Diffusive limit of the two-band k.p model for semiconductors

ABSTRACT. We derive semiclassical diffusive equations for the densities of electrons in the two energy bands of a semiconductor, as described by a k·p Hamiltonian. The derivation starts from a quantum kinetic (Wigner) description and resorts to the Chapman-Enskog method as well as to the quantum version of the minimum entropy principle. Four different regimes are investigated, according to different scalings of the k·p band-coupling and band-gap parameters with respect to the scaled Planck constant. Keywords: Quantum drift-diffusion · k·p model · Quantum entropy principle