Growth kinetics in a strained crystal film on a wavy patterned substrate

We study the combination of the Asaro-Tiller-Grinfeld morphological instability of a strained film and the organizing effect of an underlying patterned substrate. We use a continuum description of surface diffusion accounting for elasticity, surface energy and wetting interactions. We solve both the mechanical equilibrium and the growth dynamics during annealing at linear order in the film modulation amplitude. We characterize the kinetic phase diagram as a function of time, the film thickness and the ratio between the substrate and the instability wavelengths. We find that the film surface can skip from a configuration in phase with the substrate to either an out-of-phase or a non-ordered configuration, depending on the pattern wavelength and annealing time.