MATH+ project AA2-1:
Hybrid models for the electrothermal behavior of organic semiconductor devices

Project heads: Annegret Glitzky, Matthias Liero
Staff: Grigor Nika
Funding period: January 2019 – December 2020
Application area: Nano- and optoelectronics (WIAS), Materials, Light, Devices (MATH+)


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.


The idea is to develop a hybrid model for the electrothermal description of multi-dimensional structured organic devices by combining models for device substructures with different model complexity. The two main building blocks are (1.) the Energy-Drift-Diffusion (EDD) modeling of organic devices, where the interplay of charge and heat flow is described via a van Roosbroeck system adapted to organic semiconductors coupled to a heat equation with Joule and recombination heat sources (see [2,5]) and (2.) p(x)-Laplace thermistor (TH) models for organic semiconductor devices as introduced in [9]. Within the project we aim to derive models of type (TH) as limit models from (EDD), formulate and investigate from an analytical point of view hybrid models with varying model complexity in the substructures of the devices including the transfer conditions at boundaries between device substructures, and finally discuss numerical approximations and implementation of hybrid models.
Fig. 1: Perspective for multi-scale and multi-physics modeling of organic devices.



Manuel Landsdorfer, Jürgen Fuhrmann, Dirk Peschka, Markus Kantner, Uwe Bandelow, Thomas Koprucki (all WIAS)
Rupert Klein, Burkhard Schmidt (FU Berlin)


Axel Fischer, Hans Kleemann, Sebastian Reineke, Reinhard Scholz (all Dresden Integrated Center for Applied Physics and Photonic Materials (DC-IAPP) TU Dresden)

Project publications

  1. A. Glitzky, M. Liero, G. Nika: Dimension reduction of thermistor models for large-area organic light-emitting diodes, WIAS Preprint 2719 (2020)
  2. 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)
  3. A. Glitzky, M. Liero, G. Nika: Analysis of a hybrid model for the electro-thermal behavior of semiconductor heterostructures, WIAS Preprint 2636 (2019)
  4. 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)
  5. A. Glitzky, M. Liero, G. Nika: An existence result for a class of electrothermal drift-diffusion models with Gauss--Fermi statistics for organic semiconductors, to appear in Analysis and Applications,
    WIAS Preprint 2593 (2019)
  6. 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.
  7. 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.

Project related literature

  1. 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)
  2. 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)
  3. 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)
  4. 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.
  5. 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)
  6. 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.
  7. 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.
  8. 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)
  9. 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)
  10. 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.
  11. 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