Spherical-harmonic type expansion for the Boltzmann equation in semiconductor devices

The Boltzmann equation for an electron gas in a semiconductor is considered. The electron energy is assumed to have a very general form, so that, for instance, parabolic or non parabolic band approximations can be treated. A technique, which recalls the classical moment method due to Grad, to deduce an approximate quasi-hydrodynamical model is shown and compared with the spherical harmonic expansion. Some characteristics of the model, as entropy inequality, are explicitly presented