A simple model for the interfacial free energy of a semi-coherent interface was used to derive expressions for the interface stresses. An analysis of the thermodynamics of thin-film epitaxy was presented which incorporated the effects of free surface and interface stresses, and an expression was obtained for the critical thickness for thin-film epitaxy. On the basis of this analysis, the concept of an effective pressure exerted by the thin-film free surface and film/substrate interface was introduced. When it was assumed that misfit dislocations were generated at the film/substrate interface, as a result of the glide of threading dislocations, the thermodynamics and kinetics of stress relaxation could be considered in terms of a balance of the Peach-Koehler forces which acted upon the threading dislocations due to the surface and interface pressures as well as to the coherency stress. An example was provided which showed that, if the film had a relatively large surface pressure which opposed lattice-matching, then the dependence of the coherency strain upon film thickness could be very different to that deduced from conventional analyses which ignored the effects of a free surface. In particular, the largest equilibrium coherency strain having the same sign as the misfit could be much smaller than the total misfit, and a so-called anomalous coherency strain having a sign opposite to that of the misfit could be thermodynamically favourable at small film thicknesses. The analysis which was used to obtain the critical thickness for thin-film epitaxy was extended in order to furnish an expression for the critical thickness for misfit dislocation generation at the interface between a substrate and a superlattice thin film. It was shown that this critical thickness depended upon a superlattice pressure which was associated with the interlayer interface stress; in addition to the free-surface and film/substrate interface pressures.

Simple Model for Interface Stresses with Application to Misfit Dislocation Generation in Epitaxial Thin Films R.C.Cammarata, K.Sieradzki, F.Spaepen: Journal of Applied Physics, 2000, 87[3], 1227-34