Numerical Simulation of Charge Transport in Semiconductor Devices Using Mixed Finite Elements
In this lecture, we present the basic mathematical and numerical tools for semiconductor device simulation using the Drift-Diffusion model. The Gummel’s decoupled fixed point map is first reviewed, and then the dual-mixed Formulation of the diffusion-advection-reaction (DAR) differential problems resulting from decoupling is considered. The Galerkin finite element discretization of the weak mixed form is discussed, with a proper treatment of the flux mass matrix that leads to a mixed finite volume approximation of the DAR equation. Several numerical examples are included to validate the proposed procedure.
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- F. Brezzi, L. D. Marini, S. Micheletti, P. Pietra, R. Sacco, S. Wang, Discretization of Semiconductor Device Problems (I), 317–441, Handbook of Numerical Analysis, Vol. XIII, P.G. Ciarlet Ed., W.H.A. Schilders, E.J.W. ter Maten, Guest Eds., Elsevier North-Holland, Amsterdam (2005).Google Scholar
- J.W. Jerome, Analysis of Charge Transport, Springer-Verlag Berlin Heidelberg (1996).Google Scholar
- P. A. Markowich, The Stationary Semiconductor Device Equations, Springer-Verlag, Wien New York, 1986).Google Scholar
- P.A. Raviart, J.M. Thomas, A mixed finite element method for second order elliptic problems, in Mathematical Aspects of the Finite Element Method (I. Galligani, E. Magenes, eds.), Lecture Notes in Math., Springer-Verlag, New York, 606, 292–315 (1977).Google Scholar
- S. Selberherr, Analysis and Simulation of Semiconductor Devices, Springer-Verlag, Wien New York, 1984.Google Scholar
- R.S. Varga, Matrix Iterative Analysis, Prentice-Hall, Englewood Cliffs, New Jersey (1962).Google Scholar