Space homogeneous solutions of the Boltzmann equation describing electron-phonon interactions in semiconductors

Abstract

Abstract We study the collision operator of the Boltzmann equation for a semiconductor under the assumption of electron-phonon scattering processes. We assume the transition probability to be proportional to the distribution δ(ε (k′)−ε (k) ±hω), where ε(k) is the single-particle energy and ω the polar optical phonon frequency. We prove the existence of a numerable set of collision invariants and obtain an “H—theorem”. Moreover we analyze the initial value problem for spatially homogeneous distribution functions and we obtain an existence and uniqueness theorem. Our results can be applied to several situations and easily generalized.