Abstract
In this work we are interested in a sufficiently accurate approximation of the steady-state potentials in a Metal Semiconductor Field Effect Transistor (MESFET), which can be obtained with the so-called depletion region approximation (see [5]). We propose a robust method based on the shape optimization techniques to analyze and compute the depletion boundary as a function of the applied voltage and the geometry material properties of the device. During the optimization process several intermediate direct problems are solved using the boundary element method (BEM). To accelerate the solutions of of these systems we use a strategy of subdividing the domain into a number of smaller subdomains [11,9]. The scheme is iterative and each subdomain is handled by a separate node in parallel. Test runs comparing the performance of the parallel with the serial code, and other numerical discussions are presented.
Similar content being viewed by others
References
J. Abouchabaka, R. Aboulaich, O. Guennoun, A. Nachaoui and A. Souissi, Shape optimization for a simulation of a semiconductor problem, Math. Comput. Simulation 56(1) (2001) 1–16.
C.A. Brebbia and J. Dominguez, Boundary Elements. An Introductory Course (Comp. Mech. Pub./McGraw-Hill, New York, 1992).
G.F. Carey, W.R. Richardson, C. Reed and B. Mulvaney, Circuit Device and Process Simulation (Wiley, Chichester, UK, 1996).
A. Chakib and A. Nachaoui, Nonlinear programming approach for transient free boundary flow problem, Appl. Math. Comput. 160 (2005) 317–328.
A. Ellabib and A. Nachaoui, On the numerical solution of a free boundary identification problem, Inverse Problems Engrg. 9(3) (2001) 235–260.
A. Friedman, Mathematics in Industrial Problems, Part 9, The IMA Volumes in Mathematics and Its Applications, Vol. 88 (Springer, New York, 1997).
W. Gropp, E. Lusk and A. Skjellum, Using MPI: Portable Parallel Programming with the Message-Passing Interface (MIT Press, London, 1994).
M. Lundstrum, Fundamentals of Carrier Transport (Addison-Wesley, Reading MA, 1990).
A. Nachaoui, A. Stefanutti and C. Saadi, Simulation of a free boundary problem in a distributed memory environment, in: PMAA'02: Parallel Matrix Algorithms and Applications, Neuchtel, Switzerland (9–10 November 2002).
L.F. Pavarino and A. Toselli, Recent Developments in Domain Decomposition Methods, Lecture Notes in Computational Science and Engineering, Vol. 23 (Springer, Berlin, 2002).
A. Quarteroni and A. Valli, Domain Decomposition Methods for Partial Differential Equations, Numerical Mathematics and Scientific Computation, Vol. XV (Clarendon Press, Oxford, 1999).
S. Wagner, Computational Fluid Dynamics on Parallel Systems, Notes on Numerical Fluid Mechanics, Vol. 50 (Vieweg, Braunschweig, 1995).
Author information
Authors and Affiliations
Corresponding author
Additional information
Communicated by H. Sadok
AMS subject classification
65N55, 65N38, 65K10, 78A55.
A. Nachaoui: Corresponding author.
Rights and permissions
About this article
Cite this article
Nachaoui, A., Abouchabaka, J. & Rafalia, N. Parallel solvers for the depletion region identification in metal semiconductor field effect transistors. Numer Algor 40, 187–199 (2005). https://doi.org/10.1007/s11075-005-1531-5
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/s11075-005-1531-5