An analytical model for the kinetics of threading dislocations during the hetero-epitaxial growth of thin films was here applied to the special case of selective-area growth, in which mesas of limited lateral extent were grown on a substrate. Threading dislocation ensembles were treated very much like chemical species in chemical reaction kinetics. A simulation approach which incorporated specific threading-dislocation crystallography, and considered individual reactions between them, was used to supplement the analytical results. The model was applied to 3 mesa geometries, which included squares as well as a rectangle. It was found that the density of threading dislocations decayed exponentially with increasing film growth. This was consistent with experiment.

A Theoretical Model for Threading Dislocation Reduction during Selective Area Growth. G.E.Beltz, M.Chang, M.A.Eardley, W.Pompe, A.E.Romanov, J.S.Speck: Materials Science and Engineering A, 1997, 234-236, 794-7