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Zeitschrift für angewandte Mathematik und Physik

, Volume 66, Issue 6, pp 2957–2977 | Cite as

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

  • Matthias LieroEmail author
  • Thomas Koprucki
  • Axel Fischer
  • Reinhard Scholz
  • Annegret Glitzky
Article

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.

Mathematics Subject Classification

35J92 65M08 35D30 35G60 35J57 35Q79 80M12 80A20 

Keywords

p-Laplace Stationary thermistor model Nonlinear coupled system Finite-volume approximation Existence and boundedness Self-heating Arrhenius-like conductivity law Organic light-emitting diode 

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Copyright information

© Springer Basel 2015

Authors and Affiliations

  • Matthias Liero
    • 1
    Email author
  • Thomas Koprucki
    • 1
  • Axel Fischer
    • 2
  • Reinhard Scholz
    • 2
  • Annegret Glitzky
    • 1
  1. 1.Weierstrass InstituteBerlinGermany
  2. 2.Institut für Angewandte PhotophysikTU DresdenDresdenGermany

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