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Theoretical Investigation of Wave-Vector-Dependent Analytical and Numerical Formulations of the Interband Impact-Ionization Transition Rate for Electron in Bulk Silicon and GaAsThe electron interband impact-ionization rate for both silicon and gallium arsenide is calculated using an ensemble Monte Carlo simulation with the expressed purpose of comparing different formulations of the interband ionization transition rate. Specifically, three different treatments of the transition rate are examined: the traditional Keldysh formula, a new k-dependent analytical formulation first derived by W. Quade, E Scholl, and M. Rudan, and a more exact, numerical method of Y. Wang and K. F. Brennan. Although the completely numerical formulation contains no adjustable parameters and as such provides a very reliable result, it is highly computationally intensive. Alternatively, the Keldysh formula, although inherently simple and computationally efficient, fails to include the k dependence as well as the details of the energy band structure. The k-dependent analytical formulation of Quade and co-workers overcomes the limitations of both of these models but at the expense of some new parameterization. It is found that the k-dependent analytical method of Quade and co-workers produces very similar results to those obtained with (he completely numerical model for some quantities. Specifically, both models predict that the effective threshold for impact ionization in GaAs and silicon is quite soft, that the majority of ionization events originate from the second conduction band in both materials, and that the transition rate is k dependent. Therefore, it is concluded that the k-dependent analytical model can qualitatively reproduce results similar to those obtained with the numerical model yet with far greater computational efficiency. Nevertheless, there exist some important drawbacks to the k-dependent analytical model of Quade and co-workers: These are that it does not accurately reproduce the quantum yield data for bulk silicon, it requires determination of a new parameter, related physically to (he overlap integrals of the Bloch state which can only be adjusted by comparison to experiment, and fails to account for any wave-vector dependence of the overlap integrals. As such [he transition rate may be overestimated at those points for which "near vertical," small change in k, transitions occur.
Document ID
20000019587
Acquisition Source
Headquarters
Document Type
Reprint (Version printed in journal)
External Source(s)
Authors
Kolnik, Jan
(Georgia Inst. of Tech. Atlanta, GA United States)
Wang, Yang
(Georgia Inst. of Tech. Atlanta, GA United States)
Oguzman, Ismail H.
(Georgia Inst. of Tech. Atlanta, GA United States)
Brennan, Kevin F.
(Georgia Inst. of Tech. Atlanta, GA United States)
Date Acquired
August 19, 2013
Publication Date
September 15, 1994
Publication Information
Publication: Journal of Applied Physics
Publisher: American Inst. of Physics
Volume: 76
Issue: 6
ISSN: 0021-8979
Subject Category
Atomic And Molecular Physics
Funding Number(s)
CONTRACT_GRANT: E-21-H36
CONTRACT_GRANT: BNR-125A3J
CONTRACT_GRANT: NAGw-2753
Distribution Limits
Public
Copyright
Other

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