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VLSI Design
Volume 9 (1999), Issue 4, Pages 315-323

Semi-classical Limit in a Semiconductor Superlattice

Univ. Nice, Lab. J. A. Dieudonné URM 6621 du CNRS, Parc Valrose, Nice F-06108, France

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.


In this paper, we perform a mathematical study of a semiconductor superlattice. Since the thickness of the layers is very small, quantization plays an important role. The modelling is therefore given by a Schrödinger equation with a periodic potential. The scaled lattice thickness is denoted by a small parameter ℇ which is of the same order of magnitude as the Planck constant. When this parameter tends to zero, i.e., the semi-classical limit, we obtain classical transport of the charge carriers described by a Vlasov equation.