6.12 Strain Effects on the Band Structure
171
Fig. 6.48 a Dependence of the band gap of Ga 0.92 In 0.08 As alloy (squares) and nitrogen-doped (Ga,In)As on (compressive) hydrostatic pressure, determined by photomodulated transmission at T = 295 K. b Pressure dependence of band
gap for two (Ga,In)(As,N) samples together with model calculation (6.62). The coupling parameter is V = 0.12 eV
(0.4 eV) for a nitrogen content of 0.9% (2.3%). Adapted from [538]
Fig. 6.49 Dependence of the direct V
15 – C
1 and indirect V
15 –X C
1 band gap of GaAs (T = 300 K) on pressure. Solid
lines are interpolations of experimental data, dashed line is extrapolation to p = 0. The crossing of the direct and indirect
band gap occurs at 4.2 GPa. The arrow denotes the pressure of the phase transition from zincblende to an orthorhomic
structure around 17 GPa. Adapted from [537]
E
2
= b
2
/2
xx − yy
2 +
yy − zz
2 + ( xx − zz )
2
+ d
2
2
xy +
2
yz +
2
xz
,
where E
0
v denotes the bulk valence-band edge. b and d are the optical deformation potentials. For
compressive strain the heavy-hole band is above the light-hole band. For tensile strain there is strong
mixing of the bands (Fig. 6.50). In Table 6.7 the deformation potentials for some III–V semiconductors
are listed. Typical values are in the eV regime.
In a wurtzite crystal, seven (or eight) deformation potentials are needed that are termed a (for the
change of band gap with hydrostatic strain, again a = a C − a V ) and D 1 –D 6 (for the valence band
structure) [539, 540].
In Si and Ge, three deformation potentials, termed a, b, d, are needed for the valence band and two
for each conduction band minimum, u and d [541]. The energy position of the i-th conduction-band
edge (with unit vector a i pointing to the valley) is