  We present an experimental study of electron-electron exchange interaction in
self-assembled CdTe/ZnTe quantum dots based on the photoluminescence
measurements. The character and strength of this interaction are obtained by
simultaneous observation of various recombination channels of a doubly
negatively charged exciton, including previously unrecognized emission lines
related to the electron-singlet configuration in the final state. A typical
value of the electron singlet-triplet splitting, which corresponds to the
exchange integral of electron-electron interaction, has been determined as 20.4
meV with a spread of 1.4 meV across the wide population of quantum dots. We
also evidence an unexpected decrease of energy difference between the singlet
and triplet states under a magnetic field in Faraday geometry.
