SiGe - Silicon Germanium

Mechanical Properties, Elastic Constants, Lattice Vibrations

Basic Parameters
Elastic Constants
Acoustic Wave Speeds
Phonon Frequencies

Basic Parameters

Si1-xGex   Remarks Referens
Density (2.329+3.493x-0.499x2)g cm-3 300 K Schaffler F. et al.(2001)
 
Surface microhardness (1150 - 350x) kg mm-2 300 K, using Knoop's pyramid test Schaffler F. et al.(2001)
Lattice constant a(x) ( 5.431 + 0.20x + 0.027x2) A 300 K Dismukes et al. (1964b)

Elastic constants at 300 K.

Si1-xGex. Elastic constants at 300 K. Remarks Referens
C11 (165.8 - 37.3x ) GPa 300 K Schaffler F. et al.(2001)
C12 (63.9 - 15.6 x ) GPa 300 K  
C44 (79.6 - 12.8 x ) GPa 300 K  

Si1-xGex. Bulk modulus (compressibility-1) For T = 300 K  
  Bs=(C11+2C12)/3 Bs = (97.9 - 22.8x) GPa Schaffler F. et al.(2001)
  Anisotropy factor    
  C'=(C11-C12)/2C44 A = (0.64 - 0.04x)  
  Shear modulus    
  C'=(C11-C12)/2 C' = (51.0 - 10.85x) GPa  
  [100] Young's modulus    
  Y0=(C11+2C12)·(C11-C12)/(C11+C12) Y0 = (130.2 - 28.1x) GPa Wortman & Evans (1965)
Y0=(C11+2C12)·(C11-C12)/(C11+C12) Y0 = 748 GPa (Gmelins Handbuch (1959))
Y0 = 392-694 GPa (Harris et al.(1995c)		 Y0 = 748 GPa (Gmelins Handbuch (1959))
Y0 = 392-694 GPa (Harris et al.(1995c)
  [100] Poisson ratio       σo=C12/(C11+C12) σo = (0.278- 0.005x) Wortman & Evans (1965)
Si, Ge. Young's modulus vs. direction in the (001) plane.
Wortman & Evans (1965)
Si, Ge. Poisson ratio vs. direction in the (001) plane.
Wortman & Evans (1965)

Acoustic Wave Speeds

SiGe. No data
see also Si.Acoustic Wave Speeds and Ge.Acoustic Wave Speeds

Phonon frequencies

phonon wavenumbers:   Remarks Referens
Si  νLTO(Γ25') 15.5 1012 Hz T=300K see also Si. Phonon frequencies
  νTA(X3) 4.5 1012 Hz    
  νLAO(X1) 12.3 1012 Hz    
  νTO(X4 ) 13.9 1012 Hz    
  νTA (L3) 3.45 1012 Hz    
  νLA(L2') 11.3 1012 Hz    
  νLO(L1) 12.6 1012 Hz    
  νTO(L3') 14.7 1012 Hz    
 
Ge νLTO(Γ25') 9.02 1012 Hz T=300K Nillsson & Nelin (1972)
  νTA(X3) 2.385 1012 Hz   see also Ge. Phonon frequencies
  νLAO(X1) 7.14 1012 Hz    
  νTO(X4 ) 8.17 1012 Hz    
  νTA (L3) 1.87 1012 Hz    
  νLA(L2') 6.63 1012 Hz    
  νLO(L1) 7.27 1012 Hz    
  νTO(L3') 8.55 1012 Hz    
Si. Dispersion curves for acoustic and optical phonons.
Dolling (1963) and Tubino et al. (1972)
Ge. Dispersion curves for acoustic and optical phonons.
Weber (1977)
For a wide composition range three optical phonon modes dominate the Raman spectra of Si1-xGex alloys. They are attributed to local vibrations of Si-Si, Si-Ge, and Ge-Ge atom pairs. Their relative intensities are roughly proportional to the abundance of the respective pairs-that is, (1 - x)2, 2x(l - x), and x2, respectively.
Si1-xGex. Optical phonon Raman signals associated with local Si-Si, Si-Ge and Ge-Ge modes vs. composition
 Alonso & Winer (1989)