Spatiotemporal distribution of nucleation events during crystal growth - art. no. 056102

We consider irreversible second-layer nucleation that occurs when two adato ms on a terrace meet. We solve the problem analytically in one dimension fo r zero and infinite step-edge barriers, and numerically for any value of th e barriers in one and two dimensions. For large barriers, the spatial distr ibution of nucleation events strongly differs from rho (2), where rho is th e 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 visite d lattice site.