The Child-Langmuir limit for semiconductors : a numerical validation
Cáceres, María-José ; Carrillo, José-Antonio ; Degond, Pierre1
1 MIP, UMR CNRS 5640, Université Paul Sabatier, 118, route de Narbonne, 31062 Toulouse Cedex, France.
ESAIM: Modélisation mathématique et analyse numérique, Tome 36 (2002) no. 6, pp. 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 : 10.1051/m2an:2003011
Classification : 35L65, 65M99, 82D37
Mots-clés : Boltzmann-Poisson system, Child-Langmuir limit, WENO schemes, semiconductor devices
Cáceres, María-José  ; Carrillo, José-Antonio  ; Degond, Pierre 1

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