Title
Generalized phonon-assisted Zener tunneling in indirect semiconductors with non-uniform electric fields : a rigorous approach Generalized phonon-assisted Zener tunneling in indirect semiconductors with non-uniform electric fields : a rigorous approach
Author
Faculty/Department
Faculty of Sciences. Physics
Publication type
article
Publication
New York, N.Y. :American Institute of Physics ,
Subject
Physics
Source (journal)
Journal of applied physics / American Institute of Physics. - New York, N.Y., 1937, currens
Volume/pages
109(2011) :12 , p. 124503,1-124503,12
ISSN
0021-8979
1089-7550
Article Reference
124503
Carrier
E-only publicatie
Target language
English (eng)
Full text (Publishers DOI)
Affiliation
University of Antwerp
Abstract
A general framework to calculate the Zener current in an indirect semiconductor with an externally applied potential is provided. Assuming a parabolic valence and conduction band dispersion, the semiconductor is in equilibrium in the presence of the external field as long as the electron-phonon interaction is absent. The linear response to the electron-phonon interaction results in a non-equilibrium system. The Zener tunneling current is calculated from the number of electrons making the transition from valence to conduction band per unit time. A convenient expression based on the single particle spectral functions is provided, enabling the evaluation of the Zener tunneling current under any three-dimensional potential profile. For a one-dimensional potential profile an analytical expression is obtained for the current in a bulk semiconductor, a semiconductor under uniform field, and a semiconductor under a non-uniform field using the WKB (Wentzel-Kramers-Brillouin) approximation. The obtained results agree with the Kane result in the low field limit. A numerical example for abrupt p-n diodes with different doping concentrations is given, from which it can be seen that the uniform field model is a better approximation than the WKB model, but a direct numerical treatment is required for low bias conditions.
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