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

In: Analysis, Modeling and Simulation of Multiscale Problems

Author

Listed:
  • 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
    Universität Bonn, Institut für Angewandte Mathematik)

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.

Suggested Citation

  • Lev Balykov & Vladimir Chalupecky & Christof Eck & Heike Emmerich & Ganeshram Krishnamoorthy & Andreas Rätz & Axel Voigt, 2006. "Multiscale Modeling of Epitaxial Growth: From Discrete-Continuum to Continuum Equations," Springer Books, in: Alexander Mielke (ed.), Analysis, Modeling and Simulation of Multiscale Problems, pages 65-85, Springer.
    • Handle: RePEc:spr:sprchp:978-3-540-35657-8_3
    DOI: 10.1007/3-540-35657-6_3
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