High Field Approximations of the SphericalHarmonics Expansion

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 eld. The Hilbert and Chapman-Enskog expansions are performed and the dependence of macro-scopic parameter-functions such as the mobility and the diiusivity 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.