Capture-zone areas in submonolayer nucleation: effects of dimensionality and short-range interactions

Simulation results for the asymptotic scaled capture-zone distribution (CZD) for the case of irreversible nucleation and growth of point islands are presented for substrate dimension d=1 , 2, 3, and 4 and compared with a recent conjecture based on the Wigner distribution. Poor agreement is found between the predicted Wigner distributions and the asymptotic CZD in the limit of infinite DF (corresponding to the ratio of monomer hopping rate D to deposition rate F ). Our results also indicate that for d=2 and 3 the asymptotic CZD for point islands is independent of model details and dimension. However, for d=1 and d=4 the resulting distribution is significantly more sharply peaked. We also find that in contrast to the island-size distribution, for which mean-field-like behavior is observed in d=3 and above, the asymptotic CZD is significantly broadened by fluctuations even in d=4 .