Self-organized nanostructures in multi-phase epilayers

Recent experiments have shown that multi-phase epilayers may self-organize into ordered nanoscale patterns on a solid substrate. In this paper, we present a phase field model for the self-assembly of three-phase epilayers. Nanoscale patterns are developed by two competing actions: coarsening due to phase boundary energy and refining due to substrate-mediated elastic interaction. The continuum phase field approach leads to a set of nonlinear diffusion equations, which couples the two concentration fields in the epilayer and the stress field in the substrate. Numerical simulations reveal remarkably rich dynamics in the self-assembly of multi-phase epilayers. An epilayer may evolve into various patterns, suggesting a significant degree of experimental control in growing nanoscale structures.