ON A HIERARCHY OF MACROSCOPIC MODELS FOR SEMICONDUCTORS

This paper shows that various models of electron transport in semicond uctors that have been previously proposed in the literature can be con nected one with each other by the diffusion approximation methodology. We first investigate the diffusion limit of the semiconductor Boltzma nn equation towards the so-called ''spherical harmonic expansion model ,'' under the assumption of dominant elastic scattering. Then, this mo del is again connected, either to the energy-transport model or to a ' 'periodic spherical harmonic expansion model'' through a diffusion app roximation, respectively making electron-electron or phonon scattering large. We provide the mathematical background which makes the Hilbert expansions associated with these various diffusion limits rigorous. ( C) 1996 American Institute of Physics.