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The initial time layer problem and the quasineutral limit in the semiconductor drift-diffusion model

Published online by Cambridge University Press:  13 August 2001

INGENUIN GASSER ,
C. DAVID LEVERMORE ,
PETER A. MARKOWICH  and
CHRISTIAN SCHMEISER
INGENUIN GASSER
Affiliation:
Fachbereich Mathematik, Universität Hamburg, Bundesstraße 55, D-20146 Hamburg, Germany
C. DAVID LEVERMORE
Affiliation:
Department of Mathematics, University of Maryland, College Park, MD 20742-4015, USA
PETER A. MARKOWICH
Affiliation:
Institut für Mathematik, Universität Wien, Boltzmanngasse 9, A-1090 Wien, Austria
CHRISTIAN SCHMEISER
Affiliation:
Institut für Angewandte und Numerische Mathematik, Technische Universität Wien, Wiedner Hauptstraße 6-10, A-1040 Wien, Austria
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Abstract

The classical time-dependent drift-diffusion model for semiconductors is considered for small scaled Debye length (which is a singular perturbation parameter). The corresponding limit is carried out on both the dielectric relaxation time scale and the diffusion time scale. The latter is a quasineutral limit, and the former can be interpreted as an initial time layer problem. The main mathematical tool for the analytically rigorous singular perturbation theory of this paper is the (physical) entropy of the system.

Type
Research Article
Information
European Journal of Applied Mathematics , Volume 12 , Issue 4 , August 2001 , pp. 497 - 512
Copyright
2001 Cambridge University Press

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