Insights on heterogeneity in blinking mechanisms and non-ergodicity using sub-ensemble statistical analysis of single quantum-dots

Abstract

Photo-luminescence (P-L) intermittency (or blinking) in semiconductor nanocrystals (NCs), a phenomenon ubiquitous to single-emitters, is generally considered to be temporally random intensity fluctuations between "bright" ("On") and "dark" ("Off") states. However, individual quantum-dots (QDs) rarely exhibit such telegraphic signal, and yet, the vast majority of single-NC blinking data are analyzed using a single fixed threshold (FT) which generates binary trajectories. Further, blinking dynamics can vary dramatically over NCs in the ensemble, and it is unclear whether the exponents ( ) of single-particle On-/Off-time distributions ( ), which are used to validate mechanistic models of blinking, are narrowly distributed. Here, we sub-classify an ensemble based on the emissivity of QDs, and subsequently compare the (sub)ensembles" behaviors. To achieve this, we analyzed a large number (>1000) of blinking trajectories for a model system, Mn +2 doped ZnCdS QDs, which exhibits diverse blinking dynamics. An intensity histogram dependent thresholding method allowed us to construct distributions of relevant blinking parameters (such as, ). Interestingly, we find that single QD s follow either truncated power law or power law, and their relative proportion vary over sub-populations. Our results reveal a remarkable variation in amongst as well as within sub-ensembles, which implies multiple blinking mechanisms being operational amongst various QDs. We further show that the obtained via cumulative single-particle is distinct from the weighted mean value of all single-particle , an evidence for the lack of ergodicity. Thus, investigation and analyses of a large number of QDs, albeit for a limited time-span of few decades, is crucial to characterize possible blinking mechanisms or heterogeneity therein.

Core-Size-Dependent Trapping and Detrapping Dynamics in CdSe/CdS/ZnS Quantum Dots

“…In PDD analysis, the ON-to-OFF-transition (τ c ON ) and OFF-to-ON-transition (τ c OFF ) disclose the information about the trapping and detrapping kinetics, respectively. The charge trapping rate constant ( k t ) is calculated by taking the inverse of τ c ON , while the detrapping rate constant ( k d ) is obtained by the inverse of τ c OFF . ,,− The ratio of τ c ON to τ c OFF is equivalent to k d / k t in a single QD. The values for the power-law exponents for ON- and OFF-events of the four sets of QDs are provided in Table S2.…”

“…In the present study, we are focusing on the truncated part (exponential part) of the PDDs of ON- and OFF-events indicating the process such as trapping-induced charging (Auger photoionization) and detrapping-induced discharging (neutralization), respectively. The diffusion-controlled electron transfer (DCET) model proposed by Marcus and co-workers explains that the inverse of truncation time is equal to the energetic parameters of the corresponding process with a unit of s –1 , indicating that the process follows first-order kinetics. , The truncated power-law model has been widely used by several groups wherein the inverse of ON- and OFF-event truncation time is related to trapping and detrapping rates, both having a unit of second inverse. ,− In the present case, the PDDs are fitted with the ubiquitous truncated power-law (TPL) function, P ON ( t ) for the ON-state (eq ) and P OFF ( t ) for OFF-states (eq ) as where m represents the power-law exponent and τ c the truncation time (ON and OFF in the superscripts represent corresponding ON- and OFF-events, respectively). The function mentioned above describes a blinking process that can be modeled by a power-law function at the short times and an exponential function at the longer times (traces in the right column, Figure ).…”

Near-Ergodic CsPbBr3 Perovskite Nanocrystal with Minimal Statistical Aging

“…The PDD of both ON and OFF event durations of all 100 individual PNCs could be fitted well with the same truncated power-law equation (see p S7 of Supporting Information). , In the literature, the PDDs (of say ON event duration) of different subensembles of the same batch of QDs have been fitted with different kinds of equations . Thus, we may conclude that extent of heterogeneity in the quality of the nanocrystal and/or associated physical processes is minimal in our PNC system than the QDs reported in the literature.…”

“…It is important to estimate whether the deviation of the average statistical value of a physical parameter is minimal from what is obtained from a single nanocrystal. If that is true, then the system would be termed ergodic , or else it is non- ergodic . − Although single quantum dots (QDs) could be observed nearly three decades ago, to date there are very few reports investigating ergodicity in photoluminescence (PL) blinking of QDs. − Another important parameter, namely, statistical aging , measures the time evolution of PL intensity of individual QD. Optoelectronic applications rely mostly on the ergodic nature and minimal statistical aging of the QDs.…”

“…Comparatively lower magnitude of the COV for p values of OFF event distributions (Table 1) further confirms that the extent of variation in OFF → ON switching processes is lesser than that of ON → OFF switching processes. 5 ON/OFF event durations are correlated with trapping and detrapping rates. 21,22,27−29 Relatively more disperse ON event distribution as compared to OFF event distribution suggests that trapping rates are broadly distributed in comparison to detrapping rates.…”