A Two-Layer Epitaxial Composite Strained by an Array of Misfit Dislocations Accommodating the Lattice Mismatch

Abstract

The plane-strain-problem of a two-layer composite A/B/C, in which C is the infinite substrate, is investigated when the material is deformed by a regular array of misfit dislocations (MDs) that accommodate a lattice mismatch. For the first time, a capped layer structure is treated when each medium has its own isotropic elastic constants. It is assumed that the interface A/B has no stress source, whereas at the B/C heterointerface MDs accommodate parameter or/and angular misfits. Exact closed-form formulae are derived for the displacement field and the stored elastic energy. The key of the solution is the analytical inversion of two fundamental systems of 10 × 10 and 5 × 5 linear equations that express the limiting boundary conditions. The solution is illustrated by stress contours and elastic energy calculations for the composite SiO 2 /Si/(001)GaAs deformed by an array of edge 90° MDs at the Si/(001)GaAs heterointerface.