Energy-Diffusion Equation in Hot-Electron Problems: Disturbance of the Polar-Optical-Phonon Distribution

Abstract

In polar semiconductors, the emission of polar optical phonons by electrons with $\mathcal{E}>\hslash {\omega }_0$ is a major energy-relaxation process. At low temperatures, the large number of emitted phonons disturbs the polar mode distribution. The energy-diffusion equation for carrier flow in energy space can be used to solve the energy distribution function of the carriers. This function is then used to solve for the disturbed phonon distribution. A phonon quasitemperature is introduced to aid in the calculation of the disturbed phonon density and the hot-electron energy distribution function. At high values of the electric field, tailing of the energy distribution function occurs primarily due to the phonon disturbance. The theories are applied to $n$-type InSb. All optical-phonon-emission and -absorption processes are considered, even at low temperatures since the absorption processes are important for determining a balance in the distribution function. Scattering by acoustic deformation potential, piezoelectric, and ionized impurities are also considered.