Computer simulation of threading dislocation density reduction in heteroepitaxial layers

In the heteroepitaxial growth of films with large misfit with the underlying substrate, the generation of misfit dislocations and threading dislocations (TDs) is ubiquitous for thicknesses well in excess of the equilibrium critical thickness. Experimental data suggests that, after an entanglement region near the film-substrate interface, there is a fall-off in TD density that is inversely proportional to the film thickness h (applicable to densities in the approximate range 107-109 cm-2), followed by saturation or weak decay of the TD density with further increase in film thickness. In this paper, we build upon a recent framework for understanding TD reduction in terms of their effective lateral motion with increasing film thickness, coupled with the probability that certain pairs of TDs annihilate, reacting to form a single TD, or undergoing a change in line direction. A computer simulation approach is presented that augments a recent theoretical prediction of both the 1/h scaling behaviour and the saturation of TD densities. Specific cases are considered involving TD distributions typical of surface nucleation, island periphery nucleation and combinations thereof. In addition, an analysis is made of the propensity for various TDs to cluster together. Results are presented which suggest that longrange fluctuations in the net Burgers vector content of the local TDs are a cause for saturation behaviour.