Monte Carlo study of the step flow to island nucleation transition for close packed structures

Using joined super-lattice Kinetic Monte Carlo and continuous simulations we study the transition between step flow and two-dimensional island nucleation growth on stepped surfaces for close packed crystalline structures. The numerical analysis is performed in terms of misorientation cut, deposition rate and temperature. We compare the results of the atomistic approach with the predictions of the standard and generalized Burton-Cabrera-Frank (BCF) continuous model. The generalization consists in the explicit inclusion in the theory of the formation and dissolution of mobile dimers on the terraces. We show that the BCF-like continuous theories break down for low temperatures, large off-angle cuts and high deposition rates. In view of these results we critically discuss the basic assumptions of the continuous models.