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dc.contributor.authorRätz, Andreas-
dc.date.accessioned2012-03-19T11:51:33Z-
dc.date.available2012-03-19T11:51:33Z-
dc.date.issued2012-03-19-
dc.identifier.urihttp://hdl.handle.net/2003/29391-
dc.identifier.urihttp://dx.doi.org/10.17877/DE290R-4705-
dc.description.abstractIn this work, we consider epitaxial growth of thin crystalline films. Thereby, we propose a new diffuse-interface approximation of a semi-continuous model resolving atomic distances in the growth direction but being coarse-grained in the lateral directions. Mathematically, this leads to a free boundary problem proposed by Burton, Cabrera and Frank for steps separating terraces of different atomic heights. The evolution of the steps is coupled to a diffusion equation for the adatom (adsorbed atom) concentration fulfilling Robin-type boundary conditions at the steps. Our approach allows to incorporate an Ehrlich-Schwoebel barrier as well as diffusion along step edges into a diffuse-interface model. This model results in a Cahn-Hilliard equation with a degenerate mobility coupled to diffusion equations on the terraces with a diffuse-interface description of the boundary conditions at the steps. We provide a justification by matched asymptotic expansions formally showing the convergence of the diffuse-interface model towards the sharp-interface model as the interface width shrinks to zero. The results of the asymptotic analysis are numerically reproduced by a finite element discretisation.en
dc.language.isoen-
dc.relation.ispartofseriesMathematical Preprints ; 2012-03en
dc.subject.ddc610-
dc.titleA new diffuse-interface model for step flow in epitaxial growthen
dc.typeTextde
dc.type.publicationtypepreprinten
dcterms.accessRightsopen access-
Appears in Collections:Preprints der Fakultät für Mathematik

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