Skip to main content

Some Examples of Singular Perturbation Problems in Device Modeling

  • Conference paper
Semiconductors

Part of the book series: The IMA Volumes in Mathematics and its Applications ((IMA,volume 59))

  • 374 Accesses

Abstract

In this article we give a brief survey of some recent asymptotic results obtained for three singular perturbation problems arising in device modeling. The emphasis will be to obtain some rather explicit representations of the solutions and the input-output characteristics for these three ‘typical’ problems.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. A. Gnudi, F. Odeh, M. Rudan, Non-Local Effects in Small Semiconductor Devices, European Transactions on Telecommunications, 3, 1 (1990), pp. 307–312.

    Article  Google Scholar 

  2. S. Howison, J. King, Explicit Solutions to Six Free-Boundary Problems in Fluid Flow and Diffusion, IMA J. Appl. Math, 42 (1989), pp. 155–176.

    Article  MathSciNet  MATH  Google Scholar 

  3. P. Markowich, The Stationary Semiconductor Device Equations, Springer-Verlag, Vienna-New York, 1986.

    Google Scholar 

  4. P. Markowich, C. Ringhofer, C. Schmeiser, The Semiconductor Equations, Springer-Verlag, Vienna-New York, 1990.

    Book  Google Scholar 

  5. M. Mock, An Example of Nonuniqueness of Stationary Solutions in Semiconductor, Device Models, COMPEL (1982), pp. 165–174.

    Google Scholar 

  6. C. Please, An Analysis of Semiconductor P-N Junctions, IMA J. Appl. Math, 28 (1982), pp.301–318.

    Article  Google Scholar 

  7. I. Rubinstein, Multiple Steady State Solutions in One-Dimensional Electrodiffusion with Local Electroneutrality, SIAM J. Appl. Math, 47 (1987), pp. 1076–1093.

    Article  MathSciNet  Google Scholar 

  8. C. Schmeiser, On Strongly Reverse Biased Semiconductor Diodes, SIAM J. Appl. Math, 49 (1989), pp. 1734–1748.

    Article  MathSciNet  MATH  Google Scholar 

  9. H. Steinrück, A Bifurcation Analysis of the One-Dimensional Steady State Semiconductor Device Equations, SIAM J. Appl. Math, 49 (1989), pp. 1102–1121.

    Article  MathSciNet  MATH  Google Scholar 

  10. H. Steinrück, An Asymptotic Analysis of the Current-Voltage Curve of a PNPN Semiconductor Device, IMA J. Appl. Math, 43 (1990), pp. 243–261.

    Article  Google Scholar 

  11. M. Ward, F. Odeh, D. Cohen, Asymptotic Methods for Metal Oxide Semiconductor Field-Effect Transistor Modeling, SIAM J. Appl. Math, 50 (1990), pp. 1099–1126.

    Article  MathSciNet  MATH  Google Scholar 

  12. M. Ward, Singular Perturbations and a Free Boundary Problem in the Modeling of Field-Effect Transistors, SIAM J. Appl. Math., 52 (1992), pp. 112–139.

    Article  MathSciNet  MATH  Google Scholar 

  13. M. Ward, L. Reyna, F. Odeh, Multiple Steady State Solutions in a Multi-Junction Semiconductor Device, SIAM J. Appl. Math, 51 (1991), pp. 90–123.

    Article  MathSciNet  MATH  Google Scholar 

  14. L. Reyna, M. Ward, Drift Dominated Current Flow in Forward Biased Semiconductor Devices, IMA J. Appl. Math., 48 (1992), pp. 1–21.

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1994 Springer-Verlag New York, Inc.

About this paper

Cite this paper

Ward, M.J., Reyna, L., Odeh, F. (1994). Some Examples of Singular Perturbation Problems in Device Modeling. In: Coughran, W.M., Cole, J., Lloyd, P., White, J.K. (eds) Semiconductors. The IMA Volumes in Mathematics and its Applications, vol 59. Springer, New York, NY. https://doi.org/10.1007/978-1-4613-8410-6_23

Download citation

  • DOI: https://doi.org/10.1007/978-1-4613-8410-6_23

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4613-8412-0

  • Online ISBN: 978-1-4613-8410-6

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics