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VLSI Design
Volume 10 (2000), Issue 4, Pages 415-435
http://dx.doi.org/10.1155/2000/91289

The Chapman-Enskog Expansion and the Quantum Hydrodynamic Model for Semiconductor Devices

Department of Mathematics, Arizona State University, Tempe 85287-1804, AZ, USA

Received 16 December 1998; Accepted 14 December 1999

Copyright © 2000 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

A “smooth” quantum hydrodynamic (QHD) model for semiconductor devices is derived by a Chapman-Enskog expansion of the Wigner-Boltzmann equation which can handle in a mathematically rigorous way the discontinuities in the classical potential energy which occur at heterojunction barriers in quantum semiconductor devices. A dispersive quantum contribution to the heat flux term in the QHD model is introduced.