Surface area of solids - Thin films. Crystal growth

This article discusses the phenomena occurring at the interface between a solid and its surrounding medium, both at equilibrium and during solid growth. The common feature is the meeting, at the interface, of two opposing material flows: one consisting of molecules that deposit there before being incorporated into the crystal lattice, the other consisting of molecules that leave the interface toward the surrounding medium. At equilibrium, the intensity of the two flows is equal and depends on interfacial kinetics, which is itself governed by the properties of the phases in the immediate vicinity of the interface. At supersaturation, represented by the difference in chemical potentials between the two phases, the growth flux predominates; however, there is no linear relationship between the net flux and supersaturation, as one might have expected by analogy with electrodynamics, treating the interface as a passive resistor.

The approach we propose to take therefore involves examining the equilibria at the interface between a crystal and its surrounding medium, which reveal the microscopic mechanisms at saturation, before addressing the interfacial kinetics of growth, whose dependence on supersaturation can be quite complex. Two observations arise from this procedure.

— The approach used is exclusively molecular-statistical. Compared to the approach based on classical thermodynamics and continuum mechanics , the chosen method has the advantage of providing a clearer visualization of the physical phenomena, at the cost of some concessions to mathematical rigor. Furthermore, it proves to be better suited for analyzing systems with high surface energy and strong anisotropy, such as a crystal growing from its vapor.

— It should be noted that the overall growth kinetics depend as much on interfacial kinetics as on the kinetics of mass transport from the bulk to the interface. However, the mechanisms of transport within the bulk are common to other processes (chemical engineering, combustion, etc.) and are addressed in detail by fluid mechanics, which is why we have chosen not to go beyond the scope of interfacial phenomena in this article.