We consider irreversible second-layer nucleation that occurs when two adatoms on a terrace meet. We solve the problem analytically in one dimension for zero and infinite step-edge barriers, and numerically for any value of the barriers in one and two dimensions. For large barriers, the spatial distribution of nucleation events strongly differs from ${\rho }^2$, where $\rho$ is the stationary adatom density in the presence of a constant flux. Theories of the nucleation rate $\omega$ based on the assumption that it is proportional to ${\rho }^2$ are shown to overestimate $\omega$ by a factor proportional to the number of times an adatom diffusing on the terrace visits an already visited lattice site.

• Received 14 September 2000

DOI:https://doi.org/10.1103/PhysRevLett.87.056102