Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Generalized phonon-assisted Zener tunneling in indirect semiconductors
  with non-uniform electric fields : a rigorous approach   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 electronphonon
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 numerical calculation of the Zener
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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The categories of this paper are: eess
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The categories of this paper are: chem-ph
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The categories of this paper are: nucl-th
33
The categories of this paper are: plasm-ph
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The categories of this paper are: hep-lat
37
The categories of this paper are: supr-con
31
The categories of this paper are: ao-sci
32
The categories of this paper are: atom-ph
20
The categories of this paper are: acc-phys
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The categories of this paper are: nlin
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The categories of this paper are: patt-sol
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The categories of this paper are: bayes-an
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The categories of this paper are: math
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The categories of this paper are: funct-an
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The categories of this paper are: econ
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The categories of this paper are: nucl-ex