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

  • Finite Volumes for Complex Applications IX -- Methods, Theoretical Aspects, Examples -- FVCA 9, Bergen, June 2020, R. Klöfkorn, E. Keilegavlen, F.A. Radu, J. Fuhrmann, eds., vol. 323 of Springer Proceedings in Mathematics & Statistics, Springer International Publishing, Cham et al., 2020, pp. 173--182, DOI 10.1007/978-3-030-43651-3_14 .

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