On some numerical problems in semiconductor device simulation
We recall in the introduction the main features of the drift-diffusion model for semiconductor devices, pointing out its physical meaning, its possible derivation, and its limits. Then, in Section 2, we present a mixed finite element method for the discretization of this model. Finally, using asymptotic analysis techniques, we compare the qualitative behaviour of the mixed method with other methods (classical conforming Galerking method and harmonic average methods). This asymptotic analysis provides some indication of the advantages of the mixed method.
KeywordsMixed Method Mixed Finite Element Method Order Elliptic Problem Harmonic Average Mixed Approximation
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- F.Brezzi-L.D. Marini-P.Pietra: Two-dimensional exponential fitting and applications to drift-diffusion models. (To appear in SIAM J.Numer.Anal.).Google Scholar
- F.Brezzi-L.D. Marini-P.Pietra: Numerical simulation of semiconductor devices. (To appear in Comp.Meths.Appl. Mech.and Engr.).Google Scholar
- B.X. Fraeijs de Veubeke: Displacement and equilibrium models in the finite element method. In: Stress Analysis, O.C. Zienkiewicz and G. Hollister eds., Wiley, New York, 1965.Google Scholar
- L.D.Marini-P.Pietra: New mixed finite element schemes for current continuity equations. (Submitted to COMPEL).Google Scholar
- P.A.Markowich: The Stationary Semiconductor Device Equations. Springer, 1986.Google Scholar
- P.A.Markowich-C.Ringhofer-C.Schmeiser: Semiconductor equations. Springer, 1989. (To appear).Google Scholar
- F.Poupaud: On a system of nonlinear Boltzmann equations of semiconductor physics. (To appear in SIAM J. Math. Anal.).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, Lecture Notes in Math. 606, 292–315, Springer, 1977.Google Scholar
- S.Selberherr: Analysis and simulation of semiconductor devices. Springer, 1984.Google Scholar