WIAS Preprint No. 2787, (2020)

Assessing the quality of the excess chemical potential flux scheme for degenerate semiconductor device simulation


  • Abdel, Dilara
    ORCID: 0000-0003-3477-7881
  • Farrell, Patricio
    ORCID: 0000-0001-9969-6615
  • Fuhrmann, Jürgen
    ORCID: 0000-0003-4432-2434

2010 Mathematics Subject Classification

  • 35Q81 35K57 65N08


  • degenerate semiconductors, drift-diffusion equations, finite volume method, flux discretization, Scharfetter--Gummel scheme




The van Roosbroeck system models current flows in (non-)degenerate semiconductor devices. Focusing on the stationary model, we compare the excess chemical potential discretization scheme, a flux approximation which is based on a modification of the drift term in the current densities, with another state-of-the-art Scharfetter-Gummel scheme, namely the diffusion-enhanced scheme. Physically, the diffusion-enhanced scheme can be interpreted as a flux approximation which modifies the thermal voltage. As a reference solution we consider an implicitly defined integral flux, using Blakemore statistics. The integral flux refers to the exact solution of a local two point boundary value problem for the continuous current density and can be interpreted as a generalized Scharfetter-Gummel scheme. All numerical discretization schemes can be used within a Voronoi finite volume method to simulate charge transport in (non-)degenerate semiconductor devices. The investigation includes the analysis of Taylor expansions, a derivation of error estimates and a visualization of errors in local flux approximations to extend previous discussions. Additionally, drift-diffusion simulations of a p-i-n device are performed.

Appeared in

  • Opt. Quantum Electron., 53 (2021), pp. 163/1--163/10.

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