Stochastic nucleation and growth of islands on surfaces with the theory of non-classical nucleation

In order to study the irreversible growth and dynamics of islands on surfaces in metal-on (1 0 0) metal homoepitaxy at low temperatures and small coverage, a stochastic element in the theory of non-classical nucleation is introduced. The order parameter is the fractional change in the mass density σ=(ρ−ρ₀)/ρ₀ of the system. The local and non-local free energy densities are functionals of σ. The size distribution of the islands is extracted and compared with the experimental distribution and with the distribution obtained from other simulations. The time dependence of the average island size is also studied. The results are in relatively good agreement with the experimental results and with the results obtained from other simulations.