Effect of the shell on the blinking statistics of core-shell quantum dots ...

PHYSICAL REVIEW B 75, 125431 共2007兲

Effect of the shell on the blinking statistics of core-shell quantum dots: A single-particle fluorescence study Colin D. Heyes,1,* Andrei Yu. Kobitski,1 Vladimir V. Breus,1 and G. Ulrich Nienhaus1,2,* 1Department

of Biophysics, University of Ulm, Albert Einstein Allee 11, 89069 Ulm, Germany Department of Physics, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA 共Received 24 July 2006; revised manuscript received 17 January 2007; published 28 March 2007兲

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Fluorescence blinking of single quantum dots 共QDs兲 under constant illumination has attracted a great deal of attention from both experimentalists and theoreticians. To explain the power-law behavior in the distribution of both “on” and “off” times, several models have been proposed, in which the charge carrier is either ejected from the QD to an external trap or localized at a trapping site within the QD. To gain insight into the blinking mechanism, we have studied the role of the shell of CdSe-ZnS core-shell QDs. For two sets of samples varying in the fluorescence quantum yield of the core, we systematically varied the thickness of the shell and analyzed the blinking behavior of a statistically significant number of single QDs. In both cases, the distributions of on and off times were independent of the ZnS shell thickness. These data can be explained with a recently introduced model 关Frantsuzov and Marcus, Phys. Rev. B 72, 1553211 共2005兲兴. After photoinduced creation of an electron-hole pair, the hole is trapped in a deep surface state of the CdSe core, and the excess energy is transferred to the electron in an Auger process, raising it from the 1Se to the 1Pe state. The energy gap between these electronic states is assumed to perform stochastic diffusion so that it can be either in resonance or out of resonance with the energy gap between the hole states. This model explains the power-law behavior of the on and off times distribution, the exponential cutoff of the power-law dependence at long on times and the lacking dependence of the blinking kinetics on the shell thickness. It also explains our observation that the overall quantum yield of an ensemble is mainly governed by the fraction of nonemitting particles in the sample. DOI: 10.1103/PhysRevB.75.125431

PACS number共s兲: 78.67.Hc, 73.22.⫺f

I. INTRODUCTION

Quantum dots 共QDs兲 are direct-band gap semiconductor nanomaterials that have received a great deal of attention in recent years due to their unique properties, which lie between the atomic and bulk material extremes. Photoexcitation creates an electron-hole pair 共exciton兲 that is confined to a space smaller than its Bohr radius, resulting in quantum confinement effects. The electronic and optical properties can be fine-tuned via the size and shape of the nanoparticles, which makes them attractive for various electro- and quantumoptical applications 共Lasers,1 LEDs,2,3 optical storage,4 photovoltaic/solar cells,3,5 single-photon sources,6 etc.兲, supramolecular mesoscale self-assembled arrays,7 and highly sensitive luminescent probes in biological and biophysical applications.8–11 Their high luminescence efficiency and photostability allow easy observation of single QDs 共Refs. 12 and 13兲 and, hence, also single QD-labeled biomolecules10,14 for long periods of time. A particularly interesting phenomenon observed in individual light-emitting entities, whether these are organic dye molecules,15 fluorescent protein molecules,16,17 or nanoparticles12,18 is fluorescent intermittency, also called “flickering” or “blinking,” an intriguing effect that is completely obscured in ensemble measurements. The exact origins of blinking vary from species to species but, in general, involve transitions to nonemissive, metastable states. Blinking of QDs limits their application as devices in nanotechnology or the life sciences. To devise strategies to minimize or even suppress blinking completely, it is important that its physical mechanism be well understood. The optical properties of QDs can be improved by coating the particles with a protective shell made from a semicon1098-0121/2007/75共12兲/125431共8兲

ductor material with a wider band gap. The most common core-shell QD system consists of a CdSe core and a ZnS shell. The shell performs two main functions. The first function is to reduce the number of CdSe surface dangling bonds, which confines the electron and hole wave functions away from the surface, thereby increasing the quantum yield.19,20 The second function is to enable subsequent chemical modification 共e.g., for solubilization or conjugation with biomolecules兲 without affecting the optical properties of the core. In an effort to better understand the blinking mechanism of the nanoparticle, we have systematically investigated the effect of the shell on the blinking dynamics of individual QDs. Blinking can be conveniently studied by recording a fluorescence emission time trajectory, i.e., the emission intensity of single, immobilized QDs, as a function of time. An intensity threshold is set to determine the periods in which the QDs are in their on and off states. From these data, distributions of time periods spent in either of the two states are calculated for a particular QD ensemble. It has been suggested that an off state is transiently created if one of the charge carriers is ejected from the particle, leaving behind a charged QD.21 Any excitons formed during this time recombine by a radiationless Auger process, which has a lifetime of 1 – 100 ps, strongly depending on the QD size,22 compared to the ⬃10 ns radiative lifetime. Measurements of QD charging upon laser illumination were reported by Krauss and Brus using electrostatic force microscopy.23,24 The off to on transition was also found to be accompanied by spectral diffusion of the QD emission due to a redistribution of the local electric field following blinking.25 The shapes of the distributions of on and off times have become a source of much debate in recent years. Various models have been proposed to

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explain them. The initial theory of photoionization leading to the dark state predicted exponential probability densities for the duration of both on and off times.21 However, for the off times, power-law dependencies have been reported, extending over several orders of magnitude in time.12,18,26–28 These observations were explained by an ensemble of trap states with wide distributions of the energy and distance. For the probability densities of on times, the experimental findings have been ambiguous. Power-law behavior has been observed by some,28,29 others report power-law behavior with a cutoff tail at long times,18 whereas Verberk et al.30 have observed a single-exponential distribution for uncapped CdS QDs and a power law for capped CdS QDs. They postulated that three states are present, 共i兲 the normal emitting state, 共ii兲 a positively charged particle state in which the electron has been ejected from the particle into an external trap, leaving the hole to quench any emission by Auger processes 共charged and nonemitting兲, and 共iii兲 a state in which the electron remains ejected, but the hole is localized in an internal trap at the surface of the shell 共charged but emitting兲. It was argued that Coulomb blockade effects would prevent further electron ejection, thereby causing long on times. More recently, Zhang et al.31 have analyzed fluorescence time traces of streptavidin-coated commercial CdSe-ZnS QDs and reported a continuous distribution of emissive states of different intensity and fluorescence lifetime. Pelton et al.32 observed that the power spectral density of QD blinking is identical whether in solution or immobilized on glass slides, suggesting that the blinking mechanism is not sensitive to the environment. This result sheds doubt on models that involve trapping of electrons in external, structurally, and energetically heterogeneous states in the vicinity of the QD. At the same time, a theoretical model, in which the trap states rendering the QD in an off state reside only in the core and shell,33 was shown to be able to adequately fit the experimental data of Shimizu et al.18 A surface-trapping model was also reported by Tang and Marcus,34 and recently, Frantsuzov and Marcus35 presented a mechanism for QD blinking that does not involve long-lived electron traps, but rather hole trapping in surface states, accompanied by electron excitation within the conduction band by an Auger mechanism. The reported diversity of experimental data and physical models requires further exploration of the blinking process. To this end, systematic variation of the shell properties may be an attractive approach to gain further insight and to distinguish between the different models. In this study, we have chosen to investigate the same CdSe cores upon varying the thickness of the ZnS capping layer. Furthermore, we have measured CdSe preparations with different initial quantum yields to investigate the effect of CdSe core quality. Variable parameters that affect the optical properties include crystallinity, surface passivation, shape and size distribution, and method of synthesis, which are sometimes not reported with the blinking data. II. EXPERIMENTAL METHODS AND DATA ANALYSIS

We prepared two samples of CdSe quantum dots with different quantum yields and varied the ZnS shell thickness

of each sample by adding Zn and S precursors to the cores, the amounts of which were calculated based on the density of ZnS and the size of the CdSe core 共2.9 nm兲 to yield up to eight monolayers 共ML兲 of ZnS 共1 ML of ZnS shell corresponds to an increase in the QD diameter of 2 ⫻ 3.1 Å兲. We have analyzed the blinking behavior of uncapped CdSe and compared it to the various ZnS capped samples. After preparation of the uncapped CdSe using CdO and TOPSe precursors in trioctylphosphine oxide 共TOPO兲/hexadecylamine 共HDA兲 as previously described,36,37 the CdSe nanoparticle sample was divided into two fractions, one of which was measured as prepared 共uncapped CdSe兲, the other one was used as the core for the capping process. After slow addition of stoichiometric amounts of diethyl zinc and hexamethyldisilylthiane at 170– 180 ° C,20,38 samples were withdrawn at regular intervals. Samples were characterized by transmission electron microscopy 共TEM兲 using an EM 301 microscope 共Philips, Amsterdam, The Netherlands兲 operating at an acceleration voltage of 80 kV. A copper TEM grid 共Plano, Wetzlar, Germany兲 was coated with a thin layer of amorphous carbon onto which a drop of particles dissolved in CHCl3 was deposited and left to dry. Additionally, the optical properties were determined for each sample, including absorption and fluorescence spectra and the quantum yield. The latter was determined by referencing the integrated fluorescence emission of an optically thin QD sample 共peak absorbance ⬍20 mOD兲 to that of rhodamine 6G in ethanol with the same peak optical density. Both samples were excited at 500 nm. QD samples, diluted in toluene to picomolar concentration, were mixed in a 1:1 ratio with 4% 共w/v兲 poly 共methylmethacrylate兲共PMMA兲 in 2-butanone. The solutions were spin cast onto glass coverslips at 2000 rpm. We used total internal reflection fluorescence microscopy 共TIRFM兲 with excitation at 532 nm and detection by an intensified CCD camera, which is an excellent method for obtaining data from a statistically significant ensemble within a relatively short acquisition time.39 We have measured four to five areas of 80 ␮m ⫻ 80 ␮m for each of the eight samples for several hundred seconds to obtain good statistics. A typical intensity time trace 共with 100 ms time binning兲 is shown in Fig. 1共a兲, with an intensity histogram in the right frame. The background intensity was determined locally around each particle; it follows a Poissonian distribution with a standard deviation, ␴, of ⬃25 Hz. A threshold separating on states from off states is set to multiples of ␴ to ensure that background noise does not generate any false short on events. For thresholds between 2␴ and 4␴, we found no effect on the blinking statistics 共data not shown兲, since the emission frequency of QDs in the on state is ⬃200– 400 Hz in our experiments. For all subsequent analyses, the threshold was set to 70 Hz. Furthermore, the spot shapes were analyzed to ensure that only single QDs 共no larger than their point spread function兲, well separated from neighboring spots, were included in the analysis. The on and off times distributions were extracted for each QD preparation at an excitation power of 400 W / cm2. Figure 1共b兲 shows typical distributions of the on and off times observed. The total duration of the traces from which the distributions were extracted was 550 s at 100 ms resolution, allowing an analysis window between

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EFFECT OF THE SHELL ON THE BLINKING…

FIG. 1. 共a兲 Black—typical fluorescence time trajectory of a single QD with 100 ms binning. Gray—local background calculated from a set of pixels immediately surrounding the single QD spot. 共b兲 Typical on and off time distributions showing a power-law behavior of the off times and a power law with exponential cutoff for on times. The vertical lines represent the analysis window based on the time binning and the trace length.

300 ms and 50 s. Traces were also measured for 275 s with 50 ms resolution 共not shown兲, allowing the window to be shifted to shorter times accordingly. The off times distributions were fitted with a power law, as shown previously12,18,26–28 Pof f = At␣ ,

共1兲

where ␣ is the power-law exponent, and A is a scaling coefficient. The on times were fitted with a power law with an

FIG. 3. 共a兲 Fluorescence spectra of two samples of uncapped and ZnS-capped CdSe QDs 共after adding 7 ML of ZnS to the cores兲, 共b兲 wavelength of fluorescence peak, ␭max, 共c兲 fluorescence linewidth 共full width at half maximum, FWHM兲 and 共d兲 quantum yield, as a function of ZnS added to the CdSe cores.

exponentially decaying tail, thereby limiting very long on times34,35

FIG. 2. TEM images of 共a兲 uncapped CdSe and 共b兲–共d兲 upon capping CdSe cores with increasing amounts of ZnS. For each image, magnification is 190 k. The insets are fourfold magnification of a single particle 共inset size is 15 nm⫻ 15 nm兲.

冉冊

pon = At␣exp −

t . ␶

Here ␶ is the relaxation time of the exponential tail.

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FIG. 4. The on and off times probability distributions for sample 1 共a, b兲 and sample 2 共c, d兲 with varying amounts of ZnS shell added to the CdSe cores. III. RESULTS

The increase in the ZnS shell upon capping was monitored by TEM. The images, presented in Figs. 2共a兲–2共d兲, show that the uncapped particles have excellent size homogeneity. The particles increase in size following capping, indicating growth of the shell around the cores, which can be seen more clearly from the inset of each frame highlighting a single particle 共size of the inset is 15⫻ 15 nm兲. The good size homogeneity of the particles is also maintained upon capping. Due to the low contrast of the TEM images of uncapped particles 关Fig. 2共a兲兴, the particle boundary is blurred and it is difficult to obtain an accurate average size, but a systematic calibration of CdSe sizes measured by high resolution TEM with their absorption and emission spectra has been previously published.40 The average size of the CdSe particles increases from 2.9 nm when uncapped to 4.6 nm in Fig. 2共b兲共equal to 2.6 ML of ZnS兲, 5.0 nm in Fig. 2共c兲共3.5 ML ZnS兲 and 7.2 nm in Fig. 2共d兲共7.0 ML ZnS兲. However, the low contrast of the TEM images does not allow a complete characterization of the shell homogeneity, and variations in the shell thickness within individual particles cannot be excluded. Capping of CdSe QDs with ZnS also alters their optical properties. Specifically, the fluorescence spectrum redshifts by up to 8 nm, the width of the emission peak increases and the quantum yield increases with ZnS shell thickness, as shown in Figs. 3共a兲–3共d兲. Sample 1 showed a quantum yield of 20% before capping. It increased to 44% after 3.5 ML of ZnS were added and then decreased again slightly upon adding more ZnS. Sample 2 had a quantum yield of 7% before capping; it reached 41% after adding 3.5 ML of ZnS and then decreased to 35% at 7 ML. Lattice mismatches due to differences in bond lengths between Cd-Se and Zn-S 共⬃13% 兲 create strain at the core-shell interface, which affects the quantum yield by providing additional non-radiative pathways.19,20,41 Other factors limiting the quantum yield include the extent of lattice disorder and ligand coverage. The key variables in our study are the core quality and the shell thickness, both of which were independently varied.

FIG. 5. Power-law slope of 共a兲 the off times distribution and 共b兲 the on times distribution, 共c兲 characteristic time of the exponential cutoff in the on times distribution with varying amounts of ZnS shell added to the CdSe cores. The thick lines show the average obtained from all data points. The thin lines are least-squares linear fits to the data. The slopes obtained from these fits are, for panel a: −0.027± 0.015, b: 0.020± 0.013, and c: −0.147± 0.209.

In Fig. 4, the on and off times distributions are compared for different capping thicknesses. A slight scatter is visible in the slopes and in the exponential tails, but both distributions show no systematic variation with capping thickness up to 7 ML of ZnS. This holds true for both the cores of higher quality, sample 1, and lower quality, sample 2. The slopes, ␣, for the on and off times and ␶ for the on times, are plotted as a function of capping thickness in Fig. 5. The averages over all values of these parameters are shown as thick lines on the graphs, which pass though the error bars for the majority of points. The average ␣ for the off times is −1.6 共±0.1兲; for the on times it is −1.9 共±0.1兲. For the on times, the exponential role off is characterized by ␶ ⬇ 5.5 共±1.4兲 s. More importantly, it shows no dependence on either sample quality or shell thickness. In the figure, we also show the results of linear least-squares fits to the data. Their slopes are all close to zero. Therefore, we conclude that ␣ and ␶ do not depend on the presence or thickness of the ZnS shell. Shimizu et al.18 also found that the power-law exponent is the same for uncapped and ZnS capped CdSe. However, we have not observed an increase of the exponential cutoff tail characteristic time, ␶, upon capping with ZnS. Remarkably, the parameters ␣ and ␶ for both samples 1 and 2 are identical within the experimental uncertainty, suggesting that the overall quan-

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FIG. 6. Dependence of the average on count rate, 具I典on, on the ensemble quantum yield for traces measured with 50 ms resolution and 100 ms resolution. The solid line is the fit taking all points into account. The dashed and dotted lines are fits taking only the 100 and 50 ms data, respectively, into account.

tum yield of the CdSe cores is not related to the blinking statistics. The increase in quantum yield observed either with higher quality cores or upon capping must arise from an increase either in the fraction or the average quantum yield of the emitting particles. It has been shown previously that single fluorescing QDs have quantum yields that are much higher than the ensemble quantum yield of the sample they were taken from,42 and that a QD sample contains a fraction of nonemitting QDs.42–44 Recently, Yao et al. found a direct correlation between the observed bright fraction and ensemble quantum yield for commercially available core-shell QDs containing both a polymer and a streptavidin coating on their surface.43 We have calculated the average count rate of the ensemble of single QDs in the on state, 具I典on, at constant laser excitation power 共400 W / cm2兲具I典on = 兺 NI ” 兺 N.

共3兲

Here, I is the intensity of a given time bin above the threshold intensity of 70 Hz and N is the number of bins with that intensity summed over all QDs investigated. In Fig. 6, we have plotted 具I典on as a function of the ensemble quantum yield of the QD preparation. There is a relatively large distribution of on intensities, since the quantum dots, which are randomly distributed within the PMMA film, are exposed to varying strengths of the evanescent field. It can be seen from Fig. 6 that the average intensity of the on state has a slight dependence on the ensemble quantum yield. The slope of the average on intensity versus ensemble quantum yield is also dependent on the time binning. This effect is expected, since longer time binning averages out fast blinking events, reducing the average counts per second. However, even for the data binned in 50 ms intervals, an increase in quantum yield by a factor of 2 only increases the average on count rate by a factor of 1.4. This lends further support to the claim that the ensemble quantum yield is correlated largely to changes in the ratio of radiant 共bright兲 to non-radiant 共dark兲 QDs in the

FIG. 7. Energy level diagram of the CdSe states used in the model of Frantsuzov and Marcus35 to explain power-law blinking kinetics without external traps. Diffusion of the conduction band energy levels is represented as a band with its energy randomly fluctuating with time 共thin jagged line within the shaded band兲. The energy differences are based on previous spectroscopic experiments 共see text兲.

sample and only slightly to the individual-particle quantum yield.42,43 IV. DISCUSSION

The absence of systematic effects of the shell thickness on the QD blinking statistics suggests that electron tunneling through the shell to or from an external trap is unlikely as the key mechanism for the intermittency in photon emission. This observation is in agreement with the observed lack of sensitivity of blinking to the QD environment,32 but is at variance with several reports which have been explained by an external trapping model. Examples of such studies include observations of charging of the QD upon illumination23 and of a correlation between off time distributions and the dielectric coefficient of the medium surrounding the particles.45 For an electron tunneling mechanism, an exponential decrease in the tunneling rate with shell thickness would be expected, leading to longer on and off times for the QD emission.46 By the same argument, tunneling to the external surface of the QD shell also seems unlikely. The model proposed by Shimizu et al.18 considers a random walk in phase space through a transition point separating dark and bright states. Diffusion of the transition point, as deduced from spectral diffusion experiments,25 leads to power-law statistics. The exponential cutoff tail in the on times was suggested to result from a secondary mechanism, such as photoassisted charge ejection due to Auger ionization followed by external trapping, whereas the increase in the characteristic time of the exponential cutoff for capped QDs was proposed to be due to a reduction in the number of trap states. The model recently introduced by Frantsuzov and Marcus35 develops this idea further without using external trap sites and can be applied to explain our data. The scheme in Fig. 7 shows the QD energy levels relevant to this model. A key ingredient is the presence of multiple hole trap states above the 1S3/2 valence band level, as shown by infrared absorption spectroscopy, even in ZnS capped QDs.47 The width of the

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band associated with the hole states was found to be ⬃200 meV, with the first trap state lying ⬃300 meV above the1S3/2 state.47 For a 3 nm QD, ⬃200 Cd, and ⬃200 Se atoms, from a total of 1000 atoms, reside at the surface. Frantsuzov and Marcus argued that there is one dangling bond per Se atom, as TOPO binds primarily to Cd,48,49 leading to the presence of ⬃200 trap states, each separated by 1 meV. Following QD excitation, the hole can be trapped in one of these states, and the energy released in this process is transferred to the electron, which is promoted from 1Se to 1Pe by an Auger mechanism 共Fig. 7兲. The 1Pe – 1Se energy gap, ␧0, was experimentally determined as ⬃300 meV, with a width of ⬃140– 220 meV depending on QD size.50 In the model, the 1Pe–1Se gap undergoes light-induced stochastic fluctuations, with the probability distribution of the transition energy, ␧, with time given by a Gaussian function.35 In Fig. 7, we have schematically depicted fluctuating conduction band levels from which the gap fluctuations originate. Evidence supporting diffusive gap fluctuations is provided by measurements of the homogeneous linewidth of the band associated with the 1Pe – 1Se transition of ⬃3 meV,51 whereas the width is ⬃200 meV.50 Auger-assisted hole trapping requires matching energy gaps for the electron and hole transitions, and therefore, the rate of hole trapping depends strongly on the electron energy gap fluctuations. The expression for the hole-trapping rate, kt, based on Fermi’s Golden Rule, is essentially a step function, as kt increases over several orders of magnitude within a narrow range of energy, ␧, for which the electron energy gap is sufficiently large to match the gap between the 1S3/2 and the hole trap states. A threshold value of the 1Pe – 1Se gap, ␧*, denotes the onset of high trapping rates. If the fluctuating energy gap ␧ is below ␧*, the trapping rate is small and the QD fluoresces. Conversely, if the energy gap is above ␧*, the trapping rate is large, and the QD is quenched. Assuming that the energy fluctuations obey the diffusion equation, the theory yields a power-law dependence of both the on and off times distribution with ␣ = −1.5, with an exponential cutoff at times longer than the diffusional relaxation time, ␶D, given by35

␶D =

⌬2 , D

共4兲

where ⌬2 is the variance of the distribution of ␧ 共⬃50 meV兲, and D is the diffusion coefficient. Experimentally, the cutoff time of the power-law distribution of the off times is ⬃1000 s,52 while we 共and others previously18兲 have shown that the cutoff time for the on times is ⬃6 s. We have observed a power-law exponent of −1.6 for the off times distribution, in excellent agreement with theory.35 However, our exponent for the on times distribution is −1.9, significantly larger than the theoretical value of −1.5.35 A variation in reported power-law exponents for the on times has been noted 共see Table V in Tang and Marcus34兲. The power-law exponent of the on times may be sensitive to the QD environment or sample preparation.35 In any case, a major result from our study is that the power-law exponents for both the on and off times, and the exponential cutoff of the on times

are independent of ZnS capping and independent of the ensemble quantum yield of the CdSe core particles. The independence of the blinking statistics on the capping thickness can be explained as follows. Upon capping the QD, the ensemble quantum yield increases, which has been previously attributed to be the result of a reduction in the average number of surface trap states.19,20,38,41 However, due to lattice strain at the core-shell interface, a relatively large number of surface trap states persist. This hypothesis is supported by the presence of a long-lived 共microseconds兲 transient infrared absorption at ⬃300 meV following photoexcitation, which was attributed to transitions within the hole trap states, even in ZnS-capped CdSe QDs.47 It is reasonable to assume that the number of trap states and the energy between the 1S3/2 level and the first trap state varies from QD to QD. If a QD has its first trap state at a relatively low energy with respect to the 1Pe – 1Se transition energy, then the 1Pe – 1Se transition energy will always be in resonance with the 1S3/2 to hole trap transition. In these particles, Auger-assisted quenching will always occur following photoexcitation and, thus, the particle will never emit a photon 共dark QD兲. Capping with ZnS results in a larger fraction of QDs that have a number of traps above this threshold, resulting in a decrease in the dark fraction, but that there is still an appreciable number of hole trap states that can be populated if the 1Pe – 1Se energy gap crosses its threshold between the on and off states, ␧*. There are, therefore, two populations of QDs that exist in a given sample—dark QDs that are never on 共dark fraction兲 and QDs that are on and blinking 共bright fraction兲. The ensemble quantum yield is mainly governed by this ratio. A slight dependence of the ensemble quantum yield on the average on intensity was shown in Fig. 6, suggesting that samples with higher overall quantum yield do contain particles with slightly higher individual quantum yield. This effect, however, is not large enough to account for the increase in the ensemble quantum yield. A similar result was also observed using correlated atomic force microscopy 共AFM兲 and fluorescence microscopy measurements.42 It may be possible that not all of the trap states in this model are, in fact, surface states. Lattice defects in the CdSe crystal volume may also contribute to the number of trap states, as is suggested by the fact that QDs of the same size can have dramatically different ensemble quantum yields, depending on the method of synthesis. In general, synthesis at higher temperatures 共or post-preparative annealing兲 results in higher quantum yield particles. Reducing the surface defects by capping initially increases the bright fraction until lattice mismatch effects at the CdSe– ZnS interface increases the number of trap states to render the QD dark again. This may explain the observation that forming a ZnS shell thicker than ⬃4 ML results in a slight reduction of the ensemble quantum yield. In contrast to our results, Shimizu et al.18 reported a slight dependence of the power-law cutoff time upon capping CdSe with 6 ML of ZnS. However, it is clear from their data that the power-law exponent for the uncapped and ZnS capped QDs are identical within the experimental error, and that only the cutoff time was affected by capping. Various explanations have been invoked to address why the cutoff time from power-law statistics is much shorter 共⬃2 to 3 orders of

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magnitude兲 for the on times than the off times.18,28,34,35 Two arguments were derived from the model of Frantsuzov and Marcus.35 One hypothesis is that the diffusion coefficient, D, of the stochastic motion of the 1Pe – 1Se transition in the on state is higher than in the off state, effectively leading to deviations from the idealized Gaussian probability distribution function of ␧. Based on the values of ␶D reported previously for the off times52 and for the on times reported here, D ⬃ 2.5 meV2 / s for the off state and ⬃410 meV2 / s for the on state. This difference may be the result of more pronounced rearrangements of atoms or bonds in the excited state QD relative to the ground state QD. Another possibility is that the 1De – 1Se transition 共see Fig. 7兲 also undergoes stochastic diffusion. If the 1Pe – 1Se transition energy is significantly reduced, then the 1De – 1Se energy may come into resonance with the hole trap state energy, resulting in a second Auger-assisted trapping route. The effect of the shell was not explored by Frantsuzov and Marcus.35 The observed increase in the cutoff time of the on times in ZnS capped QDs reported by Shimizu et al.18 could be a result of their capping procedure reducing the number of trap states to a low enough number that the first trap state is high enough above 300 meV that the stochastic diffusion of ␧ with time, crosses ␧* less frequently 共i.e., ␧* is moved up in energy with respect to ␧0兲, whereas the QDs capped in our laboratory may still have many traps at the core-shell interface. However, the dependence of the displacement of ␧* from ␧0, on the powerlaw exponent has not yet been investigated. In the model of Shimizu et al.,18 which contains the possibility of external trapping, limiting the amplitude of the diffusion of the transition point between bright and dark states would have a similar effect on the on times exponential cutoff as the model of Frantsuzov and Marcus.35 It is interesting to note that Kuno et al.28 found no exponential cutoff at all in the on times distribution for their CdSe particles under even higher excitation power densities than used here and used by Shimizu et al.18 The variation in power-law exponents and exponential cutoff behavior reported for the on times by different groups may reflect either a dependence on QD preparation of the position of the first trap state 共estimated at ⬃300 meV above 1S3/2兲, effectively leading to a displacement of ␧* with respect to ␧0, or the position and diffusion of the 1De state offering a second Auger route to quench the fluorescence, as discussed above. While the power-law slope was unaffected by capping in our work and that of Shimizu et al.,18 Issac et al.45 found that the power-law exponent depended on the dielectric constant of the surrounding medium. The data of Isaac et al.45 are also at variance to the results of Pelton et al.32 who found that the blinking was independent of whether the QDs were in solution or immobilized on a glass slide. In fact, the data in Fig. 5 show that there may be a slight dependence of the powerlaw exponent in the off and on times with ZnS shell thickness on approximately the same order of magnitude as was reported for the off times by Issac et al.,45 but this is difficult to determine unambiguously. Additionally, due to low con-

trast, the TEM images in Fig. 2 could not provide conclusive proof that the QDs were capped completely uniformly. No TEM images of the QDs were published in the studies of Shimizu et al.,18 Verberk et al.,30 Pelton et al.,32 and Issac et al.,45 and sample-to-sample variations in the shells for the different reports likely explain the differences in the results. It should be noted that our data can be explained without the external trap hypothesis, whereas the observation of QD charging upon illumination23 is difficult to rationalize without ejection of a charge carrier from the QD. It is thus possible, and now seems probable, that several mechanisms may be responsible for blinking. Blocking one of the mechanisms, e.g., by increasing the tunneling distance by coating the core with a thick shell, may eliminate one mechanism, but blinking could still arise from an alternative remaining mechanism, such as hole trapping at the core-shell interface. V. CONCLUSIONS

In summary, the lacking dependence of QD blinking statistics on the shell thickness of CdSe– ZnS core-shell QDs observed here suggest that tunneling to an external trap is not the primary mechanism responsible for blinking. We have invoked the recent model of Frantsuzov and Marcus35 to explain the statistical behavior of QD blinking. By extending the model to the idea of a threshold number of trap states rendering the QD either “permanently dark” or “bright and blinking,” it is possible to explain the correlation between ensemble quantum yield and bright fraction, including a microscopic description of the increase of ensemble quantum yield upon capping CdSe with ZnS. The exact physical mechanisms underlying the deviations of the power-law exponent from −1.5 and the cutoff time at which the power-law behavior collapses to an exponential behavior have not yet been fully elucidated. However, clues have arisen as to their origin, such as possible deviations of the probability density function of ␧ from Gaussian and/or differences in the position and bandwidth of trap states relative to the 1Pe – 1Se energy gap. Controversy still exists in the literature as to the physical origin of blinking, which may be related to sample variations, multiple underlying physical mechanisms, or both. By extending our present studies to other QD systems and capping materials, further insight into the physical mechanism governing QD intensity fluctuations will be gained. This knowledge may allow the design and production of nonblinking QDs, which are highly desirable for a wide spectrum of applications. ACKNOWLEDGMENTS

We are extremely grateful to Paul Walther for help with the TEM imaging. C.D.H. would like to thank the International Human Frontiers Science Program and the Alexander von Humboldt Foundation for their support. Financial support for this work by the Deutsche Forschungsgemeinschaft 共SFB569兲 and the Fonds der Chemischen Industrie are gratefully acknowledged.

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