Correlation versus mean-field contributions to excitons, multiexcitons, and charging energies in semiconductor quantum dots

Single-dot spectroscopy is now able to resolve the energies of excitons, multiexcitons, and charging of semiconductor quantum dots with $\lesssim 1$ meV resolution. We discuss the physical content of these energies and show how they can be calculated via quantum Monte Carlo (QMC) and configuration interaction (CI) methods. The spectroscopic energies have three pieces: (i) a “perturbative part” reflecting carrier-carrier direct and exchange Coulomb energies obtained from fixed single-particle orbitals, (ii) a “self-consistency correction” when the single particle orbitals are allowed to adjust to the presence of carrier-carrier interaction, and (iii) a “correlation correction.” We first apply the QMC and CI methods to a model single-particle Hamiltonian: a spherical dot with a finite barrier and single-band effective mass. This allows us to test the convergence of the CI and to establish the relative importance of the three terms (i)–(iii) above. Next, we apply the CI method to a realistic single-particle Hamiltonian for a CdSe dot, including via a pseudopotential description the atomistic features, multiband coupling, spin-orbit effects, and surface passivation. We include all bound states (up to 40 000 Slater determinants) in the CI expansion. Our study shows that (1) typical exciton transition energies, which are $\sim 1$ eV, can be calculated to better than 95% by perturbation theory, with only a $\sim 2$ meV correlation correction; (2) typical electron addition energies are $\sim 40$ meV, of which correlation contributes very little $(\sim 1$ meV); (3) typical biexciton binding energies are positive and $\sim 10$ meV and almost entirely due to correlation energy, and exciton addition energies are $\sim 30$ meV with nearly all contribution due to correlation; (4) while QMC is currently limited to a single-band effective-mass Hamiltonian, CI may be used with much more realistic models, which capture the correct symmetries and electronic structure of the dots, leading to qualitatively different predictions from effective-mass models; and (5) CI gives excited state energies necessary to identify some of the peaks that appear in single-dot photoluminescence spectra.