Kinetics of nucleation in surfactant-mediated epitaxy

The theory of atomistic nucleation is developed to account for the presence of surface active species (surfactants) on the crystal surface. A cluster consisting of surfactant atoms is formed on top of the crystal nucleus owing to segregation of the surfactant on the crystal surface. In effect, two factors account for the presence of the surfactant. The first is the decrease of the edge energy of the nucleus owing to the saturation of the dangling bonds at the nucleus periphery by the atoms of the surfactant. The second is the edge energy of the cluster consisting of surfactant atoms. The two factors influence inversely the process of nucleation. The decrease of the nucleus edge energy requires less work for nucleus formation and a smaller number of atoms in the critical nucleus. The edge energy of the surfactant cluster lends to larger work of nucleus formation and a greater number of atoms in the critical nucleus. Thus the presence or absence of a surfactant may result in a different number of atoms in the critical nucleus at one and the same supersaturation. An expression for the nucleation rate is derived and the saturation nucleus density is calculated on the assumption that the latter is determined by overlapping of nucleation exclusion (depleted) zones around the growing nuclei. The work needed for formation of kinks at the steps edges is calculated. It is shown that the latter, as well as the step free energy and the roughening temperature are determined by the surfactant efficiency. That efficiency is defined as the relative difference of the interfacial energy per bond and the energy of the dangling bonds and can be evaluated directly from the slope of an Arrhenius plot of the kink density.