On the conditioning of the steady state semiconductor device problem

U. Ascher, Peter Markowich, C. Schmeiser, H. Steinrück, R. Weiss

Research output: Contribution to journalReview articlepeer-review

Abstract

In this paper we carry out a conditioning analysis for the steady state semiconductor device problem. We consider various quasilinearizations as well as Gummel-type iterations and obtain stability bounds which may allow ill-conditioning' in general. These bounds are exponential in the potential variation, and are sharp e.g. for a thyristor. But for devices where each smooth subdomain has an Ohmic contact, e.g. a pn-diode, moderate bounds guaranteeing well-conditioning are obtained. Moreover, the analysis suggests how various row and column scalings should be applied in order for the measured condition numbers of the linearized discrete problem to correspond more realistically to the true loss of significant digits in the calculations.

Original languageEnglish (US)
Pages (from-to)19-23
Number of pages5
JournalCOMPEL - The International Journal for Computation and Mathematics in Electrical and Electronic Engineering
Volume6
Issue number1
DOIs
StatePublished - Jan 1 1987

ASJC Scopus subject areas

  • Computer Science Applications
  • Computational Theory and Mathematics
  • Electrical and Electronic Engineering
  • Applied Mathematics

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