Asymptotic methods for transient semiconductor device equations
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Peter Szmolyan [1]
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[1] Vienna University of Technology
Vienna University of Technology
Innere Stadt, Austria
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- Localización: Compel: International journal for computation and mathematics in electrical and electronic engineering, ISSN 0332-1649, Vol. 8, Nº 2, 1989, págs. 113-122
- Idioma: inglés
- Enlaces
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Resumen
The singular perturbation character of the semiconductor device problem is well known by now. Various results on the structure of solutions (i.e. existence of spatial and temporal layers) have been obtained by means of singular perturbation theory. We use a rescaled form of the equations, which describes the evolution on the fast time scale, and discuss the asymptotic behavior of this system, i.e. its relationship to the initial layer problem, to the corresponding stationary problem and to the reduced problem. We show that the transient semiconductor problem fits in the framework of ‘fast reaction‐slow diffusion’ type equations, which are known from the analysis of chemical reacting systems. We use a multiple time scale expansion to give a new ‘dynamical’ derivation of the reduced problem.
