The formation of nanoscale clusters – nanofilms / quantum dots predicted using a capillary model of nucleation

Abstract

This paper describes the theoretical and simulation studies of both homogenous and heterogeneous nucleation, the phenomena that refers to the formation of stable nuclei prior to the growth of nanoclusters including nanofilms and quantum dots. Essentially, a single cluster may contain few thousand of atoms, and interaction with the surface may be preceded via processes, such as diffusion, hopping, sorption and coalescences. These complicated physical-chemical phenomena require in-depth theoretical understanding on how the various interacting quantities can be formulated and then resolved using specific mathematical approximation. In the case of a capillary model for heterogeneous nucleation, the nuclei are assumed to be in spherical shapes, which increase in both energies and diameters, and finally reach their critical points and settled to oval shapes prior to dome-like wetting on the substrate, essentially just like water droplet resting on a surface. The net change of energy, ΔG for the formation of cluster is found to be the functions of nucleus volume, surface area of atomic-nucleus interface, surface area of nucleus-surface interface and energy lost at substrate-atomic interface. The results for ΔG, ΔG*, r* and Ω and their respective changes with r, s and T were obtained and experimentally verified using existing data.