Browsing by Author "Kutter, Michael"

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    A two scale model for liquid phase epitaxy with elasticity
    (2015) Kutter, Michael; Rohde, Christian (Prof. Dr.)
    Epitaxy, a special form of crystal growth, is a technically relevant process for the production of thin films and layers. It gives the possibility to generate microstructures of different morphologies, such as steps, spirals or pyramids. These microstructures are influenced by elastic effects in the epitaxial layer. There are different epitaxial techniques, one is the so-called liquid phase epitaxy. Thereby, single particles are deposited out of a supersaturated liquid solution on a substrate where they contribute to the growth process. The thesis studies a two scale model including elasticity, introduced in [Ch.Eck, H.Emmerich. Liquid-phase epitaxy with elasticity. Preprint 197, DFG SPP 1095, 2006]. It consists of a macroscopic Navier-Stokes system and a macroscopic convection-diffusion equation for the transport of matter in the liquid, and a microscopic problem that combines a phase field approximation of a Burton-Cabrera-Frank model for the evolution of the epitaxial layer, a Stokes system for the fluid flow near the layer and an elasticity system for the elastic deformation of the solid film. Suitable conditions couple the single parts of the model. As main result, existence and uniqueness of a solution is proven in suitable function spaces. Furthermore, an iterative solving procedure is proposed, which reflects on the one hand the strategy of the proof of the main result via fixed point arguments and, on the other hand, can be a basis for an numerical algorithm.