MISFIT DISLOCATION DISTRIBUTIONS IN CAPPED (BURIED) STRAINED SEMICONDUCTOR LAYERS

An elastic continuum model is used to investigate distributions of mis fit dislocations in a capped layer structure. Effects of the free surf ace at the top of the cap and of interactions between dislocations hav e been rigorously incorporated, making the study applicable to structu res with caps of arbitrary thickness and to the process of strain rela xation in layers already containing misfit dislocations. Two dislocati on types are considered in detail: single dislocations (singles) resid ing at the lower interface, between the strained layer and the substra te, and dislocation dipoles, i.e., pairs of parallel dislocations with opposite Burgers vectors, one at the lower interface and the other at the upper interface, between the strained layer and the cap. Although singles cause unwanted long-range distortion in the cap, which is not caused by dipoles, dipoles give rise to increased localised distortio n, due to the presence of the additional dislocation, at the upper int erface. Hence singles and dipoles compete as misfit dislocation types in capped layers, with the dominant type being determined by the param eters of the layer structure. It is demonstrated that interactions bet ween dislocations are crucial, and that experimental observations cann ot be explained by consideration of an isolated single or dipole. Inte ractions between singles in an array at the lower interface result in a buildup of strain energy in the cap. The rapidity of this buildup wi th dislocation density demands a transition from relaxation by singles to relaxation by arrays of dipoles; such a transition would not be pr edicted by a consideration of isolated singles or dipoles. Energy eval uations are performed to incorporate such interactions between disloca tions while providing a sequential view of strain relaxation, with sin gles and dipoles entering the structure one at a time. It is thus demo nstrated that a mixture of singles and dipoles is expected in many cap ped layers of practical interest. An example calculation predicts a mi xture that is consistent with experimental observation.