Effects of cluster diffusion on the island density and size distribution in submonolayer island growth

The effects of cluster diffusion on the submonolayer island density and island-size distribution are studied for the case of irreversible growth of compact islands on a 2D substrate. In our model we assume instantaneous coalescence of circular islands, while the cluster mobility is assumed to exhibit power-law decay as a function of island size with exponent μ. Results are presented for μ=1/2,1, and 3/2 corresponding to cluster diffusion via Brownian motion, correlated evaporation condensation, and edge diffusion respectively, as well as for higher values including μ=2,3, and 6. We also compare our results with those obtained in the limit of no cluster mobility (μ=∞). In agreement with theoretical predictions of power-law behavior of the island-size distribution (ISD) for μ<1, for μ=1/2 we find N(s)(θ)~s(-τ) [where N(s)(θ) is the number of islands of size s at coverage θ] up to a crossover island-size S(c). However, the value of the exponent τ obtained in our simulations is higher than the mean-field (MF) prediction τ=(3-μ)/2. Similarly, the measured value of the exponent ζ corresponding to the dependence of S(c) on the average island-size S (e.g., S(c)~S(ζ)) is also significantly higher than the MF prediction ζ=2/(μ+1). A generalized scaling form for the ISD [N(s)(θ)=θ/S(1+τζ)f(s/S(ζ))] is also proposed for μ<1, and using this form excellent scaling is found for μ=1/2. However, for finite μ≥1 neither the generalized scaling form nor the standard scaling form N(s)(θ)=θ/S(2)f(s/S) lead to scaling of the entire ISD for finite values of the ratio R of the monomer diffusion rate to deposition flux. Instead, the scaled ISD becomes more sharply peaked with increasing R and coverage. This is in contrast to models of epitaxial growth with limited cluster mobility for which good scaling occurs over a wide range of coverages.