Continuous analytical solutions for strain applied to quantum dot and rings

Several analytical strain matrix component solutions for quantum dot (QD) various geometries have been derived using principles of continuous mechanics. These strain calculations were used to determine the shift in electron energies for various QD and ring configurations and sizes (see, for instance, M. Grundmann et al. PRB 52, 11969 (1995)). In the presented work we propose simplified strain approximation for such calculations. This approximation is accompanied by the band gap model given in I. Filikhin et al. PRB 73, 205332 (2006). The results of our calculation are compared to those of previous ones. Besides, comparisons are made between 2D and 3D electron energy calculations. Finally the limits of continuous strain calculations are discussed.