Universal ratio of coulomb interaction to geometric quantization in (In, Ga)As/GaAs quantum dots

We study the photoluminescence of self-assembled (In, Ga)As/GaAs quantum dot ensembles with varying confinement potential height. The low energy shift of the $s$-shell emission with increasing excitation power gives a measure of the Coulomb interaction in these structures as it results from carrier-carrier interactions between the optically injected exciton complexes. When dividing this shift by the dot level splitting, determined by the geometric confinement, we obtain a universal function of the number of involved excitons that is independent of the confinement potential height. This shows an identical scaling of Coulomb interaction and geometric quantization with varying confinement.