Multiscale Modeling of Epitaxial Growth: From Discrete-Continuum to Continuum Equations

Lev Balykov (), Vladimir Chalupecky (), Christof Eck (), Heike Emmerich (), Ganeshram Krishnamoorthy (), Andreas Rätz () and Axel Voigt ()
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Lev Balykov: Crystal Growth group, research center caesar
Vladimir Chalupecky: Czech Technical University, Department of Mathematics, Faculty of Nuclear Sciences and Physical Engineering
Christof Eck: Universität Erlangen-Nürnberg, Institut für Angewandte Mathematik
Heike Emmerich: RWTH Aachen, Computational Materials Engineering, Center for Computational Engineering, Science and Institute of Minerals Engineering
Ganeshram Krishnamoorthy: RWTH Aachen, Computational Materials Engineering, Center for Computational Engineering, Science and Institute of Minerals Engineering
Andreas Rätz: Crystal Growth group, research center caesar
Axel Voigt: Crystal Growth group, research center caesar

A chapter in Analysis, Modeling and Simulation of Multiscale Problems, 2006, pp 65-85 from Springer

Abstract: Summary Imposed by the crystal lattice, at the surface of a crystal, there exist atomic steps, which separate exposed lattice planes that differ in height by a single lattice spacing. These steps are long-living lattice defects, which make them suitable as a basis for the description of surface morphology on a mesoscopic length scale and thus are an ideal approach to overcome the different length scales, which range from several atoms in lateral direction to micrometers in horizontal direction. This paper summerizes an approach how the thermodynamics and kinetics of atomic steps can be coarse grained to continuum models for the evolving surface. We discuss phase-field approximations to the step dynamics model and apply them to various growth procedures.

Keywords: Molecular Beam Epitaxy; Epitaxial Growth; Screw Dislocation; Multiscale Modeling; Liquid Phase Epitaxy (search for similar items in EconPapers)
Date: 2006
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DOI: 10.1007/3-540-35657-6_3

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