Mixed-RKDG Finite Element Methods for the 2-D Hydrodynamic Model for Semiconductor Device Simulation

Zhangxin Chen, Bernardo Cockburn, Joseph W. Jerome, Chi Wang Shu

Research output: Contribution to journalArticle

39 Scopus citations

Abstract

In this paper we introduce a new method for numerically solving the equations of the hydrodynamic model for semiconductor devices in two space dimensions. The method combines a standard mixed finite element method, used to obtain directly an approximation to the electric field, with the so-called Runge-Kutta Discontinuous Galerkin (RKDG) method, originally devised for numerically solving multi-dimensional hyperbolic systems of conservation laws, which is applied here to the convective part of the equations. Numerical simulations showing the performance of the new method are displayed, and the results compared with those obtained by using Essentially Nonoscillatory (ENO) finite difference schemes. From the perspective of device modeling, these methods are robust, since they are capable of encompassing broad parameter ranges, including those for which shock formation is possible. The simulations presented here are for Gallium Arsenide at room temperature, but we have tested them much more generally with considerable success.

Original languageEnglish (US)
Pages (from-to)145-158
Number of pages14
JournalVLSI Design
Volume3
Issue number2
DOIs
StatePublished - 1995

Keywords

  • MESFET
  • conservation laws
  • finite element methods
  • finite volume methods
  • hydrodynamic model
  • mixed methods

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