Simple model for interface stresses with application to misfit dislocation generation in epitaxial thin films

A simple model for the interfacial free energy of a semicoherent interface is used to develop expressions for interface stresses, which are surface thermodynamic quantities associated with solid-solid interfaces. An analysis of the thermodynamics of thin film epitaxy is presented that incorporates the effects of free surface and interface stresses, and an expression for the critical thickness for thin film epitaxy is obtained. Based on this analysis, the concept of effective pressures exerted by the thin film free surface and film-substrate interface is introduced. If it is assumed that misfit dislocations are generated at the film-substrate interface as a result of glide of threading dislocations, the thermodynamics and kinetics of stress relaxation can be discussed in terms of a balance of Peach-Koehler forces acting on the threading dislocations owing to the surface and interface pressures as well as to the coherency stress. An example is given that shows that, if the film has a relatively large surface pressure that opposes lattice matching, the dependence of the coherency strain on film thickness can be very different from that obtained from conventional analyses which ignore the effect of the free surface; specifically, the largest equilibrium coherency strain of the same sign as the misfit can be much smaller than the total misfit, and an "anomalous" coherency strain of sign opposite that of the misfit can be thermodynamically favorable at small film thicknesses. The analysis used to obtain the critical thickness for thin film epitaxy is extended to give an expression for the critical thickness for misfit dislocation generation at the interface between a substrate and a superlattice thin film. It is shown that this critical thickness depends on a superlattice pressure associated with the interlayer interface stress in addition to the free surface and film-substrate interface pressures.