Band to Band Generation
Thermal or photon energy is absorbed
Fig. 8.2
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Fig. 8.2 |
Band to Band Recombination
Photons are almost mass less  very small momentum
Therefore, photon assisted transition  vertical on E-k plot
In GaAs direct bandgap semiconductor, there is little change in momentum is needed for recombination process to proceed. Conservation of energy and momentum is simply met by release of photon.
Fig. 8.3
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Fig. 8.3 |
In an indirect bandgap semiconductor there is a change of crystal momentum associated with a recombination process. The emission of a photon will conserve energy but not momentum. For Band to Band recombination in an indirect bandgap semiconductor to proceed a photon must be emitted or absorbed - lattice vibration.
Fig. 8.4
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Fig. 8.4 |
Band to Band process in indirect semiconductors is complicated. This means that a diminished rate band to -band recombination in indirect semiconductors. In indirect semiconductors R-G, center recombination dominates.
All info on band to band radiative recombination optical absorption coefficient  .
(Direct BG)
Fig. 8.5
Photon  electron hole.
generation rate  Planck's radiantion law
Radiative recombination rate 
Thermal equilibrium 
Therefore, 
The excess carrier Radiative recombination rate
Let
 and 
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and
rate at which electrons and holes disappear.
 has units of sec-1 and so we can define 
as carriers lifetime (minority carrier)
Radiative recombination lifetime 
n type semiconductor Donor  .
At high level injection 
at 300K.
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