Farrell, PatricioPatricioFarrellPeschka, DirkDirkPeschka2021-11-092021-11-092019-12-15Computers and Mathematics with Applications 78 (12): 3731-3747 (2019-12-15)http://hdl.handle.net/11420/10848We study different discretizations of the van Roosbroeck system for charge transport in bulk semiconductor devices that can handle nonlinear diffusion. Three common challenges corrupting the precision of numerical solutions will be discussed: boundary layers, discontinuities in the doping profile, and corner singularities in L-shaped domains. We analyze and benchmark the error and the convergence order of finite difference, finite-element as well as advanced Scharfetter–Gummel type finite-volume discretization schemes. The most problematic of these challenges are boundary layers in the quasi-Fermi potentials near ohmic contacts, which can have a drastic impact on the convergence order. Using a novel formal asymptotic expansion, our theoretical analysis reveals that these boundary layers are logarithmic and significantly shorter than the Debye length.en0898-122120191237313747Convergence orderFinite element methodFinite volume methodNonlinear diffusion and diffusion enhancementScharfetter–Gummel schemeVan Roosbroeck system for semiconductorsJournal Article10.1016/j.camwa.2019.06.007Other