Comparison of Scharfetter-Gummel Flux Discretizations Under Blakemore Statistics

  • Patricio Farrell
  • Thomas Koprucki
  • Jürgen Fuhrmann
Conference paper
Part of the Mathematics in Industry book series (MATHINDUSTRY, volume 26)


We discretize the semiconductor device equations assuming a Blakemore distribution function using a finite volume scheme and compare three thermodynamically consistent Scharfetter-Gummel type flux discretizations, namely the exact solution to a two-point boundary value probem and two fluxes incorporating certain averages. In order to do this, we simulate an n-i-n semiconductor device and study the electron densities as well as the total current. While the diffusion-enhanced flux approximation using logarithmic averaging of the nonlinear diffusion enhancement behaves somewhat similarly to the exact solution of the two-point boundary value problem (the generalized Scharfetter-Gummel scheme), the scheme based on averaging the inverse activity coefficients scheme exhibits a noticeably different behavior.


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Copyright information

© Springer International Publishing AG, part of Springer Nature 2017

Authors and Affiliations

  • Patricio Farrell
    • 1
  • Thomas Koprucki
    • 1
  • Jürgen Fuhrmann
    • 1
  1. 1.Weierstrass Institute (WIAS)BerlinGermany

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