitaxial layer.

To overcome these shortcomings, ultra-high vacuum chemical vapor deposition (UHVCVD) was introduced by Meyerson and co-workers at IBM T. J. Watson Research Center in 1986 (Meyerson, 1986). In a UHVCVD system, the base pressure of the chamber is usually in the range of 10−<sup>8</sup> <sup>∼</sup> <sup>10</sup>−<sup>9</sup> torr when idling and 10−<sup>3</sup> torr during growth. At this ultra high vacuum environment, the contamination can be well controlled at a very low level. For example, the system induced background partial pressure of contaminants such as water vapor, oxygen, and hydrocarbons is limited to values in the range of 10−<sup>11</sup> torr (Meyerson, 1992). As a result of the superior condition of ambient and substrate surface, the germanium and GeSi epitaxial growth is performed at relatively low temperatures (400∼700◦C) without requiring extensive high temperature hydrogen pre-bake. UHVCVD technique is suitable for manufacturing owing to its high throughput multiple-wafer growth process. The early work of GeSi UHVCVD epitaxy focused on high silicon content GeSi alloy films driven by the demands for mobility enhancement by strained GeSi in CMOS transistors (Meyerson, 1990). There are numerous work on this type of GeSi epitaxy, however it is not our primary interest in the photonic applications described in this chapter. There was some UHVCVD germanium epitaxy reports in the early 1990s (Kobayashi et al., 1990), while the extensive development of pure germanium epitaxy by UHVCVD began in the early to late 1990s (Currie et al., 1998; Luan et al., 1999) as a result of the booming photonics research.

On the other hand, germanium can also be grown with very high carrier (mainly hydrogen gas) flow rate at relaxed chamber base pressure. Rapid growth rate and surface passivation as a result of high carrier flow rate reduces of the chance of impurities contamination. The base pressure during growth e.g. tens of Torrs, is much higher than that in the UHVCVD case while lower than atmospheric pressure thereby this approach is called reduced pressure

Silicon Photonics 5

Germanium-on-Silicon for Integrated Silicon Photonics 7

dislocations on SiO2 sidewalls and leave the overgrown germanium above Si/SiO2 layer with reduced dislocation densities. The disadvantage of this approach is the difficulty of surface morphology control and the inconvenience of using the fine patterned Si/SiO2 surface in

The electronic band structure of bulk germanium at room temperature is shown in Fig. 1. The valence band is composed of a light-hole band, a heavy-hole band, and a split-off band from spin-orbit interaction. The light-hole band and the heavy-hole band are degenerate at wave vector **k** = 0 or Γ point which is at the maximal energy of the valence band. The minimal energy of the conduction band is located at **k** =< 111 > or *L* point. The energy difference between the conduction band at *L* point and the valence band at Γ point determines the narrowest band gap in germanium: *Eg* = 0.664 eV. This type of band gap is called an indirect band gap since the referred energies do not occur at the same **k**. On the other hand, the two energy gaps between the two local minima of the two conduction bands and the maximum of the valence band at the same Γ point, i.e. *E*Γ<sup>1</sup> and *E*Γ<sup>2</sup> in Fig. 1, are called direct band gaps. Because the energy gap *E*Γ<sup>2</sup> is much larger than *E*Γ<sup>1</sup> and *Eg*, there is barely any electrons at such high energy levels so that it has negligible effect on the light-matter interaction in most cases. Therefore, people usually refer the direct band gap to *E*Γ<sup>1</sup> thus the author denotes *Eg*<sup>Γ</sup> ≡ *E*Γ<sup>1</sup> and *EgL* ≡ *Eg* in the chapter. The part of the conduction band near Γ point is usually called direct valley or Γ valley while the part near *L* point is called indirect valley or *L* valley. In germanium crystal, the energy is 4-fold degenerate with regard

many cases.

**1.3 Germanium band structure**

Fig. 1. Ge band structure at 300K.(M.Levinstein et al., 1996)

chemical vapor deposition (RPCVD). Epitaxial germanium film with comparable threading dislocation density has been successfully grown on silicon using this approach (Hartmann et al., 2004). This approach quickly became popular as the maturely developed epitaxy reactors for (high silicon content) SiGe growth can be directly used with modified processes. It's also an approach compatible with manufacturing owing to its mature technique and rapid growth rate.

Besides the widely used UHVCVD and RPCVD approaches, there are a few other ways to grow germanium and high germanium content GeSi epitaxial films on silicon. Similarly to graded GeSi layers, GeSn can also be used as a buffer layer for germanium growth (Fang et al., 2007) though the research of the GeSn material system is still at its early stage. Epitaxial germanium has also been grown on silicon using a newly developed low energy plasma enhance chemical vapor deposition (LEPECVD) approach with low dislocation density (Osmond et al., 2009). The lack of germanium growth selectivity (between on silicon and on dielectrics) of this approach limits its use in many types of photonic devices. Besides direct epitaxy on silicon, an alternative way to form crystalline germanium on dielectrics through a so-called rapid melt growth (RMG) was introduced (Liu, Deal & Plummer, 2004). In this approach, amorphous germanium is deposited on top of dielectrics with a small window to expose crystalline silicon below the dielectrics. The germanium film is then capped with oxides and melt for a short time by rapid thermal annealing (RTA). Single crystalline germanium can be grown from the exposed silicon seed window through liquid-phase epitaxy (LPE) process. The RTA temperature profile is critical to the success of this approach though good quality of germanium film can be achieved.

As stated previously, the biggest challenge to grow high quality epitaxial germanium films with sufficient thickness is the lattice constant mismatch between germanium and silicon. To solve this problem a few approaches have been developed. A straightforward solution is to grow a graded GeSi layer or layers with the composition gradually changed from silicon to germanium. This approach was at first attempted in MBE growth (Fitzgerald et al., 1991) and was later introduced to UHVCVD growth (Samavedam & Fitzgerald, 1997) and RPCVD. It has been demonstrated that with a sufficiently thick graded layer high quality and low dislocated germanium films can be successfully grown on silicon (Currie et al., 1998).

A thick graded GeSi layer complicates epitaxial growth and device fabrication, so an alternative approach which uses a low temperature germanium layer (called buffer layer or seed layer) was developed (Colace et al., 1997). The low temperature buffer layer is used to kinetically prevent germanium from islanding and to plastically release lattice strain energy with misfit dislocations at Ge/Si interface when germanium thickness is beyond Stranski-Krastanov (S-K) critical thickness. In addition, another benefit of using low temperature is to make growing surface hydrogen act as surfactant to reduce island nucleation (Eaglesham et al., 1993). A thicker germanium film is then homo-epitaxially grown on the relaxed Ge buffer at higher temperatures for better growth rate. Therefore this approach is sometimes called two-step growth. The quality of germanium films by this type of growth is generally worse than the graded GeSi layer case, while the dislocations in the epitaxial film can be greatly minimized by a proper post annealing process (Luan et al., 1999).

Graded GeSi layer and low temperature Ge layer can both be used as buffer layer in germanium epitaxy and the required thickness of graded GeSi layer can be greatly reduced. Overgrowing germanium on a patterned silicon/SiO2 surface is another way to reduce dislocations resulted from Ge/Si lattice mismatch (Langdo et al., 2000). The "epitaxial necking" process as a result of selective germanium growth on silicon and SiO2 terminates dislocations on SiO2 sidewalls and leave the overgrown germanium above Si/SiO2 layer with reduced dislocation densities. The disadvantage of this approach is the difficulty of surface morphology control and the inconvenience of using the fine patterned Si/SiO2 surface in many cases.

#### **1.3 Germanium band structure**

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

chemical vapor deposition (RPCVD). Epitaxial germanium film with comparable threading dislocation density has been successfully grown on silicon using this approach (Hartmann et al., 2004). This approach quickly became popular as the maturely developed epitaxy reactors for (high silicon content) SiGe growth can be directly used with modified processes. It's also an approach compatible with manufacturing owing to its mature technique and rapid

Besides the widely used UHVCVD and RPCVD approaches, there are a few other ways to grow germanium and high germanium content GeSi epitaxial films on silicon. Similarly to graded GeSi layers, GeSn can also be used as a buffer layer for germanium growth (Fang et al., 2007) though the research of the GeSn material system is still at its early stage. Epitaxial germanium has also been grown on silicon using a newly developed low energy plasma enhance chemical vapor deposition (LEPECVD) approach with low dislocation density (Osmond et al., 2009). The lack of germanium growth selectivity (between on silicon and on dielectrics) of this approach limits its use in many types of photonic devices. Besides direct epitaxy on silicon, an alternative way to form crystalline germanium on dielectrics through a so-called rapid melt growth (RMG) was introduced (Liu, Deal & Plummer, 2004). In this approach, amorphous germanium is deposited on top of dielectrics with a small window to expose crystalline silicon below the dielectrics. The germanium film is then capped with oxides and melt for a short time by rapid thermal annealing (RTA). Single crystalline germanium can be grown from the exposed silicon seed window through liquid-phase epitaxy (LPE) process. The RTA temperature profile is critical to the success of this approach though

As stated previously, the biggest challenge to grow high quality epitaxial germanium films with sufficient thickness is the lattice constant mismatch between germanium and silicon. To solve this problem a few approaches have been developed. A straightforward solution is to grow a graded GeSi layer or layers with the composition gradually changed from silicon to germanium. This approach was at first attempted in MBE growth (Fitzgerald et al., 1991) and was later introduced to UHVCVD growth (Samavedam & Fitzgerald, 1997) and RPCVD. It has been demonstrated that with a sufficiently thick graded layer high quality and low dislocated

A thick graded GeSi layer complicates epitaxial growth and device fabrication, so an alternative approach which uses a low temperature germanium layer (called buffer layer or seed layer) was developed (Colace et al., 1997). The low temperature buffer layer is used to kinetically prevent germanium from islanding and to plastically release lattice strain energy with misfit dislocations at Ge/Si interface when germanium thickness is beyond Stranski-Krastanov (S-K) critical thickness. In addition, another benefit of using low temperature is to make growing surface hydrogen act as surfactant to reduce island nucleation (Eaglesham et al., 1993). A thicker germanium film is then homo-epitaxially grown on the relaxed Ge buffer at higher temperatures for better growth rate. Therefore this approach is sometimes called two-step growth. The quality of germanium films by this type of growth is generally worse than the graded GeSi layer case, while the dislocations in the epitaxial film

Graded GeSi layer and low temperature Ge layer can both be used as buffer layer in germanium epitaxy and the required thickness of graded GeSi layer can be greatly reduced. Overgrowing germanium on a patterned silicon/SiO2 surface is another way to reduce dislocations resulted from Ge/Si lattice mismatch (Langdo et al., 2000). The "epitaxial necking" process as a result of selective germanium growth on silicon and SiO2 terminates

germanium films can be successfully grown on silicon (Currie et al., 1998).

can be greatly minimized by a proper post annealing process (Luan et al., 1999).

growth rate.

good quality of germanium film can be achieved.

Fig. 1. Ge band structure at 300K.(M.Levinstein et al., 1996)

The electronic band structure of bulk germanium at room temperature is shown in Fig. 1. The valence band is composed of a light-hole band, a heavy-hole band, and a split-off band from spin-orbit interaction. The light-hole band and the heavy-hole band are degenerate at wave vector **k** = 0 or Γ point which is at the maximal energy of the valence band. The minimal energy of the conduction band is located at **k** =< 111 > or *L* point. The energy difference between the conduction band at *L* point and the valence band at Γ point determines the narrowest band gap in germanium: *Eg* = 0.664 eV. This type of band gap is called an indirect band gap since the referred energies do not occur at the same **k**. On the other hand, the two energy gaps between the two local minima of the two conduction bands and the maximum of the valence band at the same Γ point, i.e. *E*Γ<sup>1</sup> and *E*Γ<sup>2</sup> in Fig. 1, are called direct band gaps. Because the energy gap *E*Γ<sup>2</sup> is much larger than *E*Γ<sup>1</sup> and *Eg*, there is barely any electrons at such high energy levels so that it has negligible effect on the light-matter interaction in most cases. Therefore, people usually refer the direct band gap to *E*Γ<sup>1</sup> thus the author denotes *Eg*<sup>Γ</sup> ≡ *E*Γ<sup>1</sup> and *EgL* ≡ *Eg* in the chapter. The part of the conduction band near Γ point is usually called direct valley or Γ valley while the part near *L* point is called indirect valley or *L* valley. In germanium crystal, the energy is 4-fold degenerate with regard

Silicon Photonics 7

Germanium-on-Silicon for Integrated Silicon Photonics 9

Fig. 2. Comparison of germanium absorption from different published sources. The experimental data (Source 1 to 4 in the figure) are obtained from (Braunstein et al., 1958; Dash & Newman, 1955; Frova & Handler, 1965; Hobden, 1962), respectively. The fitting

than the direct gap. A calculation based on the above theoretical model (Equation 3) with *<sup>A</sup>* <sup>=</sup> 2.0 <sup>×</sup> 104 eV1/2/cm is shown with black solid line and fits well with the experimental

For an integrated optical interconnect and transmission system on silicon platform, any wavelength above silicon absorption edge (about 1.1 *μ*m) can be adopted for photon carriers as silicon is the guiding material. Shorter wavelengths can also be used if other compatible materials (e.g. silicon nitride) are used for wave guiding however silicon is a preferred material for the miniaturization reason owing to the high refractive index contrast between silicon and cladding materials (e.g. silicon oxide). But wavelengths near 1.55 *μ*m (fiber optics C-band) are commonly used because the communication design tool boxes at this wavelength band are mature in fiber optics technology. But germanium has weak absorption at 1.55 *μ*m which is about its direct band gap energy as described in the band diagram earlier.

Semiconductor band structure is associated with the crystal structure which can be altered by the existence of strain. This effect can be calculated using a strain-modified *k* · *p* method Chuang (1995). Pikus-Bir Hamiltonian and Luttinger-Kohn's model are used in the method to describe the degenerate bands in germanium. This calculation shows that strain changes the energy levels of the direct Γ valley, the indirect *L* valleys, the light-hole band, and the heavy-hole band relative to vacuum level.2 As a result, the direct band gap and indirect band gap are changed and the light-hole and the heavy-hole bands become non-degenerate with separation at Γ point. A band structure comparison of unstrained germanium and 0.2%

based on the theoretical model is drawn with a black solid line.

**2. Waveguide integrated germanium photodetector**

Germanium strain engineering has been adopted to address this issue.

<sup>2</sup> The energy levels of other bands such as spin-orbit split-off band are also changed.

**2.1 Tensile strain engineering of germanium**

tensile-strained germanium is shown in Fig. 3.

data.

to the changes of the secondary total angular-momentum quantum number at *L* point, four *L* valleys are considered in the following calculations. <sup>1</sup>

#### **1.4 Germanium optical absorption**

In the study of germanium in optoelectronic and photonic applications, one of the most important properties is the optical absorption. The band-to-band optical absorption is a process that transferring the energy of an incoming photon to an electron in valence band and make the electron jump to conduction band and leave a hole in valence band. When this process occurs in a crystalline material, both energy and momentum are conserved for the system. Therefore, the rate of such event is much lower in an indirect band-to-band transition compared to a direct band-to-band transition due to the need of one or more phonons to conserve momentum. The band structure described earlier indicates that the optical absorption of bulk germanium is substantial at any wavelengths less than 1.55 *μm* (corresponding to 0.80 *eV* direct band gap energy) and the direct optical absorption is what matters in most of the applications studied here.

The direct gap absorption of a semiconductor can theoretically modeled by solving the electron-photon scattering in crystalline potential with Fermi's golden rule. The detailed mathematical derivation is skipped the only the result is shown here:

$$\alpha(h\nu) = \frac{e^2 hc\mu\_0}{2m\_e^2} \frac{|p\_{c\upsilon}|}{n} \frac{1}{h\nu} \rho\_I (h\nu - E\_\mathbb{g}),\tag{1}$$

where |*pcv*| is related to an element of optical transition operator matrix and *n* is index of refraction, both of which are material properties and may be considered as constants within a small range of wavelengths. *hν* and *Eg* are the energy of photon and band gap respectively. *ρ<sup>r</sup>* is the joint density of states of the conduction band (Γvalley) and the valence band. A quadratic approximation is usually adapted to describe the density of states near an extremum of any energy band in semiconductor and *ρ<sup>r</sup>* is subsequently calculated

$$
\rho\_r(h\nu - E\_{\mathcal{S}}) = 2\pi \left(\frac{2m\_r}{h^2}\right)^{3/2} \sqrt{h\nu - E\_{\mathcal{S}'}} \tag{2}
$$

where *mr* = *mcmv*/(*mc* + *mv*) is the reduced effective mass as an expression of the effective masses of conduction band (*mc*) and the valence band (*mv*).

In a concise form, the direct gap absorption can be approximately written as

$$\alpha(h\nu) = A \frac{\sqrt{h\nu - E\_{\mathcal{S}}}}{h\nu} \,\,\,\,\,\,\tag{3}$$

where *A* is a constant usually determined from experiments.

Some experimental optical absorption data of intrinsic and unstrained germanium at photon energies around its direct band gap (Braunstein et al., 1958; Dash & Newman, 1955; Frova & Handler, 1965; Hobden, 1962) are shown in Fig. 2. The sharp absorption drop at a photon energy of 0.8 *eV* from all the data sources indicates the energy of the direct gap. The data from (Dash & Newman, 1955) and (Hobden, 1962) show good agreement at photon energies more

<sup>1</sup> Degeneracy with regard to the changes of electron spin quantum number is not explicitly accounted here though it is considered in density of states calculations.

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

to the changes of the secondary total angular-momentum quantum number at *L* point, four *L*

In the study of germanium in optoelectronic and photonic applications, one of the most important properties is the optical absorption. The band-to-band optical absorption is a process that transferring the energy of an incoming photon to an electron in valence band and make the electron jump to conduction band and leave a hole in valence band. When this process occurs in a crystalline material, both energy and momentum are conserved for the system. Therefore, the rate of such event is much lower in an indirect band-to-band transition compared to a direct band-to-band transition due to the need of one or more phonons to conserve momentum. The band structure described earlier indicates that the optical absorption of bulk germanium is substantial at any wavelengths less than 1.55 *μm* (corresponding to 0.80 *eV* direct band gap energy) and the direct optical absorption is what

The direct gap absorption of a semiconductor can theoretically modeled by solving the electron-photon scattering in crystalline potential with Fermi's golden rule. The detailed

> |*pcv*| *n*

where |*pcv*| is related to an element of optical transition operator matrix and *n* is index of refraction, both of which are material properties and may be considered as constants within a small range of wavelengths. *hν* and *Eg* are the energy of photon and band gap respectively. *ρ<sup>r</sup>* is the joint density of states of the conduction band (Γvalley) and the valence band. A quadratic approximation is usually adapted to describe the density of states near an extremum

> 2*mr h*2

where *mr* = *mcmv*/(*mc* + *mv*) is the reduced effective mass as an expression of the effective

Some experimental optical absorption data of intrinsic and unstrained germanium at photon energies around its direct band gap (Braunstein et al., 1958; Dash & Newman, 1955; Frova & Handler, 1965; Hobden, 1962) are shown in Fig. 2. The sharp absorption drop at a photon energy of 0.8 *eV* from all the data sources indicates the energy of the direct gap. The data from (Dash & Newman, 1955) and (Hobden, 1962) show good agreement at photon energies more

<sup>1</sup> Degeneracy with regard to the changes of electron spin quantum number is not explicitly accounted

3/2

*<sup>h</sup><sup>ν</sup>* <sup>−</sup> *Eg*

1 *hν*

*ρr*(*hν* − *Eg*), (1)

*hν* − *Eg*, (2)

*<sup>h</sup><sup>ν</sup>* , (3)

valleys are considered in the following calculations. <sup>1</sup>

matters in most of the applications studied here.

mathematical derivation is skipped the only the result is shown here:

*<sup>α</sup>*(*hν*) = *<sup>e</sup>*2*hcμ*<sup>0</sup>

of any energy band in semiconductor and *ρ<sup>r</sup>* is subsequently calculated

*ρr*(*hν* − *Eg*) = 2*π*

In a concise form, the direct gap absorption can be approximately written as

*α*(*hν*) = *A*

masses of conduction band (*mc*) and the valence band (*mv*).

where *A* is a constant usually determined from experiments.

here though it is considered in density of states calculations.

2*me* 2

**1.4 Germanium optical absorption**

Fig. 2. Comparison of germanium absorption from different published sources. The experimental data (Source 1 to 4 in the figure) are obtained from (Braunstein et al., 1958; Dash & Newman, 1955; Frova & Handler, 1965; Hobden, 1962), respectively. The fitting based on the theoretical model is drawn with a black solid line.

than the direct gap. A calculation based on the above theoretical model (Equation 3) with *<sup>A</sup>* <sup>=</sup> 2.0 <sup>×</sup> 104 eV1/2/cm is shown with black solid line and fits well with the experimental data.

#### **2. Waveguide integrated germanium photodetector**

#### **2.1 Tensile strain engineering of germanium**

For an integrated optical interconnect and transmission system on silicon platform, any wavelength above silicon absorption edge (about 1.1 *μ*m) can be adopted for photon carriers as silicon is the guiding material. Shorter wavelengths can also be used if other compatible materials (e.g. silicon nitride) are used for wave guiding however silicon is a preferred material for the miniaturization reason owing to the high refractive index contrast between silicon and cladding materials (e.g. silicon oxide). But wavelengths near 1.55 *μ*m (fiber optics C-band) are commonly used because the communication design tool boxes at this wavelength band are mature in fiber optics technology. But germanium has weak absorption at 1.55 *μ*m which is about its direct band gap energy as described in the band diagram earlier. Germanium strain engineering has been adopted to address this issue.

Semiconductor band structure is associated with the crystal structure which can be altered by the existence of strain. This effect can be calculated using a strain-modified *k* · *p* method Chuang (1995). Pikus-Bir Hamiltonian and Luttinger-Kohn's model are used in the method to describe the degenerate bands in germanium. This calculation shows that strain changes the energy levels of the direct Γ valley, the indirect *L* valleys, the light-hole band, and the heavy-hole band relative to vacuum level.2 As a result, the direct band gap and indirect band gap are changed and the light-hole and the heavy-hole bands become non-degenerate with separation at Γ point. A band structure comparison of unstrained germanium and 0.2% tensile-strained germanium is shown in Fig. 3.

<sup>2</sup> The energy levels of other bands such as spin-orbit split-off band are also changed.

Silicon Photonics 9

Germanium-on-Silicon for Integrated Silicon Photonics 11

Fig. 4. The direct and the indirect band gaps of germanium with in-plane strain. *Eg*<sup>Γ</sup>*hh* and *Eg*<sup>Γ</sup>*lh* are energy gaps between the Γ valley and the heavy-hole band and the light-hole band respectively. *EgLhh* and *EgLlh* are energy gaps between the *L* valley and the heavy-hole band

The direct and the indirect band gaps of strained germanium can be obtained using Eq. 4−7 with the experimental results of *ac*<sup>Γ</sup> = −8.97 eV and *b* = −1.88 eV from reference (Liu, Cannon, Ishikawa, Wada, Danielson, Jongthammanurak, Michel & Kimerling, 2004) *C*<sup>11</sup> = 128.53 GPa and *C*<sup>12</sup> = 48.26 GPa from reference (Madelung & et al, 1982), and the calculated results of *acL*=-2.78 eV and *av*=1.24 eV from reference (de Walle, 1989). These energy gaps are calculated and shown in Fig. 4. We can see both the direct band gap and the indirect band gap shrink with tensile strain (positive *�xx*) and the direct band gap decreases faster than the indirect band gap does due to |*ac*Γ| > |*acL*|. The direct band gap becomes equal to the indirect band gap at *�* ≈ 1.8% where Ge becomes a direct band gap material. The energy gaps from the conduction band (equal for both direct Γ valley and indirect *L* valley) to the light-hole and the heavy-hole band are 0.53 eV and 0.66 eV respectively.It is noted that there are two kinds of energy gaps at both Γ point and *L* point due to the separation of the light-hole band and the heavy-hole band. The optical band gap is determined by the smaller gap with respect to the light-hole band. We refer the band gap to this energy gap in the following

The absorption edge of tensile strain germanium moves towards lower energy because of the shrinkage of the direct band gap. Since the light-hole band and the heavy-hole band separate under strain, two optical transitions corresponding to the two energy gaps contribute the overall optical absorption. Therefore the absorption spectrum of tensile-strain germanium

> *hν* − *Eg*<sup>Γ</sup>*lh hν*

+ *k*<sup>2</sup>

�

*hν* − *Eg*<sup>Γ</sup>*hh hν*

⎞

⎠ , (12)

where *C*<sup>11</sup> and *C*<sup>12</sup> are the elements of the elastic stiffness tensor.

and the light-hole band respectively.

discussion unless explicitly stated otherwise.

*α*(*hν*) = *A*

⎛ ⎝*k*<sup>1</sup> �

can be expressed as

Fig. 3. Comparison of the band structures of (a) unstrained germanium and (b) strained germanium.

The direct band gap and indirect band gap under strain can be calculated using this method3

$$E\_{\mathcal{S}\Gamma hh} = a\_{\mathcal{C}\Gamma} (\varepsilon\_{xx} + \varepsilon\_{yy} + \varepsilon\_{zz}) + P + Q \tag{4}$$

$$E\_{\rm g\Gamma\hbar} = a\_{\rm c\Gamma}(\varepsilon\_{xx} + \varepsilon\_{yy} + \varepsilon\_{zz}) + P - Q/2 + E\_{\rm so}/2 - \sqrt{E\_{\rm so}^2 + 2E\_{\rm so}Q + 9Q^2} \tag{5}$$

$$E\_{\rm gLhh} = a\_{\rm cL}(\varepsilon\_{xx} + \varepsilon\_{yy} + \varepsilon\_{zz}) + P + Q \tag{6}$$

$$E\_{\rm gLlh} = a\_{\rm cL}(\varepsilon\_{xx} + \varepsilon\_{yy} + \varepsilon\_{zz}) + P - Q/2 + E\_{\rm so}/2 - \sqrt{E\_{\rm so}^2 + 2E\_{\rm so}Q + 9Q^2} \tag{7}$$

where

$$P = -a\_{\upsilon}(\mathfrak{e}\_{\text{xx}} + \mathfrak{e}\_{yy} + \mathfrak{e}\_{zz}) \tag{8}$$

$$Q = -b(\epsilon\_{xx}/2 + \epsilon\_{yy}/2 - \epsilon\_{zz})\tag{9}$$

. *Eg*<sup>Γ</sup>*hh* and *Eg*<sup>Γ</sup>*lh* are energy gaps between the Γ valley and the heavy-hole band and the light-hole band respectively. *EgLhh* and *EgLlh* are energy gaps between the *L* valley and the heavy-hole band and the light-hole band respectively. *xx*, *yy*, and *zz* are strain components. *Eso* is the energy difference between valence bands and spin-orbit split-off band at Γ point. *ac*Γ, *acL*, *av* and *b* are deformation potentials for Γ valley, *L* valleys, the average of three valence bands (light-hole, heavy-hole and spin-orbit split-off) and a strain of tetragonal symmetry. They are material properties which can be either calculated from first-principle calculation or determined by experiments.

For epitaxial germanium films, the strain is usually induced by in-plane stress from adjacent layers. If a biaxial stress is applied, i.e.

$$
\epsilon\_{\rm xx} = \epsilon\_{yy} \tag{10}
$$

the relation of the stress tensors for the isotropic material can be determined from Hooke's law in tensor form:

$$
\epsilon\_{zz} = -2\mathsf{C}\_{12}/\mathsf{C}\_{11}\epsilon\_{xx} \tag{11}
$$

<sup>3</sup> Shear strain *xy*(*x*�=*y*), which is negligible in the thin film material, is not considered here.

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

(a) (b)

The direct band gap and indirect band gap under strain can be calculated using this method3

. *Eg*<sup>Γ</sup>*hh* and *Eg*<sup>Γ</sup>*lh* are energy gaps between the Γ valley and the heavy-hole band and the light-hole band respectively. *EgLhh* and *EgLlh* are energy gaps between the *L* valley and the heavy-hole band and the light-hole band respectively. *xx*, *yy*, and *zz* are strain components. *Eso* is the energy difference between valence bands and spin-orbit split-off band at Γ point. *ac*Γ, *acL*, *av* and *b* are deformation potentials for Γ valley, *L* valleys, the average of three valence bands (light-hole, heavy-hole and spin-orbit split-off) and a strain of tetragonal symmetry. They are material properties which can be either calculated from first-principle calculation or

For epitaxial germanium films, the strain is usually induced by in-plane stress from adjacent

the relation of the stress tensors for the isotropic material can be determined from Hooke's

<sup>3</sup> Shear strain *xy*(*x*�=*y*), which is negligible in the thin film material, is not considered here.

*Eg*<sup>Γ</sup>*hh* = *ac*Γ(*xx* + *yy* + *zz*) + *P* + *Q* (4)

*EgLhh* = *acL*(*xx* + *yy* + *zz*) + *P* + *Q* (6)

 *E*2

 *E*2

*P* = −*av*(*xx* + *yy* + *zz*) (8) *Q* = −*b*(*xx*/2 + *yy*/2 − *zz*) (9)

*xx* = *yy*, (10)

*zz* = −2*C*12/*C*<sup>11</sup>*xx*, (11)

*so* + 2*EsoQ* + 9*Q*<sup>2</sup> (5)

*so* + 2*EsoQ* + 9*Q*<sup>2</sup> (7)

Fig. 3. Comparison of the band structures of (a) unstrained germanium and (b) strained

*Eg*<sup>Γ</sup>*lh* = *ac*Γ(*xx* + *yy* + *zz*) + *P* − *Q*/2 + *Eso*/2 −

*EgLlh* = *acL*(*xx* + *yy* + *zz*) + *P* − *Q*/2 + *Eso*/2 −

germanium.

where

determined by experiments.

law in tensor form:

layers. If a biaxial stress is applied, i.e.

where *C*<sup>11</sup> and *C*<sup>12</sup> are the elements of the elastic stiffness tensor.

Fig. 4. The direct and the indirect band gaps of germanium with in-plane strain. *Eg*<sup>Γ</sup>*hh* and *Eg*<sup>Γ</sup>*lh* are energy gaps between the Γ valley and the heavy-hole band and the light-hole band respectively. *EgLhh* and *EgLlh* are energy gaps between the *L* valley and the heavy-hole band and the light-hole band respectively.

The direct and the indirect band gaps of strained germanium can be obtained using Eq. 4−7 with the experimental results of *ac*<sup>Γ</sup> = −8.97 eV and *b* = −1.88 eV from reference (Liu, Cannon, Ishikawa, Wada, Danielson, Jongthammanurak, Michel & Kimerling, 2004) *C*<sup>11</sup> = 128.53 GPa and *C*<sup>12</sup> = 48.26 GPa from reference (Madelung & et al, 1982), and the calculated results of *acL*=-2.78 eV and *av*=1.24 eV from reference (de Walle, 1989). These energy gaps are calculated and shown in Fig. 4. We can see both the direct band gap and the indirect band gap shrink with tensile strain (positive *�xx*) and the direct band gap decreases faster than the indirect band gap does due to |*ac*Γ| > |*acL*|. The direct band gap becomes equal to the indirect band gap at *�* ≈ 1.8% where Ge becomes a direct band gap material. The energy gaps from the conduction band (equal for both direct Γ valley and indirect *L* valley) to the light-hole and the heavy-hole band are 0.53 eV and 0.66 eV respectively.It is noted that there are two kinds of energy gaps at both Γ point and *L* point due to the separation of the light-hole band and the heavy-hole band. The optical band gap is determined by the smaller gap with respect to the light-hole band. We refer the band gap to this energy gap in the following discussion unless explicitly stated otherwise.

The absorption edge of tensile strain germanium moves towards lower energy because of the shrinkage of the direct band gap. Since the light-hole band and the heavy-hole band separate under strain, two optical transitions corresponding to the two energy gaps contribute the overall optical absorption. Therefore the absorption spectrum of tensile-strain germanium can be expressed as

$$\alpha(h\nu) = A \left( k\_1 \frac{\sqrt{h\nu - E\_{\text{g}}\tau\mu}}{h\nu} + k\_2 \frac{\sqrt{h\nu - E\_{\text{g}}\tau\mu}}{h\nu} \right), \tag{12}$$

Silicon Photonics 11

Germanium-on-Silicon for Integrated Silicon Photonics 13

As silicon substrate is always much thicker than germanium epitaxial layer, the tensile strain

where, *T*<sup>0</sup> and *T*<sup>1</sup> are room temperature and growth temperature respectively, and *α*Ge = *α*Ge(*T*) and *α*Si = *α*Si(*T*) are thermal expansion coefficients of germanium and silicon respectively. In general, these coefficients are a function of temperature and the relations are

*<sup>α</sup>*Si(*T*) = 3.725 <sup>×</sup> <sup>10</sup>−<sup>6</sup> <sup>×</sup> [<sup>1</sup> <sup>−</sup> exp(−5.88 <sup>×</sup> <sup>10</sup>−<sup>3</sup> <sup>×</sup> (*<sup>T</sup>* <sup>+</sup> 149.15))] + 5.548 <sup>×</sup> <sup>10</sup>−10*T*(*oC*−1).

Fig. 7. Ge direct energy gaps versus tensile strain measured by X-ray diffraction (XRD) and

From the above formula, different tensile strain can be achieved with different growth temperature and the experimental results of germanium grown at various temperatures are also plotted in Fig. 7. The energy gaps are measured by photoreflectance (PR) experiment and the tensile strain is obtained from crystal lattice constant measurement by X-ray diffraction

photoreflectance (PR) experiments. (Liu, Cannon, Ishikawa, Wada, Danielson,

Jongthammanurak, Michel & Kimerling, 2004)

*<sup>α</sup>*Ge(*T*) = 6.050 <sup>×</sup> 106 <sup>+</sup> 3.60 <sup>×</sup> 109*<sup>T</sup>* <sup>−</sup> 0.35 <sup>×</sup> <sup>10</sup>−12*T*2(*oC*−1), (14)

(*α*Ge − *α*Si)*dT*, (13)

(15)

 *T*<sup>1</sup> *T*0

Fig. 6. Illustration of tensile strain formation in germanium on silicon epitaxy.

*�*// =

experimentally determined (Singh, 1968) and (Okada & Tokumaru, 1984):

*�*// in germanium caused by in-plain stress can be obtained using

Fig. 5. The experimental result and the theoretical fitting of the optical absorption of 0.2% tensile-strained germanium. The optical absorption of unstrained germanium is shown with a black dash line for comparison.

where *k*<sup>1</sup> = *mrlh*3/2/(*mrlh*3/2 + *mrhh*3/2) and *k*<sup>2</sup> = *mrhh*3/2(*mrlh*3/2 + *mrhh*3/2) are coefficients attributing to the difference between the two transitions due to the different reduced effective masses. *k*<sup>1</sup> and *k*<sup>2</sup> are normalized so that *k*<sup>1</sup> + *k*<sup>2</sup> = 1. *k*<sup>1</sup> = 0.68168 and *k*<sup>2</sup> = 0.31832 are calculated for germanium. The measured absorption spectrum of 0.2% tensile-strained germanium is shown in Fig. 5 and *<sup>A</sup>* <sup>=</sup> 1.9 <sup>×</sup> 104 eV1/2/cm is calculated by fitting the experimental result using Eq. 12. The *A* of strained germanium is approximately the same as that of unstrained germanium which underlies that applied strain is too small to affect the optical transition matrix of Fermi's golden rule.

Introduction of tensile strain in germanium is not intuitive in germanium-on-silicon epitaxy. It is usually understood that strain is induced from the lattice mismatch between epitaxial and substrate materials. In such way, epitaxial germanium is compressively strained as the lattice constant of germanium (5.658 Å) is greater than that of silicon (5.431 Å). However, the above analysis is only applied to the case that an epitaxial layer is thinner than its critical thickness on a certain substrate. Beyond this thickness, the elastic strain of the epitaxial film releases plastically by introducing misfit dislocations near material interface region. Another possible result beyond critical thickness is that three dimensional growth (islanding) occurs to balance elastic strain energy with surface tension.

In the two-step growth described earlier, the buffer layer is grown at low temperature to prevent such islanding process by reducing the mobility of adsorbed atoms on growing surface. Thus the following germanium layer grown at higher temperatures layer is on a strain-relaxed surface of the buffer layer, the thickness which is more than critical thickness. The epitaxial germanium and the silicon substrate shrink as the substrate temperature is cooled down to room temperature. Germanium shrinks more due to its larger coefficient of thermal expansion than that of silicon therefore in-plain tensile strain is accumulated in the germanium film as illustrated in Fig. 6.

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

Fig. 5. The experimental result and the theoretical fitting of the optical absorption of 0.2% tensile-strained germanium. The optical absorption of unstrained germanium is shown with

where *k*<sup>1</sup> = *mrlh*3/2/(*mrlh*3/2 + *mrhh*3/2) and *k*<sup>2</sup> = *mrhh*3/2(*mrlh*3/2 + *mrhh*3/2) are coefficients attributing to the difference between the two transitions due to the different reduced effective masses. *k*<sup>1</sup> and *k*<sup>2</sup> are normalized so that *k*<sup>1</sup> + *k*<sup>2</sup> = 1. *k*<sup>1</sup> = 0.68168 and *k*<sup>2</sup> = 0.31832 are calculated for germanium. The measured absorption spectrum of 0.2% tensile-strained germanium is shown in Fig. 5 and *<sup>A</sup>* <sup>=</sup> 1.9 <sup>×</sup> 104 eV1/2/cm is calculated by fitting the experimental result using Eq. 12. The *A* of strained germanium is approximately the same as that of unstrained germanium which underlies that applied strain is too small to affect the

Introduction of tensile strain in germanium is not intuitive in germanium-on-silicon epitaxy. It is usually understood that strain is induced from the lattice mismatch between epitaxial and substrate materials. In such way, epitaxial germanium is compressively strained as the lattice constant of germanium (5.658 Å) is greater than that of silicon (5.431 Å). However, the above analysis is only applied to the case that an epitaxial layer is thinner than its critical thickness on a certain substrate. Beyond this thickness, the elastic strain of the epitaxial film releases plastically by introducing misfit dislocations near material interface region. Another possible result beyond critical thickness is that three dimensional growth (islanding) occurs to balance

In the two-step growth described earlier, the buffer layer is grown at low temperature to prevent such islanding process by reducing the mobility of adsorbed atoms on growing surface. Thus the following germanium layer grown at higher temperatures layer is on a strain-relaxed surface of the buffer layer, the thickness which is more than critical thickness. The epitaxial germanium and the silicon substrate shrink as the substrate temperature is cooled down to room temperature. Germanium shrinks more due to its larger coefficient of thermal expansion than that of silicon therefore in-plain tensile strain is accumulated in the

a black dash line for comparison.

optical transition matrix of Fermi's golden rule.

elastic strain energy with surface tension.

germanium film as illustrated in Fig. 6.

Fig. 6. Illustration of tensile strain formation in germanium on silicon epitaxy.

As silicon substrate is always much thicker than germanium epitaxial layer, the tensile strain *�*// in germanium caused by in-plain stress can be obtained using

$$
\varepsilon\_{//} = \int\_{T\_0}^{T\_1} (\mathfrak{a\_{\rm Ge}} - \mathfrak{a\_{\rm Si}}) dT \,\tag{13}
$$

where, *T*<sup>0</sup> and *T*<sup>1</sup> are room temperature and growth temperature respectively, and *α*Ge = *α*Ge(*T*) and *α*Si = *α*Si(*T*) are thermal expansion coefficients of germanium and silicon respectively. In general, these coefficients are a function of temperature and the relations are experimentally determined (Singh, 1968) and (Okada & Tokumaru, 1984):

$$\varkappa\_{\rm Ge}(T) = 6.050 \times 10^6 + 3.60 \times 10^9 T - 0.35 \times 10^{-12} T^2 (^{\circ} \text{C}^{-1}),\tag{14}$$

$$\mathfrak{a}\_{\mathfrak{H}}(T) = 3.725 \times 10^{-6} \times \left[1 - \exp\left(-5.88 \times 10^{-3} \times (T + 149.15)\right)\right] + 5.548 \times 10^{-10} T (^{\circ}\text{C}^{-1}). \tag{15}$$

Fig. 7. Ge direct energy gaps versus tensile strain measured by X-ray diffraction (XRD) and photoreflectance (PR) experiments. (Liu, Cannon, Ishikawa, Wada, Danielson, Jongthammanurak, Michel & Kimerling, 2004)

From the above formula, different tensile strain can be achieved with different growth temperature and the experimental results of germanium grown at various temperatures are also plotted in Fig. 7. The energy gaps are measured by photoreflectance (PR) experiment and the tensile strain is obtained from crystal lattice constant measurement by X-ray diffraction

Silicon Photonics 13

Germanium-on-Silicon for Integrated Silicon Photonics 15

where *<sup>μ</sup>* <sup>=</sup> 3.7 <sup>×</sup> <sup>10</sup>3*cm*2/*<sup>V</sup>* · *<sup>s</sup>* is the electron mobility and *<sup>n</sup>* <sup>=</sup> 2.5 is a coefficient determined empirically. The saturation velocity of electrons in germanium is about 6 <sup>×</sup> <sup>10</sup><sup>6</sup> cm/s while

Fig. 8. Experimental result and theoretical fitting of the electron drift velocity in germanium

Based on this formula, the calculated 3dB bandwidth contour of a germanium diode with respect to its depletion width and device area is shown in Fig. 9. In general, the transit time limits the maximal thickness of depletion width which is close to the germanium thickness for a fully depleted vertical P-I-N junction diode. The RC delay, on the other hand, limits the maximal device area. In the calculation, a termination resistance of 50 Ω is used for the compatibility of common impedance and no parasitics is considered. When the series resistance and parasitic capacitance (e.g. contact pad capacitance) are taken into account, the

Dark current is another important parameter of photodetectors. Germanium photodetector usually suffers from a larger dark current as a result of its narrow indirect band gap and poor surface passivation capability. A narrow band gap leads to higher density of intrinsic carriers and higher trap assisted generation rate through Shockley-Read-Hall (SRH) process. The surface passivation of germanium, i.e. termination of the dangling bonds or surface states, is generally more different than silicon as germanium oxide is much less robust than silicon dioxide. Therefore people use other materials such as hydrogenate amorphous silicon (aSi:H), hydrogen-rich silicon nitride (Si3N4), germanium oxynitride (Ge(ON)*x*) and etc. to passivate germanium surface. The dark current associated with material quality (e.g. defects)

<sup>2</sup> + 1/ *ftr*

2

. (19)

When both RC delay and transit time are considered the overall 3dB bandwidth is

*<sup>f</sup>*3*dB* <sup>=</sup> <sup>1</sup> 1/ *fRC*

(1/(*vsat*)*<sup>n</sup>* <sup>+</sup> 1/(*μE*)*n*)1/*<sup>n</sup>* , (18)

*vd* <sup>=</sup> <sup>1</sup>

formula:

the value is a little less for holes.

versus electric field.

3dB bandwidth is reduced.

(XRD) (Liu, Cannon, Ishikawa, Wada, Danielson, Jongthammanurak, Michel & Kimerling, 2004). The direct-gap deformation potentials of germanium can then be calculated from fitting the experimental data. The calculated two direct energy gaps, i.e. from the direct Γ valley to the light-hole band (indicated by lh) and to the heavy-hole band (indicated by hh) respectively, of germanium as a function of tensile strain are shown in Fig. 7 with the fitted deformation potentials.

If post-growth thermal annealing is performed, germanium epitaxial layer is further relaxed at the annealing temperature therefore more tensile-strain is possibly obtained at room temperature. In practice, it is found that the tensile strain in germanium cease to increase at temperatures beyond about 750 ◦C and the measured strain is usually less than the theoretical values calculated from above formula (Cannon et al., 2004). It is believed that the existence of residual compressive strain retrains the full relaxation of germanium.

#### **2.2 Germanium photodetector**

Germanium has been investigated as an efficient photodetector on silicon platform since the germanium MBE was realized. Although the early work of germanium on silicon photodetector was in 1980s (Luryi et al., 1984), it only became extensively researched since late 1990s aligned with the boom of CVD epitaxy of germanium on silicon (Colace et al., 2000; 1998; Dehlinger et al., 2004; Hartmann et al., 2004; Liu, Michel, Giziewicz, Pan, Wada, Cannon, Jongthammanurak, Danielson, Kimerling, Chen, Ilday, Kartner & Yasaitis, 2005; Luan et al., 2001).

Early epitaxial germanium photodetectors are mostly vertical P-N or P-I-N junction devices designed for surface optical incidence for the ease of fabrication. There is a trade-off between optical absorption and carrier transit time for this type of photodetector and many of devices are designed for a 3dB bandwidth less or around 10GHz for 10 Gb/s applications (Colace et al., n.d.; Liu, Michel, Giziewicz, Pan, Wada, Cannon, Jongthammanurak, Danielson, Kimerling, Chen, Ilday, Kartner & Yasaitis, 2005; Morse et al., 2006). A lateral P-I-N junction design can be adopted to reduce carrier transit time for very high speed applications though the photo responsivity is usually compromised (Dehlinger et al., 2004). Therefore, waveguide coupled germanium photodetectors are favored in high speed applications especially for devices working at 1.55 *μ*m in which longer germanium absorption length is required due to weaker absorption.

The speed of photodetectors is characterized by its 3dB bandwidth which is usually limited by a combination of Resistive-capacitive (RC) delay and carrier transit time. The RC delay limited 3dB bandwidth is

$$f\_{\rm RC} = \frac{1}{2\pi \text{RC}}.\tag{16}$$

It be can proved that the carrier transit time limited 3dB bandwidth is

$$f\_{tr} = 0.44 \times \frac{v\_d}{d} \,\tag{17}$$

where *vd* is the average drift velocity of carriers (electrons or holes) and *d* is the junction depletion width in germanium. *vd* is generally a function of electric field (and temperature) but it approaches the saturation velocity *vsat* when applied electric field is sufficiently large. The experimentally measured electron drift velocity in germanium as a function of electric field (Jacoboni et al., 1981) is shown in Fig. 8. This relation can be described by an empirical formula:

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

(XRD) (Liu, Cannon, Ishikawa, Wada, Danielson, Jongthammanurak, Michel & Kimerling, 2004). The direct-gap deformation potentials of germanium can then be calculated from fitting the experimental data. The calculated two direct energy gaps, i.e. from the direct Γ valley to the light-hole band (indicated by lh) and to the heavy-hole band (indicated by hh) respectively, of germanium as a function of tensile strain are shown in Fig. 7 with the fitted deformation

If post-growth thermal annealing is performed, germanium epitaxial layer is further relaxed at the annealing temperature therefore more tensile-strain is possibly obtained at room temperature. In practice, it is found that the tensile strain in germanium cease to increase at temperatures beyond about 750 ◦C and the measured strain is usually less than the theoretical values calculated from above formula (Cannon et al., 2004). It is believed that the existence of

Germanium has been investigated as an efficient photodetector on silicon platform since the germanium MBE was realized. Although the early work of germanium on silicon photodetector was in 1980s (Luryi et al., 1984), it only became extensively researched since late 1990s aligned with the boom of CVD epitaxy of germanium on silicon (Colace et al., 2000; 1998; Dehlinger et al., 2004; Hartmann et al., 2004; Liu, Michel, Giziewicz, Pan, Wada, Cannon, Jongthammanurak, Danielson, Kimerling, Chen, Ilday, Kartner & Yasaitis, 2005; Luan et al.,

Early epitaxial germanium photodetectors are mostly vertical P-N or P-I-N junction devices designed for surface optical incidence for the ease of fabrication. There is a trade-off between optical absorption and carrier transit time for this type of photodetector and many of devices are designed for a 3dB bandwidth less or around 10GHz for 10 Gb/s applications (Colace et al., n.d.; Liu, Michel, Giziewicz, Pan, Wada, Cannon, Jongthammanurak, Danielson, Kimerling, Chen, Ilday, Kartner & Yasaitis, 2005; Morse et al., 2006). A lateral P-I-N junction design can be adopted to reduce carrier transit time for very high speed applications though the photo responsivity is usually compromised (Dehlinger et al., 2004). Therefore, waveguide coupled germanium photodetectors are favored in high speed applications especially for devices working at 1.55 *μ*m in which longer germanium absorption length is required due

The speed of photodetectors is characterized by its 3dB bandwidth which is usually limited by a combination of Resistive-capacitive (RC) delay and carrier transit time. The RC delay

*fRC* <sup>=</sup> <sup>1</sup>

*ftr* = 0.44 ×

where *vd* is the average drift velocity of carriers (electrons or holes) and *d* is the junction depletion width in germanium. *vd* is generally a function of electric field (and temperature) but it approaches the saturation velocity *vsat* when applied electric field is sufficiently large. The experimentally measured electron drift velocity in germanium as a function of electric field (Jacoboni et al., 1981) is shown in Fig. 8. This relation can be described by an empirical

*vd*

It be can proved that the carrier transit time limited 3dB bandwidth is

<sup>2</sup>*πRC*. (16)

*<sup>d</sup>* , (17)

residual compressive strain retrains the full relaxation of germanium.

potentials.

2001).

to weaker absorption.

limited 3dB bandwidth is

**2.2 Germanium photodetector**

$$v\_d = \frac{1}{(1/(v\_{sat})^n + 1/(\mu E)^n)^{1/n}},\tag{18}$$

where *<sup>μ</sup>* <sup>=</sup> 3.7 <sup>×</sup> <sup>10</sup>3*cm*2/*<sup>V</sup>* · *<sup>s</sup>* is the electron mobility and *<sup>n</sup>* <sup>=</sup> 2.5 is a coefficient determined empirically. The saturation velocity of electrons in germanium is about 6 <sup>×</sup> <sup>10</sup><sup>6</sup> cm/s while the value is a little less for holes.

Fig. 8. Experimental result and theoretical fitting of the electron drift velocity in germanium versus electric field.

When both RC delay and transit time are considered the overall 3dB bandwidth is

$$f\_{\text{3dB}} = \frac{1}{\sqrt{1/f\_{\text{RC}}^2 + 1/f\_{tr}^2}}.\tag{19}$$

Based on this formula, the calculated 3dB bandwidth contour of a germanium diode with respect to its depletion width and device area is shown in Fig. 9. In general, the transit time limits the maximal thickness of depletion width which is close to the germanium thickness for a fully depleted vertical P-I-N junction diode. The RC delay, on the other hand, limits the maximal device area. In the calculation, a termination resistance of 50 Ω is used for the compatibility of common impedance and no parasitics is considered. When the series resistance and parasitic capacitance (e.g. contact pad capacitance) are taken into account, the 3dB bandwidth is reduced.

Dark current is another important parameter of photodetectors. Germanium photodetector usually suffers from a larger dark current as a result of its narrow indirect band gap and poor surface passivation capability. A narrow band gap leads to higher density of intrinsic carriers and higher trap assisted generation rate through Shockley-Read-Hall (SRH) process. The surface passivation of germanium, i.e. termination of the dangling bonds or surface states, is generally more different than silicon as germanium oxide is much less robust than silicon dioxide. Therefore people use other materials such as hydrogenate amorphous silicon (aSi:H), hydrogen-rich silicon nitride (Si3N4), germanium oxynitride (Ge(ON)*x*) and etc. to passivate germanium surface. The dark current associated with material quality (e.g. defects)

Silicon Photonics 15

Germanium-on-Silicon for Integrated Silicon Photonics 17

and it usually between 1 <sup>×</sup> <sup>10</sup>−14cm−<sup>2</sup> to 1 <sup>×</sup> <sup>10</sup>−15cm−2. The leakage current density per unit length as a function of threading dislocation density is calculated by using *<sup>σ</sup>* <sup>=</sup> <sup>1</sup> <sup>×</sup> <sup>10</sup>−15cm−<sup>2</sup> for *NTD* <sup>=</sup> <sup>1</sup> <sup>×</sup> <sup>10</sup>7cm−<sup>1</sup> and *NTD* <sup>=</sup> <sup>1</sup> <sup>×</sup> <sup>10</sup>8cm−1, respectively. The results are shown in Fig. 10. A few experimental results (Colace et al., n.d.; Fama et al., n.d.; Liu, Cannon, Wada, Ishikawa, Jongthammanurak, Danielson, Michel & Kimerling, 2005; Samavedam et al., 1998; Sutter et al., 1994) are also presented in the figure for comparison. For the experimental results, the dark current density is divided by the germanium thickness as an approximating for the depletion width. All the experimental results fall in the two calculation curves and show good

Fig. 10. Summary of dark current density (at -1V) bias versus measured threading dislocation density from various literature (Colace et al., n.d.; Fama et al., n.d.; Liu, Cannon, Wada, Ishikawa, Jongthammanurak, Danielson, Michel & Kimerling, 2005; Samavedam et al., 1998; Sutter et al., 1994). Theoretical calculation with two conditions of generation-recombination

Waveguide coupled photodetector is adopted to break the trade-off between optical absorption and device speed as stated earlier. It also allows the realization of planar integration of photodetectors with electronics on silicon substrate. Therefore many research work on silicon waveguide coupled germanium photodetectors emerged soon after the surge of surface incidence epitaxial germanium photodetector research. The research started with polycrystalline germanium on silicon waveguide (Colace et al., 2006) followed by numerous work of waveguide coupled epitaxial germanium photodetectors around the world. In most of these work, silicon-on-insulator is the choice for substrate to form silicon waveguide with optical confinement by buried oxide and surrounding low refractive index materials (Feng et al., 2009; 2010; Masini et al., 2007; Vivien et al., 2009; 2007; Wang, Loh, Chua, Zang, Xiong, Loh, Yu, Lee, Lo & Kwong, 2008; Wang, Loh, Chua, Zang, Xiong, Tan, Yu, Lee, Lo & Kwong, 2008; Yin et al., 2007) while silicon nitride can also be adopted as waveguide to couple light into germanium (Ahn et al., 2007). Most of these photodetectors are vertical or lateral P-I-N diodes while quantum well germanium photodetectors are also investigated (Fidaner

agreement with the calculated relation.

center per unit length are shown in two solid lines.

**2.3 Integration of germanium photodetector and waveguide**

Fig. 9. Calculated 3dB bandwidth contour of a germanium diode with respect to its depletion width and device area in ideal conditions.

is sometimes called bulk leakage while that with surface condition is called surface leakage. The former one is scaled with the area of devices while the latter one is scaled with the perimeter.

As surface leakage highly depends on surface passivation processes, bulk leakage is a good measure of material quality. In many epitaxial germanium photodetectors with relatively larger size, bulk leakage dominates overall dark current. As we mentioned earlier in this chapter, misfit dislocations exist at germanium and silicon interface as a result of lattice mismatch and stress relaxation. These misfit dislocations along with other crystal imperfections are important sources of threading dislocations in germanium. These threading dislocations introduce deep level traps (SRH recombination-generation centers) which result in the majority of bulk leakage current in many cases. The effect of threading dislocation on leakage current can be obtained by calculating generation current induced by deep level traps:

$$J\_{\text{gen}}/d = \frac{e n\_i}{\pi},\tag{20}$$

where *Jgen*/*d* is the generation current per unit length, *e* is elementary charge, *ni* is intrinsic carrier density and the minority lift time *τ* is equal to

$$
\pi = \frac{1}{\sigma v\_{th} N\_D N\_{\rm TD}},
\tag{21}
$$

where *σ* is trap capture cross-section, *vth* is carrier thermal velocity, *ND* is threading dislocation density and *NTD* is the number of traps per unit length of dislocation. By substituting the expression of *τ* the current density per length

$$J\_{\rm gen}/d = en\_i \sigma v\_{th} N\_D N\_{TD}.\tag{22}$$

The above formula can be applied to either electrons or holes though one of them usually dominates the generation process. In germanium, *vth* <sup>=</sup> 2.3 <sup>×</sup> <sup>10</sup>7cm/s for electrons and *vth* <sup>=</sup> 1.7 <sup>×</sup> <sup>10</sup>7cm/s for holes. The trap capture cross section is different for different types of traps 14 Will-be-set-by-IN-TECH

Fig. 9. Calculated 3dB bandwidth contour of a germanium diode with respect to its depletion

is sometimes called bulk leakage while that with surface condition is called surface leakage. The former one is scaled with the area of devices while the latter one is scaled with the

As surface leakage highly depends on surface passivation processes, bulk leakage is a good measure of material quality. In many epitaxial germanium photodetectors with relatively larger size, bulk leakage dominates overall dark current. As we mentioned earlier in this chapter, misfit dislocations exist at germanium and silicon interface as a result of lattice mismatch and stress relaxation. These misfit dislocations along with other crystal imperfections are important sources of threading dislocations in germanium. These threading dislocations introduce deep level traps (SRH recombination-generation centers) which result in the majority of bulk leakage current in many cases. The effect of threading dislocation on leakage current can be obtained by calculating generation current induced by deep level traps:

*Jgen*/*<sup>d</sup>* <sup>=</sup> *eni*

where *Jgen*/*d* is the generation current per unit length, *e* is elementary charge, *ni* is intrinsic

*σvthNDNTD*

where *σ* is trap capture cross-section, *vth* is carrier thermal velocity, *ND* is threading dislocation density and *NTD* is the number of traps per unit length of dislocation. By

The above formula can be applied to either electrons or holes though one of them usually dominates the generation process. In germanium, *vth* <sup>=</sup> 2.3 <sup>×</sup> <sup>10</sup>7cm/s for electrons and *vth* <sup>=</sup> 1.7 <sup>×</sup> <sup>10</sup>7cm/s for holes. The trap capture cross section is different for different types of traps

*<sup>τ</sup>* <sup>=</sup> <sup>1</sup>

*<sup>τ</sup>* , (20)

, (21)

*Jgen*/*d* = *eniσvthNDNTD*. (22)

width and device area in ideal conditions.

carrier density and the minority lift time *τ* is equal to

substituting the expression of *τ* the current density per length

perimeter.

and it usually between 1 <sup>×</sup> <sup>10</sup>−14cm−<sup>2</sup> to 1 <sup>×</sup> <sup>10</sup>−15cm−2. The leakage current density per unit length as a function of threading dislocation density is calculated by using *<sup>σ</sup>* <sup>=</sup> <sup>1</sup> <sup>×</sup> <sup>10</sup>−15cm−<sup>2</sup> for *NTD* <sup>=</sup> <sup>1</sup> <sup>×</sup> <sup>10</sup>7cm−<sup>1</sup> and *NTD* <sup>=</sup> <sup>1</sup> <sup>×</sup> <sup>10</sup>8cm−1, respectively. The results are shown in Fig. 10. A few experimental results (Colace et al., n.d.; Fama et al., n.d.; Liu, Cannon, Wada, Ishikawa, Jongthammanurak, Danielson, Michel & Kimerling, 2005; Samavedam et al., 1998; Sutter et al., 1994) are also presented in the figure for comparison. For the experimental results, the dark current density is divided by the germanium thickness as an approximating for the depletion width. All the experimental results fall in the two calculation curves and show good agreement with the calculated relation.

Fig. 10. Summary of dark current density (at -1V) bias versus measured threading dislocation density from various literature (Colace et al., n.d.; Fama et al., n.d.; Liu, Cannon, Wada, Ishikawa, Jongthammanurak, Danielson, Michel & Kimerling, 2005; Samavedam et al., 1998; Sutter et al., 1994). Theoretical calculation with two conditions of generation-recombination center per unit length are shown in two solid lines.

#### **2.3 Integration of germanium photodetector and waveguide**

Waveguide coupled photodetector is adopted to break the trade-off between optical absorption and device speed as stated earlier. It also allows the realization of planar integration of photodetectors with electronics on silicon substrate. Therefore many research work on silicon waveguide coupled germanium photodetectors emerged soon after the surge of surface incidence epitaxial germanium photodetector research. The research started with polycrystalline germanium on silicon waveguide (Colace et al., 2006) followed by numerous work of waveguide coupled epitaxial germanium photodetectors around the world. In most of these work, silicon-on-insulator is the choice for substrate to form silicon waveguide with optical confinement by buried oxide and surrounding low refractive index materials (Feng et al., 2009; 2010; Masini et al., 2007; Vivien et al., 2009; 2007; Wang, Loh, Chua, Zang, Xiong, Loh, Yu, Lee, Lo & Kwong, 2008; Wang, Loh, Chua, Zang, Xiong, Tan, Yu, Lee, Lo & Kwong, 2008; Yin et al., 2007) while silicon nitride can also be adopted as waveguide to couple light into germanium (Ahn et al., 2007). Most of these photodetectors are vertical or lateral P-I-N diodes while quantum well germanium photodetectors are also investigated (Fidaner

Silicon Photonics 17

Germanium-on-Silicon for Integrated Silicon Photonics 19

(a) (b) Fig. 13. Simulated ideal responsivity versus germanium thickness for waveguide-coupled

Photonic-electronic monolithic integration requires a silicon-based light source. A silicon-based laser is arguably the most challenging element in silicon photonics because both silicon and SiGe (including pure germanium) are inefficient light emitters due to their indirect band structure. Many approaches have been investigated to solve this challenge including the efforts on porous silicon (Gelloz & Koshida, 2000; Koshida & Koyama, 1992), silicon nanostructures (Irrera et al., 2003) and SiGe nanostructures (Peng et al., 1998), silicide (Leong et al., 1997), erbium doped silicon (Zhang et al., 1994). However, all above approaches

Erbium-doped silicon dielectrics which benefit from less energy back transfer than erbium-doped silicon are potential gain media . Erbium atoms which are capable of light emission at 1.54 *μ*m have been incorporated into silicon oxide (Adeola et al., 2006; Fujii et al., 1997; Kik et al., 2000) or silicon nitride (Makarova et al., 2008; Negro et al., 2008) matrix materials. Silicon nanocrystals are sometimes introduced in these materials as recombination sensitizers. The optical gain of such extrinsic light-emitting materials is generally very small (Han et al., 2001) due to limited erbium solubility and energy up-conversion. Therefore lasing can only occur in extremely low loss resonators such as toroidal structures (Polman

are challenged by the lack of sufficient gain to surpass material loss for laser action.

photodetector with silicon thickness of (a) 0.55*μ*m and (b) 0.8*μ*m, respectively.

Fig. 12. FDTD simulation of light coupling from silicon waveguide to germanium

photodetector.

**3. Germanium light source 3.1 Silicon based light source**

et al., 2007). Among these devices, more than 30GHz 3dB bandwidth have been achieved at reasonable bias (usually -1V to -2V) with good responsivity (e.g. 0.9-1.0 A/W). These high speed photodetectors can be potential substitutes for commercially available photodetectors based on III-V materials for up to 25Gb/s digital transmission applications.

In waveguide coupled photodetectors, one of the critical design roles is to optimize waveguide to germanium optical coupling. The required length of a photodetector is determined by the coupling efficiency for an evanescent coupling. Therefore the device speed is also affected by coupling design as the capacitance of the device is scaled with its dimension. In general, the germanium is on top of an input silicon waveguide for evanescent coupling. This design is usually adopted for small silicon waveguides such as channel waveguides or small rib waveguides on SOI substrates with relatively thin device silicon layer. However, for a large rib waveguide the coupling efficiency is very sensitive to the thickness of germanium layer as shown later. Therefore it is sometimes necessary to make a mode converter to push guided light down to the slab part of the rib waveguide and couple the light from the slab to germanium photodetectors. The two different designs are schematically shown in Fig. 11.

Fig. 11. Two designs of waveguide to germanium photodetector coupling on SOI substrate.

The coupling between waveguide and germanium can be simulated by numerical methods such as finite-difference time-domain (FDTD) method. A sample simulation results is shown in Fig. 12. In the figure, the propagated electric field shows the process of evanescent coupling. By calculating the absorption in germanium in this coupling process, the ideal responsivity can be obtained. Simulated ideal responsivity as a function of germanium thickness for waveguide-coupled photodetector with two silicon thicknesses (0.55*μ*m and 0.8*μ*m) are shown in Fig. 13. The responsivity is generally a periodic function of germanium thickness as a result of coupling resonance conditions. But the sensitivity of peak responsivity on germanium thickness is higher for thicker silicon thickness. It is the reason of reducing silicon thickness for large silicon rib waveguides to avoid the sensitivity of the performance of germanium photodetectors due to processing variations. The reduction of the coupling sensitivity on the polarization state of guided modes is another design consideration. The peak coupling conditions of a transverse-electric (TE) mode and a transverse-magnetic (TM) mode are not usually aligned. Optimizing TE and TM modes or creating multiple modes in the waveguides with some mode transformers can minimize the polarization sensitivity.

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

et al., 2007). Among these devices, more than 30GHz 3dB bandwidth have been achieved at reasonable bias (usually -1V to -2V) with good responsivity (e.g. 0.9-1.0 A/W). These high speed photodetectors can be potential substitutes for commercially available photodetectors

In waveguide coupled photodetectors, one of the critical design roles is to optimize waveguide to germanium optical coupling. The required length of a photodetector is determined by the coupling efficiency for an evanescent coupling. Therefore the device speed is also affected by coupling design as the capacitance of the device is scaled with its dimension. In general, the germanium is on top of an input silicon waveguide for evanescent coupling. This design is usually adopted for small silicon waveguides such as channel waveguides or small rib waveguides on SOI substrates with relatively thin device silicon layer. However, for a large rib waveguide the coupling efficiency is very sensitive to the thickness of germanium layer as shown later. Therefore it is sometimes necessary to make a mode converter to push guided light down to the slab part of the rib waveguide and couple the light from the slab to germanium photodetectors. The two different designs are schematically shown in Fig. 11.

Fig. 11. Two designs of waveguide to germanium photodetector coupling on SOI substrate. The coupling between waveguide and germanium can be simulated by numerical methods such as finite-difference time-domain (FDTD) method. A sample simulation results is shown in Fig. 12. In the figure, the propagated electric field shows the process of evanescent coupling. By calculating the absorption in germanium in this coupling process, the ideal responsivity can be obtained. Simulated ideal responsivity as a function of germanium thickness for waveguide-coupled photodetector with two silicon thicknesses (0.55*μ*m and 0.8*μ*m) are shown in Fig. 13. The responsivity is generally a periodic function of germanium thickness as a result of coupling resonance conditions. But the sensitivity of peak responsivity on germanium thickness is higher for thicker silicon thickness. It is the reason of reducing silicon thickness for large silicon rib waveguides to avoid the sensitivity of the performance of germanium photodetectors due to processing variations. The reduction of the coupling sensitivity on the polarization state of guided modes is another design consideration. The peak coupling conditions of a transverse-electric (TE) mode and a transverse-magnetic (TM) mode are not usually aligned. Optimizing TE and TM modes or creating multiple modes in the waveguides with some mode transformers can minimize the polarization sensitivity.

based on III-V materials for up to 25Gb/s digital transmission applications.

Fig. 12. FDTD simulation of light coupling from silicon waveguide to germanium photodetector.

Fig. 13. Simulated ideal responsivity versus germanium thickness for waveguide-coupled photodetector with silicon thickness of (a) 0.55*μ*m and (b) 0.8*μ*m, respectively.

#### **3. Germanium light source**

#### **3.1 Silicon based light source**

Photonic-electronic monolithic integration requires a silicon-based light source. A silicon-based laser is arguably the most challenging element in silicon photonics because both silicon and SiGe (including pure germanium) are inefficient light emitters due to their indirect band structure. Many approaches have been investigated to solve this challenge including the efforts on porous silicon (Gelloz & Koshida, 2000; Koshida & Koyama, 1992), silicon nanostructures (Irrera et al., 2003) and SiGe nanostructures (Peng et al., 1998), silicide (Leong et al., 1997), erbium doped silicon (Zhang et al., 1994). However, all above approaches are challenged by the lack of sufficient gain to surpass material loss for laser action.

Erbium-doped silicon dielectrics which benefit from less energy back transfer than erbium-doped silicon are potential gain media . Erbium atoms which are capable of light emission at 1.54 *μ*m have been incorporated into silicon oxide (Adeola et al., 2006; Fujii et al., 1997; Kik et al., 2000) or silicon nitride (Makarova et al., 2008; Negro et al., 2008) matrix materials. Silicon nanocrystals are sometimes introduced in these materials as recombination sensitizers. The optical gain of such extrinsic light-emitting materials is generally very small (Han et al., 2001) due to limited erbium solubility and energy up-conversion. Therefore lasing can only occur in extremely low loss resonators such as toroidal structures (Polman

Silicon Photonics 19

Germanium-on-Silicon for Integrated Silicon Photonics 21


 

> 

 

 

"


 


 - -

!#


 

(a) (b) Fig. 15. Comparison of the carrier distribution and the light emission process between (a) Ge

To improve the light emission efficiency in germanium, more injected electrons are required to be pumped into Γ valley. In other words, the objective is to make germanium a direct gap material. In the germanium photodetector section, it has shown that tensile strain can used to reduce direct band gap for more optical absorption. It should also be noted that the difference

 !

 

 

 

(a) (b) Fig. 14. Comparison of the band structure and the carrier distribution between (a) Ge and (b)

radiative recombination in direct band gap materials. But the overall light emission from germanium is weak because most of the injected electrons are in the *L* valleys. Most of these electrons recombine non-radiatively as indirect phonon-assisted radiative recombination is very slow. For III-V direct gap materials, injected electrons are in the direct valley so overall

 

 

 

 


 


In0.53Ga0.47As at equilibrium.

light emission is efficient.

 



and (b) In0.53Ga0.47As under injection.

 

 

 

et al., 2004). These dielectric materials also suffer from the difficulty of electrical injection. Appreciable concentration of carriers only presents under very high electric field via effects like tunneling process (Iacona et al., 2002; Nazarov et al., 2005).

Non-linear optical effects can also produce net gain in silicon. Based on stimulated Raman scattering (SRS) effect, optically pumped silicon waveguide lasers have been realized with pulse (Boyraz & Jalali, 2004; Rong et al., 2004) and continuous-wave operation (Rong et al., 2005). Similarly, the inevitable requirement of optical injection makes them not suitable for integrated photonics.

Following a hybrid approach, researchers successfully integrated III-V semiconductor lasers on silicon substrates. The integration can be accomplished by directly growing GaAs/InGaAs on silicon with graded Si*x*Ge1−*<sup>x</sup>* buffer layers (Groenert et al., 2003) or bonding III-V materials on silicon surface for laser fabrication (Fang et al., 2006; Park et al., 2005).

Electronic-photonic monolithic integration requires a light source with the capability of electrical injection and room temperature operation based on silicon compatible materials and CMOS-compatible processes. Germanium is a very promising material for making such a light source if it can be engineered for more efficient direct gap light emission and net optical gain.

#### **3.2 Germanium band structure engineering**

The inefficiency of light emission from germanium comes from is its indirect band structure. To understand how we can engineer its band structure for more efficient light emission and even net optical gain we start with the carrier recombination analysis in germanium.

The band structure and the carrier distribution of germanium at equilibrium are drawn in the Fig. 14 (a). Most of the thermally activated electrons occupy the lowest energy states in the indirect *L* valleys governed by Fermi distribution:

$$f(E) = \frac{1}{1 + (E - E\_f) / k\_B T},\tag{23}$$

where *Ef* is equilibrium Fermi level. For a direct gap material InGaAs shown in Fig. 14 (b), most of the electrons occupy the direct Γ valley.

The carrier occupancy states determine the light emitting properties of a material. The band-to-band optical transition requires excess free carriers which are injected electrically or optically. At steady state, the carriers obey quasi Fermi distribution with respect to carrier quasi Fermi level:

$$f\_c(E) = \frac{1}{1 + (E - E\_{fc}) / k\_B T}, \text{and} \tag{24}$$

$$f\_{\nu}(E) = \frac{1}{1 + (E - E\_{fv})/k\_B T},\tag{25}$$

where *Ef c* and *Ef v* are the quasi Fermi levels of electrons and holes. A single quasi Fermi level exists for electrons or holes in steady state despite of the multi-valley band structure because of very fast inter-valley scattering process.

The carrier distribution under injection for germanium and InGaAs are shown in Fig. 15. Despite germanium is an indirect band gap material, there are still some electrons pumped to the Γ valley owing to the small energy difference (0.136 eV) between the direct band gap and the indirect band gap. The excess electrons in the Γ valley recombine radiatively with the holes in the valence band. This light emission process is as efficient as the direct 18 Will-be-set-by-IN-TECH

et al., 2004). These dielectric materials also suffer from the difficulty of electrical injection. Appreciable concentration of carriers only presents under very high electric field via effects

Non-linear optical effects can also produce net gain in silicon. Based on stimulated Raman scattering (SRS) effect, optically pumped silicon waveguide lasers have been realized with pulse (Boyraz & Jalali, 2004; Rong et al., 2004) and continuous-wave operation (Rong et al., 2005). Similarly, the inevitable requirement of optical injection makes them not suitable for

Following a hybrid approach, researchers successfully integrated III-V semiconductor lasers on silicon substrates. The integration can be accomplished by directly growing GaAs/InGaAs on silicon with graded Si*x*Ge1−*<sup>x</sup>* buffer layers (Groenert et al., 2003) or bonding III-V materials

Electronic-photonic monolithic integration requires a light source with the capability of electrical injection and room temperature operation based on silicon compatible materials and CMOS-compatible processes. Germanium is a very promising material for making such a light source if it can be engineered for more efficient direct gap light emission and net optical gain.

The inefficiency of light emission from germanium comes from is its indirect band structure. To understand how we can engineer its band structure for more efficient light emission and

The band structure and the carrier distribution of germanium at equilibrium are drawn in the Fig. 14 (a). Most of the thermally activated electrons occupy the lowest energy states in the

where *Ef* is equilibrium Fermi level. For a direct gap material InGaAs shown in Fig. 14 (b),

The carrier occupancy states determine the light emitting properties of a material. The band-to-band optical transition requires excess free carriers which are injected electrically or optically. At steady state, the carriers obey quasi Fermi distribution with respect to carrier

where *Ef c* and *Ef v* are the quasi Fermi levels of electrons and holes. A single quasi Fermi level exists for electrons or holes in steady state despite of the multi-valley band structure because

The carrier distribution under injection for germanium and InGaAs are shown in Fig. 15. Despite germanium is an indirect band gap material, there are still some electrons pumped to the Γ valley owing to the small energy difference (0.136 eV) between the direct band gap and the indirect band gap. The excess electrons in the Γ valley recombine radiatively with the holes in the valence band. This light emission process is as efficient as the direct

<sup>1</sup> + (*<sup>E</sup>* <sup>−</sup> *Ef*)/*kBT* , (23)

<sup>1</sup> + (*<sup>E</sup>* <sup>−</sup> *Ef c*)/*kBT* , and (24)

<sup>1</sup> + (*<sup>E</sup>* <sup>−</sup> *Ef v*)/*kBT* , (25)

even net optical gain we start with the carrier recombination analysis in germanium.

*<sup>f</sup>*(*E*) = <sup>1</sup>

*fc*(*E*) = <sup>1</sup>

*fv*(*E*) = <sup>1</sup>

like tunneling process (Iacona et al., 2002; Nazarov et al., 2005).

on silicon surface for laser fabrication (Fang et al., 2006; Park et al., 2005).

integrated photonics.

quasi Fermi level:

**3.2 Germanium band structure engineering**

indirect *L* valleys governed by Fermi distribution:

most of the electrons occupy the direct Γ valley.

of very fast inter-valley scattering process.

Fig. 14. Comparison of the band structure and the carrier distribution between (a) Ge and (b) In0.53Ga0.47As at equilibrium.

radiative recombination in direct band gap materials. But the overall light emission from germanium is weak because most of the injected electrons are in the *L* valleys. Most of these electrons recombine non-radiatively as indirect phonon-assisted radiative recombination is very slow. For III-V direct gap materials, injected electrons are in the direct valley so overall light emission is efficient.

Fig. 15. Comparison of the carrier distribution and the light emission process between (a) Ge and (b) In0.53Ga0.47As under injection.

To improve the light emission efficiency in germanium, more injected electrons are required to be pumped into Γ valley. In other words, the objective is to make germanium a direct gap material. In the germanium photodetector section, it has shown that tensile strain can used to reduce direct band gap for more optical absorption. It should also be noted that the difference

Silicon Photonics 21

Germanium-on-Silicon for Integrated Silicon Photonics 23


 

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and (27)

(28)
