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On p(x)-Laplace thermistor models describing electrothermal feedback in organic semiconductor devices

Dr. Matthias Liero, Weierstrass Institut, Berlino

Sala conferenze IMATI-CNR - Martedì 17 Novembre 2015 h.15:00

Abstract.  Organic semiconductor devices are thin-film multilayer structures consisting of organic, i.e. carbon-based, molecules or polymers. Nowadays, they can be found in everyday life in smartphone displays, photovoltaic cells, and TV screens. In addition, organic light-emitting diodes (OLEDs) have been identified as a promising alternative to conventional solid-state lighting.
However, several technological issues in the development of efficient large-area OLEDs exist. In lighting applications, a much higher brightness than in displays is required. At high power, a substantial self-heating in the device occurs, which leads to unpleasant brightness inhomogeneities. Although the role of electrothermal interplay has been recognized, the fundamental understanding of this mechanism is still missing. For example, there is no explanation why the highest temperature is reached at the device boundary although the heat conduction is worst at the center of the structure. Furthermore, lighting panels can show a saturation of brightness around their center at elevated self-heating, see [1].
In this talk, we present a stationary thermistor model, introduced in [2], to describe the electrothermal behavior of large-area OLEDs. The coupled system consists of the current-flow equation for the electrostatic potential and the heat equation with Joule heating term as source. The self-heating in the device is modeled by an Arrhenius-like temperature dependency of the electrical conductivity. The non-Ohmic electrical behavior of the organic material is described by a power law such that the electrical conductivity depends nonlinearly on the electric field. Notably, we allow for functional substructures with different power laws, which gives rise to a p(x)-Laplace-type problem with piecewise constant exponent. We prove the existence and boundedness of solutions in the two-dimensional case. The crucial point is to establish the higher integrability of the gradient of the electrostatic potential to treat the Joule heating term. The proof of the improved regularity is based on Caccioppoli-type estimates,
Poincaré inequalities, and a Gehring-type Lemma for the p(x)-Laplacian. Finally, Schauders fixed-point theorem is used to show the existence of solutions, see [3] for details.

The talk presents joint work with A. Glitzky and T. Koprucki (WIAS) and reports on experimental results of A. Fischer and R. Scholz (Institute of Applied Photophysics, TU Dresden). Support from the Einstein Center for Mathematics via Matheon project SE2: “Sustainable Energies: Electrothermal Modeling of Large-Area OLEDs” is gratefully acknowledged.

[1] A. Fischer, T. Koprucki, K. G ̈artner, M.L. Tietze, J. Bru ̈ckner, B. Lu ̈ssem, K. Leo, A. Glitzky, and
R. Scholz: Feel the heat: nonlinear electrothermal feedback in organic LEDs, Adv. Funct. Mater., 2014, 24, 3367
[2] M. Liero, T. Koprucki, A. Fischer, R. Scholz, and A. Glitzky: p-Laplace thermistor modeling
of electrothermal feedback in organic semiconductors, WIAS Preprint 2082, 2015, to appear in
Z. Angew. Math. Phys. DOI: 10.1007/s00033-015-0560-8
[3] A. Glitzky and M. Liero: Analysis of p(x)-Laplace thermistor models describing the electrothermal
behavior of organic semiconductor devices, WIAS Preprint 2143, 2015.

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