Fluctuation-induced mound coarsening in two dimensions

The effects of deposition noise on two-dimensional mound coarsening with slope selection are studied using both continuum and discrete models. Our continuum model may also be considered as a model of two-dimensional polycrystalline growth with a preferred facet orientation. In agreement with recent scaling arguments, we find n=β=13, where n is the mound coarsening exponent and β is the surface roughening exponent. We also find δ=13 where δ is the facet length coarsening exponent. These results are compared with simulation results obtained using a discrete model in which deposition noise and diffusion have been included, but island nucleation and mass transfer between mounds are assumed to be negligible. In the presence of an interfacet diffusion barrier, the surface exhibits a self-affine morphology and Edwards–Wilkinson scaling behavior (β=14) while the average facet length is constant (δ=0). However, in the absence of a barrier to interfacet diffusion, we again find a mound-like morphology and coarsening with n=β=13, while the average facet length increases logarithmically with film thickness. The slow growth of the facet length in this case may also explain the absence of island nucleation in polycrystalline growth. Our results may also be useful in the development of improved continuum and discrete models of polycrystalline growth.