The elastic fields of three-dimensional quantum dots, and the interaction energy between them, are determined by finite element analysis. The results from the analysis are then used in optimization of several cases of multiple dot ordering on the surface of a semiconductor. The strain energy in the model remains constant, when a certain plateau has been reached, even though dot height is increased. Furthermore, for a range of idealized geometries, the shape of the quantum dot has little impact on the strain energy, and thereby the interaction energy.
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