WIAS Preprint No. 2822, (2021)

A coarse-grained electrothermal model for organic semiconductor devices



Authors

  • Glitzky, Annegret
    ORCID: 0000-0003-1995-5491
  • Liero, Matthias
    ORCID: 0000-0002-0963-2915
  • Nika, Grigor
    ORCID: 0000-0002-4403-6908

2020 Mathematics Subject Classification

  • 35J57 35K05 78A35

Keywords

  • Drift-diffusion, charge & heat transport, electrothermal interaction, organic semiconductor, coarse-grained model, weak solutions

DOI

10.20347/WIAS.PREPRINT.2822

Abstract

We derive a coarse-grained model for the electrothermal interaction of organic semiconductors. The model combines stationary drift-diffusion based electrothermal models with thermistor type models on subregions of the device and suitable transmission conditions. Moreover, we prove existence of a solution using a regularization argument and Schauder's fixed point theorem. In doing so, we extend recent work by taking into account the statistical relation given by the Gauss--Fermi integral and mobility functions depending on the temperature, charge-carrier density, and field strength, which is required for a proper description of organic devices.

Appeared in

  • Math. Methods Appl. Sci., 45 (2022), pp. 4809--4833 (published on 26.01.2022), DOI 10.1002/mma.8072 .

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