High field approximations of the spherical harmonics expansion model for semiconductors

We present an asymptotic analysis (with the scaled mean free path as small parameter) of the spherical-harmonics expansion (SHE-) model for semiconductors in the case of a large electric field. The Hilbert and Chapman-Enskog expansions are performed and the dependence of macroscopic parameter-functions such as the mobility and the diffusivity on the details of the considered elastic and inelastic scattering processes are investigated. For example, we verify so called velocity-saturation mobility models, so far obtained by heuristic considerations, by means of an asymptotic analysis for certain scattering processes.