Theoretical analysis of plasmon, polar phonon, and hot-electron energy relaxation in nondegenerate semiconductors

Abstract

Hot-electron energy relaxation due to the Coulomb scattering in nondegenerate polar semiconductors is treated theoretically by analyzing coupled modes between the electron-hole plasma and longitudinal-optical phonon in the self-consistent-field approximation. The ratio of lattice energy in each coupled mode is calculated in terms of the dielectric functions of the phonon and carriers, by which the screening of the phonon field can be evaluated. The coupled mode consists of three branches which arise from mixing of two plasmon modes and the phonon mode. Energy loss of an electron is mainly governed by the scattering by the highest-frequency mode and individual motion of the carriers, where the latter becomes dominant with increasing carrier density. Numerical computations are made for GaAs at 300 K. It is found that the energy-loss rate $W_{e\mathrm{-}h}$ due to the carrier individual motion becomes nearly equal to that due to the coupled mode at the carrier density of ${10}^{17}$ ${\mathrm{cm}}^{\mathrm{-}3}$. For an electron with energy 3000 K, the values of $W_{e\mathrm{-}h}$ are 0.28 and 1.9 ergs/s for ${10}^{17}$ and ${10}^{18}$ ${\mathrm{cm}}^{\mathrm{-}3}$, respectively.