Super-resolution photoluminescence lifetime and intensity mapping of interacting CdSe/CdS quantum dots

Numerous optical microscopy techniques have been developed in the past two decades that surpass the resolution limits imposed by the diffraction of light such that emitters separated by less than ∼200 nm can be spatially resolved.¹ Single-molecule localization microscopy (SMLM) is a subset of these super-resolution (SR) techniques through which multiple closely spaced emitters can be resolved by locating the centroid of the emission profile of single molecules with a high degree of precision.² Resolution in the tens of nanometers is typical, and ∼1 nm resolution has been reported under favorable conditions.^3,4 Though emission is typically collected by a charge-coupled device (CCD) camera or a complementary metal-oxide semiconductor (CMOS) camera, several recent SR demonstrations have greatly improved the temporal resolution by employing single-photon avalanche photodiode (SPAD) detectors in conjunction with time-correlated single-photon counting (TCSPC) hardware.^5–7 In TCSPC, the arrival time of each registered photon relative to the start of the experiment and relative to the excitation laser pulse is recorded with a resolution down to ∼50 ps.^8,9 The simultaneous acquisition of TCSPC data and SR images allows for observation and characterization of dynamic processes that are inaccessible in conventional camera-based SR imaging.

High spatiotemporal resolution imaging has been implemented with two different detection schemes: arrays of optical fibers that are coupled to individual SPAD detectors and SPAD array detectors. The latter was used to resolve emitters spaced by ∼80 nm,⁶ and a theoretical study used photon pair correlations to accurately extract the number of noninteracting emitters in an image containing overlapping emission profiles.¹⁰ Additionally, the array's timing resolution was exploited for fluorescence lifetime imaging with a resolution that slightly exceeded the diffraction limit.⁷ Despite the large number of pixels (256–66 000) within SPAD arrays, optical fibers coupled to a small number of individual detectors (4–16) offer a competitive alternative because they have higher collection efficiencies.⁹ Optical fiber-coupled SPAD detectors have previously been implemented for tracking single molecules diffusing in viscous solutions with a lateral precision of ∼5 nm.^11–14 More recently, Israel et al. used them in the context of SR imaging to locate emission centroids based on the photons collected by 16 optical fibers coupled to SPAD detectors.⁵ In their study, the TCSPC data were used to identify and reject the contribution from multiple emitters based on photon pair correlations, and that processing method aided in resolving two emitters separated by ∼100 nm.

The present work uses a bundle of 4 optical fibers coupled to SPAD detectors to resolve multiple centroids separated by ∼12 nm based on differences in the intensity and lifetime of the centroids. The TCSPC data are used to differentiate between multi- and single-emitter systems and to monitor the emission lifetime associated with each centroid location. Simultaneous spatial mapping of the emission lifetime and intensity enables direct visualization of nanosecond dynamics. We exploit this super-resolved lifetime imaging technique to view the energy transport pathways among interacting CdSe/CdS core/shell quantum dots (QDs). Previous nonimaging studies of QD clusters indicated the presence of energy transfer from donor to acceptor QDs based on correlations between lower intensity/shorter lifetime emission and higher intensity/longer lifetime emission.^15,16 More recently, camera-based SR mapped the emission intensity from QD clusters, revealing spatial intensity variations consistent with energy transfer.¹⁷ The simultaneous super-resolved lifetime and intensity mapping reported here reveals the signature of energy transfer on the nanometer scale within the clusters, wherein different parts of the cluster can be identified as donor or acceptor regions depending on their emission intensity and lifetime.

We imaged CdSe/CdS core/shell QDs that had core diameters of ∼6 nm and total diameters of ∼9 nm. After synthesis,¹⁸ the QDs were suspended in toluene and diluted to nanomolar concentrations prior to spin coating on the coverslip. Clusters were formed by adding a small amount (1:50 parts) of methanol to a nanomolar solution of the QDs prior to spin coating. The isolated QDs and clusters were excited with 485 nm laser pulses (∼100 ps FWHM, 5 MHz repetition rate) with an average power of ∼210 nW that were delivered to the rear aperture of a 100$×$1.3 numerical aperture oil immersion objective. The focus was maintained with feedback to a piezoelectric objective mount (Mad City Labs Nano F Series). Proportional and integral feedback were provided by monitoring the image of scattered light off the coverslip surface from a 785 nm laser beam (Thorlabs LDM 785) that was directed through the side port of the microscope. The image moved as a function of the focus position due to astigmatism introduced by purposely misaligning the IR beam. Emission (peaked at 636 nm for nonclustered QDs in solution) from an isolated photoluminescent spot was collected by the same objective, and it passed through a 488 nm dichroic mirror, a 680 nm short pass filter, a 500 nm long pass filter, and a 450 mm focal length tube lens. The objective and tube lens gave a 250$×$ overall magnification, and the emission was imaged onto the center of a bundle of four square optical fibers arranged in a $2×2$ array (Fig. 1). The image of the point spread function (PSF) had a FWHM of ∼150 μm, and the fibers had dimensions of 100 $×$ 100 μm² with an additional 7.5 μm of cladding.

The output of each fiber was coupled to a separate SPAD detector, and the detector outputs were suitably conditioned and directed to a multichannel TCPSC module that recorded the arrival time and detector identity for each registered photon relative to the start of the experiment, and the elapsed time, $τ$⁠, between each excitation laser pulse and a photon arrival. For 100 ms time windows, the $τ$ values were compiled and histogrammed. The arrival time distributions were rarely monoexponential for the case of both single and clustered QDs, and there was a wide variation in the form of the distributions among different time windows. Because of the complexity and variation of the distributions, we took the average arrival time, $τ$⁠, to be a characteristic lifetime for each time window. To determine the lateral position of the emission centroid, we analyzed the counts, N, registered in each detector for 100 ms time windows using maximum likelihood estimation (MLE). The PSF, the fiber pixel dimensions and locations, and Poisson distributions for the signal and background were used as inputs in order to compute the maximum of the likelihood distribution function and locate the centroid. The precision was calculated from the standard deviation in the repeated measurements of the location of an isolated QD; it improves for longer time windows and scales as $1/N$ following the central limit theorem (Fig. S3).

Segments of the data lasting ∼200 s were selected for analysis from each photoluminescent spot so that a substantial number of blinking events were contained. Blinking events are needed to resolve multiple centroids within multiemitter systems. Unfortunately, the lateral drift of the microscope during these long durations significantly blurs the 2D mapping of the x and y positions. Correcting for the drift with frequency-based filtration techniques is problematic because the extraction of low frequencies tends to attenuate the blinking events that contribute to features of interest (step changes in the position following by long, static locations). To this end, we chose to analyze segments of the data stream over which the underlying drift velocity was approximately constant and the only correction we implemented was to remove the average drift velocity by subtracting a linear fit to each segment. Supplementary material (i)–(iii) contains further details about the experimental setup, sample preparation, and localization procedure.

To benchmark the SR lifetime imaging capabilities of the microscope, we imaged individual isolated QDs. Photon pair correlations were computed from the photon arrival times for each sample to verify that it was an isolated emitter (Fig. S10). Intensity, $τ$⁠, and position data from a selected QD are shown in Fig. 2. The intensity, with a mean photon detection rate of 105 kHz for a 200 s observation period, is plotted vs time in Fig. 2(a). The $τ$ values, with a mean of 43 ns, are plotted in Fig. 2(b). Comparison of the intensity and $τ$ values reveals synchronized changes in the two observables, with longer $τ$ values corresponding to higher intensities. The drift-corrected x position is plotted vs time in Fig. 2(c) (Figs. S6 and S7 display y positions). Using 50 kHz as a threshold to delineate blinking, we observe that the QD spends 10% of its time below the threshold in the off state. The standard deviation in positions is 4 nm in x and 5 nm in y when the QD is in the on state, for which the average number of detected photons is N ∼ 11 000 per localization (per 100 ms time window). Figure 2(d) is an intensity-scaled scatterplot showing all the x and y positions acquired. On average, we observe a single emission centroid. As expected, the distribution of individual centroid positions depends on the number of photons acquired during that time window; lower intensity corresponds to a broader distribution. A lifetime image of the QD is shown in Fig. 2(e) where the color scale represents $τ$⁠, and again we observe individual centroid positions scattered about a single mean.

The advantages of measuring intensity and $τ$ in conjunction with precisely locating the emission centroid are evident when we examine QD clusters. Figure 3 shows data from a selected cluster in which disparate emission behavior within different regions of the cluster is obvious. Analogous to Fig. 2, Figs. 3(a)–3(c) display the intensity, $τ$⁠, and x position vs time over 200 s from a small QD cluster (Figs. S8 and S9 display y positions). We observe synchronized changes in all three observables: the intensity, with an average of 180 kHz, decreases; the $τ$⁠, with an average of 18 ns, decreases; and the position moves in the positive-x direction. The synchronized changes in the intensity and position occur when one or more QDs turn on and off in the cluster, and the centroid location shifts toward the QDs that are dominating the emission. Figures 3(d) and 3(e) are composite images of the emission centroid positions for the entire 200 s data stream that are color-scaled according to intensity and $τ$⁠, respectively. We identify both a high intensity and longer $τ$ region and a low intensity and short $τ$ region. The disparate intensity and $τ$ values are used to discern two centroids. A threshold of 200 kHz was chosen by inspection to separate high and low intensity segments [Fig. 3(a)]. For the entire 200 s of data, we computed the average of the positions associated with intensities above and below that threshold. The distance between the two locations is 12.3 ± 0.3 nm. Repeating this procedure using $τ$ rather than intensity as a filter [Fig. 3(b)], a 21 ns threshold yields a separation of 12.2 ± 0.3 nm between the two emission sites.

The presence of multiple regions within the clusters associated with different $τ$ values may be caused by the ∼10% distribution of core sizes and particle sizes found within the synthesis batch (Fig. S1) that results in a distribution of bandgaps among individual QDs.^19,20 We hypothesize that the distribution of bandgaps among individual QDs allows them to take on preferred roles as either energy donors or acceptors within the clusters. Previous studies have shown that energy transfer from a donor species to an acceptor species leads to shorter lifetime and lower intensity emission from the donor because energy transfer to the acceptor is competing with the radiative relaxation of the donor.^15,21,22 For the selected QD cluster in Figs. 3(d) and 3(e), it appears that the significantly shorter $τ$ and lower intensity of the centroid located near the origin occur because QD(s) on that side of the cluster are transferring energy to the QD(s) on the left side. We speculate that the highest intensity and longest $τ$ emission are coming from the largest QD with the lowest energy bandgap, and when that QD blinks off, we observe emission from the QD with the next lowest bandgap. In that case, the centroid position shift may be between the locations of the two lowest-energy QDs within the cluster.

The relationship between intensity and $τ$ is shown in Fig. 4, which compares the behavior of the isolated QD to that of the cluster. The cluster distribution (green) has signatures of energy transfer: when radiative relaxation of donor species competes with energy transfer to acceptor species that are in off states, emission is lower in intensity and shorter in lifetime. The single QD distribution (black) exhibits a similar correlation between intensity and $τ$⁠, but its $τ$ values are significantly longer than those of the cluster, an observation consistent among all the samples we studied [Figs. S2(b) and S2(d)]. At this time, it remains unclear why even the longest lifetime contribution from clusters is shorter than that of individual QDs.

In summary, we have described a SR lifetime imaging technique capable of assessing dynamic processes within small QD clusters, such as the presence and direction of energy transfer based on lifetime and intensity mapping. We have demonstrated the ability to locate the emission centroid with a precision of ∼5 nm using 10⁴ detected photons for localization, and we have exploited differences in intensity and photon arrival time to distinguish emission centers separated by ∼12 nm. In future work, we intend to to use this aprroach to image heterostructured nanomaterials with well defined structures and compositions, as well as biological systems.

See the supplementary material for details of the experimental setup, sample preparation and characterization, and localization procedure.

We thank Joanna Casson for the TEM imaging and Farshad Abdollah-Nia for helpful discussions. This work was funded by the Los Alamos Laboratory-Directed Research and Development Exploratory Research Program (Project No. 20180189ER) and was performed, in part, at the Center for Integrated Nanotechnologies, an Office of Science User Facility operated for the U.S. Department of Energy (DOE) Office of Science. Los Alamos National Laboratory, an affirmative action equal opportunity employer, is managed by Triad National Security, LLC, for the U.S. Department of Energy's NNSA, under Contract No. 89233218CNA000001. M.K.D. is grateful for support from the Gary E. Maciel Fellowship Foundation. A.V.O. acknowledges the Los Alamos Institute for Materials Research for a Rapid Response grant that supported a summer minisabbatical in 2017. LA-UR-19-30441, unlimited release.

The authors declare no conflicts of interest.