The changes in the lifetime of a metastable energy level in Er-doped Si nanocrystals in the presence of an external source of colored noise are analyzed for different values of noise intensity and correlation time. Exciton dynamics is simulated by a set of phenomenological rate equations which take into account all the possible phenomena inherent to the energy states of Si nanocrystals and Er$^{3+}$ ions in the host material of Si oxide. The electronic deexcitation is studied by examining the decay of the initial population of the Er atoms in the first excitation level $^4$I$_{13/2}$ through the fluorescence and the cooperative upconversion by energy transfer. Our results show that the deexcitation process of the level $^4$I$_{13/2}$ is slowed down within wide ranges of noise intensity and correlation time. Moreover, a nonmonotonic behavior of the lifetime with the amplitude of the fluctuations is found, characterized by a maximum variation for values of the noise correlation time comparable to the deexcitation time. The indirect influence of the colored noise on the efficiency of the energy transfer upconversion activated from the level $^4$I$_{13/2}$ is also discussed.
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