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

  • Lev Balykov
  • Vladimir Chalupecky
  • Christof Eck
  • Heike Emmerich
  • Ganeshram Krishnamoorthy
  • Andreas Rätz
  • Axel Voigt


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.


Molecular Beam Epitaxy Epitaxial Growth Screw Dislocation Multiscale Modeling Liquid Phase Epitaxy 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Lev Balykov
    • 4
  • Vladimir Chalupecky
    • 3
  • Christof Eck
    • 1
  • Heike Emmerich
    • 2
  • Ganeshram Krishnamoorthy
    • 2
  • Andreas Rätz
    • 4
  • Axel Voigt
    • 4
    • 5
  1. 1.Institut für Angewandte MathematikUniversität Erlangen-NürnbergErlangen
  2. 2.Computational Materials Engineering, Center for Computational Engineering, Science and Institute of Minerals EngineeringRWTH AachenAachen
  3. 3.Department of Mathematics, Faculty of Nuclear Sciences and Physical EngineeringCzech Technical UniversityCzechoslovakia
  4. 4.Crystal Growth group, research center caesarBonn
  5. 5.Institut für Angewandte MathematikUniversität BonnBonn

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