Diffusion approximation of the linear semiconductor Boltzmann equation: analysis of boundary layers

This paper deals with mathematical properties of the semiconductor Boltzmann equation. We first investigate the question of existence of solutions and some basic properties of the collision operator. Then we study the connection with the drift diffusion model by using a perturbation approach, the so-called diffusion approximation. For justifying rigorously this theory, we have to deal with boundary layers. A half space problem (Milne problem) arises in the study of the boundary corrector. We prove existence and we give the asymptotic behaviour of its solutions.