Basic Parameters of Silicon Germanium (SiGe)
"The group IV silicongermanium 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 Si_{1x}Ge_{x}:
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 highquality
Si_{1x}Ge_{x} substrates. For these reasons, many of the available
data concerning the physical properties of bulk Si_{1x}Ge_{x}
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 compositiondependent dopant segregation are also the main reason for the almost
complete lack of data concerning the dopantdependence of basic material parameters,
such as carrier mobility or fundamental energy gap. Except for a few new attempts
toward employing Si_{1x}Ge_{x} : 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 lowtemperature growth techniques, such as molecular beam epitaxy
or chemical vapor deposition, and the new concepts of energy band engineering (first
emerged for IIIV materials in the seventies and eighties) led to a fast increase
of the number of groups dealing with thin Si_{1x}Ge_{x} 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 Si_{1x}Ge_{x}
film at a given composition (and other growth parameters that rule kinetic limitations),
such films can be either biaxially strained or strainrelaxed. Strainrelaxed 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 Si_{1x}Ge_{x} heterostructure
system. Many parameters, such as band gaps, band offsets, effective masses, and so
on, are strongly straindependent, 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 Si_{1x}Ge_{x} 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 highfrequency analog market segment were introduced in spring 1998".
Schaffler F. (2001)
This partiton
reflects the contrast between the technical relevance of strained Si_{1x}Ge_{x}
thin films and the quite limited interest in bulk alloys. Where straindependent 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 Si_{1x}Ge_{x}
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 Silike to Gelike 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 Si_{1x}Ge_{x} alloys.
Basic Parameters
Remarks  Referens  
Crystal structure  Si (x=0)  Diamond  300 K  see also Si. Basic Parameters 
Ge (x=1)  Diamond  300 K  see also Ge. Basic Parameters  
Si_{1x}Ge_{x}  Diamond (random alloy)  
Group of symmetry  Si (x=0)  O_{h}^{7}Fd3m  300 K  see also Si. Basic Parameters 
Ge (x=1)  O_{h}^{7}Fd3m  300 K  see also Ge. Basic Parameters  
Si_{1x}Ge_{x}  O_{h}^{7}Fd3m  
Number of atoms in 1 cm^{3}  Si (x=0)  5.0 · 10^{22}  300 K  see also Si. Basic Parameters 
Ge (x=1)  4.42 · 10^{22}  300 K  see also Ge. Basic Parameters  
Si_{1x}Ge_{x}  (5.000.58x) · 10^{22}  
Remarks  Referens  
Bulk modulus  Si_{1x}Ge_{x}  (97.9  22.8x) GPa  300 K  Schaffler F. et al.(2001) 
Si (x=0)  98 GPa  300 K  see Si. Thermal properties  
Ge (x=1)  75 GPa  300 K  see Ge. Thermal properties  
Linear thermal expansion coefficien  Si_{1x}Ge_{x}  (2.6 + 2.55x) x 10^{6} K^{1}  x <0.85, 300 K  Schaffler F. et al.(2001) 
Si_{1x}Ge_{x}  (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 K  see Si. Thermal properties  
Ge (x=1)  5.9 x 10^{6} K^{1}  300 K  see Ge. Thermal properties  
Debye temperature  Si_{1x}Ge_{x}  (640  266x) K  300 K  Schaffler F. et al.(2001) 
Si (x=0)  640 K  300 K  see Si. Thermal properties  
Ge (x=1)  374 K  300 K  see Ge. Thermal properties  
Melting point  _{Si1xGex } (solidus)  T_{s}(1412  738x + 263x^{2}) ^{o}C  solidus, 300 K  Stohr & Klemm (1954) 
_{Si1xGex } (liquidus)  T_{l} (1412  80x  395x^{2}) ^{o}C  liquidus, 300 K  Stohr & Klemm (1954)  
Si (x=0)  1412 K  300 K  see Si. Thermal properties  
Ge (x=1)  937 K  300 K  see Ge. Thermal properties  
Specific heat  Si_{1x}Ge_{x}  (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  Si_{1x}Ge_{x}  (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 K  see Si. Thermal properties  
Ge (x=1)  0.58 W cm^{1} K^{1}  300 K  see Ge. Thermal properties  
Thermal diffusivity  Si (x=0)  0.8 cm^{2} s^{}^{1}  300 K  see Si. Thermal properties 
Ge (x=1)  0.36 cm^{2} s^{}^{1}  300 K  see Ge. Thermal properties  
Thermal expansion coefficient  Si_{1x}Ge_{x}  α = (2.6 + 2.55x) x 10^{6} K^{1}  x < 0.85, 300 K  Zhdanova et al. (1967). 
Si_{1x}Ge_{x}  α = (7.53  0.89x) x 10^{6} K^{1}  x > 0.85, 300 K  Zhdanova et al. (1967). 
 
Density  Si_{1x}Ge_{x}  (2.329+3.493x0.499x^{2})g cm^{3}  300 K  Schaffler 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^{3}  300 K  see also Ge. Basic Parameters  
Surface microhardness  Si_{1x}Ge_{x}  (1150  350x) kg mm^{2}  300 K, using Knoop's pyramid test  Schaffler F. et al.(2001) 

Dielectric constant (static)  Si (x=0)  11.7  300 K  Schaffler F. et al.(2001) 
Ge (x=1)  16.2  300 K  
Si_{1x}Ge_{x}Si_{1x}Ge_{x}  11.7 + 4.5x  300 K  
Infrared refractive index n(λ)  Si_{1x}Ge_{x}Si_{1x}Ge_{x}  n 3.42 + 0.37x + 0.22 x^{2}  300K  Schaffler F. et al.(2001) 
Si (x=0)Si (x=0)  n = 3.42  300K  see Si. Refractive index  
n = 3.38(1 + 3.9·10^{5}·T)  77K < T < 400 K  
Ge (x=1)  n = 4.0  300K  see Ge. Refractive index  
Radiative recombination coefficient  Si (x=0)  1.1 x 10^{14} cm^{3} s^{1}  300 K  see Si. Optical properties 
Ge (x=1)  6.4 x 10^{14} cm^{3} s^{1}  300 K  see Ge. Optical properties  
Optical photon energy  Si_{1x}Ge_{x}  (63  8.7x) meV  Si  Si, 300 K  Schaffler F. et al.(2001) 
(35.+2.0x) meV  GeGe, 300 K  
50 meV  SiGe, 300 K  see also Si_{1x}Ge_{x}. Optical phonon Raman signals  
Si (x=0)  63 meV  300 K  see Si. Optical properties  
Ge (x=1)  37 meV  300 K  see Ge. Optical properties  

Effective electron mass (longitudinal)m_{l}  Si_{1x}Ge_{x}  0.92m_{o}  300K, x < 0.85  Schaffler F.(2001) 
0.159m_{o}  300K, x > 0.85  
Effective electron mass (transverse)m_{t}  Si_{1x}Ge_{x}  0.19m_{o}  300K, x < 0.85  Schaffler F.(2001) 
0.08m_{o}  300K, x > 0.85  
Effective mass of density of states m_{cd}=M^{2/3}
m_{c} (for all valleys of conduction band)  Si_{1x}Ge_{x}  1.06m_{o}  300K, x < 0.85  Son et al. (1994);
Son et al. (1995) 
1.55m_{o}  300K, x > 0.85  
Effective mass of the density of states m_{c}=(m_{l}+m_{t2})^{1/3} (in one valley of conduction band)  Si_{1x}Ge_{x}  0.32m_{o}  300K, x < 0.85  Son
et al. (1994); Son et al. (1995) 
0.22m_{o}  300K, x > 0.85  
Effective hole masses (heavy)
