Epitaxial growth kinetics in the presence of an Ehrlich–Schwoebel barrier: comparative analysis of different models

In the last years, much theoretical effort has been devoted to the effects of the Ehrlich–Schwoebel (ES) step-edge barrier to interlayer diffusion on epitaxial growth. In a number of models, in a frame of the rate equation approach the expressions for critical island size for second-layer nucleation have been derived and various growth mode transitions, induced by the ES barrier, have been revealed, and corresponding ‘phase diagrams’ of the growth mode in a parameter space have been constructed. The application of these models to the experimental data has been shown to result in the reasonable estimates of the ES barrier. However, in just published papers by employing kinetic MC simulations and theory, based on a concept of the residence time of an adatom on top of an island and simple statistical arguments, the expressions for critical island size and nucleation rate differing from that of the rate equation approach, have been obtained and it has been remarked that the applicability of mean field rate equations to the confined geometry on top of a small island is not obvious. This article presents a comparative analysis and reconsideration of the rate equation-based models in view of these critical comments that shows that these models are valid at least in a range of weak ES barriers where the most interesting growth phenomena are developed.