158
6 Band Structure
Table 6.4 Parameters for the temperature dependence of the band gap according to 6.33 (Si, GaAs: [505], GaN: [507],
ZnO: [508]) and (6.34) for various semiconductors
α
α B
B
(10 −4 eV/K)
(K)
(10 −4 eV/K)
(K)
Si
3.23
446
0.51
2.56
296
Ge
4.13
253
0.49
GaAs
4.77
252
0.43
5.16
310
GaN
6.14
586
0.40
4.05
370
InP
3.96
274
0.48
InAs
2.82
147
0.68
ZnSe
5.00
218
0.36
ZnO
3.8
659
0.54
5.9
616
Fig. 6.32 Band gap of
GaAs (at T = 10 K) as a
function of the Ga isotope
content. Dashed line is
linear fit. Adapted
from [509]
β =
π
2
3 (1 + 2 )
γ
2
+
3
2
− 1
4
γ
3
+
8
3
γ
4
+ γ
6
γ = 2 T // ,
where α is the high-temperature limiting magnitude of the slope (of the order of several 10
−4 eV/K),
is an effective average phonon temperature and is related to the phonon dispersion. takes typically
values between zero (Bose-Einstein model) and 3/4 [506].
6.8 Isotope Dependence of the Band Gap
The band edge slightly depends on the isotope composition of semiconductor, as shown for GaAs in
Fig. 6.32. The effect is discussed in detail in [509].
6.9 Electron Dispersion
6.9.1 Equation of Electron Motion
The equation of motion for the electron in the band structure is no longer given by Netwon’s law
F = d(mv)/dt as in vacuum. Instead, the propagation of quantum-mechanical electron wave packets
has to be considered. Their group velocity is given by (v g = ∂ω/∂k)