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boltzmann-poisson system

ESAIM: Mathematical Modelling and Numerical Analysis (1)

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The Child–Langmuir limit for semiconductors:a numerical validation
María-José Cáceres, José-Antonio Carrillo, Pierre Degond
Journal:

ESAIM: Mathematical Modelling and Numerical Analysis / Volume 36 / Issue 6 / November 2002

Published online by Cambridge University Press:

15 January 2003, pp. 1161-1176

Print publication:

November 2002
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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.