A procedure was developed for the description of the evolution of threading dislocation densities in lattice-mismatched epitaxial films. The threading dislocation ensembles were treated by analogy with chemical species during reaction kinetics. Analogous so-called reaction-rate equations were derived for a changing threading dislocation density with increasing film thickness. First-order and second-order reactions were considered. Selective area growth was used as an example of a first-order reaction. Threading dislocation annihilation, fusion, and scattering were considered to be examples of second-order reactions. Analytical models were developed for the threading dislocation behavior in relaxed homogeneous buffer layers, for selective area growth, and for strained layers.

A.E.Romanov, W.Pompe, G.E.Beltz, J.S.Speck: Applied Physics Letters, 1996, 69[22], 3342-4