Preprint 40-2014

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

Author(s) : Marion Dziwnik , Andreas Muench , Barbara Wagner

Preprint series of the Institute of Mathematics, Technische Universität Berlin
Preprint 40-2014

MSC 2000

41A60 Asymptotic approximations, asymptotic expansions

76M45 Asymptotic methods, singular perturbations

Abstract :
We propose a phase field model for solid state dewetting where the surface energy is weakly anisotropic. The evolution is based on the Cahn-Hilliard equation with degenerate mobility and 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.

Keywords : phase field model, matched asymptotic expansions, sharp interface model, free boundaries, dewetting solid films