130 CHAPTER 3. CHARGE TRANSPORT IN MATERIALS
(^10) 0.2 0.6 1 1.4 1.8
106
105
104
103
102
32 1.5 1 0.7
PHOTON ENERGY (eV)
WAVELENGTH (μm)
ABSORPTION COEFFICIENT
(cm
–1
)
GaP
InP
GaAs
In0.53Ga0.47As
Si
Figure 3.21: Absorption coefficient of some direct and indirect gap semiconductors. For the
direct gap material, the absorption coefficient is very strong once the photon energy exceeds the
bandgap. For indirect materials the absorption coefficient is small near the bandedge, but once
the photon energy is more than the direct gap, the absorption coefficient increases rapidly.
and the electron-hole pair generation rate is
RG=αΦ=
αP ̃op
ω
(3.8.7)
Under equilibrium conditions, electron occupation in the valence band is close to unity while
the occupation in the conduction band is close to zero. Assuming this is the case the absorption
coefficient for direct gap materials is
α(ω)=πe^2
2 nrcom 0(
2 p^2 cv
m 0)
Ncv(ω)
ω·
2
3
(3.8.8)
Herenris the refractive index of the material,pcvis the momentum matrix element for the
scattering process,cis the speed of light in vacuumandNcvis the joint density of states for the