By assuming that the nucleation of dislocation half-loops from the crystal growth surface was a mechanism for the generation of misfit dislocations between an epitaxial film and a substrate, critical thicknesses could be determined by calculating the zero of free energy of the system. In order to estimate the free energy, 2 analytical methods were used. One was the whole-space approximation, while another treated surface half-loops in the half-space by means of image-stress construction. In both cases, interaction between 2 dislocation glide loops which lay either in the same slip plane or in parallel slip planes, was incorporated into the analysis. It was shown that half-loop correction reduced the critical thickness. The former interaction reduced, and the latter interaction, increased it and the interaction effects became smaller by the half-space correction. It was also shown that the effect of anisotropy in the whole-space approximation tended to increase the critical thickness.

K.Shintani, H.Yonezawa: Journal of Applied Physics, 1995, 78[8], 5022-7