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The Method of Baliga-Patankar and 3-D Device Simulation

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Mathematical Modelling and Simulation of Electrical Circuits and Semiconductor Devices

Part of the book series: ISNM International Series of Numerical Mathematics ((ISNM,volume 117))

Abstract

The carrier transport in a semiconductor device is described by the classical drift-diffusion equations, which can be discretized by the method of Baliga-Patankar [6]. However, the computation of the minority charge densities is sensitive with respect to round-off errors, if the Baliga-Patankar discretization scheme is used. This will be shown by a 2-D counterexample.

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References

  1. B. R. Baliga, S. V. Patankar: A new finite-element formulation for convection diffusion problems ,Numerical Heat Transfer, vol. 3, pp. 393–409, 1980.

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  2. W. Bergner, R. Kircher: SITAR -An Efficient 3-D Simulator for Optimization of Nonplanar Trench Structures ,IEEE Transactions on computer-aided design, vol. 9, no. 11, pp. 1184–1188, Nov. 1990.

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  3. R. Bulirsch, A. Gilg, K. Merten, K. Steger: Numerische Simulation in der Halbleiterindustrie ,Informatik Forsch. Entw. vol. 5, pp. 42–56, Springer-Verlag, 1990.

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  4. R. Kircher, W. Bergner: Three Dimensional Simulation of Semiconductor De vices ,Birkhäuser, Basel-Boston-Berlin, 1991.

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  5. P. A. Markowich: The Stationary Semiconductor Device Equations ,Springer, Wien-New York, 1986.

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  6. N. Shigyo, T. Wada, S. Yasuda: Discretization Problem for Multidimensional Current Flow ,IEEE Transactions on computer-aided design, vol. 8, no. 10, pp. 1046–1050, Oct. 1989.

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Author information

Authors and Affiliations

  1. Mathematisches Institut, Technische Universität München, Arcisstraβe 21, D-80333, München, Germany

    F. Montrone

Authors
  1. F. Montrone
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Editor information

Editors and Affiliations

  1. Dept. of Mathematics, C-012, University of California, San Diego, La Jolla, CA, 92093, USA

    R. E. Bank

  2. Institut für Angewandte Analysis und Stochastik, Mohrenstr. 39, D-10117, Berlin, Germany

    H. Gajewski

  3. Mathematisches Institut der TH München, Postfach 20 24 20, D-80290, München, Germany

    R. Bulirsch

  4. ZTI DES2 Siemens AG, Otto-Hahn-Ring 6, D-81739, München, Germany

    K. Merten

  5. Siemens Corporate Research, Inc., 755 College Road East, Princeton, N. J., 08540, USA

    K. Merten

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© 1994 Springer Basel AG

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Montrone, F. (1994). The Method of Baliga-Patankar and 3-D Device Simulation. In: Bank, R.E., Gajewski, H., Bulirsch, R., Merten, K. (eds) Mathematical Modelling and Simulation of Electrical Circuits and Semiconductor Devices. ISNM International Series of Numerical Mathematics, vol 117. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8528-7_19

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  • DOI: https://doi.org/10.1007/978-3-0348-8528-7_19

  • Publisher Name: Birkhäuser, Basel

  • Print ISBN: 978-3-0348-9665-8

  • Online ISBN: 978-3-0348-8528-7

  • eBook Packages: Springer Book Archive

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