Optical investigations of individual InAs quantum dots:  Level splittings of exciton complexes

We have investigated individual InAs quantum dots embedded in GaAs using photoluminescence spectroscopy as a function of temperature and excitation power density. We also present $\mathbf{k}\cdot \mathbf{p}$ calculations including both direct and exchange interactions for systems with up to three excitons in the dot. From these calculations we are able to assign some of the many peaks observed to various few-particle states. A rate-equation model has also been developed which allows simulations of the peak intensities with excitation power density to be made and compared with experiment.