Abstract
Electro-thermal transport phenomena in semiconductors are described by the non-isothermal drift-diffusion system. The equations take a remarkably simple form when assuming the Kelvin formula for the thermopower. We present a novel, non-isothermal generalization of the Scharfetter–Gummel finite volume discretization for degenerate semiconductors obeying Fermi–Dirac statistics, which preserves numerous structural properties of the continuous model on the discrete level. The approach is demonstrated by 2D simulations of a heterojunction bipolar transistor.
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Acknowledgements
This work was funded by the German Research Foundation (DFG) under Germany’s Excellence Strategy—EXC2046: Math+ (Berlin Mathematics Research Center).
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Kantner, M., Koprucki, T. (2020). Non-isothermal Scharfetter–Gummel Scheme for Electro-Thermal Transport Simulation in Degenerate Semiconductors. In: Klöfkorn, R., Keilegavlen, E., Radu, F.A., Fuhrmann, J. (eds) Finite Volumes for Complex Applications IX - Methods, Theoretical Aspects, Examples. FVCA 2020. Springer Proceedings in Mathematics & Statistics, vol 323. Springer, Cham. https://doi.org/10.1007/978-3-030-43651-3_14
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