Point Island Models for Nucleation and Growth of Supported Nanoclusters   during Surface Deposition
  Point island models (PIMs) are presented for the formation of supported nanoclusters (or islands) during deposition on flat crystalline substrates at lower submonolayer coverages. These models treat islands as occupying a single adsorption site, although carrying a label to track their size (i.e., they suppress island structure). However, they are particularly effective in describing the island size and spatial distributions. In fact, these PIMs provide fundamental insight into the key features for homogeneous nucleation and growth processes on surfaces. PIMs are also versatile being readily adapted to treat both diffusion-limited and attachment-limited growth, and also a variety of other nucleation processes with modified mechanisms. Their behavior is readily and precisely assessed by kinetic Monte Carlo simulation. 
Y. Han, E. Gaudry, T. J. Oliveira and J. W. Evans
cond-mat.mes-hall cond-mat.stat-mech