WIAS Preprint No. 2013, (2014)

On thermodynamic consistency of a Scharfetter--Gummel scheme based on a modified thermal voltage for drift-diffusion equations with diffusion enhancement


  • Koprucki, Thomas
    ORCID: 0000-0001-6235-9412
  • Rotundo, Nella
  • Farrell, Patricio
    ORCID: 0000-0001-9969-6615
  • Doan, Duy Hai
  • Fuhrmann, Jürgen
    ORCID: 0000-0003-4432-2434

2010 Mathematics Subject Classification

  • 65N08 35K55


  • Scharfetter--Gummel scheme, thermodynamic consistency, Drift-diffusion equations, non-Boltzmann statistic distributions, diffusion enhancement




Driven by applications like organic semiconductors there is an increased interest in numerical simulations based on drift-diffusion models with arbitrary statistical distribution functions. This requires numerical schemes that preserve qualitative properties of the solutions, such as positivity of densities, dissipativity and consistency with thermodynamic equilibrium. An extension of the Scharfetter-Gummel scheme guaranteeing consistency with thermodynamic equilibrium is studied. It is derived by replacing the thermal voltage with an averaged diffusion enhancement for which we provide a new explicit formula. This approach avoids solving the costly local nonlinear equations defining the current for generalized Scharfetter-Gummel schemes.

Appeared in

  • Opt. Quantum Electron., 47 (2015) pp. 1327--1332.

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