Capture zones and scaling in homogeneous thin-film growth

The capture zones for the islands in homogeneous thin-film growth simulations are studied. A complete condensation limit is used for the growth of dendritic and circular islands. The critical island sizes examined are i=1 in the former and i=1,2,3 in the latter case. It is found that the capture zones show scaling over all of the conditions and substrate coverages studied. In the high-temperature (i>~1) regime this leads to the scaling of the island sizes themselves, and enables a semiempirical functional form derived for Voronoi networks to be assigned to the size distribution. In the low-temperature (i=1) regime the island size scaling with substrate coverage is only approximate and coincidental. These results show good agreement with previously published data from both experimental and computational studies.