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Derivation of the high field semiconductor equations [electronic resource].

Published
Washington, D.C. : United States. Dept. of Energy, 1991.
Oak Ridge, Tenn. : Distributed by the Office of Scientific and Technical Information, U.S. Dept. of Energy.
Physical Description
Pages: (28 pages) : digital, PDF file
Additional Creators
Los Alamos National Laboratory, United States. Department of Energy, and United States. Department of Energy. Office of Scientific and Technical Information
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Summary
Electron and hole densities evolve in x-z phase space according to Boltzmann equations. When the mean free path of the particles is short and electric force on the particles is weak, a well-known expansion can be used to solve the Boltzmann equation. This asymptotic solution shows that the spatial density of electrons and holes evolves according to diffusion-drift equations. As devices become smaller, electric fields become stronger, which renders the Basic Semiconductor Equations increasingly inaccurate. To remedy this problem, we use singular perturbation techniques to obtain a new asymptotic expansion for the Boltzmann equation. Like the Hilbert expansion, the new expansion requires the mean free path to be short compared to all macroscopic length scales. However, it does not require the electric forces to be weak. The new expansion shows that spatial densities obey diffusion-drift equations as before, but the diffusivity D and mobility μ turn out to be nonlinear functions of the electric field. In particular, our analysis determines the field-dependent mobilities μ(E) and diffusivities D(E) directly from the scattering operator. By carrying out this asymptotic expansion to higher order, we obtain the high frequency corrections to the drift velocity and diffusivity, and also the corrections due to gradients in the electric field. Remarkably, we find that Einsteins's relation is still satisfied, even with these corrections. The new diffusion-drift equations, together with Poissons' equation for the electric field, form the high-field semiconductor equations, which can be expected to be accurate regardless of the strength of the electric fields within the semiconductor. In addition, our analysis determines the entire momentum distribution of the particles, so we derive a very accurate first moment model for semi-conductors by substituting the asymptotically-correct distribution back into the Boltzmann equation and taking moments.
Report Numbers
E 1.99:la-ur-91-2951
E 1.99: conf-9107176--1
conf-9107176--1
la-ur-91-2951
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Other Subject(s)
Note
Published through SciTech Connect.
01/01/1991.
"la-ur-91-2951"
" conf-9107176--1"
"DE92000249"
1991 IMA semiconductor workshop, Minneapolis, MN (United States), 15 Jul - 9 Aug 1991.
Cox, R.W.; Wagner, B.A. . Dept. of Mathematics; Hagan, P.S.
Funding Information
W-7405-ENG-36
View MARC record | catkey: 14063511