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VLSI Design
Volume 6, Issue 1-4, Pages 97-101
http://dx.doi.org/10.1155/1998/39370

Moment Closure Hierarchies for the Boltzmann-Poisson Equation

Department of Mathematics, University of Arizona, Tucson, AZ 85721, USA

Copyright © 1998 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We outline a systematic nonperturbative derivation of a hierarchy of closed systems of moment equations that can be applied to any kinetic description of electrons in a semiconductor. This entropy based closure procedure extends one that was introduced in the context of gas dynamics. In the context of semiconductors, this procedure yields generalizations of socalled hydrodynamic models. It is illustrated on the semiclassical Boltzmann-Poisson equation for a single conduction band in the parabolic band approximation.