A theoretical model for threading dislocation reduction during selective area growth

An analytic model, developed earlier for understanding the reduction kinetics of threading dislocations (TDs) in the heteroepitaxial growth of thin films, is considered here for the special case of selective area growth, wherein mesas of comparatively small lateral dimension are grown on a substrate. TD ensembles are treated in close analogy with chemical species in chemical reaction kinetics. In addition, a computer simulation approach that incorporates specific TD crystallography and considers the individual geometry of and reactions between TDs is used to augment the analytic results. The model is applied to three mesa geometries, encompassing squares as well as a rectangle. It is found that the density of TDs decays exponentially with increasing film growth, consistent with the enhanced reduction noted in several experimental reports.