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p-Laplace thermistor modeling of electrothermal feedback in organic semiconductors

Please always quote using this URN:urn:nbn:de:0296-matheon-13376
  • 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.

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Metadaten
Author:Matthias Liero, Thomas Koprucki, Axel Fischer, Reinhard Scholz, Annegret Glitzky
URN:urn:nbn:de:0296-matheon-13376
Referee:Frank Schmidt
Document Type:Preprint, Research Center Matheon
Language:English
Date of first Publication:2015/02/25
Release Date:2015/02/25
Tag:Arrhenius-like conductivity law; existence and boundedness; finite-volume approximation; nonlinear coupled system; organic light-emitting diode; p-Laplace; self-heating; stationary thermistor model
Institute:Weierstraß-Institut für Angewandte Analysis und Stochastik (WIAS)
Project:D Optics and Electronics (Electronic and photonic devices) / D-SE2 Electrothermal modeling of large-area OLEDs
MSC-Classification:35-XX PARTIAL DIFFERENTIAL EQUATIONS / 35Dxx Generalized solutions / 35D30 Weak solutions
35-XX PARTIAL DIFFERENTIAL EQUATIONS / 35Gxx General higher-order equations and systems / 35G60 Boundary value problems for nonlinear higher-order systems
35-XX PARTIAL DIFFERENTIAL EQUATIONS / 35Jxx Elliptic equations and systems [See also 58J10, 58J20] / 35J57 Boundary value problems for second-order elliptic systems
35-XX PARTIAL DIFFERENTIAL EQUATIONS / 35Jxx Elliptic equations and systems [See also 58J10, 58J20] / 35J92 Quasilinear elliptic equations with p-Laplacian
35-XX PARTIAL DIFFERENTIAL EQUATIONS / 35Qxx Equations of mathematical physics and other areas of application [See also 35J05, 35J10, 35K05, 35L05] / 35Q80 PDEs in connection with classical thermodynamics and heat transfer
65-XX NUMERICAL ANALYSIS / 65Mxx Partial differential equations, initial value and time-dependent initial- boundary value problems / 65M08 Finite volume methods
80-XX CLASSICAL THERMODYNAMICS, HEAT TRANSFER (For thermodynamics of solids, see 74A15) / 80Axx Thermodynamics and heat transfer / 80A20 Heat and mass transfer, heat flow
80-XX CLASSICAL THERMODYNAMICS, HEAT TRANSFER (For thermodynamics of solids, see 74A15) / 80Mxx Basic methods / 80M12 Finite volume methods
Preprint Number:1077
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