Dynamics of Intermittent Delayed Emission in Single CdSe/CdS Quantum Dots.

Bright and fast fluorescence makes semiconductor nanocrystals, or quantum dots (QDs), appealing for applications ranging from biomedical research to display screens. However, a few percent of their fluorescence intensity is surprisingly slow. Research into this "delayed emission" has been scarce, despite undesired consequences for some applications and potential opportunities for others. Here, we characterize the dynamics of delayed emission exhibited by individual CdSe/CdS core/shell QDs and correlate these with changes in the emission spectrum. The delayed-emission intensity from a single QD fluctuates strongly during an experiment of several minutes and is thus not always "on", implying that control over delayed emission may be possible. Periods of bright delayed emission correlate with red-shifted emission spectra. This behavior is consistent with exciton polarization by fluctuating electric fields due to diffusing surface charges, which have been known to cause spectral diffusion in QDs. Our findings thus provide a stepping stone for future efforts to control delayed emission.

Research and development for over 25 years[1] has resulted in high-quality semiconductor nanocrystals (or quantum dots, QDs) of various material compositions that produce bright fluorescence useful in display screens, lighting, bioimaging, quantum optics, and other applications.[2] Nevertheless, some of their key fundamental properties remain poorly understood. For example, while the excited state of a QD usually lives no longer than a few tens of nanoseconds before it decays by emitting a photon, sometimes emission takes orders of magnitude longer.[3−15] This slow emission—or “delayed emission”—is responsible for on the order of 10% of the fluorescence from various types of QDs, including CdSe/CdS/CdZnS/ZnS core/multishells,[10] Cu-doped CdSe,[13] CuInS2,[13] and lead–halide perovskites.[14] It is typically ascribed to trapping and detrapping of excited charge carriers, which renders the excited state of the QD temporarily nonemissive. The prolonged excited-state lifetimes can be beneficial for the use of QDs in photocatalysis and photovoltaics. On the other hand, the occurrence of (temporarily) nonemissive excited states may have negative implications for the use of QDs as laser gain medium[16] or as Förster resonance energy transfer (FRET) donors.[7] Furthermore, delayed-emission trapping has been tentatively linked to fluorescence blinking of single QDs[3−6,8−11,13,15] and may lower the threshold for fluorescence saturation.[6,17]

Most of what we know about delayed emission has until now come from ensemble-scale experiments. Generally, the decay of delayed emission following pulsed excitation is characterized by a long, power-law-like slope,[3,10−13,15] indicating broadly distributed rates of charge-carrier detrapping. (De)trapping of charge carriers likely happens through tunneling, as the rates are temperature-independent.[11,13,18,19] The trapping process is thought to occur from the lowest-energy exciton state.[3−6,8−15] Based on the spectrum of delayed emission on the ensemble scale, the lowest-energy exciton is likely restored upon charge-carrier detrapping, followed by radiative recombination.[10,12−14] However, much is still unknown regarding delayed emission. For example, ensemble-scale experiments do not provide information about variations between QDs or dynamic fluctuations that likely underly the distributed dynamics of delayed emission. Moreover, ensemble-averaging masks possible correlations between the fluorescence intensity, dynamics, and spectrum, which could otherwise establish the mechanisms of trapping/detrapping and the proposed link between delayed emission and blinking.

Here, we elucidate the mechanisms underlying delayed emission in individual CdSe/CdS core/shell QDs, using a combination of single-QD spectroscopy and time-correlated single-photon counting (TCSPC). Low-dark-count detectors allow us to measure the photoluminescence (PL) decay dynamics of single QDs up to 1 μs after excitation with negligible (<20 photons/s) background. All single QDs measured have prompt PL lifetimes of approximately 30–50 ns but also show delayed emission on time scales until 1 μs. Surprisingly, the intensity of delayed emission shows strong temporal fluctuations, seemingly uncorrelated to fluctuations of the total emission intensity (i.e., blinking). We find that the QD emission spectrum is red-shifted and broadened during time periods of high delayed-emission intensity. These spectral changes are reminiscent of the response of a QD to an external electric field, due to the quantum-confined Stark effect (QCSE).[20−30] However, the QCSE alone cannot explain the very slow dynamics of delayed emission. We propose that, additionally, polarization of the exciton by the spontaneously fluctuating electric field facilitates temporary trapping of charge carriers, as was previously observed for applied external electric fields.[23] Our results establish delayed emission as yet another property of QDs with pronounced temporal fluctuations, besides the total fluorescence intensity (i.e., blinking) and their spectrum (i.e., spectral diffusion).

We synthesized CdSe/CdS core/shell quantum dots (QDs) with an ensemble emission peak at 628 nm (Figure S1) and a diameter of 8.4 ± 1.7 nm (mean ± standard deviation; Figure S2) following a procedure based on the work of Chen et al.[31] The PL decay dynamics of a typical single CdSe/CdS QD from our batch (Figure a,b) are similar to those of the ensemble (Figure S3). The decay is approximately exponential on the first 50 ns due to “prompt” radiative recombination of the exciton, i.e., directly following photoexcitation. The slower nonexponential tail is denoted “delayed emission” and is typically ascribed to temporary trapping of one (or both) charge carriers from the band-edge state, followed by detrapping and subsequent radiative recombination of the exciton.[3−5,8−15] All 10 QDs studied in detail showed nonexponential delayed emission, consistent with previous studies,[3] although the relative intensity of delayed compared to prompt emission varied between QDs (see Extended Data, Figures E1–10). Distributed dynamics are thus not only an ensemble-averaged characteristic of delayed emission but also an intrinsic property of individual QDs.

Figure 1

(a,b) Normalized PL decay curves of a single CdSe/CdS core/shell QD, displayed on (a) semilogarithmic and (b) log–log scale. The dashed lines are a biexponential fit to the data up to a delay time of 100 ns. Prompt and delayed emission are indicated with blue and red shading, respectively. (c) Total photoluminescence (PL) intensity (Itot) trace of an individual quantum dot (QD), constructed with a 10 ms bin size. Itot switches between a state of high and a state of lower intensity labeled “ON” (blue arrow) and “GRAY” (red arrow). The background intensity is 0.2 cts/10 ms. (d) Delayed-PL intensity (Idel, defined as the number of photons detected ≥200 ns after a laser pulse) trace of the same QD, binned at 10 ms. Idel fluctuates between low (3 cts/10 ms) and high (∼25 cts/10 ms) values. (e) Distributions of Idel, corresponding to (red) bins directly preceding an ON → GRAY switch (i.e., selecting all bins i for which Itot, – Itot, ≤ −70 cts/10 ms), (blue) bins directly following an GRAY → ON switch (i.e., Itot, – Itot, ≥ 70 cts/10 ms), and (black) all 10 ms time bins during which the QD is ON (Itot, ≥ 100 cts/10 ms).

Under continued photoexcitation, the CdSe/CdS QD discussed here blinks between a high-intensity state producing 137 photon counts/10 ms and a lower-intensity state with 42 photon counts/10 ms (Figure c). The characteristics of these states (see Extended Data, Figures E1–10) are consistent with an “ON” state, in which the QD exhibits a PL quantum yield (QY) of unity,[32] and a “GRAY” state, in which the QD is momentarily charged, leading to an increased radiative decay rate but a reduced PLQY because of competition with nonradiative Auger decay processes.[33,34]

In Figure d, we show the delayed-emission intensity, Idel, over the same measurement period of 30 s as shown in Figure c. For this analysis, we classify a photon as “delayed” when it is detected more than 200 ns after the laser pulse. As the PL lifetime of the ON states of our QDs is 30–50 ns, a threshold of 200 ns effectively discards >99% of the exponential prompt emission while accepting enough delayed photons to allow further analysis. We observe, surprisingly, that the delayed-emission intensity fluctuates strongly, between a low value of ∼3 counts/10 ms (due to background fluorescence and unrejected prompt emission; Figure S4) to high values of >40 counts/10 ms.

At first glance, it is difficult to identify correlations between the fluctuations in Idel and fluctuations in Itot: during ON periods, the QD can exhibit either low or high Idel (cyan and purple regions in Figure c,d, respectively). Similarly, periods in which the QD is blinking between the ON and GRAY states can exhibit either low or high Idel (green and yellow regions in Figure c,d, respectively). More quantitative statistical analysis (Figures e and S5) does not reveal correlations between Idel and Itot either, despite recent proposals for a relationship between delayed emission and blinking.[3−6,8−11,13,15] We have to stress, however, the gap in time scales between our measurements of delayed emission (between 200–1000 ns after laser excitation) and our ability to resolve blinking (10 ms). We might in fact miss the rarest and slowest delayed-emission events that are the most relevant for blinking. Only when a charge carrier is trapped for ≫1 μs would this effectively charge the QD and thereby lead to an ON → GRAY switch observable in the blinking trace of Figure c. Ensemble-scale experiments have provided evidence for such very slow detrapping processes.[10,11,13,15]

Ensemble-scale time-resolved emission spectroscopy (TRES) on our CdSe/CdS QDs dispersed in toluene yields results consistent with previous studies:[10,12−14] the spectrum emitted over the first 10 ns after photoexcitation (blue in Figure a) is nearly identical to the delayed-emission spectrum recorded from 1250 to 2000 ns (purple in Figure a). This confirms that delayed emission of our QDs involves recombination of free, rather than trapped charge carriers. In contrast, emission involving trapped charges would yield a broad spectrum red-shifted from the lowest-energy exciton recombination, due to strong electron–phonon coupling.[35−37] On intermediate time scales, between 50 and 400 ns, the spectrum is red-shifted and broadened (Figure a,b). This behavior, matching previous TRES measurements on Cd-based QDs,[10,38] is attributed in the literature to polydispersity in the QD size and corresponding variations in the prompt radiative decay rate.[39] As we will show below, spectral diffusion likely contributes to this red-shift as well.

Figure 2

(a) Time-resolved PL spectra of an ensemble of CdSe/CdS QDs dispersed in toluene, obtained by integrating the PL spectrum over delay times of 0–10 ns (blue), 170–210 ns (green), 340–400 ns (yellow), 750–1000 ns (red), 1250–2000 ns (purple), and 0–2000 ns (black). (b) PL peak positions, obtained by fitting spectra with a two-sided Gaussian (see Supporting Information, Section S2 for details). The dashed line is the peak position of the early time spectrum (0–10 ns), which is set to ΔEpeak = 0. Error bars correspond to ±1 standard error of the fit. (c) Distribution of delayed-emission intensity during simultaneous TCSPC and spectral measurements on the same single QD discussed in Figure . For this analysis, we selected only periods during which the QD was ON (i.e., total intensity Itot > 75 cts/18 ms on the single-photon detector). (d) Single-QD PL spectra as a function of Idel, obtained by selecting periods of a 296 s experiment during which the QD exhibited delayed-emission intensity (colored regions indicated in panel (c)) of Idel < 3 cts/18 ms (blue), 3 cts/18 ms ≤ Idel < 5 cts/18 ms (cyan), 5 cts/18 ms ≤ Idel < 7 cts/18 ms (green), 7 cts/18 ms ≤ Idel < 10 cts/18 ms (yellow), 10 cts/18 ms ≤ Idel < 13 cts/18 ms (orange), and 13 cts/18 ms ≤ Idel (red). (e) PL peak position and (f) full-width-at-half-maximum as a function of our selection of Idel, displayed here as the mean ± standard deviation of Lorentzian fits to the selected 18-ms-integrated spectral frames.

To correlate the spectral properties and delayed-emission dynamics of single QDs, we performed simultaneous time-correlated single-photon counting and spectroscopy by splitting the QD emission (Supporting Information, Section S2). Synchronizing the measurements provides us with the delayed-emission intensity Idel of the QD (Figure c) during the integration time of each spectral frame. Figure d shows the PL spectra for increasing Idel. Note, however, that, as the integration time for each spectral frame was 18 ms, these PL spectra always contain contributions from both prompt and delayed emission.

The single-QD PL spectrum contains a single peak for all delayed-emission intensities Idel (Figure d), resembling a Lorentzian. This indicates that delayed emission is due to recombination of delocalized, rather than trapped, charge carriers. If the delayed emission we study here was due to emission from (surface) trap states, we would expect the appearance of a second, red-shifted peak in the PL spectrum, as commonly observed for trap emission on the ensemble scale.[35,36] Nevertheless, the PL spectrum for high Idel is different from that for low Idel. It red-shifts up to 30 meV with increasing delayed-emission intensity (Figure e) and broadens (Figure f). As all spectra show a single emission peak, this red-shift corresponds to a spectral shift of both prompt and delayed emission.

The comparison between the time-resolved PL spectra of the QD ensemble (Figure a,b) and the single-QD spectra for selected Idel (Figure d–f) is not straightforward. Even during moments of the highest Idel (Idel > 13 cts/18 ms, red in Figure c), 83% of the emission is emitted at delay times <200 ns, and only 17% of the emission is emitted at delay times of 200–1000 ns. In our correlated experiments of PL spectra and dynamics, it is impossible to select the slowest delayed emission (>500 ns) exclusively. This explains why our single-QD analysis reproduces the initial red-shift and broadening of the delayed emission observed in the ensemble-scale TRES data (blue and green spectra in Figure a), but it is difficult to observe the blue-shift on time scales >250 ns (yellow, red, and purple spectra in Figure a). Of the 10 QDs studied, only one shows this blue-shift for the highest Idel (see QD 5 in the Extended Data, Figures E5 and E15). Regardless, our single-QD experiments prove that the initial red-shift is not exclusively due to sample polydispersity but occurs on the scale of individual QDs. Future experiments yielding simultaneous information on the color and delay time of each individual photon may be necessary to study the single-QD spectrum of the slowest delayed emission (>500 ns) in more detail.[40]

The spectral red-shift and broadening (see Figure ) point to an influence of the quantum-confined Stark effect (QCSE)[25,41] on delayed emission. The QCSE is the response of a nanoconfined semiconductor to an external electric field. For example, with the application of electric fields on the order of 107 V m–1,[21,23−28] the emission of QDs and nanorods red-shifts and broadens. The QCSE also underlies spectral diffusion, the spontaneous fluctuations in the PL spectrum demonstrated in various types of individual QDs at cryogenic temperatures as well as room temperature.[22,25,29,30,42−44] These are due to spontaneously fluctuating electric fields experienced by charge carriers in the QD due to, for example, surface atoms or capping ligands moving around over the QD surface.

To elucidate the possible influence of electric fields on delayed emission in our individual QDs, we analyze the PL decay dynamics in more detail. We scaled the PL decay curves of our QD for increasing Idel (Figure a,b) to the number of 18 ms time periods that were selected to generate the curve. The amplitude of the decay curve, i.e., the intensity at delay time t = 0, is then proportional to the radiative decay rate of the QD (Supporting Information, Section S3). With increasing Idel (from blue to red in Figure a,b), the PL decay becomes slower, and the amplitude of the decay curve decreases. Figure c shows a linear relation between the early time PL decay rate and the amplitude of the decay curve. This can be qualitatively explained in terms of the QCSE, wherein a fluctuating electric field polarizes the exciton wave function (Figure d). Exciton polarization reduces the electron–hole overlap and thereby the radiative recombination rate krad, to which the amplitude of the decay curve is proportional (Supporting Information, Section S3).

Figure 3

(a) Background-subtracted single-QD PL decay curves from selected periods with increasing delayed-emission intensity Idel, corresponding to the six delayed-emission categories indicated in Figure c. We select only periods in which the QD is ON (total emission is >75 cts/18 ms). (b) Zoom-in of the PL decay curves of panel (a) on a semilogarithmic scale. Solid lines are monoexponential fits. (c) Amplitude and decay rates obtained from fits of monoexponential decay to the experimental decay curves depicted in (a,b). Colors indicate the delayed-emission category (see Figure c). The solid line is a linear fit to the data points. (d) Schematic depiction of the QCSE: an external electric field perturbs the electron and hole wave functions, thereby reducing the electron–hole wave function overlap and decreasing the radiative decay rate krad.

Although the behavior of our single QD is qualitatively consistent with the QCSE, the fluctuations of krad by a factor 2.4 (Figure c) are stronger than have ever been reported. Previous experiments achieved spectral shifts of up to several tens of meV in colloidal QDs and nanorods,[24,26−28] induced by electric fields of up to 50 MV m–1 applied using external electrodes. The spectral fluctuations of our QD (up to ∼35 meV; Figure e) are thus consistent with spontaneously fluctuating electric fields with strengths of up to a few tens of MV m–1, which could originate from a few elementary charges diffusing around on the QD surface (see Supporting Information, Section S4 for further discussion of this). However, such fields were previously reported to increase the PL lifetime of individual CdSe/CdS QDs by no more than 5%,[24] while the PL lifetime of individual CdSe/ZnS QDs became shorter by ∼10% or longer by ∼10%, depending on the particular QD.[26] These weak lifetime changes are at odds with the strong fluctuations of up to a factor of 2.4 that we observe. The slowest photon emission events in our experiments (e.g., at t = 500–1000 ns in Figure a) are even more difficult to reconcile with the expectedly limited effect of the QCSE on the fluorescence lifetime.

To better understand the expected effect of the QCSE on the PL lifetime, we performed simple quantum-mechanical effective-mass calculations (Figure ). We approximated our QDs as spherical particles with a core of 2 nm radius and a shell of 2 nm thickness and calculated the spectral shift and radiative decay rate with increasing homogeneous electric field. The electric field polarizes the exciton wave function (Figure a,b), decreases the exciton energy (Figure c), and reduces the electron–hole overlap integral and thereby the radiative decay rate (Figure d).[28] We calculate that a homogeneous field of approximately 20 MV m–1 induces a Stark shift of approximately 35 meV, which is close to the maximum peak shift we and others[24,26−28] observed experimentally (see Figure e). The corresponding PL decay rate, however, is only slower by 25% compared to the zero-field situation. These calculations confirm that the QCSE alone cannot explain the strong fluctuations in lifetime observed experimentally (Figure e). Note that in the experiment, the QD may never experience exactly zero electric field, but this does not affect the expected correlation between exciton energy and radiative lifetime based on the QCSE model.

Figure 4

(a,b) Calculated (a) electron and (b) hole charge densities in a CdSe/CdS core/shell QD experiencing a homogeneous electric field in the vertical direction (see arrow) with a strength of 14 MV m–1. See Supporting Information, Section S4 for details of the model. (c) Calculated Stark shift ΔE as a function of electric-field strength. (d) Calculated normalized radiative decay rate, krad, as a function of electric-field strength. (e) Calculated relation between krad and ΔE for our QD geometry due to the quantum-confined Stark effect (QCSE, solid line), and experimental single-QD data (colored symbols). Symbol colors refer to the delayed-emission category (see Figure c); error bars correspond to ±1 standard deviation in the fitted Stark shifts.

To reconcile the apparent link between the QCSE and delayed emission with the quantitative mismatch between the emission time scales, we propose a mechanistic link between charge-carrier trapping/detrapping and the QCSE. The spontaneously fluctuating electric fields, which induce the QCSE,[22,25,29,30] may—if sufficiently strong—also promote temporary trapping of charge carriers. Indeed, several delayed-emission characteristics on the ensemble and single-QD levels clearly point to charge-carrier trapping/detrapping. For example, the single-QD PL decay curves at high Idel contain lifetime components that are an order of magnitude slower than the prompt lifetime of 40.7 ns (see delay times of 500–1000 ns in Figure a), which cannot be understood in terms of the QCSE alone. Moreover, the ensemble-scale emission spectrum at delay times of >400 ns is nearly identical to prompt emission, indicating emission from a nonpolarized exciton.

Our interpretation is supported by previous experiments, which demonstrated that external electric fields can not only induce the QCSE[24,26−28] but also influence charge-carrier trapping.[23] In fact, a transition has been shown for individual CdSe/ZnS nanorods where weak applied electric fields (<20 MV m–1) result in the QCSE while stronger fields (>20 MV m–1) cause charge-carrier trapping.[27] We propose that spontaneous electric-field fluctuations due to a moving surface charge could have similar effects. Weak fluctuating fields result in red-shifted and broadened PL and a reduced radiative recombination rate due to the QCSE. Stronger fluctuating fields result in temporary charge-carrier trapping,[23] giving rise to the red-shifted and unusually slow emission on 100–400 ns time scales. The slowest delayed emission (>400 ns), which is not red-shifted, can be explained as follows: the strongest fluctuating fields induce charge-carrier trapping but may also prevent detrapping (as observed in ref (23) for externally applied electric fields). Hence, charge carriers cannot detrap until after the field disappears spontaneously. This could lead to the slowest delayed-emission events that have the same spectrum as prompt emission. Indeed, correlation analysis on delayed photons (Figure S6) demonstrates fluctuations in delayed-emission intensity, hence, electric-field fluctuations, on microsecond time scales. These electric-field fluctuations would be responsible for keeping charges trapped for prolonged times of 400 ns and longer.

The delayed-emission characteristics of individual CdSe/CdS QDs and QD ensembles thus provide evidence for a mechanistic link between delayed emission and spectral fluctuations due to the QCSE. Although we studied CdSe/CdS QDs here, exciton wave functions are polarizable by surface charges in other types of QDs as well. This mechanism could thus contribute to the delayed emission observed in many types of QDs, including CuInS2 and perovskites.[11,14] Our findings suggest strategies to control or even eliminate the occurrence of delayed emission from colloidal QDs.[10,13,14] A high-bandgap shell around the emissive QD core would increase the separation from diffusing surface charges and reduce their effect on the exciton. However, charge-carrier delocalization—as in our CdSe/CdS QDs with a quasi-type-I band alignment—counteracts this beneficial effect, because it increases the exciton polarizability and hence the response to external fields. Recently, CdSe/CdZn1–Se core/shell QDs have been reported, with a type-I band alignment that confines both charge carriers to the core and prevents increased exciton polarizability.[45] Indeed, these QDs showed reduced spectral diffusion due to the QCSE. Future research will have to establish whether such new core/shell QD designs can suppress delayed emission. This might, for example, be important to increase the saturation threshold of QDs,[17] making them better suited for high-power and laser applications.