Homogenization and two-scale models for liquid phase epitaxy |
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Authors: | Ch Eck and H Emmerich |
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Institution: | 1.IANS, University of Stuttgart,Stuttgart,Germany;2.CME/GHI, RWTH Aachen University,Aachen,Germany |
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Abstract: | We consider models for liquid phase epitaxy without and with elasticity. The models are based on continuum models for fluid
flow and transport of adatoms in the liquid solution and a BCF–model for the growth of the solid phase. Using homogenization
by formal asymptotic expansion, we obtain two–scale models that are appropriate to describe the evolution of microstructures
in the solid phase for processes of technically relevant macroscopic length scales. The two–scale models consist of macroscopic
equations for fluid flow and solute transport in the liquid and microscopic cell problems for the growth and elastic deformation
of the solid. For the case without elasticity and a phase field approximation of the BCF–model, an estimate of the model error
is presented. |
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Keywords: | |
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