SINGULAR PERTURBATION APPROACH FOR THE ANALYSIS OF THE FUNDAMENTAL SEMICONDUCTOR EQUATIONS.

Peter A. Markowich, Christian Ringhofer, Siegfried Selberherr, Marianela Lentini

Research output: Contribution to journalArticle

25 Citations (Scopus)

Abstract

Singular perturbation theory allows to distinguish between regions of strong and of weak variation of solutions, so called layers and smooth regions, and to describe solutions qualitatively in these regions. This information is used to analyze the stability and convergence of the discretization scheme. Particular emphasis is put on the construction of efficient grids. It is shown that the Scharfetter-Gummel method is uniformly convergent, i. e. , the global error contribution coming from the continuity equations is small when the maximal mesh size is small, independent of the gradient of the solution.

Original languageEnglish (US)
Pages (from-to)1165-1180
Number of pages16
JournalIEEE Transactions on Electron Devices
VolumeED-30
Issue number9
StatePublished - Sep 1982
Externally publishedYes

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Semiconductor materials
perturbation
continuity equation
mesh
perturbation theory
grids
gradients

ASJC Scopus subject areas

  • Electrical and Electronic Engineering
  • Physics and Astronomy (miscellaneous)

Cite this

SINGULAR PERTURBATION APPROACH FOR THE ANALYSIS OF THE FUNDAMENTAL SEMICONDUCTOR EQUATIONS. / Markowich, Peter A.; Ringhofer, Christian; Selberherr, Siegfried; Lentini, Marianela.

In: IEEE Transactions on Electron Devices, Vol. ED-30, No. 9, 09.1982, p. 1165-1180.

Research output: Contribution to journalArticle

Markowich, Peter A. ; Ringhofer, Christian ; Selberherr, Siegfried ; Lentini, Marianela. / SINGULAR PERTURBATION APPROACH FOR THE ANALYSIS OF THE FUNDAMENTAL SEMICONDUCTOR EQUATIONS. In: IEEE Transactions on Electron Devices. 1982 ; Vol. ED-30, No. 9. pp. 1165-1180.
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