The Child–Langmuir limit for semiconductors: a numerical validation
Departamento de Matemática Aplicada, Universidad de Granada, 18071 Granada, Spain. email@example.com., firstname.lastname@example.org.
2 MIP, UMR CNRS 5640, Université Paul Sabatier, 118, route de Narbonne, 31062 Toulouse Cedex, France. email@example.com.
Revised: 10 July 2002
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.
Mathematics Subject Classification: 35L65 / 65M99 / 82D37
Key words: Boltzmann-Poisson system / Child-Langmuir limit / WENO schemes / semiconductor devices.
© EDP Sciences, SMAI, 2002