DIFFUSION AND HOMOGENIZATION APPROXIMATION FOR SEMICONDUCTOR BOLTZMANN–POISSON SYSTEM

Abstract

In this paper, the diffusion and homogenization approximation of the Boltzmann–Poisson system in the presence of a spatially oscillating electrostatic potential is studied. By analyzing the relative entropy, the uniform energy estimate for a well-prepared boundary data is proved. An averaging lemma and two-scale convergence techniques are used to prove rigorously the convergence of the scaled Boltzmann equation (coupled to Poisson) to a homogenized drift–diffusion-Poisson system.