Blinking Kinetics of Single CdSe / ZnS Nanocrystals by Photon-Counting Statistics at High Temporal Resolution

Fluorescence intermittency (blinking) of semiconductor nanocrystals (NCs) is interpreted in terms of single photon-counting at high temporal resolution of tens of kiloframes per second (kfps) by fast imaging on ZnSovercoated CdSe (CdSe/ZnS) NCs. We report herein a characterization method based on the threshold resulting from a double exponential distribution as a function of the photon interval to discriminate between “on” (bright) and “off” (dark) states. Histograms of both the resolved “on” and “off” lengths show that they obey single Poisson distributions with their duration constants, contrary to the conventional power-law distributions. We suggest that this characterization gives us more potential power to elucidate blinking kinetics of single CdSe/ZnS NCs on their physicochemical surroundings. [DOI: 10.1380/ejssnt.2009.701]


I. INTRODUCTION
Semiconductor nanocrystals (NCs) are one of fascinating materials for both fundamental studies and technical applications such as solar cells [1], quantum-dot memories [2], and biological labeling probes [3] due to their optical properties of size-dependent tunability [4], fluorescence intermittency, and high quantum yield.The single-NC fluorescence intermittency (blinking) under continuous excitation was first discovered by Nirmal et al., which has been understood as a phenomenon involved in the nonradiative Auger relaxation process of a photoionized NC accompanied by neutralization [5].An ejected carrier (electron or hole) can be trapped on the photoionized NC surface, giving rise to changes in the blinking profile of a NC such as substrate-dependent blinking [6], and the effects of its shell and capping layer on blinking profiles [7,8].However, all of the previous results have revealed that the blinking kinetics obeys universal inverse power-law distributions in "on" and "off" lengths for a single NC of CdSe [8][9][10][11], and "off" lengths for single NCs of CdTe [11] and CdS [12], contrary to the predictable exponential distributions [13].Thus, several efforts have been made to explain this unexpected nonexponential blinking kinetics by employing non-single-trap models such as the multiple-trap model [9,10,14], and the model involving a uniform distribution of multiple traps [12].These methods, however, could explain the power-law distribution for the "off" length only.Osad'ko et al. have also proposed a similar multiple-trap model reflecting the multiple-localized state in a NC as a doorway for the ejected carrier to explain the power-law distribution of "on" lengths [15].However, they also encountered difficulty in explaining the experimental incompatibilities at room temperature and under high excitation [11], as well as the further ionization of a charged NC.Moreover, a recent study has revealed the NC blinking statistics to be independent of the shell thickness [16], and all discussed models remain controversial.Lippitz et al. have pointed out that a temporal resolution ten times higher than the blinking rate is necessary to fully resolve the blinking events, which implies that employment of a sufficiently short bin size can lead to Poisson distributions [17].Verberk et al. suggested a charged "on" state in terms of trap depth [12].Extending the prolonged "on" state to a three-state model, recent reports [18,19] have suggested that emission states of single NCs are governed by not two levels ("on" and "off") but numerous intermediate levels of continuous distribution.However, we noted that the temporal resolutions of these previous studies were limited to 10-100 ms/bin.We demonstrate herein a measurement designed for the 1,000 times higher temporal resolution in a photoncounting regime than that used in conventional measurements to analyze the distributions of "on" (bright state) and "off" (dark state) lengths, which are discriminated by the thresholds evaluated from a double exponential distribution of temporal intervals between single photon emissions (photon intervals).Consequently, the blinking kinetics is considered to be a single exponential distri- bution, thus suggesting the potential possibility of this characterization for blinking statistics of NCs under their various physicochemical surroundings.

II. EXPERIMENTAL METHODS
Two kinds of colloidal CdSe/ZnS NCs capped with tri-n-octylphosphine oxide (TOPO) in toluene were purchased from Evident Technologies Inc. (USA).These NCs have the emission peaks of 560 nm (core size, 2.6 nm) and 620 nm (core size, 5.2 nm), respectively.As a polymer matrix for embedding NCs, polystyrene (PS) (Sigma-Aldrich Co. Ltd., USA) was used without further purification.The molecular weight of PS had a narrow distribution of 18,700 (g/mol).Phenyltrimethoxysilane (PTMS) was purchased from Tokyo Chemical Industry Co., Ltd.(Japan).Toluene for a solvent, and reagent-grade concentrated sulfuric acid (H 2 SO 4 ) and certified 30% hydrogen peroxide (H 2 O 2 ) for piranha solution were purchased from Kanto Chemical Co., Inc. (Japan).Cover glasses with a diameter of 18 mm (Matsunami Ind., Ltd., Japan), and p-type Si(100) (Shin-Etsu Chemical Co., Ltd., Japan) wafers were employed as substrates for fluorescence and thickness measurements of films, respectively.
The cover glasses and Si wafers split into 10×20 mm were thoroughly cleaned with piranha solution (H 2 SO 4 :H 2 O 2 = 7:3 v/v) at 98 • C for 1 h.The cleaned substrates were placed in the glass vessel with its lid; subsequently, the vessel containing a 30 mm-wide Petri dish filled with 100 µL PTMS and 700 µL toluene was heated at 105 • C for 1 h, which led to PTMS silanization of substrates.Each colloidal CdSe/ZnS NC of different core size was prepared at concentrations of 0.8 nM (core size, 5.2 nm) and 4 nM (core size, 2.6 nm), respectively.These colloids were continuously diluted to concentrations of 0.008 nM (core size, 5.2 nm) and 0.04 nM (core size, 2.6 nm).Each of the prepared colloidal NC solutions was added to PS matrix dissolved in toluene at a concentration of 1 mg/mL.The PS matrix containing the colloidal NCs was spin-coated on PTMS-modified substrates at 2,000 rpm for 20 s.The spin-coated NC films were dried overnight under ambient conditions without being baked.
The thickness measurements of the spin-coated PS films and the silanized PTMS films were taken using an M-2000UI ellipsometer (J.A. Woollam Co., Inc., USA).The PS and PTMS films had the thickness of 3.69 nm and 2.10 nm, respectively.
Fast imaging on the NC films by wide-field microscopy was carried out using the high-frame-rate video camera (FASTCAM-MAX 120K, Photron Ltd., Japan) equipped with an image intensifier unit (customized C8600-03: response time of sub microseconds, Hamamatsu Photonics K.K., Japan) via the TIRFM at a temporal resolution of 87.6 kiloframes per second (kfps) for 18 s.The obtained image size was 128×32 pixels, and the intensity of each pixel was exhibited in a range of 8-bit (0 to 255).The number of images for one measurement (stack) was about 1.5 million for 18 s.
The standard deviation and the summation of intensity trajectory for each pixel in the image stack were investigated using the ImageJ (NIH, USA) macro to figure out the pixels standing for blinking single NCs.The time traces of the selected pixels were monitored to pick up the frames of single photon emissions among all frames via the ImageJ macro.The intervals between the single photon emissions (photon intervals) were numerically computed, and the histogram of the photon intervals and time lengths ("on" and "off" states) with thresholds for each pixel were statistically evaluated using MATLAB (The MathWorks, Inc., USA).

A. Confirmation of a single NC distribution
It has been known that only a single NC can exhibit a blinking phenomenon because ensemble NCs can average out their individual blinking phenomena [5,10,14,19].However, Yu et al. pointed out that ensemble NCs such as a cluster composed of two or more NCs and multiple isolated NCs can also show blinking phenomena [20].These conflicting findings indicate that an optical microscopy can bring about a technical difficulty in resolving a single NC among ensemble NCs due to the limitation in its resolving power.We controlled the concentrations of single NCs embedded in a PS matrix to suppress this difficulty, and two kinds of NCs with their different emission peaks were mixed and spin-coated to confirm single NC measurements.The 3CCD images of NC/PS films are shown in Figs.1(a), 1(b), and 1(c).The isolated individual emissions were observed at a low NC/PS concentrations (0.01 µg/mg), as shown in Fig. 1(b), while high concentrations (1 µg/mg) led to yellowish emissions, implying the presence of multiple isolated NCs with short interdistances (Fig. 1(a)).
On the basis of our estimation of a single NC weight [21], the average distance between single NCs was computed to be ∼3 µm.We assumed that 55 single NCs existed in an irradiated circular area 25 µm in diameter.Surprisingly, we found 45 blinking spots in an imaged area 25 µm in diameter (Fig. 1(c)).

B. Determination of single photons
The fluorescence lifetime in a single NC is known to be in the range of several tens of nanoseconds [22,23], while the mean photon-absorption time is estimated to be up to sub microseconds at an excitation intensity of 15 W/cm 2 .This suggests a technical difficulty in the proper monitoring of single photons from a blinking NC with the conventional measurement at a high excitation power.However, we attempted to employ 87.6 kfps (11.416 µs/bin) as the temporal resolution for characterization of blinking statistics.One frame of a raw image stack, which has white noises, background-emissions and photon-emissions, is illustrated in Fig. 2 the background-emissions with white noises in the raw image stack leads to a calibrated image stack, which has effectively photon-emissions as shown in Fig. 2(b).This calibration process was regulated automatically by the high-frame-rate video camera.
The intensity trajectory of one spot among 48 pixels is shown in Fig. 3 which satisfies the following condition: where I n and I n−1 are the fluorescence intensities at "n"th and "n-1"-th bins of the calibrated image stack for a selected spot, respectively.The tailed decreases in Fig. 3(b) are regarded as residual lags in photon detection.However, we noted that photon interval of the unit bit has been counted 86 times as a maximum frequency via the above condition (1).On the basis of the above logical flow, the discrete pulselike profile for the spot was interpreted into the photon stream as a function of time (Figs.3(b: inset) and 4(a)) [24].The distribution of photon intervals was revealed to obey double exponential function with time constants of τ on and τ off , as follows (Fig. 4(b)): where P (t) is the probability function of the photon interval, and A on and A off are arbitrary constants.The P (t) is composed of and

C. Time constants and threshold
Considering that the photon-emission rate is inversely proportional to the number of counted photons per unit http://www.sssj.org/ejssnt(J-Stage: http://www.jstage.jst.go.jp/browse/ejssnt/) time, or fluorescence intensity, it is clear that the shortterm state is related to the "on" event.Consequently, the distribution of detected photon intervals can be expressed by the combination of Poisson functions of P on (t) and P off (t), which stand for the occurrence probabilities for "on" and "off" episodes, respectively, as a function of the photon interval.Thus, the time constants, τ on and τ off , represent the mean times of photon intervals for "on" and "off" states, which are computed as 192 µs and 2.6 ms, respectively.In terms of statistics, these time constants imply that 5,208 and 384 photons can be counted for a unit second as the fluorescence intensities of "on" and "off" states.Figure 4(b) strongly demonstrates that emissions of single NCs flow between two levels ("on" and "off" states) contrary to the previous reports of continuous distribution in emission intensity [18,19].
The relationship between the photon-emission rate and the number of counted photons leads us to take simply the harmonic mean of τ on and τ off as a threshold to discriminate between "on" and "off" states.However, we cannot ignore the error probabilities induced by a combination of two probability functions.Thus, the probabilities for P on (t) and P off (t) in their counter-regions were taken as their errors (Fig. 4(b: inset)).The normalized probability of taking "on" as "off" with P on (t) and that of taking "off" as "on" with P off (t) must be identical, as in Eq. ( 5): which can be simplified into Eq.( 6).
where τ th is the critical threshold to discriminate between "on" and "off" states.The critical threshold can be numerically evaluated from Eq. ( 6) by the Newton-Raphson method, which was computed to 381 µs from 192 µs and 2.6 ms.This value slightly deviates from the harmonic mean (358 µs) of 192 µs and 2.6 ms.On the basis of the threshold, the events whose lengths are shorter than 381 µs can be regarded as the "on" state, and the others can be regarded as the "off" state (Fig. 4(c)).

D. On and off durations, and duration constants
As shown in Fig. 4(c), the above threshold gives us a more precise definition of "on" and "off" events than the conventional threshold [9,10,14].This definition indicates that the conventional definitions of "on" and "off" events can ignore the short-term events, which can distinctly contribute to an "on" or "off" event.According to the definition, "off" duration (or the length of "off" state) should be larger than the threshold of 358 µs.However, "on" duration (or the length of "on" state) is not restricted to the threshold.
As a result of the evaluation, each of the "on" and "off" events was collected and distributed respectively as a function of the time length (interval or duration).The distributions of "on" and "off" lengths are shown in Figs.5(a) and 5(b).Both of the distributions are described by single exponential functions of P on (∆t) and P off (∆t) as a function of the time length (∆t), as follows: and where B on and B off are arbitrary constants and ∆τ on and ∆τ off are the mean durations of the "on" and "off" states, respectively.Figures 5(a) and 5(b) show that the distributions of the "on" and "off" lengths obey single exponential functions with the ∆τ on of 280 µs and the ∆τ off of 10.4 ms, respectively.These results support the postulate that only the neutralized NC can emit a photon, and the charged NC prefers to undergo neutralization rather than further ionization [13].We believe that our results can explain blinking kinetics based on a single-photon regime.http://www.sssj.org/ejssnt(J-Stage: http://www.jstage.jst.go.jp/browse/ejssnt/) e-Journal of Surface Science and Nanotechnology  4(a), illustrating "on" (blue columns) and "off" events according to the τ th : double-headed blue arrows indicate "off" durations (the length of "off" states).

E. Comparison with conventional analysis
Contrary to the CdSe NC, the other fluorescent intermittent cores such as the green fluorescent protein (GFP) and the Cy5-maleimide molecule (Cy5) are known to obey a Poisson distribution at conventional low temporal resolutions [25,26].These findings imply that the blinking rate of CdSe NC is much faster than those of the GFP and the Cy5.We found that bin size, or temporal resolution, can play an important role in determining the distribution profile of blinking statistics.In order to monitor the conventional temporal trajectory of the fluorescence intensity, a certain number of bins (Fig. 4(a)) can be summed into a large bin size, as in Fig. 6(a).In this measurement, 8,760 bins and 4,380 bins were summed up as unit bins of 100 ms and 50 ms, respectively.Thus, 63 events for the temporal resolution of 50 ms/bin and 28 events for 100 ms/bin were generated from the summation of 11.416 µs-bins.Considering the conventional threshold (Fig. 6(a)), the upper side of each I th simply stands for the "on" state, while the bottom side of each I th represents the "off" state.However, it is clear that the conventional low temporal resolution can screen numerous short-term events, judging from the photon-counting regime at high temporal resolutions of tens of microseconds.
Hence, fluorescence trajectories as a function of the regenerated temporal resolution from the summation of bins were investigated to elucidate the effects of temporal resolution.As shown in Fig. 6(b), the blinking profile at lower temporal resolution than 87.6 kfps (11.4 µs/bin) can be expressed in terms of a time-dependent intensity.We can apparently see that the blinking profiles parade discrete pulselike streams at the resolutions lower than 100 fps (10 ms/bin).As a temporal resolution is increasing, it is inevitable to switch the interpretative variable to photon interval.Similarly, Lippitz et al. have suggested a ten times higher temporal resolution than the blinking rate as a proper resolution [17]; they did not, however, speculate on the proper resolution for blinking NCs.Thus, we propose that a 100 to 1,000 times higher temporal resolution is necessary for precise characterization in light of the loss of short-term photon-emissions at a low temporal resolution.

IV. CONCLUSION
We introduced the photon-counting statistics based on the threshold of photon intervals for the blinking single NCs embedded in PS film at a temporal resolution of 87.6 kfps.The blinking statistics were interpreted as an interval-dependent stream of single photons, while the conventional characterization translated the blinking phenomenon as a stepwise continuous fluctuation of fluorescence.Consequently, the histogram of the photon intervals from a blinking NC was described by a double exponential function, whose time constants represent the mean times for "on" and "off" states.This double exponential distribution strongly reflects that the blinking phenomenon of a single NC can be described by short interval ("on") and long interval ("off") states.The threshold based on the photon interval was estimated from the probability functions and two time constants.We computed the threshold to 381 µs at 87.6 kfps.The histograms of the collected "on" and "off" events were expressed in single exponential functions whose time constants were 280 µs and 10.4 ms, respectively.These results indicate that the stream of each state ("on" or "off") obeys a single exponential distribution.
Although further considerations on the trap model may be necessary to visualize our results, we hope that our analytical method will be powerful enough to characterize the blinking statistics of single NCs in various physicochemical surroundings.The numerical demonstration of temporal resolution effect will prove our suggestion soon or later.
FIG. 1: 3CCD-TIRFM images of CdSe/ZnS NC embedded in PS films on PTMS surfaces for (a) 2.6 nm core of 4 nM and 5.2 nm core of 0.8 nM: the dotted circles show yellowish emissions indicating two kinds of NCs existing close to each other; (b) 2.6 nm core of 0.04 nM and 5.2 nm core of 0.008 nM: the dotted circles show reddish emissions indicating individual NCs existing separately; and (c) the imaged area of 25 µmdiameter (dotted circle) irradiated by an Ar ion laser at a concentration of NCs for (b).
FIG. 2: The frames (32×128 pixels) of (a) a raw image stack having white noises, background-emissions and photonemissions, and (b) the compensated image stack having photon-emissions only: the background-emissions with white noises have been ruled out via calibration.Each inset in Figs.2(a) and 2(b) indicates histogram of intensity in 8-bit scale for the corresponding frame: the gray part in each inset indicates the range of intensity larger than background emission; the non-gray part in Fig. 2(a) indicates the range of background emission.The nine gray spots in Figs.2(a) and 2(b) indicate the pixels in the range of intensity higher than the background emission (the gray region in each inset).Note that the scale of the histogram is not absolute but relative.

FIG. 3 :
FIG. 3: Analyzed profiles at 87.6 kfps: (a) intensity trajectory of a blinking single NC; (b) the magnified region of Fig. 3(a), illustrating how to determine single photon at "n"-th frame (bin) via ImageJ macro: the dotted circles indicate the determined single photons satisfying the condition of In > In−1, and the inset indicates the time trace of the determined photon stream at the frames of the dotted circles.

FIG. 4 :
FIG. 4: Analyzed profiles at 87.6 kfps: (a) time trace of a photon stream evaluated from Fig. 3(a) via the logical flow in Fig. 3(b); (b) double exponential distribution of photon intervals: the solid curve indicates fitted P (t); the dashed green line illustrates a cross-section line indicating threshold τ th ; and the inset shows error probabilities [the red part for Pon(t), and the blue part for P off (t)] of Pon(t) (the dotted blue line) and P off (t) (the dotted red line) in their counter-regions; and (c) the magnified region of Fig.4(a), illustrating "on" (blue columns) and "off" events according to the τ th : double-headed blue arrows indicate "off" durations (the length of "off" states).