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Title: Comparison of thermodynamically consistent charge carrier flux discretizations for Fermi-Dirac and Gauss-Fermi statistics
Authors: Farrell, PatricioPatriarca, MatteoFuhrmann, JürgenKoprucki, Thomas
Publishers Version: https://doi.org/10.20347/WIAS.PREPRINT.2424
Issue Date: 2017
Published in: Preprint / Weierstraß-Institut für Angewandte Analysis und Stochastik , Volume 2424, ISSN 2198-5855
Publisher: Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik
Abstract: We compare three thermodynamically consistent ScharfetterGummel schemes for different distribution functions for the carrier densities, including the FermiDirac integral of order 1/2 and the GaussFermi integral. The most accurate (but unfortunately also most costly) generalized ScharfetterGummel scheme requires the solution of an integral equation. We propose a new method to solve this integral equation numerically based on Gauss quadrature and Newtons method. We discuss the quality of this approximation and plot the resulting currents for FermiDirac and GaussFermi statistics. Finally, by comparing two modified (diffusion-enhanced and inverse activity based) ScharfetterGummel schemes with the more accurate generalized scheme, we show that the diffusion-enhanced ansatz leads to considerably lower flux errors, confirming previous results (J. Comp. Phys. 346:497-513, 2017).
Keywords: Scharfetter–Gummel schemes; (organic) semiconductors; nonlinear diffusion; thermodynamic consistency; finite volume scheme; Gauss–Fermi integral; Fermi–Dirac integral
DDC: 510
License: 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.
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Appears in Collections:Mathematik



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