Spatio-temporal distribution of nucleation events during crystal growth

Details Spatio-temporal distribution of nucleation events during crystal growth Spatio-temporal distribution of nucleation events during crystal growth

2001-02-12

arxiv.org/abs/cond-mat/0102212v2

Phys. Rev. Lett. 87, 056102 (2001)

Physics

Condensed Matter

Statistical Mechanics

4 pages, 3 figures; accepted for publication on PRL

Scientific paper

10.1103/PhysRevLett.87.056102

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.

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