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On the applicability of a semi-analytical approach to determining the transient electron transport response of gallium arsenide, gallium nitride, and zinc oxide

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Abstract

We critically examine the applicability of the semi-analytical approach of Shur (M. Shur, Electron Lett 12, 615 (1976)) in evaluating the transient electron transport response of gallium arsenide, gallium nitride, and zinc oxide. In particular, we contrast results obtained using this semi-analytical approach of Shur with those obtained using Monte Carlo simulations of the electron transport. Our approach will be to examine the response of an ensemble of electrons to the application of a constant and uniform applied electric field. For the purposes of this analysis, three aspects of the transient electron transport response will be considered: (1) the dependence of the electron drift velocity on the time elapsed since the onset of the applied electric field, (2) the dependence of the average electron energy on the time elapsed since the onset of the applied electric field, and (3) the dependence of the average electron displacement on the time elapsed since the onset of the applied electric field. The results obtained show that this semi-analytical approach of Shur produces results that are very similar to those produced using Monte Carlo simulations. Thus, this semi-analytical approach of Shur should be applicable for the treatment of non-uniform and time-varying electric fields, making it a useful tool for the treatment of the transient electron transport response within electron device configurations.

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Notes

  1. In the Kane model, the energy bands are assumed to be non-parabolic, spherical, and of the form \(\frac{\hbar^{2} k^{2}}{2 {m}^{*}} = E \left( 1 + \alpha E \right)\), where \(\hbar k\) denotes the crystal momentum, E represents the energy, m* is the effective mass of the electrons within this valley, and α is the non-parabolicity coefficient [49].

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Acknowledgments

The authors gratefully acknowledge financial support from the Natural Sciences and Engineering Research Council of Canada. The work at Rensselaer Polytechnic Institute (M. S. Shur) was supported primarily through the Engineering Research Centers program of the National Science Foundation under the NSF Cooperative Agreement No. EEC-0812056 and in part by New York State under NYSTAR contract C090145.

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Authors and Affiliations

  1. Department of Electrical and Computer Engineering, University of Windsor, 401 Sunset Avenue, Windsor, ON, N9B 3P4, Canada

    Walid A. Hadi

  2. Department of Electrical, Computer, and Systems Engineering, Rensselaer Polytechnic Institute, Troy, NY, 12180-3590, USA

    Michael S. Shur

  3. School of Engineering, The University of British Columbia, 3333 University Way, Kelowna, BC, V1V 1V7, Canada

    Stephen K. O’Leary

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  1. Walid A. Hadi
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Correspondence to Stephen K. O’Leary.

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Hadi, W.A., Shur, M.S. & O’Leary, S.K. On the applicability of a semi-analytical approach to determining the transient electron transport response of gallium arsenide, gallium nitride, and zinc oxide. J Mater Sci: Mater Electron 24, 1624–1634 (2013). https://doi.org/10.1007/s10854-012-0986-0

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