Inter-layer diffusion and motion of adatoms in the vicinity of steps

Kinetic Monte Carlo simulations are extensively used to simulate the aggregation of atoms deposited on a surface during epitaxial growth. In almost all cases the rate constants for the displacements of the adsorbed atoms are guessed with the help of simple rules. Here we use effective medium theory to calculate the activation energies controlling the rates, for Pt atoms deposited on Pt(lll). While the calculations are not highly accurate it is hoped that they represent qualitatively the relative magnitudes of the rates and are an improvement over simple rules (e.g. bond counting) used so far. We calculate the activation energy for a particle that starts on top of an island and descends from it onto the surface on which the island is located. The rate and the mechanism of this process depend on the step type and island size. At one type of the step the particle descends most rapidly from the island by rolling over the edge; at the other it inserts itself into the island by pushing an edge atom away. If the islands are very small the descent rate is very high, since the insertion process takes place with ease. The diffusion of an atom on the terrace towards the island is accelerated as the atom approaches the island, as inferred by Wang and Ehrlich. The diffusion of an atom along the two kinds of island edges differs little from one edge to another. This small difference is, however, essential for explaining why island shape is very sensitive to growth temperature.