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Entropy 2015, 17(2), 528-538;

A New Telegrapher’s-Poisson System in Semiconductor Theory: A Singular Perturbation Approach

Dipartimento di Scienza Applicata e Tecnologia, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy
Received: 3 December 2014 / Revised: 20 January 2015 / Accepted: 21 January 2015 / Published: 29 January 2015
(This article belongs to the Special Issue Entropic Aspects in Statistical Physics of Complex Systems)
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In the theory of energy and momentum relaxation in semiconductor devices, the introduction of two temperatures and two mean velocities for electron and phonons is required. A new model, based on an asymptotic procedure for solving the kinetic equations of electrons and phonons is proposed, which naturally gives the displaced Maxwellian at the leading order. After that, balance equations for the electron number, energy densities and momentum densities are constructed, which constitute now a system of five equations for the chemical potential of electrons, the temperatures and the drift velocities. Moreover, Poisson’s equation is coupled, in order to calculate the self-consistent electric field. In Bloch’s approximation, we derive a telegrapher’s-Poisson system for the electron number density and the electric potential, which could allow simple semiconductor calculations, but still including wave propagation effects. View Full-Text
Keywords: semiconductors; kinetic theory; telegrapher’s equation semiconductors; kinetic theory; telegrapher’s equation
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Rossani, A. A New Telegrapher’s-Poisson System in Semiconductor Theory: A Singular Perturbation Approach. Entropy 2015, 17, 528-538.

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