Abstract
We start with a Hamiltonian containing electron-hole Coulomb, electron (hole)-phonon, and electron-hole photon interactions to derive effectively renormalized interactions appropriate to recombination in the indirect-band-gap semiconductors with the use of canonical transformations. It is found that a phonon-induced Auger process and a radiative process involving electron-hole-phonon-photon interaction leads to relaxation in the indirect-band-gap semiconductors. The electron-hole pair self-energy for these processes is calculated. The imaginary part of the self-energy which leads to the relaxation time is deduced for these processes for optical as well as acoustic phonons. The theory is applied to the electron-hole drop recombination relaxation in Ge. The predicted relaxation times for the optical phonons which dominate in Ge for both the radiative process and the phonon-induced Auger process are in reasonable agreement with the experimental values.
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