Elastic Fields of Quantum Dots in Multilayered Semiconductors: A Novel Green’s Function Approach

We present an efficient and accurate continuum-mechanics approach to predict the elastic fields in multilayered semiconductors due to buried quantum dots (QDs). Our approach is based on a novel Green’s function solution in anisotropic and linearly elastic multilayers, derived within the framework of generalized Stroh formalism and Fourier transforms, in conjunction with the Betti’s reciprocal theorem. By using this approach, the induced elastic fields due to QDs with general misfit strains are expressed as a volume integral over the QDs domains. For QDs with uniform misfit strains, the volume integral involved is reduced to a surface integral over the QDs boundaries. Further, for QDs that can be modeled as point sources, the induced elastic fields are then derived as a sum of the point-force Green’s functions. In the last case, the solution of the QD-induced elastic field is analytical, involving no numerical integration, except for the evaluation of the Green’s functions. As numerical examples, we have studied a multilayered semiconductor system of QDs made of alternating GaAs-spacer and InAs-wetting layers on a GaAs substrate, plus a freshly deposited InAs-wetting layer on the top. The effects of vertical and horizontal arrays of QDs and of thickness of the top wetting layer on the QD-induced elastic fields are examined and some new features are observed that may be of interest to the designers of semiconductor QD superlattices.