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Semi-classical Limit in a Semiconductor Superlattice
Philippe Bechouche
11Univ. Nice, Lab. J. A. Dieudonné URM 6621 du CNRS, Parc Valrose, France
Abstract
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.
Copyright
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.
