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 ρ2, where ρ is the
stationary adatom density in the presence of a constant flux. The probability
Q(t) that nucleation occurs at time t after the deposition of the second
adatom, decays for short time as a power law [Q(t)∼t−1/2] in d=1 and
logarithmically [Q(t)∼1/ln(t/t0)] in d=2; for long time it decays
exponentially. Theories of the nucleation rate ω based on the assumption
that it is proportional to ρ2 are shown to overestimate ω by a
factor proportional to the number of times an adatom diffusing on the terrace
visits an already visited lattice site.Comment: 4 pages, 3 figures; accepted for publication on PR