Elasticity theory of straight dislocations in a multilayer

The question of describing the displacement and stress fields associated with straight misfit dislocations (MD's) located in a multilayer involving any N heterointerfaces or free surfaces is reduced, as well as other related problems, to the inversion of two independent sets of linear equations. The displacement field u of a single translation dislocation (TD) is obtained as the limit of an infinite spacing between two MD's. The multilayer can be limited by one or two free surfaces (epitaxy, thin foils). The simplicity and the power of the method is illustrated in solving classical but yet unsolved questions: the stress field associated with an edge interfacial TD in a layer interfacial edge TD's in a thin bicrystal (N=3), and the stress field associated with a multilayer formed by alternating GaAs and Si layers (N=5) containing a single array of edge MD's along one of the heterointerfaces.