We develop a theory of nucleation on top of two-dimensional islands bordered by steps with an additional energy barrier $\Delta E_S$ for descending atoms. The theory is based on the concept of the residence time of an adatom on the island, and yields an expression for the nucleation rate which becomes exact in the limit of strong step-edge barriers. This expression differs qualitatively and quantitatively from that obtained using the conventional rate-equation approach to nucleation [J. Tersoff et al., Phys. Rev. Lett. $72,$ 266 (1994)]. We argue that rate-equation theory fails because nucleation is dominated by the rare instances when two atoms are present on the island simultaneously. The theory is applied to two distinct problems: the onset of second-layer nucleation in submonolayer growth, and the distribution of the sizes of top terraces of multilayer mounds under conditions of strong step-edge barriers. Application to homoepitaxial growth on Pt(111) yields the estimate $\Delta E_S>~0.33$ eV for the additional energy barrier at CO-decorated steps.

• Received 22 December 1999

DOI:https://doi.org/10.1103/PhysRevB.61.14037