Page 153 - A Comprehensive Guide to Solar Energy Systems

154 A CoMPrehensIVe GuIde To soLAr enerGy sysTeMs

FIGURE 8.2 Carrier generation by photon absorption in the energy band scheme. (A) Direct band structure. (B) Indirect
band structure.
valence band and the energy minimum in the conductive band have the same momen-
tum. examples of “direct” semiconductors include GaAs, CdTe, and CuInse 2 . Fig. 8.2A also
illustrates the transition of an electron from the valence band to the conductive band fol-
lowing the absorption of a photon with energy hν > W g . As the photon momentum h/λ ≈ 0,
the generated electron and hole have practically the same momentum. Increasing photon
energy also increases the kinetic energy of the electrons and the holes generated. To reach
thermal equilibrium, the excess energy is lost to the lattice vibration as heat as the elec-
trons and holes are scattered from lattice vibrations (phonons), as indicated in Fig. 8.2A.
This process is called thermalization. The excess energy dissipation is fast; it takes in the
order of 10 −12 s. In the case of the direct transitions, for hν > W g the absorption coefficient
−1
4
α(λ) shows a steep rise with the photon energy up to levels in order 10 cm (penetration
depth x L in order 1 µm).
The so-called indirect band structure is shown in Fig. 8.2B. The minimum of electron
energy in the conductive band and the maximum of energy in the valence band have a
different momentum value. examples of “indirect” semiconductors are si, Ge, and GaP.
In this case, the transition between the maximum of valence band to the minimum of the
conductive band is not possible with only the absorption of photon with energy hν close
to the bandgap W g . As the photon momentum h/λ ≈ 0, the transitions can be realized only
with the absorption of the photon and simultaneous absorption or emission of the pho-
non (interaction with the lattice vibration). The requirement of simultaneous electron–
photon–phonon interaction in the case of “indirect transitions” results in a relatively small
absorption coefficient α in comparison with the case of “direct” transitions. The absorp-
tion coefficient increases relatively slowly with the photon energy. For sufficiently high
photon energy, “direct” transitions can also be realized in the “indirect” band structure,
as indicated in Fig. 8.2B. This results in a steeper increase of the absorption coefficient at
higher photon energies. The effect of generated carrier thermalization occurs in indirect
semiconductors, too.