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Islands in the Stream: Electromigration-Driven Shape Evolution with Crystal Anisotropy

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Multiscale Modeling in Epitaxial Growth

Part of the book series: ISNM International Series of Numerical Mathematics ((ISNM,volume 149))

Abstract

We consider the shape evolution of two-dimensional islands on a crystal surface in the regime where mass transport is exclusively along the island edge. A directed mass current due to surface electromigration causes the island to migrate in the direction of the force. Stationary shapes in the presence of an anisotropic edge mobility can be computed analytically when the capillary effects of the line tension of the island edge are neglected, and conditions for the existence of non-singular stationary shapes can be formulated. In particular, we analyse the dependence of the direction of island migration on the relative orientation of the electric field to the crystal anisotropy, and we show that no stationary shapes exist when the number of symmetry axes is odd. The full problem including line tension is solved by time-dependent numerical integration of the sharp-interface model. In addition to stationary shapes and shape instability leading to island breakup, we also find a regime where the shape displays periodic oscillations.

This work was supported by DFG within SFB 616 Energiedissipation an Oberflächen.

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Author information

Authors and Affiliations

  1. Fachbereich Physik, Universität Duisburg-Essen, D-45117, Essen, Germany

    Philipp Kuhn

  2. Institut für Theoretische Physik, Universität zu Köln, Zülpicher Strasse 77, D-50937, Köln, Germany

    Joachim Krug

Authors
  1. Philipp Kuhn
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  2. Joachim Krug
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Editor information

Editors and Affiliations

  1. Crystal Growth group, research center caesar, Ludwig-Erhard-Allee 2, D-53175, Bonn, Germany

    Axel Voigt

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© 2005 Birkhäuser Verlag Basel/Switzerland

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Kuhn, P., Krug, J. (2005). Islands in the Stream: Electromigration-Driven Shape Evolution with Crystal Anisotropy. In: Voigt, A. (eds) Multiscale Modeling in Epitaxial Growth. ISNM International Series of Numerical Mathematics, vol 149. Birkhäuser Basel. https://doi.org/10.1007/3-7643-7343-1_10

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