Phase field model of stress-induced surface instabilities: Surface diffusion

We present a phase field model for the surface corrugation of elastically stressed films where the surface diffusion is a dominant mass-transport mechanism. The conserved order parameter is used to describe the state of system and the phase mobility is defined as a function of the order parameter in order to make the mass transport occur only in interfacial regions. We conduct the matched asymptotic expansion analysis and demonstrate that our phase field model reduces to the before-existing sharp interface model of the Asaro–Tiller–Grinfeld instability in the sharp interface limit. By performing the two-dimensional numerical stability analysis, the model is verified to reproduce the instability of elastically stressed surface and have a same dependency with the results of linear-stability analysis.