The energy of finite systems of misfit dislocations in epitaxial strained layers

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Abstract
Previous approaches to calculating the energy of a system of misfit dislocations in epitaxial strained layers have assumed that the system is infinite in the plane of the epitaxial interface and that the dislocations are uniformly spaced. Here a method is presented which is capable of dealing with finite systems of nonuniformly spaced dislocations of the type observed experimentally. The principle of the method is to explicitly account for the interactions between pairs of misfit dislocations. When the dislocations are infinite and uniformly spaced the present approach is shown to be equivalent to an earlier exact treatment. The present approach applied to finite systems of uniformly spaced dislocations shows that the energy per unit area converges to that of the infinite system very slowly; particularly when the spacing of the dislocations is less than the thickness of the epitaxial layer. Typically, systems must be larger than 30×30 dislocations for their energy per unit area to be within 10% of that of the infinite system. Similarly the infinite system will overestimate the energy of a 10×10 array by about 30%.