Models for diffusion and island growth in metal monolayers
A model that describes self diffusion, island nucleation and film growth on FCC(001) metal substrates is presented. The parameters of the model are optimized to describe Cu diffusion on Cu(001), by comparing activation energy barriers to a full set of barriers obtained from semi-empirical potentials via the embedded atom method. It is found that this model (model I), with only three parameters, provides a very good description of the full landscape of hopping energy barriers. These energy barriers are grouped in four main peaks. A reduced model (model II) with only two parameters, is also presented, in which each peak is collapsed into a single energy value. From the results of our simulations, we find that this model still maintains the essential features of diffusion and growth on this model surface. We find that hopping rates along island edges are much higher than for isolated atoms (giving rise to compact island shapes) and that vacancy mobility is higher than adatom mobility. We observe substantial dimer mobility (comparable to the single atom mobility) as well as some mobility of trimers. Mobility of small islands affects the scaling of island density $N$ vs. deposition rate $F$, $N ~ F^γ$, as well as the island size distribution. In the asymptotic limit of slow deposition, scaling arguments and rate equations show that $γ= i*/(2 i* + 1)$ where $i*$ is the size of the largest mobile island. Our Monte Carlo results, obtained for a range of experimentally relevant conditions, show $γ= 0.32$ for the EAM, 0.33 for model I and 0.31 for model II barriers. These results are lower than the anticipated $γ>= 0.4$ due to dimer (and trimer) mobility.