A finite element study of the stress and strain fields of InAs quantum dots embedded in GaAs

We report on a stress and strain analysis, using the finite element method, of the heterosystem of InAs quantum dots embedded in GaAs. The methodology of using the finite element method to simulate the lattice mismatch is discussed and a three-dimensional (3D) model of the heterostructure shows the 3D stress distribution in the InAs islands embedded in a matrix of GaAs substrate and cap layer. The initial shape of the InAs islands is pyramidal. The stress and strain distribution calculated corresponds well with the strain induced by the lattice mismatch. Factors such as the height of the spacer layer and the height of the island are found to play an important role in the stress and strain distribution. With the island having the shape of a truncated pyramid, the stress and strain distribution deviates from that of a full pyramidal island showing the effects that a change of shape in the islands has on the stress field. The stress distribution contributes to the driving force for the mechanism of surface diffusion in molecular beam epitaxy. The effects of anisotropy on the strain distribution are also studied.