  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.
