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Drift‐diffusion problems with Gauss–Fermi statistics and field‐dependent mobility for organic semiconductor devices
Author(s) -
Glitzky Annegret,
Liero Matthias
Publication year - 2019
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201900050
Subject(s) - organic semiconductor , diffusion , charge carrier , semiconductor , nonlinear system , condensed matter physics , charge (physics) , electron mobility , field (mathematics) , statistical physics , electric field , physics , gauss , fermi level , field dependence , materials science , quantum mechanics , mathematics , magnetic field , electron , pure mathematics
We consider a drift‐diffusion model for organic semiconductor devices including Gauss–Fermi statistics and application‐specific mobility functions. The charge transport in organic materials is realized by hopping of carriers between adjacent energetic sites and is described by complicated mobility laws with a strong nonlinear dependence on temperature, carrier densities and the electric field strength. We report on the existence of weak solutions to the stationary problem as well as global weak solutions to the instationary problem. Moreover, L ∞ bounds for the solutions are established.