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A PDE Model for Electrothermal Feedback in Organic Semiconductor Devices

  • Matthias Liero
  • Axel Fischer
  • Jürgen Fuhrmann
  • Thomas Koprucki
  • Annegret Glitzky
Conference paper
Part of the Mathematics in Industry book series (MATHINDUSTRY, volume 26)

Abstract

Large-area organic light-emitting diodes are thin-film multilayer devices that show pronounced self-heating and brightness inhomogeneities at high currents. As these high currents are typical for lighting applications, a deeper understanding of the mechanisms causing these inhomogeneities is necessary. We discuss the modeling of the interplay between current flow, self-heating, and heat transfer in such devices using a system of partial differential equations of thermistor type, that is capable of explaining the development of luminance inhomogeneities. The system is based on the heat equation for the temperature coupled to a p(x)-Laplace-type equation for the electrostatic potential with mixed boundary conditions. The p(x)-Laplacian allows to take into account non-Ohmic electrical behavior of the different organic layers. Moreover, we present analytical results on the existence, boundedness, and regularity of solutions to the system. A numerical scheme based on the finite-volume method allows for efficient simulations of device structures.

Notes

Acknowledgements

A.G. and M.L. gratefully acknowledge the funding received via Research Center Matheon supported by ECMath in project D-SE2.

References

  1. 1.
    Bradji, A., Herbin, R.: IMA J. Numer. Anal. 28(3), 469 (2008). doi:10.1093/imanum/drm030MathSciNetCrossRefGoogle Scholar
  2. 2.
    Bulíček, M., Glitzky, A., Liero, M.: SIAM J. Math. Anal. 48, 3496 (2016). doi:10.1137/16M1062211MathSciNetCrossRefGoogle Scholar
  3. 3.
    Bulíček, M., Glitzky, A., Liero, M.: Thermistor systems of p(x)-laplace-type with discontinuous exponents via entropy solutions. Discrete Contin. Dyn. Syst. S 10(4), 697–713 (2017). doi:10.3934/dcdss.2017035MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Diening, L., Harjulehto, P., Hästö, P., Ružička, M.: Lebesgue and Sobolev Spaces with Variable Exponents. Lecture Notes in Mathematics, vol. 2017. Springer, Berlin (2011). doi:10.1007/978-3-642-18363-8Google Scholar
  5. 5.
    Fischer, A., Pahner, P., Lüssem, B., Leo, K., Scholz, R., Koprucki, T., Gärtner, K., Glitzky, A.: Phys. Rev. Lett. 110, 126601/1 (2013). doi:10.1103/PhysRevLett.110.126601Google Scholar
  6. 6.
    Fischer, A., Koprucki, T., Gärtner, K., Brückner, J., Lüssem, B., Leo, K., Glitzky, A., Scholz, R.: Adv. Funct. Mater. 24, 3367 (2014). doi:10.1002/adfm.201303066CrossRefGoogle Scholar
  7. 7.
    Glitzky, A., Liero, M.: Nonlinear Anal. Real World Appl. 34, 536 (2017). doi:10.1016/j.nonrwa.2016.09.015MathSciNetCrossRefGoogle Scholar
  8. 8.
    Liero, M., Koprucki, T., Fischer, A., Scholz, R., Glitzky, A.: Z. Angew. Math. Phys. 66(6), 2957 (2015). doi:10.1007/s00033-015-0560-8MathSciNetCrossRefGoogle Scholar
  9. 9.
    Si, H., Gärtner, K., Fuhrmann, J.: Comput. Math. Math. Phys. 50(1), 38 (2010). doi:10.1134/S0965542510010069MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2017

Authors and Affiliations

  • Matthias Liero
    • 1
  • Axel Fischer
    • 2
  • Jürgen Fuhrmann
    • 1
  • Thomas Koprucki
    • 1
  • Annegret Glitzky
    • 1
  1. 1.Weierstrass Institute for Applied Analysis and StochasticsBerlinGermany
  2. 2.Dresden Integrated Center for Applied Physics and Photonic Materials (IAPP)DresdenGermany

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