The luminescence dynamics in ensembles of nanocrystals are complicated by a variety of processes, including the size-dependence of the radiative and non-radiative rates in inhomogeneous broadened samples and interparticle interactions. This results in a non-exponential decay, which for the specific case of silicon nanocrystals (SiNCs) has been widely modeled with a Kohlrausch or "stretched exponential" (SE) function. We first derive the population decay function for a luminescence decay following exp[- (t/τ)β]. We then compare the distributions and mean times calculated by assuming that either the luminescence decay or the population decay follows this function and show that the results are significantly different for β much below 1. We then apply these two types of SE functions as well as other models to the luminescence decay data from two thermally grown SiNC samples with different mean sizes. The mean lifetimes are strongly dependent on the experimental setup and the chosen fitting model, none of which appears to adequately describe the ensemble decay dynamics. Frequency-resolved spectroscopy (FRS) techniques are then applied to SiNCs in order to extract the lifetime distribution directly. The rate distribution has a half width of ~ 0.5 decades and mainly resembles a somewhat high-frequency-skewed lognormal function. The combination of TRS and FRS methods appear best suited to uncovering the luminescence dynamics of NC materials having a broad emission spectrum.
Keywords: Frequency-resolved spectroscopy; Lifetimes; Lognormal; Silicon nanocrystals; Stretched exponential; Time-resolved spectroscopy.