A new diffuse-interface model for step flow in epitaxial growth
| dc.contributor.author | Rätz, Andreas | |
| dc.date.accessioned | 2012-03-19T11:51:33Z | |
| dc.date.available | 2012-03-19T11:51:33Z | |
| dc.date.issued | 2012-03-19 | |
| dc.description.abstract | In 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.identifier.uri | http://hdl.handle.net/2003/29391 | |
| dc.identifier.uri | http://dx.doi.org/10.17877/DE290R-4705 | |
| dc.language.iso | en | |
| dc.relation.ispartofseries | Mathematical Preprints ; 2012-03 | en |
| dc.subject.ddc | 610 | |
| dc.title | A new diffuse-interface model for step flow in epitaxial growth | en |
| dc.type | Text | de |
| dc.type.publicationtype | preprint | en |
| dcterms.accessRights | open access |