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Journal of Engineering Physics and Thermophysics

, Volume 70, Issue 1, pp 161–168 | Cite as

Algorithms for solving algebrized transfer equations

  • S. S. Belyavskii
  • S. G. Mulyarchik
  • A. V. Popov
Article
  • 16 Downloads

Abstract

Algorithms for solving algebrized transfer equations on a continuous rectangular grid are proposed. The efficiency of the methods proposed is illustrated by performing a numerical two-dimensional simulation of a submicron bipolar transistor in the high injection-level mode.

Keywords

Iterative Refinement Iteration Cost Auger Recombination Mechanism Microelectronic Structure Silicon VLSI 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notation

ε

relative dielectric constant

ψ

electrostatic potential

ρ

charge

n, p

concentrations of electrons and holes

t

time

jn, jp

densities of electron and hole currents

R

excess of recombination rate of charge carriers over generation rate

q

elementary charge

μn, μp

electron and hole mobilities

k

Boltzmann constant

T

absolute temperature

C

resulting dopantt concentration

Qss

bound charge at the Si/SiO2 interface

tm, ta

performance times for floating-point multiplication and addition operations

ce

collector-emitter

be

base-emitter

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References

  1. 1.
    L. Heigeman and D. Young, Applied Iterative Methods [Russian translation], Moscow (1986).Google Scholar
  2. 2.
    R. Fletcher, Lect. Notes Math., No. 506, 73–89 (1976).Google Scholar
  3. 3.
    P. Sonneveld, SIAM J. Sci. Stat. Comput., 10, No. 1,36–52(1969).CrossRefGoogle Scholar
  4. 4.
    H. A. van der Vorst, SIAM J. Sci. Stat. Comput., 13, No. 2, 631–644 (1992).MATHCrossRefGoogle Scholar
  5. 5.
    C. den Heijer, in: Simulation of Semiconductor Devices and Processes, Swansea (1984), pp. 267–285.Google Scholar
  6. 6.
    G. Heiser, C. Pommerell, J. Weis, and W. Fichtner, IEEE Trans., CAD-10, No. 10, 1218–1230 (1991).Google Scholar
  7. 7.
    P. Joly and R. Eymard, J. Comput. Phys., 91, No. 2, 298–309 (1990).MATHCrossRefGoogle Scholar
  8. 8.
    E. F. D’Azevedo, P. A. Forsyth, and W.-P. Tang, BIT, 32, No. 3, 442–463 (1992).MATHCrossRefGoogle Scholar
  9. 9.
    G. E. Schneider and M. Zedan, Numer. Heat Transfer, 4, No. 1, 1–19 (1981).CrossRefGoogle Scholar
  10. 10.
    V. A. Nikolaeva, V. I. Ryzhii, and B. N. Chetvertushkin, Inzh.-Fiz. Zh., 51, No. 3, 492–501 (1986).Google Scholar
  11. 11.
    S. G. Mulyarchik, S. S. Bielawski, and A. V. Popov, J. Comput. Phys., 110, No. 2, 201–211 (1994).MATHCrossRefGoogle Scholar
  12. 12.
    S. S. Belyavskii, S. G. Mulyarchik, and A. V. Popov, Differents. Uravn., 29, No. 9, 1575–1584 (1993).Google Scholar
  13. 13.
    J. A. Meijerink and H. A. van der Vorst, Math. Comput., 31, No. 137, 1480162 (1977).Google Scholar
  14. 14.
    S. G. Mulyarchik, Numerical Simulation of Microelectronic Structures [in Russian], Minsk (1989).Google Scholar
  15. 15.
    S. Selberherr, Analysis and Simulation of Semiconductor Devices, New York (1984).Google Scholar

Copyright information

© Plenum Publishing Corporation 1997

Authors and Affiliations

  • S. S. Belyavskii
    • 1
  • S. G. Mulyarchik
    • 1
  • A. V. Popov
    • 1
  1. 1.Belarusian State UniversityMinskBelarus

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