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Simulation of a Steady-State Electron Shock Wave in a Submicron Semiconductor Device Using High-Order Upwind Methods

  • Emad Fatemi
  • Carl L. Gardner
  • Joseph W. Jerome
  • Stanley Osher
  • Donald J. Rose
Chapter
Part of the The Springer International Series in Engineering and Computer Science book series (SECS, volume 113)

Abstract

The hydrodynamic model treats electron flow in a semiconductor device through the Euler equations of gas dynamics, with the addition of a heat conduction term. Thus the hydrodynamic model PDEs have hyperbolic, parabolic, and elliptic modes.

The nonlinear hyperbolic modes support shock waves. Numerical sim-ulations of a steady-state electron shock wave in a semiconductor device are presented, using steady-state second upwind and high-order time-dependent upwind methods. For the ballistic diode (which models the channel of a MOSFET), the shock wave is fully developed in Si (with a 1 volt bias) at 300 K for a 0.1 micron channel and at 77 K for a 1.0 micron channel.

Keywords

Shock Wave Hydrodynamic Model Subsonic Flow Transonic Flow Laval Nozzle 
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.

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References

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    C. L. Gardner, J. W. Jerome, and D. J. Rose, “Numerical methods for the hydrodynamic device model: Subsonic flow,” IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, vol. 8, pp. 501–507, 1989.CrossRefGoogle Scholar
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    C. L. Gardner, “Numerical simulation of a steady-state electron shock wave in a submicron semiconductor device,” to appear.Google Scholar
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    K. Blotekjaer, “Transport equations for electrons in two-valley semiconductors,” IEEE Transactions on Electron Devices, vol. ED-17, pp. 38–47, 1970.CrossRefGoogle Scholar
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    G. Baccarani and M. R. Wordeman, “An investigation of steady-state velocity overshoot effects in Si and GaAs devices,” Solid State Electronics, vol. 28, pp. 407–416, 1985.CrossRefGoogle Scholar
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    C. L. Gardner, P. J. Lanzkron, and D. J. Rose, “A parallel nonlinear block iterative method for the hydrodynamic device model,” to appear.Google Scholar
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    E. Fatemi, J. W. Jerome, and S. Osher, “Solution of the hydrodynamic device model using high-order non-oscillatory shock capturing algorithms,” IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, to appear.Google Scholar

Copyright information

© Springer Science+Business Media New York 1991

Authors and Affiliations

  • Emad Fatemi
    • 1
  • Carl L. Gardner
    • 2
  • Joseph W. Jerome
    • 3
  • Stanley Osher
    • 1
  • Donald J. Rose
    • 2
  1. 1.Department of MathematicsUCLALos AngelesUSA
  2. 2.Department of Computer ScienceDuke UniversityDurhamUSA
  3. 3.Department of MathematicsNorthwestern UniversityEvanstonUSA

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