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.
Mots clés : Boltzmann-Poisson system, Child-Langmuir limit, WENO schemes, semiconductor devices
@article{M2AN_2002__36_6_1161_0,
author = {C\'aceres, Mar{\'\i}a-Jos\'e and Carrillo, Jos\'e-Antonio and Degond, Pierre},
title = {The {Child-Langmuir} limit for semiconductors : a numerical validation},
journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique},
pages = {1161--1176},
publisher = {EDP-Sciences},
volume = {36},
number = {6},
year = {2002},
doi = {10.1051/m2an:2003011},
zbl = {1028.35102},
mrnumber = {1958663},
language = {en},
url = {http://www.numdam.org/articles/10.1051/m2an:2003011/}
}
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: Modélisation mathématique et analyse numérique PY - 2002 SP - 1161 EP - 1176 VL - 36 IS - 6 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/m2an:2003011/ DO - 10.1051/m2an:2003011 LA - en ID - M2AN_2002__36_6_1161_0 ER -
%0 Journal Article %A Cáceres, María-José %A Carrillo, José-Antonio %A Degond, Pierre %T The Child-Langmuir limit for semiconductors : a numerical validation %J ESAIM: Modélisation mathématique et analyse numérique %D 2002 %P 1161-1176 %V 36 %N 6 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/m2an:2003011/ %R 10.1051/m2an:2003011 %G en %F M2AN_2002__36_6_1161_0
Cáceres, María-José; Carrillo, José-Antonio; Degond, Pierre. The Child-Langmuir limit for semiconductors : a numerical validation. ESAIM: Modélisation mathématique et analyse numérique, Tome 36 (2002) no. 6, pp. 1161-1176. doi : 10.1051/m2an:2003011. http://www.numdam.org/articles/10.1051/m2an:2003011/
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