DC FieldValueLanguage
dc.contributor.authorFarrell, Patricio-
dc.contributor.authorPeschka, Dirk-
dc.date.accessioned2021-11-09T11:13:53Z-
dc.date.available2021-11-09T11:13:53Z-
dc.date.issued2019-12-15-
dc.identifier.citationComputers and Mathematics with Applications 78 (12): 3731-3747 (2019-12-15)de_DE
dc.identifier.issn0898-1221de_DE
dc.identifier.urihttp://hdl.handle.net/11420/10848-
dc.description.abstractWe 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.en
dc.language.isoende_DE
dc.relation.ispartofComputers and mathematics with applicationsde_DE
dc.subjectConvergence orderde_DE
dc.subjectFinite element methodde_DE
dc.subjectFinite volume methodde_DE
dc.subjectNonlinear diffusion and diffusion enhancementde_DE
dc.subjectScharfetter–Gummel schemede_DE
dc.subjectVan Roosbroeck system for semiconductorsde_DE
dc.titleNonlinear diffusion, boundary layers and nonsmoothness: Analysis of challenges in drift–diffusion semiconductor simulationsde_DE
dc.typeArticlede_DE
dc.type.diniarticle-
dcterms.DCMITypeText-
tuhh.abstract.englishWe 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.de_DE
tuhh.publisher.doi10.1016/j.camwa.2019.06.007-
tuhh.publication.instituteMathematik E-10de_DE
tuhh.type.opus(wissenschaftlicher) Artikel-
dc.type.driverarticle-
dc.type.casraiJournal Article-
tuhh.container.issue12de_DE
tuhh.container.volume78de_DE
tuhh.container.startpage3731de_DE
tuhh.container.endpage3747de_DE
dc.identifier.scopus2-s2.0-85067271720-
datacite.resourceTypeJournal Article-
datacite.resourceTypeGeneralText-
item.grantfulltextnone-
item.openairecristypehttp://purl.org/coar/resource_type/c_6501-
item.creatorGNDFarrell, Patricio-
item.creatorGNDPeschka, Dirk-
item.openairetypeArticle-
item.fulltextNo Fulltext-
item.cerifentitytypePublications-
item.creatorOrcidFarrell, Patricio-
item.creatorOrcidPeschka, Dirk-
item.languageiso639-1en-
item.mappedtypeArticle-
crisitem.author.deptMathematik E-10-
crisitem.author.orcid0000-0001-9969-6615-
crisitem.author.orcid0000-0002-3047-1140-
crisitem.author.parentorgStudiendekanat Elektrotechnik, Informatik und Mathematik-
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