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combination of processes with nucleation dominating at high hit rates. This is analogous to the ( N − 1) Y + X → C$_{N}$ process in the mean-field model. The point of crossover between the regimes increases with increasing critical size and corresponds to a roughening transition as is illustrated in Fig. 4b. Note that for the smallest critical cluster size, the transition region is too small to see in this figure. For critical clusters larger than 2 and for small supersaturations, the roughness is virtually independent of the critical cluster size and increases slowly with the supersaturation while at higher supersaturation, the transition to the rapid growth regime is also signaled by a dramatic increase in roughness. 

Finally, Fig. 5 shows the growth rate when no defect is present. The main difference from the previous results is that at low supersaturations, the growth rate is very small since growth only occurs after the nucleation of a super-critical cluster. Once such a cluster forms, the growth of a new layer of crystal is quite rapid so that the overall growth rate is dominated by the nucleation rate. Nevertheless, a clear crossover from this slow growth regime, where most mass is added by step growth, to a fast regime, where nucleation plays an important role in adding mass, is evident. 

