Inter-shell exchange interaction in CdTe/ZnTe quantum dots: magneto-photoluminescence of X, X2- and XX-

We present a comprehensive photoluminescence study of exchange interaction in self-assembled CdTe/ZnTe quantum dots. We exploit the presence of multiple charge states in the photoluminescence spectra of single quantum dots to analyze simultaneously fine structure of different excitonic transitions, including recombination of neutral exciton/biexciton, doubly charged negative exciton and negatively charged biexciton. We demonstrate that the fine structure results from electron-hole exchange interaction and that spin Hamiltonians with effective exchange constants $\delta_i$ can provide a good description of each transition in magnetic field for Faraday and Voigt field geometry. We determine and discuss values of the effective exchange constants for a large statistics of quantum dots.