Dynamics of nanoscale pattern formation of an epitaxial monolayer

A two-phase monolayer grown on an elastic substrate may form stripes or dots on the scale of nanometers. Sometimes these stripes and dots order into superlattices. This paper reports on a simulation on the basis of a model proposed by the authors recently. The size selection and spatial ordering result from two competing actions: the phase boundary energy tends to coarsen the phases, and the concentration-dependent surface stress tends to refine the phases. A nonlinear diffusion equation couples the concentration field in the epilayer and the stress field in the substrate. The simulation reveals remarkably rich dynamics. An epilayer may evolve into various patterns, suggesting a significant degree of experimental control in growing nanoscale superlattices, just as in growing atomic crystals.