Modeling of Threading Dislocation Density Reduction in Heteroepitaxial Layers

The “effective kinetics” of threading dislocations (TDs) in growing epitaxial films is developed on the basis of the crystallographic and geometrical considerations from Part I of the paper. A system of coupled first-order nonlinear differential equations for twenty-four families of TDs is derived and solved for several initial conditions for TD densities. Numerical solutions demonstrated two general types of asymptotic behavior with increasing film thickness: linear decrease or saturation of total TD density. This behavior agrees with experimental data on TD reduction in mismatched homogeneous buffer layers.