Abstract
We introduce an empirical PDE model for the electrothermal description of organic semiconductor devices by means of current and heat flow. The current flow equation is of p(x)-Laplace type, where the piecewise constant exponent p(x) takes the non-Ohmic behavior of the organic layers into account. Moreover, the electrical conductivity contains an Arrhenius-type temperature law. We present a hybrid finite-volume/finite-element discretization scheme for the coupled system, discuss a favorite discretization of the p(x)-Laplacian at hetero interfaces, and explain how path following methods are applied to simulate S-shaped current-voltage relations resulting from the interplay of self-heating and heat flow.
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Acknowledgements
A.G. and M.L. gratefully acknowledge the funding received via Research Center Matheon supported by ECMath in project D-SE2.
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Fuhrmann, J., Glitzky, A., Liero, M. (2017). Hybrid Finite-Volume/Finite-Element Schemes for p(x)-Laplace Thermistor Models. In: Cancès, C., Omnes, P. (eds) Finite Volumes for Complex Applications VIII - Hyperbolic, Elliptic and Parabolic Problems. FVCA 2017. Springer Proceedings in Mathematics & Statistics, vol 200. Springer, Cham. https://doi.org/10.1007/978-3-319-57394-6_42
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DOI: https://doi.org/10.1007/978-3-319-57394-6_42
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