Charge transport in semiconductors with degeneracy effects

Abstract

It has been a common procedure to derive a model for charge transport in degenerate semiconductor material by incorporating a Fermi–Dirac distribution into the classical drift–diffusion model. In this work a Boltzmann equation with a non-linear collision term is considered. A new fluid dynamical model is derived by considering small perturbations of the thermal equilibrium. The analysis contains an existence and uniqueness proof for the Boltzmann equation, a justification of the perturbation argument and a study of initial boundary value problems for the new fluid dynamical model.