Influence of quantum dot geometry on p-shell transitions in differently charged quantum dots

Absorption spectra of neutral, negatively and positively charged semiconductor quantum dots are studied theoretically. We provide an overview of the main energetic structure around the p-shell transitions, including the influence of nearby nominally dark states. Based on the envelope function approximation, we treat the four-band Luttinger theory as well as the direct and short range exchange Coulomb interactions within a configuration interaction approach. The quantum dot confinement is approximated by an anisotropic harmonic potential. We present a detailed investigation of state mixing and correlations mediated by the individual interactions. Differences and similarities between the differently charged quantum dots are highlighted. Especially large differences between negatively and positively charged quantum dots become evident. We present a visualisation of energetic shifts and state mixtures due to changes in size, in-plane asymmetry and aspect ratio. Thereby we provide a better understanding of the experimentally hard to access question of quantum dot geometry effects in general. Our findings show a new method to determine the in-plane asymmetry from photoluminescense excitation spectra. Furthermore, we supply basic knowledge for tailoring the strength of certain state mixtures or the energetic order of particular excited states via changes in the shape of the quantum dot, which is highly interesting e.g. to understand relaxation paths.