Effects of elastic strain field on the self-organized ordering of quantum dot superlattices

Self-organized vertical ordering in self-assembled quantum dot superlattices is based on the long-range elastic interactions between growing dots on the surface and those buried in the previous superlattice layers. These interactions may lead to a corrected dot nucleation and to the formation of ordered superstrsuctures. In this paper, we present a systematic investigation of the strain distribution of self-organized lens-shaped quantum dot for the case of growth direction on (001) substrate. The three-dimension finite element analysis for an array of dots is used for the strain calculation. The dependences of the strain energy density distribution on the thickness of capping layer are investigated in detail when the elastic characteristics of the matrix material are anisotropic. It is showed that the elastic anisotropic greatly influences the stress, strain and strain energy density in the quantum dot structures. The anisotropic ratio of the matrix material and the combination with different thickness of the capping layer may lead different strain energy density minimum on the capping layer surface, which can result in various vertical ordering phenomena for the next layer of quantum dots, they are partial alignment, random alignment and complete alignment.