The Child–Langmuir Law for the Boltzmann Equation of Semiconductors

DOI10.1137/S0036141093246567zbMath0828.35131MaRDI QIDQ4698912

Naoufel Ben Abdallah, Pierre Degond

Publication date: 11 June 1995

Published in: SIAM Journal on Mathematical Analysis (Search for Journal in Brave)

zbMATH Keywords

existenceuniquenessboundary value problemcollision operatorinternal boundary layersChild-Langmuir asymptoticscharged particle transport in semiconductor devicesChild-Langmuir currentone- dimensional unipolar semiconductor structurestationary Vlasov-Poisson equationstationary Vlasov-Poisson- Boltzmann equations

Mathematics Subject Classification ID

Integro-ordinary differential equations (45J05) PDEs in connection with optics and electromagnetic theory (35Q60) Motion of charged particles (78A35) Applications of statistical mechanics to specific types of physical systems (82D99) General theory for ordinary differential equations (34A99)

Related Items (12)

On a mathematical model for hot carrier injection in semiconductors ⋮ Unnamed Item ⋮ The Child‐Langmuir asymptotics for semiconductors including phonon interactions ⋮ The quantum Child-Langmuir problem ⋮ A two-surface problem of the electron flow in a semiconductor on the basis of kinetic theory ⋮ Initial-boundary value problems of the Boltzmann equation at zero temperature ⋮ Computational macroscopic approximations to the one-dimensional relaxation-time kinetic system for semiconductors ⋮ The Child–Langmuir limit for semiconductors: a numerical validation ⋮ LOW AND HIGH FIELD SCALING LIMITS FOR THE VLASOV– AND WIGNER–POISSON–FOKKER–PLANCK SYSTEMS ⋮ LOW AND HIGH FIELD SCALING LIMITS FOR THE VLASOV– AND WIGNER–POISSON–FOKKER–PLANCK SYSTEMS ⋮ Particle simulation and asymptotic analysis of kinetic equations for modeling a Schottky diode ⋮ A geometric level-set formulation of a plasma-sheath interface

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