The geometry of these non-equilibrium defects, which were generated due to stress relaxation in thin films, was studied in order to facilitate their reduction during hetero-epitaxial growth. The present work considered the geometrical possibilities of reactions, between threading dislocations, due to film growth. It was demonstrated that effective threading dislocation motion and reaction were responsible for their overall reduction. The reactions became possible if pairs of threading dislocations came within a critical separation. These critical separations were assumed to be different for annihilation reactions, fusion reactions and scattering reactions. The model was used to explain the experimentally observed dependence of the threading dislocation density upon the reciprocal of the film thickness. The crystallographic behavior, and possible reactions between threading dislocations in the case of the (001) growth of face-centered cubic semiconductor films, were analyzed.

Modeling of Threading Dislocation Density Reduction in Hetero-Epitaxial Layers – I. Geometry and Crystallography. A.E.Romanov, W.Pompe, G.Beltz, J.S.Speck: Physica Status Solidi B, 1996, 198[2], 599-613