Models were developed for threading dislocation reduction via the introduction of an intentionally strained layer. Three different types of dislocation were considered: misfit dislocations, mobile threading dislocations, and threading dislocations whose glide motion was blocked by a misfit dislocation which crossed the glide path of the threading dislocation (immobile threading dislocations). The models were based upon misfit dislocation formation via a process of lateral threading dislocation motion. Strain-induced threading dislocation motion led to possible annihilation reactions of mobile threading dislocations with other mobile threading dislocations or with blocked threading dislocations, or via reactions in which a mobile threading dislocation was converted to an immobile threading dislocation by a blocking reaction with a misfit dislocation. The evolution of the density of mobile and blocked threading dislocations, and of the misfit dislocation density, was represented by 3 coupled non-linear first-order differential equations. When blocking of threading dislocations by misfit dislocations was not considered, the equations had an analytical solution which showed that the final threading dislocation density should decrease exponentially, with the argument of the exponent being proportional to the product of the reaction radius between threading dislocations (the annihilation radius) and the nominal misfit strain. The no-blocking limit represented the maximum possible threading dislocation reduction due to the introduction of a strained layer; regardless of whether this layer had a discrete step in strain, was step-graded or exhibited continuous strain-grading. When only blocking reactions were considered (no annihilation), analytical solutions to the equations were again obtained which yielded the maximum possible plastic strain relaxation for a discretely strained layer.

A.E.Romanov, W.Pompe, S.Mathis, G.E.Beltz, J.S.Speck: Journal of Applied Physics, 1999, 85[1], 182-92