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Coherent coupling and formation of molecular orbitals in vertically coupled quantum-dot molecules is studied for a seven-dot InAs/GaAs system. The electron states are computed using a nanoelectronic modelling tool NEMO-3D. The tool optimizes atomic positions in the sample with up to 64 million atoms in the frame of the atomistic VFF model. The resulting optimal interatomic distances are then used to formulate the 20-band sp3d5s* tight-binding Hamiltonian defined on a subdomain large enough to guarantee a correct treatment of confined orbitals. It is found that in the absence of strain (VFF optimization turned off), a clear and highly symmetric miniband structure of the seven-dot orbitals is formed. It maintains a high degree of symmetry even if the dots are taken to be realistically non-identical, where the dot size increases in the growth direction. However, the inclusion of strain breaks this symmetry completely. The simulations demonstrate the important interplay of strain engineering and size engineering in the design of quantum dot stacks.

Atomistic simulations of long-range strain and spatial asymmetry molecular states of seven quantum dots