An analytical model for the elastic energy of a system of conical heteroepitaxial quantum dots of finite slope is presented. An expression for the surface tractions at the dot—substrate interface is proposed. This includes a singularity in the stress field at the radial perimeter of the dot. The significance of this singularity increases as the slope of the dot increases. This dramatically increases the elastic interaction between dots. The stability of a hexagonal array of dots is found to be highly dependent on the strength of the stress singularity, with a system of highly sloped dots predicted to be metastable at much lower coverages than previously predicted. This could help explain the stability of bimodal island size distributions observed in some quantum dot systems.
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