A lattice gas model of strained epitaxy and self-organization of small clusters

We consider the Frenkel–Kontorova model of coherent strained epitaxy. We show that the model can be mapped onto a lattice gas model with cluster multiatom interactions. The latter is solved exactly in the case of pair, trio, and four-atom interactions. The method of solution can be extended to account for larger clusters. The solution shows the possibility of self-assembly of atoms into clusters with very narrow size distribution. The clusters themselves are distributed randomly at small covering but can be ordered at higher densities. In the two-dimensional (2D) case this may lead to surface reconstruction which is illustrated by Monte Carlo simulation of a 2D generalization of the model.