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Charge transport in semiconductors with degeneracy effects
Author(s) -
Poupaud Frédéric,
Schmeiser Christian
Publication year - 1991
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.1670140503
Subject(s) - boltzmann equation , uniqueness , degeneracy (biology) , degenerate energy levels , mathematics , boundary value problem , charge (physics) , boltzmann constant , perturbation (astronomy) , fermi–dirac statistics , work (physics) , partial differential equation , statistical physics , mathematical physics , mathematical analysis , physics , quantum mechanics , bioinformatics , biology , electron
It has been a common procedure to derive a model for charge transport in degenerate semiconductor material by incorporating a Fermi–Dirac distribution into the classical drift–diffusion model. In this work a Boltzmann equation with a non‐linear collision term is considered. A new fluid dynamical model is derived by considering small perturbations of the thermal equilibrium. The analysis contains an existence and uniqueness proof for the Boltzmann equation, a justification of the perturbation argument and a study of initial boundary value problems for the new fluid dynamical model.