The dependence of saturation nucleus density on deposition rate and substrate temperature in the case of complete condensation

A new analytical method is given for calculating the saturation nucleus density, N s, when vapour is condensed onto a substrate with no adatom desorption occurring. The calculations allow for a non-uniform distribution of nuclei on the substrate and for a time-dependent nucleation rate. Further, the capture of adatoms by already-formed nuclei leading to a decreased nucleation probability in their vicinity is taken into consideration by solving the appropriate diffusion problem. The resulting dependence of N s on substrate temperature and on deposition rate when the critical nucleus size is both one adatom and an adatom pair is compared with the previous results of Lewis and Campbell (1967), Logan (1969) and Joyce, Bradley and Booker (1967), and disagreements are discussed.