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The changes in the lifetime of a metastable energy level in Er-doped Sinanocrystals in the presence of an external source of colored noise areanalyzed for different values of noise intensity and correlation time. Excitondynamics is simulated by a set of phenomenological rate equations which takeinto account all the possible phenomena inherent to the energy states of Sinanocrystals and Er$^{3+}$ ions in the host material of Si oxide. Theelectronic deexcitation is studied by examining the decay of the initialpopulation of the Er atoms in the first excitation level $^4$I$_{13/2}$ throughthe fluorescence and the cooperative upconversion by energy transfer. Ourresults show that the deexcitation process of the level $^4$I$_{13/2}$ isslowed down within wide ranges of noise intensity and correlation time.Moreover, a nonmonotonic behavior of the lifetime with the amplitude of thefluctuations is found, characterized by a maximum variation for values of thenoise correlation time comparable to the deexcitation time. The indirectinfluence of the colored noise on the efficiency of the energy transferupconversion activated from the level $^4$I$_{13/2}$ is also discussed.

Enhancement of the lifetime of metastable states in Er-doped Si nanocrystals by external coloured noise