In this paper, we present a detailed exposition of the functional form of capture numbers that we found using an extended-island model. Our results suggest that the assumption ${\sigma }_s={\sigma }_1$ for all s is only valid up to a time that scales like ${O(R}^{-1/2}).\mathrm{}$ After this time, a better approximation is ${\sigma }_s=as+b+\mathrm{small}$ correction and we show that in the limit $\overrightarrow{R}\infty ,$ ${\sigma }_s\to as+b.\mathrm{}$ We link the functional form to the amount of nucleation of new islands on the surface and explain the differences between what is obtained with our extended-island model to what is obtained with a point-island model. Finally, we use our results to derive scaling laws for the adatom and total number densities. We found that the scaling in R remains unchanged, but that the time evolution is influenced by the functional form of the capture numbers.

• Received 15 April 2002

DOI:https://doi.org/10.1103/PhysRevB.67.155403