Threading dislocation reduction in strained layers

In this article, we have developed models for threading dislocation (TD) re duction due to the introduction of an intentionally strained layer. Three d ifferent types of dislocations have been considered in this model: misfit d islocations (MDs), mobile TDs, and TDs whose glide motion has been blocked by a MD crossing the glide path of the TD (immobile TDs). The models are ba sed on MD formation by the process of lateral TD motion. The strain-induced TD motion leads to possible annihilation reactions of mobile TDs with eith er other mobile TDs or blocked TDs, or reactions in which a mobile TD is co nverted to an immobile TD by a blocking reaction with a MD. The evolution o f the density of mobile and blocked TDs and the MD density is represented b y three coupled nonlinear first order differential equations. When blocking of TDs by MDs is not considered, the equations have an analytical solution that shows that the final TD density should decrease exponentially where t he argument of the exponent is proportional to the product of the reaction radius between TDs (the annihilation radius r(A)) and the nominal misfit st rain epsilon(m). The no-blocking limit represents the maximum possible TD r eduction through the introduction of a strained layer, regardless whether t his layer has a discrete step in strain, step-grade, or continuous strain g rading. When only blocking reactions are considered (no annihilation), agai n analytic solutions to the equations are obtained which show the maximum p ossible plastic strain relaxation for a discretely strained layer. Several examples of numerical solutions to the three coupled differential equations are described for cases that include both blocking and annihilation reacti ons. (C) 1999 American Institute of Physics. [S0021-8979(99)04901-4].