Some properties of the semiconductor Boltzmann collision operator

The goal of this paper is to introduce, and make a preliminary discussion of the mathematical properties of the Boltzmann Collisional Operator which describes the electron flow in a semiconductor device. The collision operator of the Boltzmann equation models the scattering processes between electrons and phonons which are assumed in thermal equilibrium. Due to the particular nature of the scattering mechanisms in the semiconductor case, the collision operator assumes a distinct aspect