Enhanced elastic interactions between conical quantum dots

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 perimeter of the dot. The strength of this singularity increases as the slope of the dot increases. This dramatically enhances the elastic interaction between dots and the metastability of a quantum dot array. This could help explain the stability of bimodal island size distributions observed in some quantum dot systems.