P-Laplace thermistor modeling of electrothermal feedback in organic semiconductor devices

Abstract

In large-area organic light-emitting diodes (OLEDs), spatially inhomogeneous luminance at high power due to inhomogeneous current flow and electrothermal feedback can be observed. To describe these self-heating effects in organic semiconductors, we present a stationary thermistor model based on the heat equation for the temperature coupled to a p-Laplace-type equation for the electrostatic potential with mixed boundary conditions. The p-Laplacian describes the non-Ohmic electrical behavior of the organic material. Moreover, an Arrhenius-like temperature dependency of the electrical conductivity is considered. We introduce a finite-volume scheme for the system and discuss its relation to recent network models for OLEDs. In two spatial dimensions, we derive a priori estimates for the temperature and the electrostatic potential and prove the existence of a weak solution by Schauder’s fixed-point theorem.