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 D∕F (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.