Diffusive semiconductor moment equations using Fermi-Dirac statistics

Diffusive moment equations with an arbitrary number of moments are formally derived from the semiconductor Boltzmann equation employing a moment method and a Chapman-Enskog expansion. The moment equations are closed by employing a generalized Fermi-Dirac distribution function obtained from entropy maximization. The current densities allow for a drift-diffusion-type formulation or a "symmetrized" formulation, using dual-entropy variables from nonequilibrium thermodynamics. Furthermore, drift-diffusion and new energy-transport equations based on Fermi-Dirac statistics are obtained and their degeneracy limit is studied.