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Ultrafast Laser Studies of Two-Photon Excited Fluorescence Intermittency in Single CdSe/ZnS Quantum Dots David J. Nesbitt, and Kevin T Early Nano Lett., Just Accepted Manuscript • DOI: 10.1021/acs.nanolett.5b01139 • Publication Date (Web): 06 Nov 2015 Downloaded from http://pubs.acs.org on November 9, 2015
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Ultrafast Laser Studies of Two-Photon Excited Fluorescence Intermittency in Single CdSe/ZnS Quantum Dots Kevin T. Early* and David J. Nesbitt JILA, National Institute of Standards and Technology and University of Colorado, Department of Chemistry and Biochemistry, University of Colorado Boulder, CO 80309 * Current affiliation: 3M, St. Paul, MN 55144
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Abstract Two-photon fluorescence microscopy of single quantum dots conditions has been reported by several groups,1-3 with contrasting observations regarding the kinetics and dynamics of fluorescence intermittency or “blinking”. Here we investigate the power dependence, kinetics, and statistics of two photon-excited fluorescence intermittency from single CdSe/ZnS quantum dots in a solid PMMA film as a function of sub-bandgap laser intensity at 800 nm. Fluorescence intermittency is observed at all excitation powers and a quadratic (n = 1.97(3)) dependence of the shot noise-limited fluorescence intensity on the incident laser power is verified, confirming essentially zero background contribution from one-photon excitation processes. Such analyses permit two photon absorption cross sections for single quantum dots to be extracted quantitatively from the data, which reveal good agreement with those obtained from previous two-photon FCS measurements. Strictly inverse power law-distributed off-state dwell times are observed for all excitation powers, with a mean power law exponent = 1.65(4) in excellent agreement with the behavior observed under one-photon excitation conditions. Finally, a superquadratic (n = 2.3(2)) rather than quartic (n = 4) power dependence is observed for the on-state
blinking dwell times, which we kinetically analyze and interpret in terms of a novel 2 + 1 “hot” exciton ionization/blinking mechanism due to partially saturated 1-photon sub-bandgap excitation out of the 2-photon single exciton state. The kinetic results are consistent with quantum dot photoionization quantum yields from “hot” exciton states (4(1) x 10-6) comparable with experimental estimates (10-6-10-5) of Auger ionization efficiencies out of the biexcitonic state. Keywords: quantum dots, ultrafast, kinetics, photoionization, exciton, intraband
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Introduction Two photon-excited fluorescence microscopy has become a standard technique for biological sample imaging since its first demonstration.4 Based on these early studies, two photon excitation (2PE) microscopy has been extended to single organic dye molecules,5-9 semiconductor quantum rods,10 gold plasmonic nanostructures,11 and colloidal quantum dots.1-3 2PE microscopy benefits from a smaller effective focal volume, reduced out-of-focus molecular photobleaching probability, and deeper sample penetration compared to standard one photon excitation (1PE) microscopy.12 Furthermore, the blueshifted emission can be filtered very efficiently from the excitation line, leading to lower background counts. On the other hand, two photon absorption cross sections are generally much lower, on the order of 101 – 104 GM (1 GM = 10-50 cm4-s/photon),9, 13 thus necessitating very high peak photon fluences to generate appreciable fluorescence signals. Ever since the initial reports by Nirmal et al.14, fluorescence intermittency in single colloidal quantum dots has been studied extensively under 1PE conditions,15-17 with detailed analysis revealing non-exponential kinetics in the switching process between ‘on’ and ‘off’ states.18 The precise picture for the mechanisms underlying photoluminescence switching are still the subject of active research. Early models suggested Auger quenching of emission in photo-charged quantum dots as being responsible for ‘off states’ in photoluminescence.15 However, recent studies have also shown trion and multiexciton emission to be important aspects of complete charge carrier dynamics models.19, 20 In addition, careful measurements of laser repetition rate effects on blinking have shown these higher exciton states to be intimately related to intermittency.21, 22 Studies of blinking fluorophores are typically studied by examination of histograms of both off- and on-time durations. Specifically, probability densities were shown to obey a simple inverse power law over several decades in probability and time,16 and models involving distributed kinetics have been developed to describe such behavior.16, 23 By way of contrast, 2PE fluorescence intermittency has received comparatively little attention, even though non-linear studies of quantum dot dynamics have proven enormously useful in disentangling questions of multiexciton and
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trion emission.21 For example, 2PE fluorescence correlation spectroscopy of water-soluble quantum dots in aqueous solution has claimed a marked suppression in blinking behavior down to the 100 ns time scale,1 as evidenced by a lack of short-time intensity fluctuations commonly associated with triplet-state formation.24 Although much progress has been made toward incorporating such distributed kinetics into these models,25-27 no parameter-free closed form expression currently exists to describe power lawdistributed fluctuations in fluorescence autocorrelation curves. Other 2PE experiments on single quantum dots immobilized on surfaces in PMMA2 and in aqueous environments3 have also shown blinking, but with no attempts reported to quantitatively characterize the underlying kinetics. In this work, we present a quantitative study and analysis for the two photon-excited (2PE) fluorescence intermittency statistics of single colloidal quantum dots in a solid PMMA matrix. As expected, a quadratic dependence of fluorescence intensity on excitation intensity is verified for single nanoparticles, with the distributions of ‘on’ and ‘off’ blinking dwell times found to obey power law statistics, with exponents in quantitative agreement with the values observed for one photon excitation. At higher excitation powers, a clear power dependent roll off in the ‘on’ time probability density is seen, in good agreement with observations in 1PE experiments.28-31 However the physical mechanism for such blinking recovery dynamics clearly differs between 1PE and 2PE conditions, as shown by detailed analysis of the relationship between i) power dependence and ii) the exponential time constant at which roll off starts to dominate the probability densities. In summary, these studies offer first quantitative measure of 2PE fluorescence intermittency dynamics at the single quantum dot level and thus help clarify discrepancies between existing reports.
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Experimental Setup Samples are prepared on ozone-cleaned microscope coverslips (No. 1-1/2) by spin coating a 500 pM solution of quantum dots (Qdot 565 ITK, Invitrogen Corp.) in toluene at 1500 RPM, followed by an overcoat of 1 mg/mL PMMA/toluene solution to suppress photooxidation effects. PMMA overcoated coverslips with quantum dots are then loaded onto a microscope-mounted xyz-piezo stage and observed under ambient conditions without further preparation. The experimental setup is shown schematically in Figure 1. Single quantum dots are excited by a mode-locked Ti:sapph laser operating at f = 92 MHz repetition rate with a wavelength centered at exc = 800 nm focused to the diffraction limit. This excitation wavelength corresponds to Ephoton/Egap = 0.71, where Ephoton and Egap are the excitation photon energy and quantum dot band gap energy, respectively. At 800 nm, the one-photon absorption cross section is negligible for the quantum dots studied here. The beam is expanded using a 4:1 telescopic lens pair to over-fill the back aperture of a 1.4 NA, 60X oil immersion objective. A 10:90 non-polarizing beam splitter is then used to reflect 10% of the incident beam into the objective, with a series of neutral density filters to adjust the average laser power between 90 and 570 W (180 kW/cm2 – 1.2 MW/cm2) measured at the focus of the objective. A fused silica prism pair compensates as much as possible for group delay dispersion of the 50 fs laser pulse due to the telescope, broadband dielectric mirrors, beam splitter, and objective lens, which is estimated to be ~4500 fs2 including all microscope elements.32 This results in a broadened pulse width of p = 250 fs, a duty factor f × p = 2.3 × 10-5, and peak photon fluxes of 8.6 x 1027 – 5.4 × 1028 photons-cm-2s-1 delivered to the sample. The resulting fluorescence is then collected back through the same objective, transmitted through the 90% transmissive beam splitter, and sent through a confocal pinhole located at the microscope side port. To reject laser light and sample autofluorescence, the emitted light is filtered using a combination of a 580/50 nm bandpass filter and 700 nm short pass filters before being focused onto an avalanche photodiode (APD). Photon counts are processed using a time-correlated single photon counting (TCSPC) module to allow for re-binning of fluorescence photons on any desired time scale. Images are formed by
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raster scanning the piezo stage and collecting fluorescence as a function of sample position. To collect single quantum dot fluorescence “trajectories” (i.e., fluorescence intensity as a function of time), a specific quantum dot is moved back under the laser focus and maintained using closed-loop positioning.
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Results Fluorescence trajectories at exc = 800 nm for the same single quantum dot at three different excitation powers (107 W, black; 218 W, red; 436 W, green) are shown in figure 2A, along with count rate histograms at each power level (binned at 1 ms intervals). These trajectories represent only small portions of the total fluorescence collection times, which are typically in excess of 1 ksec. In all three trajectories, blinking events are observed on a variety of time scales, with more rapid blinking (i.e., shortened changes in on- and off-state dwell times) observed at higher excitation intensities and discussed in more detail below. Interestingly, the quantum dots studied under 2PE conditions exhibited considerable robustness to photobleaching effects over many hours of continuous 800 nm near-IR excitation at a variety of laser powers, although we have made no attempts in the present experiment to quantify this phenomenon. At the highest excitation powers studied, however, quantum dot fluorescence intensity did exhibit irreversible photodegradation down to background levels, most likely arising from photooxidation due to oxygen permeation through the protective PMMA overcoat layer. Single quantum dots are identified by the presence of two-state telegraph blinking and shot-noise limited ‘on’ state fluorescence at moderate excitation powers. In these initial studies, no attempts have been made to verify single emitter behavior by photon antibunching measurements. Average high quantum yield (‘on’ state) intensities as a function of average laser power P for 51 quantum dots are plotted on a log-log scale in figure 2B, where uncertainties represent the standard deviation of the mean at each power level. A linear least squares fit to = C*Pv the data yields = 1.97(3). This is consistent with a nearly perfect quadratic dependence of on P and affirming that the observed fluorescence arises from a two photon absorption process, with negligible contribution from finite one-photon absorption cross section at 800 nm out of the ground state. 2PE fluorescence count rates fl (counts/second) are given by fl = (2) I2 p f, where is the experimental collection efficiency (measured to be 0.065(5) using a dye calibration under one photon excitation), is the quantum yield,
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(2) is the two photon absorption cross section in cm4s/photon, and I is the peak excitation intensity in photons/cm2s. In pulsed experiments, this peak intensity is given by
I
P 1 , p f hc A
(1)
where
is the average laser power, p is the pulse width, f is the laser repetition rate, is the wavelength, h is Planck’s constant, c is the speed of light, and A = 2/4ln(2) = 1.81 x 10-9 cm2 is the effective area of the laser spot for a Gaussian profile with FWHM . With an approximate pulse width p = 250 fs after the microscope objective, the two photon cross section for this sample can be estimated to be (2) = 1.53(20) x 10-47 cm4-s = 1530(200) GM , which is commensurate with values measured via two photon FCS.13 To quantify the two photon-induced blinking kinetics in the PMMA matrix, dwell time probability densities have been generated for single quantum dots under a variety of excitation powers. Figure 3A shows an ‘off’ dwell time (off) distribution for a single quantum dot generated from a 100 second fluorescence trajectory binned at 1 ms intervals at P = 436 W. Both ‘on’ and ‘off’ dwell times are determined by making a count rate histogram of the binned fluorescence trajectory and setting the threshold at ( - )/2. The data is plotted on a log-log scale to demonstrate the inverse power law nature of the distribution, which has also been observed for one-photon excitation of quantum dots under nearly all experimental conditions. The data span over a factor of 105 in ‘off’ time probability and 103fold in time. A linear least squares fit to log[P(off)] = log[const.] - moff log[off] yields a power law exponent moff = 1.67(3) for this particle, which is in very good agreement with values for the one-photon case. More quantitatively, figure 3B displays a histogram of individual moff values for 43 quantum dots, showing an average 2PE blinking exponent of = 1.65(4), which is in excellent agreement with the power law values reported from previous 1PE blinking studies.16-18, 23
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It is particularly significant that we observe negligible change in the off state dwell time power law exponents under 2PE vs. 1PE conditions. Indeed, this provides valuable insight into possible mechanisms for off-to-on state blinking recovery under 2PE conditions. Specifically, we have previously performed extensive 1PE studies of blinking and blinking recovery for quantum dots under modulated light conditions, which clearly demonstrated that blinking recovery occurred via both i) slow dark and ii) fast light assisted processes, but that the light assisted recovery pathway completely dominated under normal 1PE illumination conditions.33 One plausible off-to-on recovery mechanism revealed by such systems would therefore involve 1-photon excitation out of a localized surface trap state, which facilitates rapid charge neutralization of the quantum dot core and therefore recovery to the normal “on” state. It is therefore noteworthy that we see completely indistinguishable behavior in the power law recovery exponent between 1PE at 532 nm and 2PE conditions at 800 nm. This would be consistent with, for example, excitation/reneutralization of the trap state charge energetically necessitating only 1-photon energies (800 nm) below the CdSe band gap. These previous modulated light studies also revealed that the initial on-to-off blinking event to clearly be a light induced process33 with the present work confirming this to be valid under 2PE as well as 1PE conditions. We can explore this further by examining the power law blinking behavior for the ontime distributions as a function of laser power. For example, the ‘on’ dwell time distribution for a single quantum dot is shown in figure 4A on a log-log plot for P = 436 W. At such high average excitation intensities, the probability densities for two-photon induced intermittency clearly deviate from pure power law behavior at long dwell times. This has also been observed for one-photon excitation in a number of reports28, 29, 31, 34 and has been ascribed to the enhanced probability of multiple exciton generation followed by rapid Auger ionization to form a trapped surface charge state. Although no analytic kinetic model has been reported to date to describe such roll off behavior, the data can be empirically fit by a product of i) an inverse power law term and ii) an exponential decay term that serves to truncate the
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distribution at long times. The distribution takes the form P(on) = A on-mon exp(- on / c), where c = 1/kc is the critical time at which roll off begins to dominate the dwell time distribution. Unlike the ‘off’ dwell time distributions, which are largely insensitive to experimental conditions, the ‘on’ time distributions exhibit a clear dependence on laser excitation power. Specifically, figure 4B shows the average roll off rate constant for 34 quantum dots at a series of laser excitation powers, and which can be well fit to a I power law functional form with = 2.3(2). This phenomenon has been the subject of several recent studies on fluorescence intermittency under 1PE conditions,30, 31, 34-36with the above data representing the first such demonstration of such behavior for 2PE with sub-band gap photons. For one photon excitation, kc has been shown to scale quadratically with incident laser power, consistent with the anticipated dependence of a biexcitonic state on I2. It is interesting to note, therefore, that the experimentally observed power dependence for the roll off rate constants for 2PE now becomes kc I2.3(2), which is clearly faster than quadratic but nevertheless appreciably slower than the quartic dependence expected from simple extrapolation of the biexciton model. Potential reasons for such a deviation are briefly considered below. Discussion Simply summarized, on-to-off blinking transitions under two photon excitation clearly appear to be governed by different rate processes than for one photon excitation. Evidence from previous onephoton induced blinking studies indicates that photoionization, thought to be the driver for on-to-off blinking transitions, is induced by low-probability generation of a biexcitonic state.31 In one mechanistic picture, the biexciton decays via Auger relaxation to a charge separated off state, wherein further excitations relax non-radiatively (i.e., thermally).17 These photoionization events have been shown to scale quadratically with one-photon excitation flux.31 Straightforward extrapolation of this model for twophoton excitation would predict a quartic dependence of the photoionization probability on excitation flux; that is, simultaneous 4-photon excitation is required to generate the requisite biexciton state for
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charge ejection. However, as shown in figure 4 and described in the text, the observed photoionziation probability scales as I, where = 2.3(2). Here we attempt to elucidate a kinetic picture consistent with the observed data. Under the intense peak excitation fluxes required for two photon excitation, quantum dots within the laser excitation volume undergo two-photon absorption events to generate excitons relatively rarely. However, a large number of sub-bandgap 800 nm photons are always present at the same time. One scenario for charge ejection proceeds via two 2-photon absorptions to generate a biexciton. However, such a pure 4-photon absorption event would predict a quartic dependence on the laser power, which is clearly inconsistent with the slightly higher than quadratic kinetic dependence observed experimentally. A more plausible scenario to consider is charge ejection from a single exciton state that has been energized by absorption of a single sub-bandgap photon. This pathway shares conceptual similarities to resonance-enhanced multiphoton ionization (2+1 REMPI) for state-selective ionization of gas phase molecules. It is useful to examine the limiting cases of such a process. For a saturating flux of sub-bandgap photons, the kinetics will become rate-limited by the rare 2-photon excitation step, with ionization from abundant sub-gap photons proceeding with some small but finite quantum yield () out of the single exciton state. In this regime, the photoionization kinetics should follow essentially an I2 dependence. Conversely, in the case where linear absorption of the third photon occurs at a rate much slower than the 2-photon excitation process, the kinetics should recover the full I3 scaling. In the case of roll off of the blinking on-time photoionization observed here, we observe an intermediate power scaling between the two limiting cases described above, indicative of i) an unsaturated 2-photon excitation followed by ii) a partially but incompletely saturated one-photon process. More quantitatively, the rate equations for the system above can be modeled by
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.
N 0 N 0 k 01 N1k fl N1k (1 ) N k n .
N 1 N 0 k 01 N1k fl N1k
(2)
.
N N1k N k n where the subscripts 0, 1, and + refer to the zero exciton, single exciton, and ionized states. In these equations, k01 is the rate for generation of the single exciton state via two-photon process given by I2(2), kfl is a typical single exciton fluorescence decay rate (1/kfl 25 ns) at room temperature, and k and kn are the rate constants for absorption from the single exciton state and charge neutralization back to the ground state, respectively. In this simplified kinetic model, we take k as a 1-photon process with k = I1, where
1 is the absorption cross section at 800 nm from a single exciton to a multiply excited state, which in turn can result in charge separation to a surface trap state with some quantum yield . If we consider ionization from the single exciton state N1, which corresponds to the kinetics observed in the on-state dwell time distribution (and not the return from the ionized state N+, which would correspond to power law-distributed off-state dwell time distributions), we can solve in the steady state approximation for the effective rate constant for loss from N1 to the ionized state. In the steady state limit of dN1/dt = 0, this effective ionization rate keff can be readily shown to be
I 1 k eff I 2 ( 2 ) k fl I 1
(3)
In the limit kfl >> I1 (where ki = I1 is the effective ionization rate from the single exciton state at 800 nm), the kinetics simplify further to keff I2 (2) I1/ kfl]. As predicted, the ionization kinetics should behave like unsaturated 2+1 photon absorption events and scale as ~ I3. In the other limit of kfl
