Threading dislocation reduction in strained layers

Abstract

In this article, we have developed models for threading dislocation (TD) reduction due to the introduction of an intentionally strained layer. Three different types of dislocations have been considered in this model: misfit dislocations (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 based on MD formation by the process of lateral TD motion. The strain-induced TD motion leads to possible annihilation reactions of mobile TDs with either other mobile TDs or blocked TDs, or reactions in which a mobile TD is converted to an immobile TD by a blocking reaction with a MD. The evolution of the density of mobile and blocked TDs and the MD density is represented by 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 the argument of the exponent is proportional to the product of the reaction radius between TDs (the annihilation radius rA) and the nominal misfit strain εm. The no-blocking limit represents the maximum possible TD reduction through the introduction of a strained layer, regardless whether this layer has a discrete step in strain, step-grade, or continuous strain grading. When only blocking reactions are considered (no annihilation), again analytic solutions to the equations are obtained which show the maximum possible 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 reactions.