The Child–Langmuir Law for the Boltzmann Equation of Semiconductors

The Child–Langmuir Law for the Boltzmann Equation of Semiconductors

We investigate the so-called Child-Langmuir asymptotics of the one-dimensional stationary Boltzmann-Poisson system. The asymptotics apply when the lattice temperature is small and leads to a singular perturbation problem. We derive the limit problem associated with these asymptotics, and prove the e...

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Veröffentlicht in:SIAM journal on mathematical analysis 1995-03, Vol.26 (2), p.364-398
Hauptverfasser: Abdallah, Naoufel Ben, Degond, Pierre
Format: Artikel
Sprache:eng
Schlagworte:
Bias
Cauchy problems
Charged particles
Crystal lattices
Integral equations
Semiconductors
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Beschreibung
Zusammenfassung:We investigate the so-called Child-Langmuir asymptotics of the one-dimensional stationary Boltzmann-Poisson system. The asymptotics apply when the lattice temperature is small and leads to a singular perturbation problem. We derive the limit problem associated with these asymptotics, and prove the existence of the Child-Langmuir current.
ISSN:0036-1410
1095-7154
DOI:10.1137/S0036141093246567