This document may be downloaded, read, stored and printed for your own use within the limits of § 53 UrhG but it may not be distributed via the internet or passed on to external parties.Dieses Dokument darf im Rahmen von § 53 UrhG zum eigenen Gebrauch kostenfrei heruntergeladen, gelesen, gespeichert und ausgedruckt, aber nicht im Internet bereitgestellt oder an Außenstehende weitergegeben werden.Koprucki, ThomasGärtner, Klaus2016-03-242019-06-2820120946-8633https://doi.org/10.34657/2258https://oa.tib.eu/renate/handle/123456789/3138Inspired 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 F(n)=1/(exp(-n)+y). 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 functionsapplication/pdfeng510Generalized Einstein relationgeneralized Scharfetter-Gummel schemedrift-diffusion equationsnon-Boltzmann statistic distributionsdiffusion enhancementReport