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

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• 作者：Matthias Liero ; Thomas Koprucki…
• 关键词：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
• 刊名：Zeitschrift f篓鹿r angewandte Mathematik und Physik
• 出版年：2015
• 出版时间：December 2015
• 年：2015
• 卷：66
• 期：6
• 页码：2957-2977
• 全文大小：845 KB
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• 作者单位：Matthias Liero (1)
  Thomas Koprucki (1)
  Axel Fischer (2)
  Reinhard Scholz (2)
  Annegret Glitzky (1)
  
  1. Weierstrass Institute, Mohrenstr?e 39, 10117, Berlin, Germany
  2. Institut für Angewandte Photophysik, TU Dresden, George-B?hr-Stra?e 1, 01069, Dresden, Germany
  
• 刊物主题：Theoretical and Applied Mechanics; Mathematical Methods in Physics;
• 出版者：Springer Basel
• ISSN：1420-9039

文摘

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