p-Laplace thermistor modeling of electrothermal feedback in organic semiconductors
- Liero, Matthias
- Koprucki, Thomas
- Fischer, Axel
- Scholz, Reinhard
- Glitzky, Annegret
2010 Mathematics Subject Classification
- 35J92 65M08 35D30 35G60 35J57 35Q79 80M12 80A20
- p-Laplace, stationary thermistor model, nonlinear coupled system, finite-volume approximation, existence and boundedness, self-heating, Arrhenius-like conductivity law, organic light-emitting diode
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.
- ZAMP Z. Angew. Math. Phys., 66 (2015) pp. 2957--2977.