WIAS Preprint No. 2664, (2019)

Non-isothermal Scharfetter--Gummel scheme for electro-thermal transport simulation in degenerate semiconductors


  • Kantner, Markus
  • Koprucki, Thomas
    ORCID: 0000-0001-6235-9412

2010 Mathematics Subject Classification

  • 35K05 35K08 35Q79, 65N08, 80M12, 82B35, 82D37


  • Scharfetter--Gummel scheme, finite volume method, Fermi--Dirac statistics, non-isothermal drift-diffusion system, electro-thermal transport, Seebeck effect, self-heating




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.

Appeared in

  • Proceedings of ``Finite Volumes for Complex Applications IX'', R. Klöfkorn, E. Keilegavlen, F.A. Radu, J. Fuhrmann, eds., vol. 323 of Springer Proceedings in Mathematics & Statistics, Springer, Cham, 2020, pp. 173--182 , DOI 10.1007/978-3-030-43651-3_14 .

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