  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. 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 [$Q(t)\sim t^{-1/2}$] in $d=1$ and
logarithmically [$Q(t)\sim 1/\ln(t/t_0)$] in $d=2$; for long time it decays
exponentially. 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.
