Coarsening of elastically stressed, strongly anisotropic driven thin films

A diffuse interface model is developed to investigate the growth and coarsening in driven thin films under the influence of strong surface energy anisotropy, misfit strain, mass deposition, and diffusion. Two high-order regularizations are used to remove the ill-posedness introduced by the strong anisotropy: a Willmore (or bending energy) regularization and a simplified linear regularization. For similar effective growth rates and regularization strengths, the two regularizations undergo similar dynamics and coarsening, as peaks (antikinks) and valleys (kinks) of the corrugated surface are removed as the film grows. Competition among the influence of elastic strains, surface energy anisotropy and the rate of deposition lead to a change in the coarsening events compared to that observed in unstressed thin films. As the rate of deposition is increased, the primary coarsening events change from a combination of both antikink-ternary and binary events at low deposition rates, to binary events at moderate rates, and finally to kink-ternary events at high rates. The kink-ternary events are the only coarsening events observed in growing unstressed films at all deposition rates. Accordingly, the coarsening dynamics of two-dimensional (2D) stressed films is much faster than for unstressed films at low deposition rates. In addition, deep grooves may form in the film due to the Asaro-Tiller-Grinfeld instability and may lead to the breakup of the film into islands. At higher deposition rates, the evolution of stressed films is found to become limited by the surface energy anisotropy and the regularizations, which inhibits groove formation. The corresponding coarsening events and rates then tend toward those observed in unstressed films. Preliminary results of 3D thin films indicate that coarsening processes in elastically stressed films are also much faster than their unstressed counterparts at low deposition rates. In three dimensions, however, the coarsening events are also found to involve saddles.