Autor(en): | Rätz, Andreas |
Titel: | A new diffuse-interface model for step flow in epitaxial growth |
Sprache (ISO): | en |
Zusammenfassung: | 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. |
URI: | http://hdl.handle.net/2003/29391 http://dx.doi.org/10.17877/DE290R-4705 |
Erscheinungsdatum: | 2012-03-19 |
Enthalten in den Sammlungen: | Preprints der Fakultät für Mathematik |
Dateien zu dieser Ressource:
Datei | Beschreibung | Größe | Format | |
---|---|---|---|---|
mathematicalPreprint-2012-03.pdf | 867.7 kB | Adobe PDF | Öffnen/Anzeigen |
Diese Ressource ist urheberrechtlich geschützt. |
Diese Ressource ist urheberrechtlich geschützt. rightsstatements.org