Three-dimensional exponentially fitted conforming tetrahedral finite elements for the semiconductor continuity equations

  • Authors:

  • Lutz Angermann;Song Wang

  • Affiliations:

  • Institut für Mathematik, Technische Universität Clausthal, Erzstraße 1, D-38678 Clausthal-Zellerfeld, Germany;Department of Mathematics and Statistics, University of Western Australia, 35 Stirling Highway, Crawley, WA 6009, Australia

  • Venue:
  • Applied Numerical Mathematics
  • Year:
  • 2003

Quantified Score

Hi-index 0.00

Visualization

Abstract

This paper presents and analyzes an exponentially fitted tetrahedral finite element method for the decoupled continuity equations in the drift-diffusion model of semiconductor devices. This finite element method is based on a set of piecewise exponential basis functions constructed on a tetrahedral mesh. The method is shown to be stable and can be regarded as an extension to three dimensions of the well-known Scharfetter-Gummel method. Error estimates for the approximate solution and its associated flux density are given. These h-order error bounds depend on some first-order seminorms of the exact solution, the exact flux density and the coefficient function of the convection terms. A method is also proposed for the evaluation of terminal currents and it is shown that the computed terminal currents are convergent and conservative.