Systems which consisted of an epitaxial film on a semi-infinite substrate made of a different material were considered, and the critical film thickness which was required to form misfit interface dislocations was derived. The energy approach was used to predict the critical thickness, the self-energy of the dislocation and the interaction energy between the dislocation and the mismatch strain. The superposition principle, and Fourier integrals, were used to derive the elastic stress field which was due to the interface dislocation. The predicted stress fields satisfied the free-surface condition at the film surface, and the continuity condition at the interface. It was found that the predicted critical film thickness for the generation of interface dislocations decreased with increasing film/substrate shear-modulus ratio.

Critical Epitaxial Film Thickness for Forming Interface Dislocations. S.Lee, S.D.Wang, C.H.Hsueh: Materials Science and Engineering A, 2001, 309-310, 473-7