Facts and Artifacts in the Blinking Statistics of Semiconductor Nanocrystals

Abstract

Since its initial discovery just over a decade ago, blinking of semiconductor nanocrystals has typically been described in terms of probability distributions for durations of bright, or "on," states and dark, or "off," states. These distributions are obtained by binning photon counts in order to construct a time series for emission intensity and then applying a threshold to distinguish on states from off states. By examining experimental data from CdSe/ZnS core/shell nanocrystals and by simulating this data according to a simple, two-state blinking model, we find that the apparent truncated power-law distributions of on times can depend significantly on the choices of binning time and threshold. For example, increasing the binning time by a factor of 10 can double the apparent truncation time and change the apparent power-law exponent by 30%, even though the binning time is only 3% of the truncation time. Our findings indicate that stringent experimental conditions are needed to accurately determine blinking-time probability distributions. Similar considerations should apply to any phenomenon characterized by time series data that displays telegraph noise.

Collective fluorescence enhancement in nanoparticle clusters

“…3a). Although it has been shown that blinking statistics are threshold dependent when the threshold is varied significantly 16,20,24 , our analysis confirms that the trends reported here hold for a wide range of reasonable thresholds (see detailed analysis of on-times for different thresholds in Methods). All results reported in the main paper were determined using a threshold of m dark + 7σ dark (red line in Fig.…”

“…Although it has been shown that blinking statistics are threshold dependent when the threshold is varied significantly 16,20,24 , our analysis confirms that the trends reported here hold over the entire threshold range tested, that is, from m dark + 5σ dark up to m dark + 8σ dark , while the absolute on-and off-time durations in the main paper depend on the exact threshold chosen, with higher thresholds yielding effectively shorter on-times (Fig. 8a).…”

“…Blinking time distributions for single nanoparticles have also been shown to depend on the time resolution of the intensity-time trace 24 . However, in this work, we compare measurements and simulations all made with the same time resolution.…”

Two-state theory of binned photon statistics for a large class of waiting time distributions and its application to quantum dot blinking

“…Parameters were not subtracted from an actual fit to the experimental WTDs due to their strong dependence on the choice of threshold. 14,17 The values of the shortest on and off timescales (t b(d) m ) have not been separately determined in experiment, and they were chosen to be identical and in the millisecond range. The possibility of lower t b(d) m cannot be ruled out as there is evidence that intensity fluctuations in CdSe/ZnS QDs may extend to 1/10 of a millisecond.…”

“…It was shown that both of these statistics can be highly biased by the two artificial quantities introduced during the analysis procedure, the bin time and intensity threshold. 14 While binned photon counting statistics have been calculated for exponential WTDs, 15 other relevant WTDs such as power laws and stretched exponentials have not yet been treated. This problem is tackled here by introducing a special kinetic scheme through which the functional form of the WTDs can be controlled.…”