such feature is blinking, which is the absence of sec ondary emission under continuous optical excitation over time intervals that may be as long as milliseconds.
ISSN 00213640, JETP Letters, 2012, Vol. 96, No. 1, pp. 17–20. © Pleiades Publishing, Inc., 2012. Original Russian Text © A.G. Vitukhnovskii, A.Yu. Pereverzev, V.V. Fedyanin, S.A. Ambrozevich, R.B. Vasiliev, D.N. Dirin, 2012, published in Pis’ma v Zhurnal Eksperimental’noi i Teoreticheskoi Fiziki, 2012, Vol. 96, No. 1, pp. 18–21.
Correlation between PhotonEmission Intervals in Blinking Luminescence of Single CdSe/CdS Nanocrystals A. G. Vitukhnovskiia, A. Yu. Pereverzeva, b, V. V. Fedyanina, c, S. A. Ambrozevicha, R. B. Vasilievd, and D. N. Dirind a
b
Lebedev Physical Institute, Russian Academy of Sciences, Moscow, 119991 Russia Moscow Institute of Physics and Technology (State University), Dolgoprudny, Moscow region, 141700 Russia c Moscow State Pedagogical University, Moscow, 119991 Russia d Faculty of Materials Science, Moscow State University, Moscow, 119992 Russia Received May 18, 2012
The statistics of luminescence from single CdSe/CdS core/shell semiconductor nanocrystals under CW laser excitation at room temperature is experimentally investigated by recording sequences of absolute arrival times of the emitted photons. It is shown that the correlation coefficient for consecutive intervals between the pho tonarrival times differs from zero. The correlation persists for photonarrival intervals separated by two or more photondetection events, until the time between the two intervals becomes, on average, as long as 180 ms, which corresponds to about 103 detected photons. A simulation of the luminescence process supports the conclusion that this correlation is linked to the blinking character of the quantumdot luminescence. DOI: 10.1134/S0021364012130139
INTRODUCTION High quantum efficiency, narrow spectral lines, and the possibility of adjusting the peak luminescence wavelength by changing the size of nanocrystals of a given chemical composition (which can be done with out changing the synthesis technology) make semi conductor nanocrystals promising for the fabrication of semiconductor lasers [1] and organic lightemitting diodes [2]. At the same time, some features typical of the lumi nescence of nanocrystals limit their applications. One such feature is blinking, which is the absence of sec ondary emission under continuous optical excitation over time intervals that may be as long as milliseconds or seconds. Blinking, i.e., the presence of long alter nating “on” and “off” periods, is also observed in the luminescence of single molecules, where this inter mittency is due to the existence of a longlived state corresponding to the triplet level [3]. However, unlike molecules, where the durations of the “on” and “off” periods are characterized by exponential distributions, nanocrystals exhibit powerlaw distributions of the “on” and “off” durations [4, 5]. The origin of this behavior is still a matter of discussion [6–8]. In partic ular, in the case of photoinduced ionization of a nanocrystal followed by its neutralization, an expo nential distribution would be obtained in disagreement with experimental data [4]. This implies that the powerlaw behavior of the blinking distributions is caused by several concurrent processes rather than by a single process. The understanding of physical mech anisms responsible for this effect may be important for
the elimination of blinking and open the way to the broad use of nanocrystals as radiative recombination centers. One of the features typical of blinking nanocrystal fluorescence is an essentially nonzero value of the lin ear (Pearson) correlation coefficient between the durations of periods of one type (“on” or “off”) with numbers i and i + k [9]: Σi ( Xi – X ) ( Xi + k – X ) Q ( k ) = . 2 2 Σi ( Xi – X ) Σi ( Xi + k – X )
(1)
Here, Xi is the duration of the ith period and X is the mean duration of periods. The fact that Q(k) differs from zero was attributed to a “memory effect” since it points to the existence of some connection between the durations of succeeding and preceding periods [9]. There is no mean for a powerlaw distribution with an exponent m < 2. So, the average duration for each experimental trajectory, which depends on the param eters of the experiment, has usually been substituted for X [10]. Such an analysis relies on arbitrary choices for the signal averaging time and the level of discrimi nation between the “on” and “off” states. Slight vari ations in these parameters lead to considerable changes in the character of the distributions thus obtained [11]. Conclusions on the existence of “memory” should be treated with caution, since different factors may result in the appearance of a correlation between the durations of the “on” and “off” periods. In particular, 17
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Fig. 1. Fragment of the luminescenceintensity trajectory of a single CdSe/CdS quantum dot obtained upon averag ing over time bins of tbin = 2 ms.
this correlation depends on how the original photon detection times are divided between the “on” and “off” periods. Nevertheless, the correlation coeffi cient proves to be a convenient tool for describing the data on the arrival of photons emitted by a single nanocrystal. In this work, instead of dealing with the timeaver aged signal of the singlenanocrystal luminescence, we analyze the sequence of individual photon detection times. The goal is to study the correlation coefficient for the time intervals between consecutive photon detection events, which is a quantity independent of any averaging procedures.
Fig. 2. Distributions of the “on” period and “off” period durations determined on the basis of the experimental luminescenceintensity trajectory of a single CdSe/CdS semiconductor nanocrystal shown in Fig. 1.
EXPERIMENT We studied CdSe/CdS semiconductor nanocrystals synthesized by a method similar to that described in [12]. The maximum of the nanocrystal luminescence spectrum corresponds to a wavelength of 615 nm, while the excitonic peak in the absorption spectrum is at 605 nm. A typical diameter of the CdSe core amounts to 3.5 nm, and the average thickness of the CdS shell is 1.0 nm. The nonuniformity in the size dis tribution does not exceed 8%. A more detailed charac terization is presented in [13]. The luminescence of single CdSe/CdS nanocrys tals was investigated at room temperature using an MT200 confocal microscope (PicoQuant, Germany), which makes it possible to record a sequence of arrival times of individual photons emitted by a nanocrystal with an accuracy of 4 ps. The dead time of the single photon detector was about 80 ns. The optical excita tion was carried out using a CW laser emitting at 376 nm. For the comparison of our results with those pre sented in other publications, the signal was averaged over time bins of size tbin = 2 ms. The number of pho tons detected within a window of this duration at dif ferent times is plotted in Fig. 1. Intensity drops are clearly seen.
The distributions of the “on” and “off” period durations (Fig. 2) corresponding to the obtained intensity trajectory exhibit a clearly pronounced powerlaw behavior. The values of the exponent for the “on” and “off” period distributions are 1.3 and 1.88, respectively, which is in agreement with the data of [7]. Figure 3 shows the correlation coefficients for the durations of consecutive “on” and “off” periods sepa rated by a number of transitions to the radiative and nonradiative states. For two adjacent “on” periods or “off” periods, the correlation coefficients are fairly large (more than 0.3). A twofold decrease in the corre lation coefficients between two “on” (“off”) periods occurs as the number of “on” (“off”) periods separat ing them approaches about 10. Since the average total duration of a pair of successive “on” and “off” periods for CdSe/CdS nanocrystals under study is about 40 ms, the correlation persists over a time of 400 ms. In the context of the novel approach suggested, we now analyze the correlation between the intervals sep arating the detection of two adjacent photons (emitted by a single CdSe/CdS nanocrystal) measured at differ ent moments of time. Figure 4 shows the correlation coefficient for this quantity, plotted as a function of the number of photons detected between the two corre sponding intervals, for two different CdSe/CdS JETP LETTERS
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Fig. 4. Correlation coefficient Q for the time intervals between the arrivals of two adjacent photons versus the number of photons k detected between the two intervals. Curves 1 and 2 show experimental results for two different quantum dots; curves 3 and 4 show the result of Monte Carlo simulation for the cases of powerlaw and exponen tial distributions of both “on” and “off” periods, respec tively; and curve 5 describes the correlation coefficient for the photonarrival intervals measured within “on” periods only. Fig. 3. Correlation coefficients Q for the durations of the “on” and “off” periods separated by k transitions to the radiative and nonradiative states.
nanocrystals (curves 1, 2). In addition, “on” periods were determined from the trajectory of the lumines cence intensity obtained after averaging over 2ms time bins (Fig. 3) and the correlation coefficient for the photonarrival intervals was determined within each such period (Fig. 4, curve 5). The correlation coefficients for the “on” periods thus obtained are expected to describe processes that are not related to blinking. DISCUSSION For two different CdSe/CdS nanocrystals, the cor relation coefficient for the photonarrival intervals exhibits similar dependences on the number of pho tons detected between them (Fig. 4, curves 1, 2). The correlation coefficient decreases by a factor of 2 when about 103 photons are detected between the two inter vals. In the case under study, the average time between two detected photons is 180 μs. Thus, the characteris tic correlation time is 180 ms. This value is comparable to the correlation time of the “on” and “off” intervals obtained for the averaged intensities. This fact may be an indication of the existence of a slow process in the system. It should be noted, however, that the average time between the detection of two successive photons has no physical meaning owing to the powerlaw behavior of the “on” and “off” interval distributions. JETP LETTERS
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In order to understand the nature of the correla tions in the intervals between successively detected photons, the correlation coefficients were calculated for the periods corresponding to the “on” states on the trajectory of the timeaveraged intensity (see Fig. 4, curve 5). No correlations between the photonarrival intervals are observed in this case; thus, any nonzero correlations are related to the blinking character of the nanocrystal luminescence. To check the validity of this conclusion, we simulated the sequence of arrival times of photons emitted by a single nanocrystal using the Monte Carlo method. The simulation was carried out in the following way. A random sequence of “on” and “off” period durations was generated according to a powerlaw dis tribution in the range of 0.1 ms to 10 s. Since the dura tions of the “on” and “off” periods were calculated independently, there were no correlations between them. Within each interval, a random sequence of photonarrival times distributed according to Poisson statistics was generated. The choice of such a distribu tion was suggested by the Poisson statistics of the pho tonarrival intervals in the “on” and “off” states that we observed experimentally. The parameters used in the calculations were equal to the average values obtained from the experimental data: the exponents in the “on” and “off” period distributions were mon = 1.5 and moff = 1.7 and the average intervals between the adjacent detected photons in the “on” and “off” states were 0.1 and 1 ms, respectively. The correlation coef ficient Q(k) for such a model sequence of photons is shown by curve 3 in Fig. 4.
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The dependence Q(k) calculated in this way has a shape typical of the experimental curves obtained for CdSe/CdS nanocrystals under study. To check the importance of the powerlaw character of the photon arrival distribution, we carried out a similar calcula tion assuming an exponential distribution of the “on” and “off” period durations with the same average val ues (Fig. 4, curve 4). In this case, the calculated Q(k) dependence differs considerably from the experimen tal one. Thus, the powerlaw distribution of the “on” and “off” periods essentially determines the shape of this dependence and, consequently, the latter does characterize in some way the process of the single nanocrystal luminescence. CONCLUSIONS The statistics of the blinking fluorescence of CdSe/CdS core/shell semiconductor nanocrystals under CW laser excitation has been studied experi mentally using for the first time an approach based on the analysis of the correlation coefficient for the time intervals between the arrivals of two adjacent fluores cence photons. The results obtained indicate that the observed correlations are related to the powerlaw character of the distribution of the “on” and “off” period durations. The time range of the correlation, which is 180 ms in the case under study, is comparable to the time range of the correlations determined for the signal averaged over 2ms time bins (400 ms). The correlation coefficient for the photonarrival intervals characterizes the blinking effect and, in contrast to the correlation in the “on” and “off” interval durations, is independent of arbitrary parameters like the binning time. We are grateful to Dr. V.I. Yudson (Institute of Spectroscopy, Russian Academy of Sciences) for use ful discussions and to N.S. Vlasova for her help in car
rying out the experiments. This study was supported by the Russian Foundation for Basic Research (project no. 120300839a) and the Ministry of Education and Science of the Russian Federation (state contract no. 16.516.11.6071). REFERENCES 1. V. I. Klimov, F. F. Mikhailovsky, X. Su, et al., Science 290, 314 (2000). 2. V. Wood, M. J. Panzer, J. M. Caruge, et al., Nano Lett. 10, 24 (2010). 3. Th. Basche, W. E. Moerner, M. Orrit, et al., Single Mol ecule Optical Detection, Imaging and Spectroscopy (Weinheim, Germany, 1997). 4. M. Kuno, D. P. Fromm, H. F. Hamann, et al., J. Chem. Phys. 115, 1028 (2001). 5. M. Kuno, D. P. Fromm, A. Gallagher, et al., Nano Lett. 1, 55 (2001). 6. I. S. Osad’ko, Chem. Phys. 316, 99 (2005). 7. P. Frantsuzov, M. Kuno, B. Janko, et al., Nature Phys. 4, 519 (2008). 8. Th. Hartmann, V. I. Yudson, and P. Reineker, J. Lumi nesc. 131, 379 (2011). 9. F. D. Stefani, X. Zhong, W. Knoll, et al., New J. Phys. 7, 197 (2005). 10. S. VolkánKacsó, P. A. Frantsuzov, and B. Jankó, Nano Lett. 10, 2761 (2010) 11. C. H. Crouch, O. Sauter, X. Wu, et al., Nano Lett. 10, 1692 (2010). 12. R. B. Vasiliev, S. G. Dorofeev, D. N. Dirin, et al., Men deleev Commun. 14 (4), 169 (2004). 13. S. Ambrozevich, M. van der Auweraer, D. Dirin, et al., J. Russ. Laser Res. 29, 526 (2008).
Translated by M. Skorikov
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