Phase-field modeling of epitaxial growth: Applications to step trains and island dynamics

In this paper, we present a new phase-field model including combined effects of edge diffusion, the Ehrlich–Schwoebel barrier, deposition and desorption to simulate epitaxial growth. A new free energy function together with a correction to the initial phase variable profile is used to efficiently capture the morphological evolution when a large deposition flux is imposed. A formal matched asymptotic analysis is performed to show the reduction of the phase-field model to the classical sharp interface Burton–Cabrera–Frank model for step flow when the interfacial thickness vanishes. The phase-field model is solved by a semi-implicit finite difference scheme, and adaptive block-structured Cartesian meshes are used to dramatically increase the efficiency of the solver. The numerical scheme is used to investigate the evolution of perturbed circularly shaped small islands. The effect of edge diffusion is investigated together with the Ehrlich–Schwoebel barrier. We also investigate the linear and nonlinear regimes of a step meandering instability. We reproduce the predicted scaling law for the growth of the meander amplitude, which was based on an analysis of a long wavelength regime. New nonlinear behavior is observed when the meander wavelength is comparable to the terrace width. In particular, a previously unobserved regime of coarsening dynamics is found to occur when the meander wavelength is comparable to the terrace width.

► A new phase field model is given, consistent with classical models of epitaxy. ► Edge diffusion, Ehrlich–Schwoebel barrier, deposition, desorption are investigated. ► A new dynamical regime occurs when meander wavelength is comparable to terrace width. ► The deposition flux is used to control the shape of a growing island.