Effect of elastic anisotropy on the elastic fields and vertical alignment of quantum dots

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Abstract
The elastic fields in the self-organized quantum dot (QD) structures are investigated in details by three-dimensional finite element analysis for an array of lens shaped QDs. Emphasis is placed on the effect of elastic anisotropy of the materials with the anisotropy ratio A ranging from 0.25 to 4.0 for both the QDs and the matrix. It is found that the elastic anisotropy strongly influences the distributions of strain, stress, and strain energy density in the QD structures. It is shown that the elastic interactions among the buried QDs play crucial role in the formation of the satellite energy minima at the cap layer surface, while the materials anisotropy and the cap layer thickness also play important roles. By changing the elastic anisotropy ratio and the cap layer thickness, substantially different distributions of strain energy minima on the cap layer surface are obtained, which may result in various QD ordering phenomena such as vertical alignment, partial alignment, or complete misalignment. Based on the calculation results, a phase diagram is constructed to show the effect of material anisotropy and cap layer thickness on the vertical correlation of QDs.