Rätz, Andreas2012-03-192012-03-192012-03-19http://hdl.handle.net/2003/2939110.17877/DE290R-4705In 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.enMathematical Preprints ; 2012-03610preprint