Nanoscale imaging of quantum dot dimers using time-resolved super-resolution microscopy combined with scanning electron microscopy

Time-resolved super-resolution microscopy was used in conjunction with scanning electron microscopy to image individual colloidal CdSe/CdS semiconductor quantum dots (QD) and QD dimers. The photoluminescence (PL) lifetimes, intensities, and structural parameters were acquired with nanometer scale spatial resolution and sub-nanosecond time resolution. The combination of these two techniques was more powerful than either alone, enabling us to resolve the PL properties of individual QDs within QD dimers as they blinked on and off, measure interparticle distances, and identify QDs that may be participating in energy transfer. The localization precision of our optical imaging technique was ∼3 nm, low enough that the emission from individual QDs within the dimers could be spatially resolved. While the majority of QDs within dimers acted as independent emitters, at least one pair of QDs in our study exhibited lifetime and intensity behaviors consistent with resonance energy transfer from a shorter lifetime and lower intensity donor QD to a longer lifetime and higher intensity acceptor QD. For this case, we demonstrate how the combined super-resolution optical imaging and scanning electron microscopy data can be used to characterize the energy transfer rate.


Introduction
Colloidal semiconductor quantum dots (QDs) have high photoluminescence (PL) quantum yields, narrow PL spectra, size tunable bandgaps, thermal stability, photostability, and ease of processing. These properties make them suitable building blocks for many optoelectronic applications including light emitting diodes [1,2], television displays [3], photovoltaics [4], lasers [5], biological labels [6,7], and other quantum technologies [8]. In many applications, the QDs are formed into close-packed assemblies, such as thin films or matrices, in which electronic interactions can occur among neighboring QDs. Such interactions may include electronic coupling [9][10][11], charge-carrier delocalization [12], resonance energy transfer [13,14], and charge carrier transfer [15]. These interactions can impact performance, either to the benefit (e.g. luminescent solar concentrators [16]) or detriment (e.g. QD-LEDs [17]) of the device application. Investigating the nature of these electronic interactions, including their mechanisms and efficiencies, improves fundamental understanding of QD behaviors and the design of practical applications.
While the behavior of single QDs and larger QD assemblies such as thin films have been studied extensively for the past 30 years [18][19][20][21][22], small QD assemblies have received less attention. Our group and several others have focused on these systems [11,[23][24][25][26][27][28]. We have used singlemolecule spectroscopic techniques to investigate inter-QD electronic interactions in isolated assemblies made up of several closely spaced QDs. One key finding is that the PL of assembled QDs is not a simple sum of their individual behaviors. Instead, the assemblies undergo switching between low and high emission intensity states that are typically accompanied by short and long PL lifetimes, respectively [24]. These observations have been explained by assuming the excitation energy is funneled via electronic energy transfer to one or more acceptor particles. Donor QDs were hypothesized to be responsible for the shorter lifetime/lower intensity emission, and acceptor QDs for the opposite behavior. However, large variations in the PL among different assemblies of QDs suggest that the structural details of each assembly play a large role in the behavior [24,25].
To address the relationship between the PL behavior and structure of the QD assemblies, we previously conducted several super-resolution studies that imaged the PL intensity with nanometer-scale precision [29,30]. Super-resolution images of QD dimers, trimers, and higher order structures captured the spatial distribution of the PL intensity, and they revealed localized regions of higher and lower intensity within the structures [29]. Scanning electron microscope (SEM) images of the same structures resolved the number of QDs, their sizes, and their relative positions, and the QDs responsible for higher and lower intensity within the superresolution images could be identified within the SEM images. Similar combinations of electron microscopy and fluorescence spectroscopy have provided complimentary insight into the relationships between the optical and structural properties of nanomaterials [31][32][33][34][35][36]. Our group also recently imaged small QD structures with time-resolved super-resolution microscopy (TSRM) [30], a technique for simultaneously imaging emitters and acquiring information about their PL lifetimes and other nanosecond timescale properties [30,[37][38][39][40][41][42][43]. In some cases, regions associated with lower PL intensities and shorter lifetimes were spatially segregated from regions associated with higher PL intensities and longer lifetimes, which was consistent with donor and acceptor interactions among the QDs.
In the present study, we acquire TSRM and SEM images of QDs to access both the PL lifetime and intensity, and the structural details, the combination of which was not captured in previous imaging studies. We demonstrate a localization precision of ∼3 nm using 0.5 s time bins with TSRM, which provides enough spatial resolution that individual QDs within an assembly can be resolved as they switch between emissive, 'on', and non-emissive, 'off', states. We focus on the behavior of assemblies containing two closely spaced QDs (i.e. QD dimers), whose SEM images agree well with the distribution of centroid positions given in the super-resolution images. This enables assignment of lifetimes and intensities to individual QDs within a dimer. In most cases, the QDs within the dimers behave as independent isolated emitters. In at least one case, however, the two QDs behave like a donor-acceptor pair. For this dimer, the combined TSRM and SEM images are used to characterize the electronic energy transfer.

QD synthesis and sample preparation
CdSe/CdS core/shell colloidal QDs were synthesized in our laboratory according to a procedure adapted from Chen et al [44]. Two samples with different CdSe core sizes were prepared, one with a 4.6 ± 0.6 nm diameter, and another with a 5.6 ± 0.6 nm core diameter. The cores were coated with CdS shells, bringing the total diameter of both samples to 9.0 ± 1.0 nm, as measured by SEM. The PL emission peaks for the QDs with smaller and larger cores were 597 and 634 nm, respectively. Octadecylamine, octadecene, and primary oleates present from the syntheses acted as stabilizing ligands. To remove excess ligand, the QDs were washed twice via precipitation with acetone, centrifugation, drying, and resuspension in hexane. After the second wash, they were resuspended in toluene.
The QDs were diluted to nanomolar concentrations and spin casted at 1000 rpm onto TEM grids with 10-or 20 nm thick silicon nitride or silicon oxide windows (SN100-A10Q33, SN100-A20Q33, and SO100-A20Q33A SiMPore). This resulted in a surface coverage of ∼0.01 photoluminescent regions per μm 2 . To create assemblies with ∼2 to 5 QDs, methanol was added to the diluted QD solution (2 parts methanol to 100 parts toluene) several minutes before spin coating. The grids were silanized with (3-aminopropyl) triethoxysilane (APTES 919-30-2) via vapor deposition prior to spin coating, resulting in a homogenous dispersion of QDs on the grid windows. Glass coverslips were wiped with ethanol to remove dust particles and plasma-treated for 5 min. The QD-coated grids were then placed face down on the cleaned glass coverslips, as shown in figure 1(a), preventing the oil immersion objectives from contacting the TEM grids during optical imaging. To keep the grid from moving during optical imaging, a flexible silicon membrane was placed on top of the grid and coverslip.

Wide-field imaging
The locations of each aggregate relative to the TEM window edges were measured with wide-field microscopy. These coordinates were used to identify the same aggregates during TSRM and SEM imaging. Figure 1(b) displays a typical wide-field image of a grid window spin-coated with QDs. The bright spots correspond to QD aggregates, the round profile illuminating most of the image is the excitation spot, and the grid edges can be seen faintly traced along the left and bottom sides of the image. Wide-field images were collected with a modified Olympus IX-71 inverted microscope with a 60 × UPlan Apo 1.5 NA oil immersion objective (Olympus). The QD samples were irradiated by a 488 nm frequencydoubled continuous-wave diode excitation laser (Coherent) at ∼20 W cm −2 in a through-objective total internal reflection configuration. The emission was collected by the same objective, filtered by a 565 nm long-pass filter, and imaged onto a ProEM 512B EMCCD Camera (Princeton Instruments) using a 250 mm focal length achromatic tube lens. The grid edges were defined based on the contrast between the background present on the TEM windows compared to the grid frame. Coordinates of the QDs relative to the frame were obtained using ThunderSTORM in ImageJ [45].

Time-resolved super-resolution imaging
After obtaining the wide-field images that would later be used to identify specific QDs during SEM imaging, the samples were moved to the TSRM (figure 2), which has been described previously [30,46]. The TSRM provides the single photon arrival times with sub-nanosecond temporal resolution in four pixels, which allows the PL lifetime, intensity, and emission centroid location to be simultaneously measured. The samples were mounted on a piezoelectric nano-positioning stage (Physik Instrumente P-733.3 with E-710.A3D driver) on an Olympus IX-71 inverted microscope with confocal excitation. Excitation light from a 485 nm pulsed picosecond diode laser (PicoQuant LDH-P-C 485 with PDL-800-B driver) at a 2.5 MHz repetition rate was attenuated to an average power of ∼100 nW using neutral density filters and was focused into a single-mode optical fiber that served as a spatial filter to remove higher order transverse modes from the beam. The spatially filtered excitation laser light was re-collimated, directed to the inverted microscope, reflected by a dichroic beamsplitter (Di01 488, Semrock), and focused onto the sample by an objective (100 × 1.3 NA oil immersion, Olympus).
The PL from the optical probe region was collected by the same objective and was then transmitted by the dichroic beamsplitter, a 488 nm long pass filter (Thorlabs), and a 680 nm short pass filter (Semrock). The PL was focused by a 450 mm lens (overall magnification ∼250×) onto the aperture of four detector pixels formed from a 2 × 2 array of square optical fibers (03208-REVA, CeramOptics). Each fiber had a width of 100 μm with an additional 7.5 μm of cladding on each side. Each of the four fiber array outputs were connected via FC fiber couplers to four single-photon counting avalanche photodiode detectors (PerkinElmer SPCM AQ4C). For each detected photon, the detectors output a TTL pulse, which was delayed (792 Dual NanoSecond Delay Module, Phillips Scientific), inverted, attenuated, and passed to a time-correlated single photon counting (TCSPC) module (Hydraharp 400, PicoQuant). For each detected photon, the TCSPC module recorded the detector that registered the count, the number of laser pulses between the count and the start of the experiment (the macro-time), and the elapsed time relative to the arrival time of the laser pulse that preceded it (the microtime). Symphotime 64 software (v2.4, PicoQuant) was used for data acquisition and control of the piezo stage. To minimize z-axis (focus) drift during an experiment, a piezoelectric z-axis objective holder (Mad City Labs Nano F Series) was used in conjunction with a CRISP autofocus unit (Applied Scientific Instrumentation) for active feedback.
Manual micrometer adjustment was used to position the TEM windows above the probe region. Next, wide scans (100 × 100 μm 2 ) with the piezo stage were done to map the locations of the PL regions relative to a corner of the TEM window, as shown in figure 1(c), where the dark edge corresponding to the grid frame can be seen along the left and bottom sides of the scan. Each PL region identified in the confocal scan was also identified in the wide-field images, and coordinates of the PL regions relative to the corner of the TEM window were obtained from the wide-field images. The coordinates were later used to identify the structures corresponding to each PL region in the SEM. Provided that the sample coverage was fairly disperse, correlating the PL regions in the wide-field images and confocal scans was straightforward, as highlighted by the constellations drawn in figures 1(b) and (c). Obtaining a confocal scan with a corner of the TEM window in the field of view was also critical for matching the orientation of the TSRM and SEM images prior to making composite TSRM/SEM images.
For each TSRM measurement, the position of the piezo sample stage was adjusted until the signal from a single PL region was maximized and each detector was receiving approximately equal counts. Then, the region was monitored for 90-1200 s. This was repeated for each PL region of interest on the grid, with each region corresponding to the emission from an individual isolated QD or from a small QD assembly. When a single QD is examined, the location of the emission centroid corresponds to the location of that QD. Alternatively, when multiple QDs in an assembly are examined, the centroid location is a weighted average of the individual QD locations. For that case, the individual QD locations cannot be resolved. However, if the QDs within an assembly blink on and off independently and the emission centroid of the assembly is repeatedly identified, its location will occasionally correspond to the locations of individual emitters. A super-resolution image can be built up from those centroid locations [47].
We identified the centroid location using maximum likelihood estimation (MLE) [48], which is commonly implemented in super-resolution analyses [49,50]. For this, a two-dimensional likelihood distribution L is generated for the emitters' centroid position in x and y given the counts collected in the four pixels during a selected time interval, the pixel geometry, the relative detector efficiencies, the background counts, and the PSF geometry. The formulation of L and procedure for characterizing the PSF have been described elsewhere [30,46]. The maximum of L corresponds to the most likely centroid location, and it was determined every 0.5 s for the data presented in this paper. The locations were not determined when the number of counts in the 0.5 s interval fell below the average number of background counts, which occurred sporadically when all the QDs in the probe region blinked off. For single QDs, this accounted for 6% of the data on average, so the centroid positions could be determined most of the time. A linear drift correction was applied to the positions to correct for the slow (<0.1 nm s −1 ) lateral drift of the imaging setup.
The localization precision s was determined from the standard deviation of centroid locations acquired from a single isolated QD. This parameter is inversely proportional to the square root of the number of counts n collected by the pixels ( ) n 1 , s µ / so it is improved by selecting longer time intervals over which to bin the data, but at the expense of averaging over dynamics that may be occurring in the samples. With the counts acquired from a QD of typical brightness in a 0.5 s integration time, the centroid could be localized with a precision of ∼3 nm. This allowed us to monitor changes in the emission centroid position over several nanometers that occurred as multiple QDs within an assembly blinked on and off.
In addition to the centroid position, we monitored the intensity and PL lifetime behavior of the QDs for each 0.5 s interval. Individual and isolated QDs exhibited multi-exponential PL decays with weights and rates that varied throughout each measurement. The average of the arrival times (the average of the micro-times)t provides a means of estimating the PL lifetime without requiring an exponential decay fit to the histogram of the microtimes. When we refer to the 'lifetime' in this paper, we are referring tot . The total number of detected counts, n, is sensitive to the position of the emitter relative to the optical fiber cladding, where incident photons do not get detected. As the emitter drifts during a measurement, n increases as more of the image is centered on the optical fibers, and n decreases as more of the image is centered on the optical fiber cladding. A better metric for the intensity than n is the total number of photons N that strike the image plane, which is independent of the emitter position relative to the optical fibers and their cladding. N is solved for when the likelihood distribution is maximized for getting the emission centroid location, and it is used to define the intensity reported in this paper.

Spatially correlated scanning electron microscopy
After TSRM, the TEM grid was removed from the glass coverslip, and the coordinates obtained from the wide-field images were used to locate the single QDs and QD aggregates in a SEM. The SEM images were acquired using a FEI Magellan 400 XHR-SEM operating in scanning transmission electron microscopy (STEM) mode at 30 kV and 0.2 nA. We could not identify the positions of the nanostructures relative to the grid edge with high enough accuracy from the SEM and wide-field imaging to overlay the TSRM and SEM images directly. However, the spatial and angular distributions of the centroid positions from the TSRM images agreed well with the underlying structure given by the SEM images, enabling us to propose plausible composite images of the dimers by translating the (x, y) coordinates.

Characterizing single QDs
To assist our interpretation of QD dimers discussed in the next section, we first characterized the behavior of individual isolated QDs. Figures 3(a)-(c) summarizes the lifetime and intensity behavior of 44 individual QDs examined with TSRM. Figure 3(a) displays histograms of the lifetimes, which are sorted based on the average lifetime from shortest (bottom) to longest (top). The shortest of the lifetime distributions is centered around ∼14 ns, the longest lifetime distribution is centered around ∼90 ns, and the mean of the averages of the lifetimes is 53 ± 17 ns. In addition to heterogeneity among the mean lifetime for each QD, the shape and width of each distribution was unique. For example, QD number 3 had the narrowest distribution, and the standard deviation of its measured lifetimes was 5 ns; QD number 26 had the broadest distribution, and the standard deviation of its measured lifetimes was 25 ns.
Notably, for QDs from the same synthesis batch that were spin-coated directly onto glass coverslips rather than TEM grids, the distribution of lifetimes among different QDs was significantly narrower, spanning only ∼10 ns, and similarly narrow distributions in the lifetime among different single QDs on glass coverslips has been observed in the past [25,30]. This suggests that the TEM grids may play a role in the exciton relaxation pathways of the excited QDs, and it complicates attempts to probe QD-QD interactions in assemblies.  the lifetime and intensity, respectively. The centroid positions have a narrow, uniform distribution characterized by standard deviations of 2 nm in x and y. The SEM image in figure 3(f) confirms that the PL was emitted by a single QD. It has the same lateral scale as the TSRM images and shows the QD has a diameter of ∼11 nm. For a theoretical point emitter, the standard deviation of the centroid locations scales inversely with the square root of the number of counts. With increasing counts, achievable with a higher intensity emitter or longer bin times, the standard deviation will get arbitrarily small. For the case of the QD in figures 3(d)-(f), the centroid locations determined with 0.5 s bin times span 2 nm about a single mean location, while the QD has an 11 nm diameter. This implies that the emission centroids are localized to a particular region of the QD. On shorter timescales, there may be dynamics associated with the centroid location that span the physical extent of the QD. However, the localization precision worsens with shorter bin times and confounds our ability to interpret the spread in centroid locations for shorter timescales. We can at least conclude that there are no dynamics occurring during the 170 s measurement that cause the emission centroid location to move further than ∼2 nm. The same is not true for the QD dimers introduced in the next section, which display changes in the centroid location as large as 30 nm during similar acquisition periods.

Characterizing QD dimers
Six isolated QD dimers were identified in our combined TSRM/SEM experiments, and their images are presented in figure 4. Dimer-1 and Dimer-2 were created by spin casting an aggregated mixture of QDs with both core sizes (see section 2.1), while the remaining Dimers 3-6 were deposited from aggregated solutions of QDs solely with the larger core size. The first column from the left in figure 4 presents the SEM images, which have been arranged, top to bottom, in order of decreasing interparticle distance. The second and third columns of figure 4 display the corresponding TSRM images, for which the centroid positions are color-coded according to the lifetime and intensity, respectively. Each TSRM image is composed of 300-500 s of data. Composite TSRM/SEM images are shown in the fourth column of figure 4, which were made by laterally translating and then overlaying intensity-scaled TSRM and SEM images.
The centroid locations determined from the TSRM are the intensity-weighted averages of the two QD positions. Consequently, for time bins when both QDs are emitting and the intensity is higher, the centroids lie between the actual locations of the QDs. Centroid locations that agree with the individual QD positions are identified when one of the QDs has blinked completely off during the time bin and the other QD remains in an emissive state. As such, these centroids are associated with lower intensity emission. This behavior is observed clearly in Dimers-1, -2, and -5 of figure 4, for which lower intensity regions of the TSRM image are associated with the positions of the individual QDs given by the SEM images, and a higher intensity region is associated with a location partway between the individual QDs. We use this interpretation when overlaying the SEM and TSRM images for these dimers, placing the higher intensity region partway between the two QD locations given by the SEM images.
The spatial distributions of the intensity are more complicated for Dimers-3, -4, and -6, and each one requires a unique interpretation. For Dimer 3, lower and higher intensity regions are associated with the left and right sides of the TSRM image, respectively. This may be observed because the QD of the left never blinked off during the measurement. As such, centroid locations associated singularly with the QD on the right would not be acquired. We use this interpretation to inform the overlay of the TSRM and SEM images for this dimer, so we placed the high intensity region partway between the two QDs and the low intensity region on top of the QD on the left. For Dimer-4 from figure 4, the bottom of the TSRM image is associated with a higher intensity and the top of the image is associated with a lower intensity. In this case, we hypothesize that the QD on the bottom has a higher intensity than the QD on the top. Dimer-6 has a similarly nonuniform intensity distribution that is correlated with its lifetime, and it is discussed in more detail below.
The time trajectories of the TSRM data can also parsed to show how the TSRM positions can represent or misrepresent the physical positions of the QD given by the SEM, depending on the intensity of the emission. This is most apparent for Dimer-1, which has the largest separation between QDs. Figures 5(a)-(d) display the lifetime, intensity, x centroid position, and y centroid position versus time for Dimer-1, and figures 5(e)-(f) display histograms of the respective trajectories. The lifetime has a Gaussian distribution (figure 5(e)) with an average of ∼60 ns, whereas the intensity is not uniform ( figure 5(f)). To simplify our interpretation of the centroid position dynamics, the (x, y) coordinates were rotated by 10°relative to the original image of Dimer-1 ( figure 4), so the interparticle axis of the two QDs points exclusively in the y-direction. Now, the centroids sample different positions exclusively in y as the QDs blink on and off. As a result, the trajectories of the rotated centroid positions in x and y (figures 5(c), (d)) have a narrow distribution in x (figure 5(g)) and a broader distribution in y ( figure 5(h)).
To examine the behavior of Dimer-1 when only one of the two QDs was on, we extracted the centroid locations for which the intensity was below a threshold (N 3.9 × 10 4 cts) that more likely corresponds to single QD emission. Histograms of the centroid locations in x and y for which N 3.9 × 10 4 cts are displayed in figures 5(i) and (j), respectively. The intensity-filtered x distribution changes little, but the filtered y distribution becomes bimodal, with two peaks separated by 27 nm. This separation is in good agreement with the 28 nm center-to-center distance measured from the SEM image of Dimer-1, which is overlaid ( figure 5(k)) on the histogram to highlight the agreement. Even lower thresholds on the intensity can be set that also return the accurate separation, at the expense of fewer data points, while higher intensity thresholds shrink the apparent separation distance as the central peak at y = −40 nm (figure 5(h)) returns. The same intensity filter can be used to extract the PL intensities and lifetimes of the individual QDs in Dimer-1. For this, we assign the filtered emission to one QD or the other if it is above or below the minimum of the bi-modal distribution in y centroid locations (figure 5(j)) at y = −33 nm. The respective lifetimes of the top and bottom QDs are 55 ± 15 ns and 49 ± 7 ns, and their intensities are both ∼29 000 cts/0.5 s. Similar intensity-based analyses can be applied to the other QD dimers from figure 4 to extract the lifetimes, positions, and intensities of the individual QDs. However, Dimer-4 and Dimer-6 present challenges because the intensity of one QD may be significantly higher than the other. Selecting for a lower intensity may yield the location of one of the QDs, but not both.Unlike the pronounced relationship between intensity and centroid position, the time trajectories of the PL lifetimes for Dimers 1-5 shown in figure 4 appear to be independent of the centroid position. However, Dimer-6 shows a correlation between position, PL lifetime, and intensity, which suggests the two QDs have significantly different lifetimes and intensities. We can apply lifetime filtering to Dimer-6 analogous to the intensity filtering applied for Dimer-1 to extract the locations, lifetimes, and intensities of the individual QDs.   lifetime is shorter than 40 ns is blue, and the data corresponding to time bins when the lifetime is longer than 40 ns is red. The selection of 40 ns gave the largest separation between the average centroid locations associated with longer and shorter lifetimes. The blue time trajectories have an average lifetime of 30 ± 7 ns, an average intensity of 1.2 (±0.4) × 10 4 cts/0.5 s, and an average y centroid position of -6.2 ± 0.3 nm relative to the origin. The red time trajectories have an average lifetime of 62 ± 10 ns, an average intensity of 2.8(±0.8) × 10 4 cts/0.5 s, and an average y centroid position -10.2 ± 0.1 nm relative to the origin.
The histograms of the y centroid location for the short lifetime (blue) and long lifetime (red) time bins (figure 6(h)) reveal a separation of 4.0 ± 0.3 nm between the mean y centroid locations associated with the shorter and longer lifetimes. This separation is significantly smaller than the center-to-center inter-QD separation of 8.7 nm measured by SEM. This can also be seen in the composite image (figure 4, 4th column) in which the short and long lifetime emitter locations are somewhat shifted towards each other along the interparticle axis compared with the SEM image. A simple explanation for the discrepancy in interparticle separation is that the longer-lifetime QD may not be completely off during some time intervals when the signal is dominated by the shorter lifetime QD, or vice versa. This would tend to skew one or both emitter locations toward some average location between the two, causing the distribution of centroid locations to be narrower than the physical separation of the two QDs. A second possibility is that the emission profile for one or both QDs in the pair may not be centrosymmetric. Further measurements of additional QD structures exhibiting this behavior will be required to address this intriguing possibility.
In previous studies of QD assemblies, our group observed correlated short lifetime/low intensity and long lifetime/high intensity emission that suggested the QDs were participating in energy transfer [24,30]. Dimer-6 shows the same correlation between lifetime and intensity, and the two QDs appear to be in direct contact in the SEM image. Given that, we hypothesize that the QDs in Dimer-6 are participating in energy transfer, and we can use the TSRM information to determine the direction and rate of energy transfer. Suppose that Dimer-6 is composed of a QD donor (D) that transfers energy with a rate F to a QD acceptor (A). In the absence of energy transfer, D and A have respective radiative decay rates R D and R .
A For the case where A blinks off (R 0 A  ), the detected emission arises exclusively from D. In this case, the lifetime is the same ast , and is determined by the reciprocal of the sum of R D and F. The intensity is proportional to the quantum yield which is equal to the product ofR t D and the proportionality constant ( ) P 0 , D which is the probability that the donor is initially excited [51]. It follows that both the lifetime and intensity decrease as F increases.
We can estimate F for Dimer-6 using equation (1) if we knowt and R . D Recalling that the average of the shorter lifetimes of Dimer-6 (figure 6(a), blue trajectory) was 30 ns, let us assumet = 30 ns. Recalling that the average lifetime of the single isolated QDs examined in figure 3(a) was 54 ± 16 ns, let us assume that R D 1 54 » ns −1 . Substituting R D andt into equation (1) gives F 0.015 » ns −1 as the rate of transfer from the QD on the left to the QD on the right ( figure 4).
A common measure of merit for comparing energy transfer rates is the Förster radius, which is the distance at which the energy transfer rate equals the radiative decay rate [52] and it is given by: where d DA is the distance between the donor and acceptor.
Using d DA = 8.7 nm measured from the SEM image, along with the values determined above for R D and F, equation (3) yields a Förster radius R 0 ≈ 8 nm. This is comparable to experimentally measured values ranging from 4 to 9 nm from other groups for energy transfer among QDs with CdSe cores and various shell compositions [28,[53][54][55].
There is an alternative explanation for the correlated lifetime/intensity of Dimer-6 which is not predicated on energy transfer. The two QDs in Dimer-6 may simply have different lifetimes and intensities where the one on the left (figure 4) has a shorter lifetime of ∼30 ns and a lower intensity of ∼1.2 cts/0.5 s, and the one on the right has a longer lifetime of ∼62 ns and a higher intensity of ∼2.8 × 10 4 cts/0.5 s. These values fall well within the range of lifetimes and intensities observed among different single QDs ( figure 3). The lifetime heterogeneity may be related to the interactions with the TEM grids, as discussed in section 3.1, and implies selection of a substrate and QD material must be done carefully if one wants to avoid QDsubstrate interactions to better facilitate the observation of QD-QD energy transfer.

Conclusions
In summary, we collected combined TSRM and SEM images of single QDs and QD dimers. SEM provides the size of the QDs and their relative positions within dimers. TSRM provides the lifetime, intensity, and emission centroid location with ∼3 nm single emitter localization precision. The TSRM images of dimers agree well with the actual configurations of the QDs given by the SEM. To our knowledge, this is the first time that combined TSRM/SEM imaging has been demonstrated. Both intensity and lifetime filters were applied to the TSRM data to extract more information. With low-pass intensity filtering, the positions, intensity, and lifetime corresponding to the individual QDs within a particular dimer were extracted. The separation distance given by the TSRM agreed with the physical separation independently measured by the SEM. With lifetime filtering, the intensities and centroid locations associated with shorter and longer lifetimes were extracted.
Of the six dimers that we examined, one exhibited behavior that was consistent with energy transfer. We estimated an energy transfer rate of 0.015 ns −1 and a Förster radius of ∼8 nm. However, due to the large heterogeneity in the lifetimes among isolated QDs when deposited on the TEM grids, we cannot rule out the possibility that the high intensity/long lifetime and low intensity/short lifetime observed in this dimer was a coincidence rather than an indication of energy transfer. Future work imaging assembled QDs on substrates that do not interact with the QDs, and thus provide a narrower distribution of lifetimes and intensities, may provide a more accurate assessment of the energy transfer properties.