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VLSI Design
Volume 9 (1999), Issue 4, Pages 339-350
http://dx.doi.org/10.1155/1999/30381

A Wignerfunction Approach to Phonon Scattering

1FB Mathematik, TU Berlin, Straße des 17. Juni 136, Berlin D-10623, Germany
2Institute for Analysis and Numerics, Altenberger Straße 69, Linz A-4040, Australia
3Department of Mathematics, Arizona State University, Tempe Az 85287-1804, USA

Received 13 August 1997; Revised 1 December 1998

Copyright © 1999 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 consider the motion of a single electron under phonon scattering caused by a crystal lattice. Starting from the Fröhlich Hamiltonian in the second quantization formalism we derive a kinetic transport model by using the Wigner transformation. Under the assumption of small electron-phonon interaction we derive asymptotically the operator representing electron-phonon scattering in the Wigner equation. We then consider some scaling limits and finally we give the connection of our result to the well known Barker-Ferry equation.