WIAS Preprint No. 2048, (2014)

A phase-field model for solid-state dewetting and its sharp-interface limit



Authors

  • Dziwnik, Marion
  • Münch, Andreas
  • Wagner, Barbara

2010 Mathematics Subject Classification

  • 34E13 74N20 74E10

Keywords

  • phase-field model, matched asymptotic expansions, sharp interface model, free boundaries, dewetting solid films

Abstract

We propose a phase field model for solid state dewetting in form of a Cahn-Hilliard equation with weakly anisotropic surface energy and a degenerate mobility together with a free boundary condition at the film-substrate contact line. We derive the corresponding sharp interface limit via matched asymptotic analysis involving multiple inner layers. The resulting sharp interface model is consistent with the pure surface diffusion model. In addition, we show that the natural boundary conditions, as indicated from the first variation of the total free energy, imply a contact angle condition for the dewetting front, which, in the isotropic case, is consistent with the well-known Young's equation.

Appeared in

  • Nonlinearity 30 (2017) pp. 1465-1496, changed title: An anisotropic phase-field model...

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