Fluctuation-induced mound coarsening in two dimensions

The e/ects 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 3nd n = � = 1 , where n is the mound coarsening exponent andis the surface roughening exponent. We also 3nd � = 1 whereis the facet length coarsening exponent. These results are compared with simulation results obtained using a discrete model in which deposition noise and di/usion have been included, but island nucleation and mass transfer between mounds are assumed to be negligible. In the presence of an interfacet di/usion barrier, the surface exhibits a self-a6ne morphology and Edwards-Wilkinson scaling behavior (� = 1 ) while the average facet length is constant (� = 0). However, inthe absen ce of a barrier to interfacet di/usion, we again 3nd a mound-like morphology and coarsening with n = � = 1 , while the average facet length increases logarithmically with 3lm 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. c