Finite size effects in nucleation processes

We have used Monte Carlo simulations to study the scaling relations describing submonolayer nucleation N proportional to F-y/D-x theta(z) as a function of system size L (where N is the nucleated island density, D the diffusion coefficient, F the flux rate, a the coverage). For island size distributions that obey scaling, the island density N can be easily related to the step density, S-D. A simple model of critical size cluster i(c)=1 is used. For a given system size L there is a minimum (D/F)(min) ratio where scaling breaks down with x=y=0. These considerations are relevant to systems with low terrace diffusion barrier or small substrate terraces.