IMPLICIT-EXPLICIT MULTISTEP FINITE ELEMENT-MIXED FINITE ELEMENT METHODS FOR THE TRANSIENT BEHAVIOR OF A SEMICONDUCTOR DEVICE

Abstract

Abstract:

The transient behavior of a semiconductor device consists of a Poisson equa-
tion for the electric potential and of two nonlinear parabolic equations for the electron
density and hole density. The electric potential equation is discretized by a mixed finite
element method. The electron and hole density equations are treated by implicit-explicit
multistep finite element methods. The schemes are very efficient. The optimal order error
estimates both in time and space are derived.

Key words: Semiconductor device, strongly A(0)-stable, multistep methods, finite ele-ment methods, mixed finite element methods

CLC Number:

65M15

CHEN Wei. IMPLICIT-EXPLICIT MULTISTEP FINITE ELEMENT-MIXED FINITE ELEMENT METHODS FOR THE TRANSIENT BEHAVIOR OF A SEMICONDUCTOR DEVICE[J].Acta mathematica scientia,Series B, 2003, 23(3): 386-.

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References

1 Douglas J Jr, Yuan Yirang. Finite difference methods for the transient behavior of a semiconductor device.
Mat Apli, 1987, 6(1): 25-38
2 Zl´amal M. Finite element solution of the fundamental equations of semiconductor devices I. Math Comp,
1986, 46(1): 27-43
3 Yuan Yirang, Ding Lanying, Yang Hong. A new method and theoretical analysis of numerical analog of
semiconductor. Chinese Science Bulletin, 1982, 27: 790-795
4 Yuan Yirang. A mixed finite element method for the transient behavior of a semiconductor device. Appl
Math J of Chinese Univ, 1992, 7(3): 452-463
5 Yuan Yirang. Finite difference method and analysis for three dimensional semiconductor device of heat
conduction. Science in China (Series A), 1996, 39(11): 1140-1151
6 Milo´s Zl´amal. Finite Element Multistep Discretizations of Parabolic Boundary Value Problems. Math of
Comp, 1975, 29: 350-359
7 Bramble J H, Pasciak J E, Sammon P H, et al. Incomplete Iterations in Multistep Backward Difference
Methods for Parabolic Problemswith Smooth and Nonsmooth Data. Math Comp, 1989, 32: 339-367
8 Georgios Akrivis, Michel Crouzeix, Charalambos Makridakis. Implicit-Explicit Multistep Finite Element
Methods for Nonlinear Parabolic Problems. Math of Comp, 1998, 67: 457-477
9 Michel Crouzeix. An Implicit-Explicit Multistep Method of the Approximationof Parabolic Equations.
Numer Math, 1980, 35: 257-276
10 Lambert J D. Computation Methods in Ordinary Differential Equations. John Wiley & Son, 1973
11 Adams R A. Sobolev Spaces. New York: Academic Press, 1975
12 Raviart P A, Thomas J M. Mixed Finite Element Method for 2nd-order Elliptic Problems. Mathematial
Aspects of The Finite Element Method, Lecture Notesin Methematics 606. Springer, 1971
13 Brezzi F. On the Existence, Uniqueness and Approximation of Saddle-point Problems Arising from La-
grangian Multipliers. R A I R O, Anal Numer, 1974, 2:129-151
14 Ciarlet P G. The Finite Element Method for Elliptic Problems. Amsterdam: North Holland, 1978
15 Chen Wei. Implicit-explicit multistep FEM for nonlinear convection-diffusion problems. Numer Meth for
PDEs, 2001, 17: 93-104
16 Chen Wei. Implicit-explicit multistep finite element methods for some nonlinear reaction-diffusion systems.
Acta Mathematica Scientia, 2002, 22A: 180-188