Phonon-assisted relaxation and tunneling in self-assembled quantum dot molecules

We study theoretically phonon-assisted relaxation processes in a system consisting of one or two electrons confined in two vertically stacked self-assembled quantum dots. The calculation is based on a k.p approximation for single-particle wave functions in a strained self-assembled structure. From these, two-particle states are calculated by including the Coulomb interaction and the transition rates between the lowest-energy eigenstates are derived. We take into account phonon couplings via deformation potential and piezoelectric interaction and show that they both can play a dominant role in different parameter regimes. Within the Fermi golden rule approximation, we calculate the relaxation rates between the lowest-energy eigenstates which lead to thermalization on a picosecond time scale in a narrow range of dot sizes.