# AMaSiS 2021 - Abstract

**Nika, Grigor**

*Derivation of an effective bulk-surface thermistor model for OLEDs*

Weierstrass Institute

We derive an effective electrothermal model for a thin-film OLED from a recently introduced fully three-dimensional *p(x)*-Laplace thermistor model describing the heat and current flow through the thin OLED [1, 2]. The OLED is mounted on a glass substrate and consists of several thin layers that scale differently with respect to the multiscale parameter *ε > 0*, which is the ratio between the total thickness and the lateral extent of the OLED. Assuming physically motivated scalings in the electrical flux functions, uniform a priori bounds are derived for the solutions of the three-dimensional system which facilitates the extraction of converging subsequences with limits that are identified as solutions of a dimension reduced system [3]. In the latter, the effective current-flow equation is given by two semilinear equations in the two-dimensional cross-sections of the electrodes and algebraic equations for the continuity of the electrical fluxes through the organic layers. The effective heat equation is formulated only in the glass substrate with Joule heat term on the part of the boundary where the OLED is mounted.

**REFERENCES**

[1] M. Liero, Th. Koprucki, A. Fischer, R. Scholz, A. Glitzky, *p-Laplace thermistor modeling of electrothermal feedback in organic semiconductor devices*, Z. Angew. Math. Phys., 66 (2015) pp. 2957--2977.

[2] M. Liero, J. Fuhrmann, A. Glitzky, Th. Koprucki, A. Fischer, S. Reineke, *3D electrothermal simulations of organic LEDs showing negative differential resistance*, Opt. Quantum Electron., 49 (2017), pp. 330/1--330/8.

[3] A. Glitzky, M. Liero, G. Nika, *Dimension reduction of thermistor models for large-area organic light-emitting diodes*, (accepted in Discrete Cont. Dyn. Sys. Ser. S) (2021).