The formation of a film from nuclei

Once a number of nuclei are formed on the surface of the substrate, the next stage of the film formation process involves the transport of nuclei or their constituent atoms across the surface in order to cover the area available to form the complete film. It is clear from the relationship between the Gibbs energy 

An empirical formula, due to Fick, shows that, under simple circumstances where the chemical potential of a component in a system is defined by the equation 

The mobility or diffusion of the atoms over the surface of the substrate, and over the film during its formation, will occur more rapidly as the temperature increases since epitaxy can be achieved, under condition of crystallographic similarity between the film and the substrate, when the substrate temperature is increased. It was found experimentally that surface diffusion has a closer relationship to an activation-dependent process than to the movement of atoms in gases, and the temperature dependence of the diffusion of gases. For surface diffusion the variation of the diffusion coefficient with temperature is expressed by the Arrhenius equation 

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