Effect of small-cluster mobility and dissociation on the island density in epitaxial growth

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Abstract
We suggest that for many systems the epitaxial growth conditions are such that the mobility of small clusters, such as dimers, substantially affects the density of the islands formed by nucleation, while the dissociation of the clusters is less important. We study the effect of small-cluster mobility on the island density formed under epitaxial growth conditions with both rate equations and computer simulations. We find that the scaling derived by Villain, Pimpinelli, Tang, and Wolf from simple rate equations is in agreement with the simulations, if great care is taken to make sure that the system has reached the scaling regime. As an application we suggest a more plausible analysis of some important recent experiments. The scaling equations can be used to extract the activation barriers for monomer and small-cluster diffusion from data on island-density dependence on temperature and deposition rate.