Theory of luminescent emission in nanocrystal ZnS:Mn with an extra electron

We consider the effect of an extra electron in a doped quantum dot ${\mathrm{Z}\mathrm{n}\mathrm{S}:\mathrm{M}\mathrm{n}}^{2+}.$ The Coulomb interaction and exchange interaction between the extra electron and the states of the Mn ion will mix the wave functions, split the impurity energy levels, break the previous selection rules, and change the transition probabilities. Using this model of an extra electron in the doped quantum dot, we calculate the energy and the wave functions, the luminescence efficiency, and the transition lifetime and compare with the experiments. Our calculation shows that two orders of magnitude of lifetime shortening can occur in the transition ${}^4{T}_1{-}^6{A}_1,$ when an extra electron is present.