Nucleation growth of thin films

Nucleation of a thin film is usually described in terms of classical nucleation theory resulting from coalescence of clusters from a random collection of atoms on a surface. The basic energetics and macroscopic kinetics of nucleation was described in some detail in Section 4.4.2 and will not be repeated here. However, it is useful to look more closely at the atomic processes that are involved in the phenomena described in Chapter 4. 

In practice, decompositions for m 2 (loss of more than one or two atoms at a time) are unlikely unless an energetic particle hits the cluster and breaks it up. Cluster aggregation where j l becomes increasingly important when the surface becomes heavily covered by clusters leaving little free space for the lattice gas, as discussed below. Actions involving monomers are generally by far the fastest and hence have the greatest values of k. 

To complete the analysis of the equations one requires an estimate of the magnitude of the rate constants k. This estimate, carried out in detail, is complex and beyond the scope of this text. However, several observations on the nature of some of the contributing terms seems reasonable. First, the rate constants include a Boltzmann-like 

Equation 10.10 represents a potentially infinite set of equations (one for each value of i) in i unknowns. Therefore, the set can be solved for each value of n given a starting condition and all relevant rate constants. Such solutions have been carried out many times in the literature. 

The process of coarsening is helped along if even relatively large clusters can move on the surface and hence can coalesce with one another. This movement is observed experimentally at sufficiently high temperatures. Cluster diffusion results from the fact that atoms may move around the perimeter of the cluster as well as leaving it to join the lattice gas. This results in random transport of atoms from one side of the cluster to the other and hence to movement of its center of mass. The larger the 

---