Noise-assisted mound coarsening in epitaxial growth

Two types of mechanisms are proposed for mound coarsening during unstable epitaxial growth: stochastic, due to deposition noise, and deterministic, due to mass currents driven by surface energy differences. Both yield the relation $H=(RWL)^2$ between the typical mound height W, mound size L, and the film thickness H. An analysis of simulations and experimental data shows that the parameter R saturates to a value which discriminates sharply between stochastic ($R\simeq1$) and deterministic ($R\ll 1$) coarsening. We derive a scaling relation between the coarsening exponent 1/z and the mound-height exponent β which, for a saturated mound slope, yields $\beta=1/z=1/4$