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A Singular Perturbation Analysis of the Transient Semiconductor Device Equations

Peter Szmolyan
SIAM Journal on Applied Mathematics
Vol. 49, No. 4 (Aug., 1989), pp. 1122-1135
Stable URL: http://www.jstor.org/stable/2102009
Page Count: 14
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A Singular Perturbation Analysis of the Transient Semiconductor Device Equations
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Abstract

This paper is concerned with the asymptotic analysis of the transient semiconductor device equations. By appropriately scaling the equations the semiconductor device problem is reformulated as a singular perturbation problem. This singular perturbation problem is analyzed by the method of matched asymptotic expansions. A formal solution that solves the equations approximately is constructed. The existence of interior and boundary layers in the transient model is shown. As a new phenomenon the existence of an initial temporal layer is shown. The existence of a "fast" timescale is proved along which certain components of the solutions decay. Equations for these components are deduced and analyzed.

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