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The Child–Langmuir limit for semiconductors:a numerical validation

Published online by Cambridge University Press:  15 January 2003

María-José Cáceres ,
José-Antonio Carrillo  and
Pierre Degond
María-José Cáceres
Affiliation:
Departamento de Matemática Aplicada, Universidad de Granada, 18071 Granada, Spain. caceresg@ugr.es., carrillo@ugr.es.
José-Antonio Carrillo
Affiliation:
Departamento de Matemática Aplicada, Universidad de Granada, 18071 Granada, Spain. caceresg@ugr.es., carrillo@ugr.es.
Pierre Degond
Affiliation:
MIP, UMR CNRS 5640, Université Paul Sabatier, 118, route de Narbonne, 31062 Toulouse Cedex, France. degond@mip.ups-tlse.fr.
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Abstract

The Boltzmann–Poisson system modeling the electron flow in semiconductorsis 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-voltagecharacteristic curves by means of a scalingprocedure 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 theBoltzmann–Poisson system and the Child–Langmuir equations in testproblems.

Keywords

Boltzmann-Poisson systemChild-Langmuir limitWENO schemessemiconductor devices.
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 36 , Issue 6 , November 2002 , pp. 1161 - 1176
Copyright
© EDP Sciences, SMAI, 2002

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