An approach to threading dislocation ‘‘reaction kinetics’’

An approach is developed to describe the evolution of threading dislocation (TD) densities in lattice-mismatched epitaxial films. TD ensembles are treated in close correspondence to chemical species in chemical reaction kinetics. ‘‘Reaction rate’’ equations are derived for changing TD density with increasing film thickness for first- and second-order reactions. Selective area growth is an example of a first-order reaction. TD annihilation, fusion, and scattering are examples of second-order reactions. Analytic models are derived for TD behavior in relaxed homogeneous buffer layers, selective area growth, and strained layers.