Quantitative characterization of the mesoscopic surface roughness in a growing island film

A quantitative description of mesoscopic surface roughness generated in thin film growing via 3D island mechanism is presented. Analysis is based on the statistical model of a random nucleation and growth of hemispherical islands accounting for their collisions at late stages. Analytical expressions for a number of surface relief parameters: the rms roughness, the roughness coefficient, the surface height (depth) distribution and the package density factor providing a rather complete quantitative description of the evolving surface morphology during growth process in different condensation regimes are derived. It is shown that the surface height distribution is a non-Gaussian with a negative skewness and that the rms roughness and the roughness coefficient kinetics can be represented as a universal (independent of a condensation regime) unimodal function of either coverage or film thickness with a maximum just prior the completed film formation. The non-monotonic surface roughness dynamics in a growth process predicted by the model is consistent with experimental data.