Skip to main content
SpringerLink
Log in

Algorithms for solving algebrized transfer equations

  • Published:
Journal of Engineering Physics and Thermophysics Aims and scope

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Abbreviations

ε:

relative dielectric constant

ψ:

electrostatic potential

ρ:

charge

n, p :

concentrations of electrons and holes

t :

time

j n , j p :

densities of electron and hole currents

R :

excess of recombination rate of charge carriers over generation rate

q :

elementary charge

μ n , μ p :

electron and hole mobilities

k :

Boltzmann constant

T :

absolute temperature

C :

resulting dopantt concentration

Qss :

bound charge at the Si/SiO2 interface

t m , t a :

performance times for floating-point multiplication and addition operations

ce:

collector-emitter

be:

base-emitter

References

  1. L. Heigeman and D. Young, Applied Iterative Methods [Russian translation], Moscow (1986).

  2. R. Fletcher, Lect. Notes Math., No. 506, 73–89 (1976).

  3. P. Sonneveld, SIAM J. Sci. Stat. Comput., 10, No. 1,36–52(1969).

    Article  Google Scholar 

  4. H. A. van der Vorst, SIAM J. Sci. Stat. Comput., 13, No. 2, 631–644 (1992).

    Article  MATH  Google Scholar 

  5. C. den Heijer, in: Simulation of Semiconductor Devices and Processes, Swansea (1984), pp. 267–285.

  6. G. Heiser, C. Pommerell, J. Weis, and W. Fichtner, IEEE Trans., CAD-10, No. 10, 1218–1230 (1991).

    Google Scholar 

  7. P. Joly and R. Eymard, J. Comput. Phys., 91, No. 2, 298–309 (1990).

    Article  MATH  Google Scholar 

  8. E. F. D’Azevedo, P. A. Forsyth, and W.-P. Tang, BIT, 32, No. 3, 442–463 (1992).

    Article  MATH  Google Scholar 

  9. G. E. Schneider and M. Zedan, Numer. Heat Transfer, 4, No. 1, 1–19 (1981).

    Article  Google Scholar 

  10. V. A. Nikolaeva, V. I. Ryzhii, and B. N. Chetvertushkin, Inzh.-Fiz. Zh., 51, No. 3, 492–501 (1986).

    Google Scholar 

  11. S. G. Mulyarchik, S. S. Bielawski, and A. V. Popov, J. Comput. Phys., 110, No. 2, 201–211 (1994).

    Article  MATH  Google Scholar 

  12. S. S. Belyavskii, S. G. Mulyarchik, and A. V. Popov, Differents. Uravn., 29, No. 9, 1575–1584 (1993).

    Google Scholar 

  13. J. A. Meijerink and H. A. van der Vorst, Math. Comput., 31, No. 137, 1480162 (1977).

    Google Scholar 

  14. S. G. Mulyarchik, Numerical Simulation of Microelectronic Structures [in Russian], Minsk (1989).

  15. S. Selberherr, Analysis and Simulation of Semiconductor Devices, New York (1984).

Download references

Author information

Authors and Affiliations

  1. Belarusian State University, Minsk, Belarus

    S. S. Belyavskii, S. G. Mulyarchik & A. V. Popov

Authors
  1. S. S. Belyavskii
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. S. G. Mulyarchik
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. A. V. Popov
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 70, No. 1, pp. 156–162, January–February, 1997.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Belyavskii, S.S., Mulyarchik, S.G. & Popov, A.V. Algorithms for solving algebrized transfer equations. J Eng Phys Thermophys 70, 161–168 (1997). https://doi.org/10.1007/s10891-997-0029-5

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10891-997-0029-5

Keywords

Search

Navigation