The Child–Langmuir limit for semiconductors : a numerical validation

María-José Cáceres; José-Antonio Carrillo; Pierre Degond[1]

  • [1] MIP, UMR CNRS 5640, Université Paul Sabatier, 118, route de Narbonne, 31062 Toulouse Cedex, France.

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique (2002)

  • Volume: 36, Issue: 6, page 1161-1176
  • ISSN: 0764-583X

Abstract

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The Boltzmann–Poisson system modeling the electron flow in semiconductors is used to discuss the validity of the Child–Langmuir asymptotics. The scattering kernel is approximated by a simple relaxation time operator. The Child–Langmuir limit gives an approximation of the current-voltage characteristic curves by means of a scaling procedure in which the ballistic velocity is much larger that the thermal one. We discuss the validity of the Child–Langmuir regime by performing detailed numerical comparisons between the simulation of the Boltzmann–Poisson system and the Child–Langmuir equations in test problems.

How to cite

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Cáceres, María-José, Carrillo, José-Antonio, and Degond, Pierre. "The Child–Langmuir limit for semiconductors : a numerical validation." ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 36.6 (2002): 1161-1176. <http://eudml.org/doc/245878>.

@article{Cáceres2002,
abstract = {The Boltzmann–Poisson system modeling the electron flow in semiconductors is used to discuss the validity of the Child–Langmuir asymptotics. The scattering kernel is approximated by a simple relaxation time operator. The Child–Langmuir limit gives an approximation of the current-voltage characteristic curves by means of a scaling procedure in which the ballistic velocity is much larger that the thermal one. We discuss the validity of the Child–Langmuir regime by performing detailed numerical comparisons between the simulation of the Boltzmann–Poisson system and the Child–Langmuir equations in test problems.},
affiliation = {MIP, UMR CNRS 5640, Université Paul Sabatier, 118, route de Narbonne, 31062 Toulouse Cedex, France.},
author = {Cáceres, María-José, Carrillo, José-Antonio, Degond, Pierre},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique},
keywords = {Boltzmann-Poisson system; Child-Langmuir limit; WENO schemes; semiconductor devices; detailed numerical comparisons; Child-Langmuir equations},
language = {eng},
number = {6},
pages = {1161-1176},
publisher = {EDP-Sciences},
title = {The Child–Langmuir limit for semiconductors : a numerical validation},
url = {http://eudml.org/doc/245878},
volume = {36},
year = {2002},
}

TY - JOUR
AU - Cáceres, María-José
AU - Carrillo, José-Antonio
AU - Degond, Pierre
TI - The Child–Langmuir limit for semiconductors : a numerical validation
JO - ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
PY - 2002
PB - EDP-Sciences
VL - 36
IS - 6
SP - 1161
EP - 1176
AB - The Boltzmann–Poisson system modeling the electron flow in semiconductors is used to discuss the validity of the Child–Langmuir asymptotics. The scattering kernel is approximated by a simple relaxation time operator. The Child–Langmuir limit gives an approximation of the current-voltage characteristic curves by means of a scaling procedure in which the ballistic velocity is much larger that the thermal one. We discuss the validity of the Child–Langmuir regime by performing detailed numerical comparisons between the simulation of the Boltzmann–Poisson system and the Child–Langmuir equations in test problems.
LA - eng
KW - Boltzmann-Poisson system; Child-Langmuir limit; WENO schemes; semiconductor devices; detailed numerical comparisons; Child-Langmuir equations
UR - http://eudml.org/doc/245878
ER -

References

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