Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



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
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Quarterly of Applied Mathematics with MSC: 82D37, 35B40, 47N20, 76P05, 76X05

Retrieve articles in all journals with MSC: 82D37, 35B40, 47N20, 76P05, 76X05

Additional Information

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

American Mathematical Society