Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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Electron transport in semiconductor superlattices


Authors: N. Ben Abdallah, P. Degond, A. Mellet and F. Poupaud
Journal: Quart. Appl. Math. 61 (2003), 161-192
MSC: Primary 82D37; Secondary 35B40, 47N20, 76P05, 76X05
DOI: https://doi.org/10.1090/qam/1955228
MathSciNet review: MR1955228
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Abstract: In this paper, we rigorously derive a diffusion model for semiconductor superlattices, starting from a kinetic description of electron transport at the microscopic scale. Electron transport in the superlattice is modelled by a collisionless Boltzmann equation subject to a periodic array of localized scatters modeling the periodic heterogeneities of the material. The limit of a large number of periodicity cells combined with a large-time asymptotics leads to a homogenized diffusion equation which belongs to the class of so-called ``SHE'' models (for Spherical Harmonics Expansion). The rigorous convergence proof relies on fine estimates on the operator modeling the localized scatters.


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DOI: https://doi.org/10.1090/qam/1955228
Article copyright: © Copyright 2003 American Mathematical Society


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