Abstract
We consider a step flow model for epitaxial growth, as proposed by Burton, Cabrera and Frank [3]. This type of model is discrete in the growth direction but continuous in the lateral directions. The effect of the Ehrlich-Schwoebel barrier, which limits the attachment rate of adatoms to a step from an upper terrace, is included. Mathematically, this model is a dynamic free boundary problem for the steps. In [6], we proposed a diffuse-interface approximation which reproduces an arbitrary Ehrlich-Schwoebel barrier. It is a version of the Cahn-Hilliard equation with variable mobility.
In this paper, we propose a discretisation for this diffuse-interface approximation. Our approach is guided by the fact that the diffuse-interface approximation has a conserved quantity and a Liapunov functional. We are lead to an implicit finite volume discretisation of symmetric structure.
We test the discretisation by comparison with the matched asymptotic analysis carried out in [6]. We also test the diffuse-interface approximation itself by comparison with theoretically known features of the original free boundary problem. More precisely, we investigate quantitatively the phenomena of step bunching and the Bales-Zangwill instability.
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© 2005 Birkhäuser Verlag Basel/Switzerland
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Otto, F., Penzler, P., Rump, T. (2005). Discretisation and Numerical Tests of a Diffuse-Interface Model with Ehrlich-Schwoebel Barrier. In: Voigt, A. (eds) Multiscale Modeling in Epitaxial Growth. ISNM International Series of Numerical Mathematics, vol 149. Birkhäuser Basel. https://doi.org/10.1007/3-7643-7343-1_9
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DOI: https://doi.org/10.1007/3-7643-7343-1_9
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