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Discretization scheme for drift-diffusion equations with strong diffusion enhancement

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Abstract

Inspired by organic semiconductor models based on hopping transport introducing Gauss-Fermi integrals a nonlinear generalization of the classical Scharfetter–Gummel scheme is derived for the distribution function \(\mathcal F_\gamma (\eta ) = 1/(\exp (-\eta )+\gamma )\). This function provides an approximation of the Fermi-Dirac integrals of different order and restricted argument ranges. The scheme requires the solution of a nonlinear equation per edge and continuity equation to calculate the edge currents. In the current formula the density-dependent diffusion enhancement factor, resulting from the generalized Einstein relation, shows up as a weighting factor. Additionally the current modifies the argument of the Bernoulli functions.

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Acknowledgments

The work of Th. Koprucki has been supported by the Deutsche Forschungsgemeinschaft (DFG) within the collaborative research center 787 “Semiconductor Nanophotonics”, project B4 “Multi-dimensional modelling and simulation of VCSELs”.

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  1. Weierstrass Institute (WIAS), Mohrenstr. 39, 10117 , Berlin, Germany

    Thomas Koprucki & Klaus Gärtner

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  1. Thomas Koprucki
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  2. Klaus Gärtner
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Correspondence to Thomas Koprucki.

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Koprucki, T., Gärtner, K. Discretization scheme for drift-diffusion equations with strong diffusion enhancement. Opt Quant Electron 45, 791–796 (2013). https://doi.org/10.1007/s11082-013-9673-5

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  • DOI: https://doi.org/10.1007/s11082-013-9673-5

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