Ii-vi Semiconductor Quantum Dot Quantum Wells: a Tight-binding Study

We have developed a symmetry-based tight-binding (TB) method for calculating the electronic structure, exciton states and optical spectra in spherical semiconductor quantum dots (QD's). It is based on the semi-empirical sp^{3}s^{*} model, including thespin-orbit interaction. The TB parameters of the QD Hamiltonian are those used to reproduce the bulk semiconductor band structure. The surface dangling bonds are passivated by hydrogen-like atoms in a controlled manner. We write the TB Hamiltonian in a block-diagonal form by using group-theoretical techniques. Exact diagonalization then yields the full single-particle spectrum including the symmetry classification of the eigenstates. We next introduce the (many-body) electron-hole interaction: both the Coulomb (direct) and exchange terms are considered. The low-energy exciton spectrum is then deduced in the configuration-interaction approach by diagonalizing the full exciton Hamiltonian in the single electron-hole pair excitation subspace of progressively increasing size until numerical convergence of the lowest excitonic energies. The electric dipole transition probabilities are also calculated. We thus obtain the low-energy fine structure characterizing the resonant and non-resonant photoluminescence Stokes shifts.