Rate equation approaches to thin film nucleation kinetics

Abstract The nucleation and growth of crystals on a substrate are discussed in terms of rate equations for the atom cluster concentrations as a function of time. Simple approximations allow this general set of equations to be reduced to three coupled equations. Many physical processes can be incorporated into these rate equations, including coalescence of clusters, and cluster mobility. The problem of increasing correlation between single atoms and stable clusters as growth proceeds is studied. It is shown that the problem can be solved self-consistently using an auxiliary diffusion equation and that approximations may be obtained which give upper and lower bounds for the cluster growth rates. These diffusion equations also give expressions which enable the cluster-cluster correlations and cluster size distributions to be discussed. With these approximations, expressions are derived for observable quantities and the expressions are compared with one experimental example. In this case, that of gold on alkali halides, it is shown that cluster mobility must be included to obtain agreement with experiment, and that the material parameters required to describe the nucleation behaviour are physically reasonable.