Three-dimensional exponentially fitted conforming tetrahedral finite elements for the semiconductor continuity equations
type: Item
instance of: scholarly article
title: Three-dimensional exponentially fitted conforming tetrahedral finite elements for the semiconductor continuity equations
zbMATH Open document ID: 1028.82024
DOI: 10.1016/S0168-9274(02)00224-6
author: L. Angermann
author: Song Wang
published in: Applied Numerical Mathematics
publication date: 2003-07-30T00:00:00Z
review text: The authors extend the triangular finite elements to tetrahedral elements in three dimensions for the semiconductor continuity equations. The continuous problem is first formulated as a weak one using a weighted inner product. The wave problem is then approximated by a Bubnov-Galerkin finite element method based on a set of novel basis functions. The basis functions are piecewise exponential, and thus the method can be regarded as an extension of the Scharfetter-Gummel scheme to 3 dimensions. This method is proved to be stable in the sense that the corresponding bilinear form is coercive, and the errors in a weighted energy norm for the approximate electron and hole concentrations are shown to be of \(O(h)\) order. Finally, a method for the evaluation of the terminal currents is presented, and the computed terminal currents from this method are shown to be convergent and conservative.
Mathematics Subject Classification ID: 82D37
Mathematics Subject Classification ID: 82-08
zbMATH DE Number: 1956717
zbMATH Keywords: 3D Scharfetter-Gummel method
Wikidata QID: Q59416214
reviewed by: Messoud Efendiev
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1956717