Geometric evolution law for modeling strongly anisotropic thin-film morphology.

The morphology of the solid-vapor interface of a nanoscale thin crystalline film is influenced by many factors including surface diffusion, attachment-detachment, deposition, and interface kinetics. Using a high-order accurate and efficient numerical method, we investigate the dynamics of two dimensional thin films when all of these effects are considered. The observed morphologies consist of facets of constant slope separated by narrow transition intervals: kinks (valleys) and antikinks (hills). The number of kinks and antikinks decreases as the system coarsens in time. Our numerical results confirm that when deposition is present, the only possible coarsening event is the kink-ternary where two kinks meet and annihilate an antikink. We characterize the total amount of coarsening, the time over which the coarsening occurs and the associated coarsening scaling laws when all effects are considered. As found in previous work that considered only attachment-detachment, or surface diffusion, there are three distinct coarsening regimes associated with increasing magnitudes of the deposition flux-fast coarsening, a regime in which periodic structures form with little or no subsequent coarsening, and a regime in which the film surface evolves chaotically. We find that the inclusion of attachment-detachment leads to additional coarsening compared to the dynamics that result from driven surface diffusion alone. When deposition and interface kinetics are both considered, the slowdown of evolution caused by the kinetic effects necessitates a decrease in the deposition flux in order to produce a nonchaotic coarsening regime. Together, these provide testable predictions for experiments of thin-film dynamics.