GaInAsP - Gallium Indium Arsenide Phosphide

Mechanical properties, elastic constants, lattice vibrations

Basic Parameter
Elastic constants
Micro Hardness
Acoustic Wave Speeds
Phonon frequencies

Basic Parameter

Bulk modulus (7.1-0.516y+0.02y2)·1011 dyn cm-2   Ga0.47In0.53AsyP1-y; 300K
Density 4.81+0.552y+0.138y2 g cm-3  

Elastic constants at 300 K

for compositions lattice-matched to InP

C11     (10.11 - 0.12y)·1011 dyn cm-2     Adachi (1992)
C12 (5.61 - 0.68y)·1011 dyn cm-2  
C44 (4.56 + 0.33y) ·1011 dyn cm-2  

Bulk modulus (compressibility-1)  
Bs=(C11+2C12)/3 Bs = (7.11-0.516y+0.02y2)·1011 dyn/cm2 Adachi (1992)
Anisotropy factor  
C'=(C11-C12)/2 A = (0.493+0.035y-0.01y2)
Shear modulus  
C'=(C11-C12)/2 C' = (2.25+0.28y)·1011 dyn/cm2
[100] Young's modulus  
Yo=(C11+2C12)·(C11-C12)/(C11+C12) Yo= (6.106+0.976y-0.344y2))·1011 dyn/cm2
[100] Poisson ratio  
σo=C12/(C11+C12) σo = (0.357-0.033y+0.006y2)

Micro Hardness

GaxIn1-xAsyP1-y. Surface microhardness (using Knoop's pyramid test)
measured on (100) plane along the <100> direction vs. concentration y for the undoped lattice-matched to InP.
Watts and Willoughby (1984)


Acoustic Wave Speeds

Wave propagation
Wave character Expression for wave speed Wave speed
(in units of 105 cm/s)
[100] VL (longitudinal) (C11/&rho)1/2
VT (transverse) (C44/&rho)1/2
[100] Vl [(C11+Cl2+2C44)/2&rho]1/2
Vt|| Vt||=VT=(C44/&rho;)1/2
Vt [(C11-C12)/2&rho]1/2
[111] Vl' [(C11+2C12+4C44)/3&rho]1/2
Vt' [(C11-C12+C44)/3&rho]1/2

Phonon frequencies

GaxIn1-xAsyP1-y lattice-matched to InP. Longitudinal optical phonon frequencie (LO) vs. composition y.
Adachi (1992)
GaxIn1-xAsyP1-y lattice-matched to InP. Transverse optical phonon frequencie (TO) vs. composition y.
The solid curves represent the calculated results using the modifed REI model.
Adachi (1992)