A Python Toolbox for Unbiased Statistical Analysis of Fluorescence Intermittency of Multilevel Emitters

Abstract

We report on a Python toolbox for unbiased statistical analysis of fluorescence intermittency properties of single emitters. Intermittency, that is, step-wise temporal variations in the instantaneous emission intensity and fluorescence decay rate properties, is common to organic fluorophores, II−VI quantum dots, and perovskite quantum dots alike. Unbiased statistical analysis of intermittency switching time distributions, involved levels, and lifetimes are important to avoid interpretation artifacts. This work provides an implementation of Bayesian changepoint analysis and level clustering applicable to time-tagged single-photon detection data of single emitters that can be applied to real experimental data and as a tool to verify the ramifications of hypothesized mechanistic intermittency models. We provide a detailed Monte Carlo analysis to illustrate these statistics tools and to benchmark the extent to which conclusions can be drawn on the photophysics of highly complex systems, such as perovskite quantum dots that switch between a plethora of states instead of just two.

Intermittency of CsPbBr$_3$ perovskite quantum dots analyzed by an unbiased statistical analysis

“…state offered to the clustering algorithm is in fact used by the algorithm, whereas Monte Carlo simulations have shown that at the photon budgets involved (5.5 × 10 6 photons) the clustering algorithm generally does not assign occupancy to more than m levels to simulated m-levels dots. 26 The occupancy diagram hence confirms the conclusion from the BIC criterion that the dot at hand requires many levels, or even a continuous set of levels, to be described.…”

“…23,41 We have extensively verified by Monte Carlo simulations the performance of CPA and level clustering for dots with many assumed discrete intensity levels in a separate work. 26,27 In brief, at small photon budgets in a total time series, only few levels can be detected, but conversely at the total photon budgets in this work, exceeding 5 • 10 6 events, clustering has a > 95% success rate in pinpointing the exact number of levels in dots with at least 10 assumed intensity levels. Moreover, for photon budgets that are too small to pinpoint all levels exactly (e.g., at 10 4 counts in a total measurement record, only up to 4 levels can be accurately discerned), clustering always returns a lower bound for the actual number of intensity states.…”

“…13,24,25,31,[35][36][37][38][39][40] We refer to Ref. 26,27 for our freely available implementation and a detailed description of benchmarking of this tool set. Here we summarize just the salient outcomes relevant for this work, obtained by extensive Monte Carlo based benchmarking to determine the performance of CPA and clustering for highly multilevel emitters.…”

“…The FDID diagrams at hand qualitatively support the continuous distribution of states hypothesized in the MRC model, and observed by Refs. 11,12,14 As quantification of the number of states involved we perform clustering analysis 23,24,26 to estimate the most likely number of intensity states describing the data on basis of Bayesian inference. A plot of the Bayesian Information Criterion as function of the number of levels n G allowed for describing the data of the specific example dot at hand is shown in Figure 4A.…”

“…These Bayesian statistics methods were first developed by Watkins and Yang [23][24][25] and have since been applied in a small set of papers to two/few-level II-VI dots, and in one recent work to CsPbBr 3 dots. 13 Our implementation is through a freely available Python-based analysis toolbox, 26,27 which we have specifically benchmarked by Monte Carlo methods for application to highly multi-state, instead of bi-modal, systems.…”