The so-called effective kinetics of threading dislocations in growing epitaxial films were developed on the basis of crystallographic and geometrical considerations. A system of coupled first-order non-linear differential equations was derived for 24 families of threading dislocations, and was solved for several initial conditions of the threading dislocation density. Numerical solutions were presented which demonstrated that there were 2 general types of asymptotic behavior with increasing film thickness. These were a linear decrease in, or saturation of, the total threading dislocation density. This behavior agreed with experimental data on threading dislocation reduction in mismatched homogeneous buffer layers.

Modeling of Threading Dislocation Density Reduction in Hetero-Epitaxial Layers – II. Effective Dislocation Kinetics. A.E.Romanov, W.Pompe, G.Beltz, J.S.Speck: Physica Status Solidi B, 1997, 199[1], 33-49