A standard theory of second-layer nucleation was extended into the regime of low temperatures, where diffusion was the limiting process. The theory took into account the fluctuations of the adatoms and the distribution of stable clusters on a surface, and yielded an expression for the nucleation rate and time evolution of the density of stable clusters. When diffusion was slow, the fluctuations of the monomer distribution played an important role and results differ qualitatively and quantitatively from those obtained using the standard rate-equation approach to nucleation. It was argued that, in this case, the standard theory failed because slow diffusion delayed nucleation and the nucleation rate depended upon the fluctuations of interatomic distances. It was shown that the final density of stable clusters depended upon the fluctuations of the monomer and stable clusters distribution and could even be independent of the deposition rate, as was experimentally observed at low temperatures.

2D Nucleation Limited by Slow Diffusion. Z.Chvoj, M.C.Tringides, Z.Chromcová: Journal of Physics - Condensed Matter, 2011, 23[21], 215307