Nonequilibrium total-dielectric-function approach to the electron Boltzmann equation for inelastic scattering in doped polar semiconductors.

Abstract

This paper describes a simple and general method for deriving the inelastic collision term in the electron Boltzmann equation for scattering from a coupled electron-phonon system and applies the method to the case of doped polar semiconductors. In the Born approximation, the inelastic differential scattering rate ${\mathit{W}}^{\mathrm{inel}}$ can be expressed in terms of the nonequilibrium total dynamic dielectric function, which includes both electronic and lattice contributions. Within the random-phase approximation ${\mathit{W}}^{\mathrm{inel}}$ separates into two components: an electron-electron interaction containing the nonequilibrium distribution function for excitations of the electron gas and a Fr\"ohlich interaction including the phonon distribution function and self-energy due to polarization of the electrons. Each of these two interactions is screened by only the electronic part of the total dielectric function, which contains the high-frequency dielectric constant, unlike commonly used expressions that contain the static dielectric constant. The detailed balance between plasmons and electron-hole pairs in steady state is used to eliminate the non- equilibrium plasmon distribution from the Boltzmann equation, resulting in a dynamically screened electron-electron collision term. The phonon self-energy modifies the longitudinal optical-phonon dispersion so that two hybrid normal modes contribute to the electron-phonon collision term.