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Erschienen in:
01.07.2013
Discretization scheme for drift-diffusion equations with strong diffusion enhancement
Erschienen in: Optical and Quantum Electronics | Ausgabe 7/2013
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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.