The Child-Langmuir limit for semiconductors : a numerical validation
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 36 (2002) no. 6, p. 1161-1176

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.

DOI : https://doi.org/10.1051/m2an:2003011
Classification:  35L65,  65M99,  82D37
Keywords: 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: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
publisher = {EDP-Sciences},
volume = {36},
number = {6},
year = {2002},
pages = {1161-1176},
doi = {10.1051/m2an:2003011},
mrnumber = {1958663},
zbl = {1028.35102},
language = {en},
url = {http://www.numdam.org/item/M2AN_2002__36_6_1161_0}
}

Cáceres, María-José; Carrillo, José-Antonio; Degond, Pierre. The Child-Langmuir limit for semiconductors : a numerical validation. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 36 (2002) no. 6, pp. 1161-1176. doi : 10.1051/m2an:2003011. http://www.numdam.org/item/M2AN_2002__36_6_1161_0/

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