Energy transport systems for semiconductors: Analysis and simulation

Moment models of carrier transport, derived from the Boltzmann equation, have made possible the simulation of certain key effects through such realistic global assumptions as energy dependent mobility functions. Some of these effects are not discerned via classical drift-diffusion models, which are primarily local in nature. In this paper, analysis and simulation of a recently developed energy transport model, the ET model, will be presented. This model, intermediate between the hydrodynamic and drift-diffusion models, was developed at the University of Illinois. The algorithms employed are the essentially non-oscillatory shock capturing algorithms, developed at UCLA during the last decade. Mathematical results will be presented as well, for the one dimensional steady state model. Informative comparisons with the hydrodynamic model will be presented. One carrier transport is studied. 1991 Mathematics Subject Classification: 35J65, 82A70, 65C20, 76N10, 35L65