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

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...

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Bibliographic Details
Published in:Zeitschrift für angewandte Mathematik und Physik 2015-12, Vol.66 (6), p.2957-2977
Main Authors: Liero, Matthias, Koprucki, Thomas, Fischer, Axel, Scholz, Reinhard, Glitzky, Annegret
Format: Article
Language:English
Subjects:
Devices
Electrostatics
Engineering
Feedback
Luminance
Mathematical Methods in Physics
Mathematical models
Organic semiconductors
Theorems
Theoretical and Applied Mechanics
Thermistors
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Summary: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.
ISSN:0044-2275
1420-9039
DOI:10.1007/s00033-015-0560-8