| Popis: |
We derive and investigate a stationary model for the electrothermal behavior of organic thin-film devices including their electrical and thermal environment. Whereas the electrodes are modeled by Ohm's law, the electronics of the organic device itself is described by a generalized van Roosbroeck system with temperature dependent mobilities and using Gauss--Fermi integrals for the statistical relation. The currents give rise to Joule heat which together with the heat generated by the generation/recombination of electrons and holes in the organic device occur as source terms in the heat flow equation that has to be considered on the whole domain. The crucial task is to establish that the quantities in the transfer conditions at the interfaces between electrodes and the organic semiconductor device have sufficient regularity. Therefore, we restrict the analytical treatment of the system to two spatial dimensions. We consider layered organic structures, where the physical parameters (total densities of transport states, LUMO and HOMO energies, disorder parameter, basic mobilities, activation energies, relative dielectric permittivity, heat conductivity) are piecewise constant. We prove the existence of weak solutions using Schauder's fixed point theorem and a regularity result for strongly coupled systems with nonsmooth data and mixed boundary conditions that is verified by Caccioppoli estimates and a Gehring-type lemma. |
