Multiband theory of multi-exciton complexes in self-assembled quantum dots

We report on a multiband microscopic theory of many-exciton complexes in self-assembled quantum dots. The single particle states are obtained by three methods: single-band effective-mass approximation, the multiband $k\cdot p$ method, and the tight-binding method. The electronic structure calculations are coupled with strain calculations via Bir-Pikus Hamiltonian. The many-body wave functions of $N$ electrons and $N$ valence holes are expanded in the basis of Slater determinants. The Coulomb matrix elements are evaluated using statically screened interaction for the three different sets of single particle states and the correlated $N$-exciton states are obtained by the configuration interaction method. The theory is applied to the excitonic recombination spectrum in InAs/GaAs self-assembled quantum dots. The results of the single-band effective-mass approximation are successfully compared with those obtained by using the of $k\cdot p$ and tight-binding methods.