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Philippe Bechouche, "Semi-classical Limit in a Semiconductor Superlattice", VLSI Design, vol. 9, Article ID 026709, 9 pages, 1999. https://doi.org/10.1155/1999/26709
Semi-classical Limit in a Semiconductor Superlattice
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.
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