##
A Finite Element Approximation Theory for the Drift-Diffusion
Semiconductor Model

#### By: Joseph W. Jerome and Thomas Kerkhoven

Two-sided estimates are derived for the approximation of
solutions to the drift-diffusion steady-state
semiconductor device system which are identified with
fixed points of Gummel's solution map.
The approximations are defined in terms of fixed
points of numerical finite element discretization maps. By use of a
calculus
developed by Krasnosel'skii and his coworkers, it is possible, both to
locate
approximations near fixed points in an ``a priori'' manner, as well as
fixed
points near approximations in an ``a posteriori'' manner. These results
thus
establish a nonlinear approximation theory, in the energy norm, with rate
keyed
to what is possible in a standard linear theory. This analysis provides a
convergence theory for typical computational approaches in current use for
semiconductor simulation.

This paper appeared in:
Siam J. Numerical Analysis 28 (1991), 403--422.

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