Analytical versus numerical approaches to the kinetics of cluster impingement in thin-film nucleation at solid surfaces

The kinetics of the island density in thin-film growth by simultaneous nucleation has been evaluated through a computer simulation. The numerical output is found to be in close agreement with the kinetics of cluster impingement previously computed by an analytical approach. The comparison between the analytical and the numerical results confirms that the 'collision series', summed up to the fourth term, is a good approximation of the collision series, namely of the impingement kinetics of the clusters. The numerical result has been used, within an approximate rate equation scheme, for determining the island density in the entire range of surface coverage for non-simultaneous nucleation.