Strain relaxation in buried strained layers by mixture of single and dipolar dislocation arrays

Abstract

The strain relaxation in buried strained layers is investigated using an elastic continuum model. The mixture of single dislocations residing at the substrate/strained layer interface (lower interface) and dipolar dislocations in which one is at the lower interface and the other at the strained layer/capping layer interface (upper interface), is proposed. In the mixture, the dislocation distributions are denoted by a parameter which is the ratio of the density of misfit dislocations at the upper interface to that at the lower interface. In a buried strained layer, relaxation of mean strain occurs by introduction of two orthogonal arrays of mixture of single and dipolar dislocations. Considering both the free surface and interactions between dislocations, the total elastic energy per unit area of buried strained layer containing two orthogonal arrays of mixture of single and dipolar dislocations is calculated. The energy is dependent on the misfit dislocation distributions. On energy minimization considerations, the expression of the misfit dislocation distributions in a buried strained layer with arbitrary strain relaxation and capping layer thickness is derived. It is demonstrated that the strain is initially relaxed by the single misfit dislocations and relaxed by the mixture of single and dipolar misfit dislocations in the final stage of strain relaxation in many buried layers of practical interest.