Basic Parameters of Silicon Germanium (SiGe)

SiGe - Silicon Germanium

"The group IV silicon-germanium random alloys differ in several respects from other material combinations treated in this volume. One of the most characteristic features of this material combination concerns bulk Si1-xGex: Si and Ge are miscible over the complete range of compositions. However, the large splitting of the solidus/liquidus phase boundary makes it almost impossible to pull bulk crystals of acceptable radial and axial homogeneity in a composition range that differs from the pure materials by more than a few atomic percent. Hence, interest in bulk alloys, which undoubtedly existed in the 1960s and early 1970s for a variety of reasons, soon waned both because of the rapid switching from Ge to Si as the dominant device material and because of the fundamental difficulties of providing high-quality Si1-xGex substrates. For these reasons, many of the available data concerning the physical properties of bulk Si1-xGex were recorded more than 30 years ago, some of them on material of doubtful crystal quality, especially in the composition range around x = 50%. Material quality and composition-dependent dopant segregation are also the main reason for the almost complete lack of data concerning the dopant-dependence of basic material parameters, such as carrier mobility or fundamental energy gap. Except for a few new attempts toward employing Si1-xGex : bulk alloys with moderate compositions for thermoelectric and optoelectronic devices, only minor activities became known in that direction in the last 20 years or so.
On the other hand, the development of low-temperature growth techniques, such as molecular beam epitaxy or chemical vapor deposition, and the new concepts of energy band engineering (first emerged for III-V materials in the seventies and eighties) led to a fast increase of the number of groups dealing with thin Si1-xGex films. These films are usually deposited on an Si substrate. Because of the inherent lattice mismatch of around 4% between pure Si and pure Ge, such films are tetragonally distorted, when grown to a thickness below the critical value for the onset of misfit dislocations. These films begin to relax to their intrinsic cubic lattice constant, once the critical thickness is exceeded. Hence depending on the thickness of a Si1-xGex film at a given composition (and other growth parameters that rule kinetic limitations), such films can be either biaxially strained or strain-relaxed. Strain-relaxed films can be considered as sort of a virtual "bulk55 substrate. With the art of epitaxial growth rapidly advancing, it was soon recognized that strain is an as important material parameter as composition in the Si1-xGex heterostructure system. Many parameters, such as band gaps, band offsets, effective masses, and so on, are strongly strain-dependent, making strain control a vital necessity for any kind of energy band engineering conceivable in these materials. The advantages gained by the introduction of thin Si1-xGex films in their basic compatibility with standard silicon technologies have made this heterostructure system an extremely interesting candidate for production devices. The first commercial products in the high-frequency analog market segment were introduced in spring 1998".                      Schaffler F. (2001)

This partiton reflects the contrast between the technical relevance of strained Si1-xGex thin films and the quite limited interest in bulk alloys. Where strain-dependent data are given, they are restricted to biaxial strain in the (001) plane, which corresponds to pseudomorphic growth on a (001)-oriented substrate. This is presently the only orientation of technical relevance, but references to other surface orientations are given, when available. Also, data that are important for the relaxation of Si1-xGex on Si, such as critical thickness or misfit dislocation glide velocities, are incorporated. The more detailed part of this chapter is preceded by a table of 300 K bulk data, which also repeats the most basic properties of elemental Si and Ge for comparison. Several parameters, such as the lattice constant, vary almost linearly between the constituents, expressing their close chemical similarity. Other parameters, such as the band gap or the effective electron masses, do not, because the general conduction band structure changes from Si-like to Ge-like at x = 85%. The variation of the room temperature bulk parameters with composition, as listed in the table, gives a quick guide to where linear variation can be expected and where not. In any case, the more detailed plots in the second part should be consulted, especially when dealing with strained films of Si1-xGex alloys.

Basic Parameters

Crystal structure Si (x=0)Diamond300 K see also Si. Basic Parameters
 Ge (x=1)Diamond300 Ksee also Ge. Basic Parameters
 Si1-xGexDiamond (random alloy)
Group of symmetry Si (x=0) Oh7-Fd3m300 K see also Si. Basic Parameters
 Ge (x=1) Oh7-Fd3m300 Ksee also Ge. Basic Parameters
 Si1-xGex Oh7-Fd3m
Number of atoms in 1 cm3 Si (x=0) 5.0 · 1022300 K see also Si. Basic Parameters
 Ge (x=1) 4.42 · 1022300 Ksee also Ge. Basic Parameters
 Si1-xGex (5.00-0.58x) · 1022
Bulk modulusSi1-xGex (97.9 - 22.8x) GPa 300 KSchaffler F. et al.(2001)
 Si (x=0)98 GPa 300 Ksee Si. Thermal properties
 Ge (x=1)75 GPa 300 Ksee Ge. Thermal properties
Linear thermal expansion coefficienSi1-xGex (2.6 + 2.55x) x 10-6 K-1 x <0.85, 300 KSchaffler F. et al.(2001)
 Si1-xGex (-0.89 + 7.53x) x 10-6 K-1 x >0.85, 300 K 
  Si (x=0) 2.6 x 10-6 K-1 300 Ksee Si. Thermal properties
 Ge (x=1) 5.9 x 10-6 K-1 300 Ksee Ge. Thermal properties
Debye temperatureSi1-xGex(640 - 266x) K300 KSchaffler F. et al.(2001)
  Si (x=0)640 K300 Ksee Si. Thermal properties
 Ge (x=1)374 K300 Ksee Ge. Thermal properties
Melting pointSi1-xGex
Ts(1412 - 738x + 263x2) oCsolidus, 300 KStohr & Klemm (1954)
Tl (1412 - 80x - 395x2) oCliquidus, 300 KStohr & Klemm (1954)
  Si (x=0)1412 K300 Ksee Si. Thermal properties
 Ge (x=1)937 K300 Ksee Ge. Thermal properties
Specific heatSi1-xGex(19.6 + 2.9x) J mol-1 K-1 Schaffler F. et al.(2001)
  Si (x=0)19.6 J mol-1 K-1
0.7 J g-1 K-1
300 K
 Ge (x=1)22.5 J mol-1 K-1
0.31 J g-1 K-1
300 K 
Thermal conductivity Si1-xGex(0.046 + 0.084x) W cm-1 K-1 0.2 < x <0.85; 300 K.
see also Thermal conductivity
vs. composition
Schaffler F. et al.(2001)
  Si (x=0)1.3 W cm-1 K-1 300 Ksee Si. Thermal properties
 Ge (x=1)0.58 W cm-1 K-1 300 Ksee Ge. Thermal properties
Thermal diffusivity Si (x=0)0.8 cm2 s-1300 Ksee Si. Thermal properties
 Ge (x=1)0.36 cm2 s-1300 Ksee Ge. Thermal properties
Thermal expansion coefficientSi1-xGex α = (2.6 + 2.55x) x 10-6 K-1x < 0.85, 300 KZhdanova et al. (1967).
 Si1-xGex α = (7.53 - 0.89x) x 10-6 K-1 x > 0.85, 300 KZhdanova et al. (1967).

DensitySi1-xGex(2.329+3.493x-0.499x2)g cm-3300 KSchaffler F. et al.(2001)
  Si (x=0)2.329 g cm-3 300 K see also Si. Basic Parameters
 Ge (x=1)5.323 g cm-3300 Ksee also Ge. Basic Parameters
Surface microhardnessSi1-xGex(1150 - 350x) kg mm-2 300 K,
using Knoop's pyramid test
Schaffler F. et al.(2001)

Dielectric constant (static) Si (x=0)11.7300 KSchaffler F. et al.(2001)
 Ge (x=1)16.2300 K 
 Si1-xGexSi1-xGex11.7 + 4.5x300 K 
Infrared refractive index n(λ)Si1-xGexSi1-xGex   n 3.42 + 0.37x + 0.22 x2 300KSchaffler F. et al.(2001)
 Si (x=0)Si (x=0)  n = 3.42300Ksee Si. Refractive index
    n = 3.38(1 + 3.9·10-5·T)77K < T < 400 K  
 Ge (x=1)  n = 4.0300Ksee Ge. Refractive index
Radiative recombination coefficient Si (x=0)  1.1 x 10-14 cm3 s-1300 Ksee Si. Optical properties
 Ge (x=1)  6.4 x 10-14 cm3 s-1300 Ksee Ge. Optical properties
Optical photon energy Si1-xGex  (63 - 8.7x) meVSi - Si, 300 KSchaffler F. et al.(2001)
    (35.+2.0x) meVGe-Ge, 300 K 
   50 meVSi-Ge, 300 Ksee also Si1-xGex. Optical phonon Raman signals
  Si (x=0)  63 meV300 Ksee Si. Optical properties
 Ge (x=1)  37 meV300 Ksee Ge. Optical properties

Effective electron mass
Si1-xGex0.92mo300K, x < 0.85 Schaffler F.(2001)
 0.159mo300K, x > 0.85
Effective electron mass
Si1-xGex0.19mo300K, x < 0.85Schaffler F.(2001)
 0.08mo300K, x > 0.85
Effective mass of density of states  mcd=M2/3 mc
      (for all valleys of conduction band)
Si1-xGex1.06mo300K, x < 0.85Son et al. (1994);
Son et al. (1995)
  1.55mo300K, x > 0.85
Effective mass of the density of states mc=(ml+mt2)1/3
    (in one valley of conduction band)
Si1-xGex 0.32mo300K, x < 0.85Son et al. (1994);
Son et al. (1995)
 0.22mo300K, x > 0.85
Effective hole masses (heavy)