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Statistics of adatom diffusion in a model of thin film growth

We study the statistics of the number of executed hops of adatoms at the surface of films grown with the Clarke-Vvedensky (CV) model in simple cubic lattices. The distributions of this number, $N$, are determined in films with average thicknesses close to $50$ and $100$ monolayers for a broad range of values of the diffusion-to-deposition ratio $R$ and of the probability $ε$ that lowers the diffusion coefficient for each lateral neighbor. The mobility of subsurface atoms and the energy barriers for crossing step edges are neglected. Simulations show that the adatoms execute uncorrelated diffusion during the time in which they move on the film surface. In a low temperature regime, typically with $Rε\lesssim 1$, the attachment to lateral neighbors is almost irreversible, the average number of hops scales as $\langle N\rangle \sim R^{0.38\pm 0.01}$, and the distribution of that number decays approximately as $\exp\left[-\left({N/\langle N\rangle}\right)^{0.80\pm 0.07}\right]$. Similar decay is observed in simulations of random walks in a plane with randomly distributed absorbing traps and the estimated relation between $\langle N\rangle$ and the density of terrace steps is similar to that observed in the trapping problem, which provides a conceptual explanation of that regime. As the temperature increases, $\langle N\rangle$ crosses over to another regime when $Rε^{3.0\pm 0.3}\sim 1$, which indicates high mobility of all adatoms at terrace borders. The distributions $P\left( N\right)$ change to simple exponential decays, due to the constant probability for an adatom to become immobile after being covered by a new deposited layer. At higher temperatures, the surfaces become very smooth and $\langle N\rangle \sim Rε^{1.85\pm 0.15}$, which is explained by an analogy with submonolayer growth.