**Project Heads**

*Annegret Glitzky, Matthias Liero*

**Project Members**

Grigor Nika (WIAS)

**Project Duration**

01.01.2019 – 31.12.2020

**Located at**

WIAS

Charge transport in disordered organic semiconductors can be modeled at very different scales, ranging from density functional theory for molecules, master equation approaches for carrier dynamics to drift-diffusion equations, see e.g. [7]. Transport properties are heavily influenced by temperature such that self-heating effects have a strong impact on the performance of e.g. organic solar cells and transistors [10,6]. Nonlinear phenomena like S-shaped current-voltage relations with regions of negative differential resistance occur. The interplay of self-heating and temperature activated hopping transport in combination with the heat balance results in spatially inhomogeneous current flow and temperature distribution in organic LEDs (OLEDs) [3,4]. Hence, models and simulations of the electrothermal interplay in multidimensional organic devices are required that are as accurate as necessary but computationally not too costly and have to work for complicated device structures.

S-shaped current-voltage curves for simple pip structure and variation of mobility

**Project Webpages**

**Selected Publications
**

- M. Bulíček, A. Glitzky, M. Liero: Thermistor systems of p(x)-Laplace-type with discontinuous exponents via entropy solutions DCDS-S,
**10**(2017) pp. 697–713. WIAS Preprint**2247**(2016) - H. D. Doan, A. Glitzky, M. Liero
*Drift-diffusion modeling, analysis and simulation of organic semiconductor devices*, Z. Angew. Math. Phys.,**70**(2019) pp. 55, WIAS Preprint**2493**(2018) - A. Fischer, Th. Koprucki, K. Gärtner, M. Tietze, J. Brückner, B. Lüssem, K. Leo, A. Glitzky, R. Scholz: Feel the heat: Nonlinear electrothermal feedback in Organic LEDs, Adv. Funct. Mater.,
**24**, issue 22 (2014) pp. 3367–3374, WIAS Preprint**1839**(2013) - A. Fischer, M. Pfalz, K. Vandewal, M. Liero, A. Glitzky, S. Lenk, S. Reineke: Full electrothermal OLED model including nonlinear self-heating effects, Phys. Rev. Applied,
**10**:014023, 2018. - A. Glitzky, M. Liero:
*Instationary drift-diffusion problems with Gauss–Fermi statistics and field-dependent mobility for organic semiconductor devices*, Comm. Math. Sci.**17**(2019) pp. 33–59, WIAS Preprint**2523**(2018) - M. P. Klinger, A. Fischer, H. Kleemann, K. Leo: Non-linear self-heating in organic transistors reaching high power densities, Scientific Reports,
**8**:9806, 2018. - P. Kordt, J. J. M. van der Holst, M. Al Helwi, W. Kowalsky, F. May, A. Badinski, C. Lennartz, D. Andrienko: Modeling of organic light emitting diodes: From molecular to device properties Adv. Func. Mater.,
**25**, pp. 1955–1971, 2015. - 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, DOI 10.1007/s11082-017-1167-4, WIAS Preprint**2420**(2017) - 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, WIAS Preprint**2082**(2015) - S. Ullbrich, A. Fischer, Z. Tang, J. Ávila, H. J. Bolink, S. Reineke, K. Vandewal: Electrothermal feedback and absorption-induced open-circuit-voltage turnover in solar cells, Phys. Rev. Applied,
**9**:051003, 2018. - F. M. Sawatzki, D. H. Doan, H. Kleemann, M. Liero, A. Glitzky, Th. Koprucki, K. Leo:
*Balance of horizontal and vertical charge transport in organic field-effect transistors,*

Phys. Rev. Applied, 10:034069, 2018. - A. Glitzky, M. Liero:
*Drift-diffusion problems with Gauss–Fermi statistics and field-dependent mobility for organic semiconductor devices,*

PAMM Proc. Appl. Mech. (2019) /DOI 10.1002/pamm.201900050. - A. Kirch, A. Fischer, M. Liero, J. Fuhrmann, A. Glitzky, S. Reineke:
*Experimental proof of Joule heating-induced switched-back regions in OLEDs,*Light: Science & Applications 9:5, 2020. - A. Glitzky, M. Liero, G. Nika:
*An existence result for a class of electrothermal drift-diffusion models with Gauss–Fermi statistics for organic semiconductors,*

Analysis and Applications, 19:2 (2021) pp. 275–304, WIAS Preprint 2593 (2019) - Y. Zheng, A. Fischer, M. Sawatzki, D. H. Doan, M. Liero, A. Glitzky, S. Reineke, S. C. B. Mannsfeld:
*Introducing pinMOS memory: a novel, non-volatile organic memory device,*Adv. Funct. Mater. 2019, 1907119, DOI: 10.1002/adfm.201907119 - D. H. Doan, A. Fischer, J. Fuhrmann, A. Glitzky, M. Liero:
*Drift-diffusion simulation of S-shaped current-voltage relations for organic semiconductor devices,*

Journal of Computational Electronic, 19:3 (2020) pp. 1164–1174, WIAS Preprint 2630 (2019) - A. Glitzky, M. Liero, G. Nika:
*Analysis of a hybrid model for the electro-thermal behavior of semiconductor heterostructures,*

J. Math. Anal. Appl., 507 (2022) p. 125815, https://doi.org/10.1016/j.jmaa.2021.125815, WIAS Preprint 2636 (2019) - J. Fuhrmann, D. H. Doan, A. Glitzky, M. Liero, G. Nika:
*Unipolar drift-diffusion simulation of S-shaped current-voltage relations for organic semiconductor devices,*in: R. Klöfkorn, E.Keilegavlen, F. Radu, J. Fuhrmann (eds) Finite Volumes for Complex Applications IX – Methods, Theoretical Aspects, Examples: FVCA 9, Bergen, Norway, June 2020, Springer Proceedings in Mathematics & Statistics, vol. 323. Springer, Cham, pp. 625–633, WIAS Preprint 2660 (2019) - A. Glitzky, M. Liero, G. Nika:
*Dimension reduction of thermistor models for large-area organic light-emitting diodes,*

DCDS-S, 14:11 (2021) pp. 3953–3971, WIAS Preprint 2719 (2020) - A. Glitzky, M. Liero, G. Nika:
*A hybrid model for the electrothermal behavior of semiconductor devices,*

PAMM Proc. Appl. Mech. (2020) /DOI 10.1002/pamm.202000028. - A. Glitzky, M. Liero, G. Nika:
*Analysis of a bulk-surface thermistor model for large-area organic LEDs,*Portugaliae Mathematica, 78:2 (2021) pp. 187–210,

WIAS Preprint 2757 (2020). - A. Glitzky, M. Liero, G. Nika:
*A coarse-grained electrothermal model for organic semiconductor devices,*

accepted for publication in Mathematical Methods in the Applied Sciences, WIAS Preprint 2822 (2021) - A. Kirch, A. Fischer, M. Liero, J. Fuhrmann, A. Glitzky, S. Reineke:
*Electrothermal tristability causes sudden burn-in phenomena in organic LEDs,*

Adv. Funct. Mater., 31 (2021) p. 2106716, /DOI 10.1002/adfm.202106716.

**Selected Pictures
**

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