Computer device modeling

  • H. K. Gummel
Part II. Invited Papers of the European Meeting of the IEEE
Part of the Advances in Solid State Physics book series (ASSP, volume 9)


The use of the computer in the study of p-n junction devices is discussed. Tow examples are presented in detail, the bipolar transistor in the high-injection region [1], and an IMPATT oscillator in the Read [2] and TRAPATT [3] modes.

For the bipolar transistor, numerical solutions for electric field and carrier concentrations for fixed collectorbase voltage and a set of collector currents exhibit the phenomena of base widening and associated high-field relocation; Webster effect, i.e. field-aided diffusion in a space-charge neutral region; and the collector current dependence of the emitter-to-collector delay time.

For network analysis programs, compact device models are needed. An appraisal of currently available models for bipolar transistors is given, and suggestions for future model development are offered. Models should be easily expandable for increased accuracy, should have few user-specified parameters (default-options for very simple models) which are structure related and represent dc as well as ac performance.

The large-signal, transit-time-mode operation of a Read diode in a single-resonance circuit is shown in a computermade movie. The computed efficiency for this diode, oscillating at 11.4 GHz with an average current density of 200 A/cm2 is 12%. A high efficiency mode of IMPATT oscillation, first reported by Prager, Chang, and Weisbrod [4] and investigated by various authors [3,5,6] has been explained in detail by Scharfetter et al. [3, 7, 8] in a series of computer-experiment bootstrap studies. The high efficiency is possible if the diode attains a high-current low voltage state during part of the cycle. This state results after a high-field, avalanche producing zone has moved through the diode and has left a hole-electron plasma in its wake. Typically, the diode executes high Q oscillation at a frequency in the transit time range while delivering power at a subharmonic frequency. A computermade movie, is shown, giving hole and electron concentrations and electric field for a diode in this mode.

In solving the differential equations expressing carrier drift and diffusion, continuity of currents, and space charge balance, the numerical techniques must be suitable to handle problems caused by the wide dynamic range and rapid spatial and temporal variations of solutions and coefficients. Conventional finite difference techniques are inadequate. Instead, an approach involving local linearization, analytic solution of linearized equations, and matching of local solutions at meshpoints is employed.


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    H. J. Prager, K. K. N. Chang, and S. Weisbrod, Proc. IEEE (letters) 55, 586 ( (April 1967).Google Scholar
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    D. L. Scharfetter, International Electron Devices Meeting, Washington, D. C. (October 1968).Google Scholar
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    D. L. Scharfetter, D. J. Bartelink, and R. L. Johnston, IEEE Solid-State Device Research Conf., Boulder, Colo., June 17–19, 1968 (to be published).Google Scholar

Copyright information

© Friedr. Vieweg + Sohn GmbH, Verlag 1969

Authors and Affiliations

  • H. K. Gummel
    • 1
  1. 1.Bell Telephone Laboratories, IncorporatedMurray Hill

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