Excitation wavelength-dependent photoluminescence decay of single quantum dots near plasmonic gold nanoparticles

Hybrid nanosystems consisting of plasmonic metal nanoparticles (NPs) and quantum dots (QDs) have been of tremendous interest for QD-related optical and optoelectronic applications, largely because plasmonic NPs offer the flexibility of modulating the photophysical properties of nearby fluorescent QDs for desired applications.¹ Plasmonic metal NPs are known for localized surface plasmon resonance (LSPR) that describes the collective oscillation of the surface conduction electrons upon electromagnetic excitation.² The created electric field near a metal NP will then enhance the absorption of fluorophores, such as QDs in the vicinity. At the meantime, a plasmonic metal NP could also accelerate the radiative excitonic recombination of nearby QDs through Purcell effect. Moreover, metal NPs could also accept energy or charges from the excited QDs, providing additional non-radiative recombination pathways to quench the photoluminescence (PL) of QDs. Thus, the overall effect of plasmonic NPs on PL intensity and lifetime of QDs is a result of multiple factors.

Plasmonic modulation of QD PL is often realized via the geometry and composition of the hybrid structure, which requires much synthetic effort. Alternatively, when the geometry and composition of a plasmonic metal NP-QD hybrid system are fixed, changing the excitation wavelength provides a simple but effective strategy to modulate the photophysical characteristics of QDs since the plasmonic effect is highly excitation wavelength-dependent. For example, it was found that when the excitation wavelength overlaps with the LSPR peak of gold (Au) NPs, the statistics of the photons emitted from nearby single QDs could switch from anti-bunched to bunched.³ Changing the excitation wavelength also has an impact on the PL decay of QDs near plasmonic nanostructures. Several groups have reported this excitation wavelength dependence at the ensemble level that the PL decay of QDs near plasmonic nanostructures tends to be faster when excited spectrally close to the LSPR peak.^4–7 This phenomenon seems to break the well-known Kasha’s rule; however, the mechanism is unclear. So far, the published studies on this excitation wavelength dependence were conducted at the ensemble level and a mechanistic understanding on the phenomenon is lacking. The ensemble averaged results may lead to ambiguity⁸ in interpreting the plasmonic effect on the PL decay mechanism.

The missing of the studies at the single QD level probably comes from the difficulties in analyzing and interpreting the data. Single QDs exhibit notorious fluorescence intensity intermittency or “blinking,”⁹ and this phenomenon is non-ergodic.¹⁰ The intensity and PL decay of a single QD are usually correlated, that the PL decay corresponding to a higher intensity level is typically slower.^11,12 The non-ergodic blinking combined with correlated intensity and PL decay could yield varied results of the PL decay curve of a single QD with finite acquisition time. Beyond the single QD level, the PL characteristics of QDs exhibit dot-to-dot variations arising from the inherent inhomogeneities in their crystal structure and surfaces. The dot-to-dot variations are further magnified by the geometry of hybrid systems as how QDs are positioned near metal NPs will substantially affect the plasmon–exciton interaction.¹³ Consequently, conclusions drawn from a few “representative” QDs, a strategy many single QD studies utilized, may not depict the true characteristics of the whole hybrid system. For these reasons, the experimental data at the single QD level should be treated integratively with mathematical rigor.

Here, we report a quantitative study on the excitation wavelength dependence of the PL decay of CdSe/CdS core/shell QDs near Au NPs at the single QD level. Using a set of statistical methods, we show with statistical rigor that the PL decay of a single QD near Au NPs is generally excitation wavelength-dependent under a mild excitation power and that it is faster when the excitation wavelength is spectrally close to the LSPR peak of Au NPs. While the rates of radiative and non-radiative recombination of QDs increase when placed near Au NPs, the increase is not necessarily excitation wavelength-dependent. The excitation wavelength dependence of the QD PL decay mainly comes from the excitation wavelength-dependent proportion of photons from biexciton emission relative to all the emitted photons.

Details on the fabrication of the Au NP-QD hybrid system have been described elsewhere³ and also in Sec. 1 of the supplementary material. Briefly, Au NPs with an average diameter of ∼100 nm were synthesized following a published protocol.¹⁴ Then, Au NPs were immobilized on a No. 1 glass cover slip pretreated with aminopropyltriethoxysilane to form a submonolayer film.¹⁵ As shown in Fig. 1(b), the extinction spectrum measured from the film of the synthesized Au NPs has a peak at ∼580 nm. A ∼25 nm thick alumina (Al₂O₃) layer was then deposited onto the Au NPs by atomic layer deposition as a spacer. The scanning electron microscopy image of the substrate can be viewed in Fig. S1. High-quality CdSe/CdS core/shell QDs dissolved in hexane were prepared following a reported protocol with minor modifications.^16,17 The synthesized QDs have an emission peak at ∼635 nm, as shown in Fig. 1(b). A very dilute QD solution was spun-cast onto the Au NP-alumina substrate and dried to form a low-density layer of QDs. The same QD solution was also deposited onto a clean glass cover slip as a reference.

The QD samples were mounted on a home-built confocal Nikon Ti–U microscope equipped with a 100× oil-immersion objective, which has a numerical aperture of 1.3. A supercontinuum pulsed laser (Solea, PicoQuant) operated at a 2.5 MHz repetition rate was used as the excitation source. Three excitation wavelengths were chosen: 580 nm that overlaps with the LSPR peak of Au NPs (“on” resonance), 530 nm that is relatively far from the LSPR peak of Au NPs (“off” resonance), and 555 nm in between. Note the extinction spectra of single Au NPs may vary from the ensemble extinction spectrum shown in Fig. 1(b). Nevertheless, 580 nm is still close to the LSPR peak of single Au NPs, while 530 nm is far from the LSPR peak of single Au NPs. The excitation power was kept low and nominally the same at ∼75 nW for three excitation wavelengths (estimated power density 9.65, 8.80, and 8.06 W/cm² for 530, 555, and 580 nm, respectively). The PL signal of QDs was split by a non-polarizing beam splitter. About 30% of the signal was directed to a spectrometer (IsoPlane SCT 320, Princeton Instruments) to resolve the PL spectrum; the rest was filtered by using a 630 ± 30 nm bandpass filter and directed to a single-photon detector (τ-SPAD, PicoQuant). The arrival times of the fluorescence photons were recorded by using a time-correlated single-photon counting module (PicoHarp300, PicoQuant) operated in a time-tagged time-resolved (TTTR) mode. All spectroscopic measurements were performed at room temperature.

Figure 2(a) shows the PL intensity trajectory of example QD-A on glass excited at 580 nm, which was recovered by binning the arrival times of fluorescence photons from raw TTTR data. During the acquisition, the QD mainly stayed in the bright intensity state but blinked to less bright intensity levels from time to time. Such high-quality QDs have a dominant bright intensity state upon photoexcitation, and the PL characteristics of the bright intensity state are well-defined.^11,18 Thus, constructing PL decay curves from the bright intensity state only at three excitation wavelengths would make a fair, meaningful comparison for the excitation wavelength dependence study. In order to properly select the bright state among the bins with statistical rigor, we adopted a trimmed likelihood approach^19,20 without applying any subjective intensity thresholds. Trimmed clustering is a model-based robust clustering analysis that trims a certain proportion α′ (0 $≤$ α′ < 100%) of data while performing model-based clustering or density estimation.²⁰ In our problem of distinguishing the bright intensity state, the number of clusters is simply one. Let N be the number of intensity bins of an intensity trajectory. For a particular trimmed proportion α′, this method aims to identify $N1−α′$ (or its nearest integer if the value is fractional) intensity bins I_i that “belong to” the bright intensity state, assuming that it is Gaussian distributed with a mean of μ and a variance of σ². Therefore, the likelihood with respect to (μ, σ²) with any 0 ≤ α′ < 100% is

where L_(i)’s are the reverse order statistics of $Li=12πσexp−12Ii−μσ2,i=1,…,N(1−α′)$⁠, satisfying $L1≥L2≥⋯≥LN(1−α′)$⁠. The parameters (μ, σ²) can then be estimated by maximum likelihood estimation. In essence, this method identifies $N1−α′$ intensity bins that can be best fitted by a normal distribution and discards the rest of the Nα′ bins. The optimal trimmed proportion α could be determined by a Bayesian information criterion (BIC). For a particular trimmed proportion α′, the parameters used in the analysis contain μ, σ², and Nα′ trimmed intensity bins, so the number of parameters is given as

Accordingly, BIC is defined as

The BIC value reaches minimum for the optimal trimmed proportion. Figure 2(c) shows the BIC value vs trimmed proportion α′ for the intensity trajectory in Fig. 2(a), and the resultant optimal trimmed proportion α is ∼9%. As a by-product, the mean intensity of the selected bright intensity state could also be obtained. The intensity bins selected by trimmed clustering are represented as blue bars in the intensity histogram shown in Fig. 2(b).

Figure 2(d) shows the PL decay curve constructed from the selected bright intensity state in Fig. 2(b). Each PL decay curve constructed was fitted by a convoluting instrument response function (IRF) with a multi-exponential decay model using the following maximum likelihood estimation:

where * denotes convolution. To ensure that a PL decay curve is properly characterized by the fitting model, we performed multi-exponential fitting with different numbers of lifetime components. Note that multi-exponential decay models are nested and that one more lifetime component corresponds to two more parameters in the model (two degrees of freedom): the lifetime component itself and its pre-exponential factor. Thus, model selection could be carried out by a likelihood ratio test (LRT). A PL decay curve was first fitted by a bi-exponential decay model and a tri-exponential decay model, from where the maximum likelihoods $LBi$⁠, $LTri$ were obtained, respectively. For LRT, the quantity λ_LR is computed as

and compared to a critical value (5.991) from the χ² distribution with two degrees of freedom at the 0.05 significance level. If λ_LR is larger than the critical value, LRT asserts that at the 0.05 significance level, the tri-exponential decay model better fits the PL decay curve. Then, a four-exponential decay model was used for fitting, and LRT was performed between the tri-exponential decay model and the four-exponential decay model. This process went on until the more complicated multi-exponential decay model failed LRT.

It turned out that most PL decay curves of the selected bright intensity state of QDs on glass or near Au NPs were best fitted by a tri-exponential decay model, with a few exceptions that were best fitted by a bi-exponential decay model. For example, the PL decay curve in Fig. 2(d) was best fitted by a tri-exponential decay model with three lifetime components τ₁ = 1.68 ns, τ₂ = 25.55 ns, and τ₃ = 47.28 ns (see the detailed fitting process in Sec. 3 of the supplementary material). The PL spectra of QDs were also recorded when acquiring the arrival times of fluorescence photons. As shown in Fig. 2(e), the PL spectrum of QD-A possesses a Gaussian shape, indicating that the recorded QD emission mostly came from band edge emission. We therefore assigned τ₁ and τ₃ to biexciton and exciton lifetimes of the QD, respectively, as they match the typical values of biexciton and exciton lifetimes of CdSe-based QDs.²¹ Since the value of τ₂ is approximately half of τ₃, it was assigned to the fast lifetime blinking process identified in this type of QDs.²² 

The same data analysis strategy was applied to QDs near Au NPs. Figure 3(a) shows the PL decay curve constructed from the selected bright intensity state of example QD-B near Au NPs excited at 580 nm. It was also best fitted by a tri-exponential decay model with three lifetime components τ₁ = 0.40 ns, τ₂ = 6.90 ns, and τ₃ = 12.17 ns. The PL spectrum of QD-B [see Fig. 3(b)] does not show observable shape changes, so we assume that there are no new emitting species. Consequently, we assigned the smallest lifetime component τ₁ to the biexciton lifetime and the largest lifetime component τ₃ to the exciton lifetime, although their values are significantly smaller than those of the QDs on glass.

Figure 4 compares the results of QD-A on glass from Fig. 2 and QD-B near Au NPs from Fig. 3 in an intuitive way. The distinct blinking feature observed in the PL intensity trajectories demonstrates that the signals came from single QDs. For QD-A on glass, the PL intensity at 530 nm excitation wavelength is the highest and that at 580 nm excitation wavelength is the lowest [see Fig. 4(a)]. In the meantime, the PL decay curves of QD-A at three excitation wavelengths are almost identical [see Fig. 4(b)]. In contrast, for QD-B near Au NPs, the PL intensity at 580 nm excitation wavelength is close to that at 530 nm excitation wavelength, while the PL intensity at 555 nm excitation wavelength is the highest [see Fig. 4(c)]. The PL decay curves of QD-B also show some differences especially at early times: the PL decay at 580 nm excitation wavelength is the fastest, followed by that at 555 nm excitation wavelength, and the PL decay at 530 nm excitation wavelength is the slowest [see Fig. 4(d)].

As mentioned earlier, conclusions drawn from the results of a few example QDs such as Fig. 4 may not properly reflect the characteristics of the whole hybrid system due to dot-to-dot variations. The results need to be viewed in an integrative perspective to yield meaningful conclusions on the excitation wavelength dependence. Note that the geometry of the hybrid Au NP-QD hybrid system cannot be precisely controlled. We observed a subpopulation of QDs on Au NP substrates that exhibit very similar behavior as those on glass, and they were excluded in the subsequent QDs near Au NPs analyses. Here, we compared the derived parameters (e.g., exciton lifetime) of the QDs on glass and near Au NPs by their absolute values and relative values. The relative-value comparison was visualized by the following procedure: for a parameter P of a QD obtained at three excitation wavelengths, two ratios P(555)/P(530) and P(580)/P(530) were calculated. Each QD was then represented by a data point in the two-dimensional P(580)/P(530) vs P(555)/P(530) mapping, and the distribution of the data points could reveal possible excitation wavelength dependence of parameter P.

Figures 5(a) and 5(b) compare PL intensities of QDs on glass and near Au NPs at three excitation wavelengths. The data points corresponding to QDs on glass fall into the region (green shaded area) enclosed by x axis, x = 1 line, and y = x line in Fig. 5(b), indicating that the PL intensity of QDs on glass has an excitation wavelength dependence: I(580) < I(555) < I(530). This excitation wavelength dependence is due to the excitation wavelength-dependent absorption, as manifested in Fig. 1(b): the absorption at 580 nm is smaller than that at 555 nm, and the absorption at 530 nm is the largest. Since the excitation power was kept the same, the resultant PL intensity at 580 nm excitation wavelength is the lowest, while that at 530 nm excitation wavelength is the highest. However, a different trend is observed for QDs near Au NPs. Although the PL intensity at 530 nm excitation wavelength is slightly enhanced compared to that of QDs on glass, the enhancement is more pronounced at 555 and 580 nm excitation wavelengths [see Fig. 5(a)] so that for a QD near Au NPs, the PL intensities at 555 and 580 nm excitation wavelengths are typically higher than that at 530 nm excitation wavelength [see Fig. 5(b)]. According to Fig. 1(b), the PL peak of QDs overlaps with the LSPR peak of Au NPs to some extent, so non-radiative energy transfer happens when placing QDs near Au NPs. Despite this non-radiative pathway, PL intensities of QDs near Au NPs still increase at three excitation wavelengths. The increase of the radiative rate of QDs near Au NPs via Purcell effect helps to compensate the increase in the rate of non-radiative processes. Meanwhile, the increase in the absorption of QDs due to an enhanced electric field from LSPR of Au NPs (vide infra) also contributes to the increase in PL intensities of QDs near Au NPs.

Figures 5(c) and 5(d) compare weighted average excitonic lifetimes of QDs on glass and near Au NPs at three excitation wavelengths. The weighted average excitonic lifetime $τ̄$ of a QD was calculated by

where τ_BX, τ_X are biexciton and exciton lifetimes assigned from multi-exponential fitting, respectively, and A_BX, A_X are the corresponding pre-exponential factors. The calculated weighted average excitonic lifetime characterizes globally how fast a PL decay is. The data points corresponding to QDs on glass distribute closely around point (1, 1) in Fig. 5(d), suggesting that the values of weighted average excitonic lifetimes of QDs on glass at three excitation wavelengths are almost identical. This phenomenon again confirms that the excited state dynamics of stand-alone QDs is not excitation wavelength-dependent. On the contrary, the results of QDs near Au NPs are totally different. Not only are the weighted average excitonic lifetimes of QDs near Au NPs considerably shorter than those of QDs on glass as manifested in Fig. 5(c), but they also exhibit consistent excitation wavelength dependence. As shown in Fig. 5(d), the data points corresponding to QDs near Au NPs fall into the region (green shaded area) enclosed by x axis, x = 1 line, and y = x line, indicating that the weighted average excitonic lifetime of QDs near Au NPs has an excitation wavelength dependence: $τ̄(580)<τ̄(555)<τ̄(530)$⁠. This observation is in line with previous studies that the PL decay of QDs near plasmonic nanostructures is faster when the excitation is spectrally close to the LSPR peak. Nevertheless, this excitation wavelength dependence may be caused by excitation wavelength-dependent multi-exciton emission or exciton lifetime or a synergistic effect. Possible factors causing the excitation wavelength dependence need to be decoupled and examined separately.

Figures 6(a) and 6(b) compare biexciton emission proportions of QDs on glass and near Au NPs at three excitation wavelengths. The biexciton emission proportion p_BX of a QD is calculated as

It quantifies the proportion of photons coming from biexciton emission in the total recorded fluorescence photons. Although the biexciton emission proportion of QDs on glass is very small as seen from Fig. 6(a), most data points corresponding to QDs on glass fall into the region (green shaded area) enclosed by x axis, x = 1 line, and y = x line in Fig. 6(b), indicating that the biexciton emission proportion of QDs on glass has an excitation wavelength dependence: p_BX(580) < p_BX(555) < p_BX(530). This excitation wavelength dependence is again due to the excitation wavelength-dependent absorption since biexciton generation in a QD depends on the number of photons absorbed in each excitation event. In contrast, the biexciton emission proportions of QDs near Au NPs are significantly larger, as manifested in Fig. 6(a), and they show a drastic reversed trend in the excitation wavelength dependence. Most data points corresponding to QDs near Au NPs fall into the region (blue shaded area) bordered by y axis, y = 1 line, and y = x line in Fig. 6(b), indicating that the biexciton emission proportion of QDs near Au NPs has an excitation wavelength dependence: p_BX(580) > p_BX(555) > p_BX(530).

This excitation wavelength dependence of biexciton emission proportion of QDs near Au NPs can be rationalized by accounting the excitation wavelength-dependent local electric field enhancement from Au NPs. The electric field enhancement factor EF is defined as EF = |E|²/|E_Inc|², where |E| is the amplitude of the electric field that a QD experiences near Au NPs and |E_Inc| is the amplitude of the incident electric field. Our previous work³ has demonstrated that EF caused by the LSPR of Au NPs is highly excitation wavelength-dependent: EF could increase multiple times from “off” resonance excitation to “on” resonance excitation. The absorption cross section of QDs near Au NPs increases by a factor of EF, leading to a higher probability of photon absorption. As proved by previous studies,²³ the higher the number of photons absorbed by the QDs, the higher the population of biexciton (and higher-order excitons) is generated. In our experiments, even though the excitation power from the laser was kept the same for different wavelengths, the generated populations of biexcitons and excitons changed due to the difference in the absorption cross section. Since EF at the “on” resonance 580 nm excitation wavelength is considerably larger than that at the “off” resonance 530 nm excitation wavelength, biexciton generation and the subsequent emission become more significant at 580 nm excitation wavelength. Because the biexciton lifetime is much shorter than the exciton lifetime, a higher biexciton emission proportion contributes to the faster PL decay at 580 nm excitation wavelength.

Finally, we examine whether the exciton lifetime of QDs near Au NPs also changes when varying the excitation wavelength. Figures 6(c) and 6(d) compare exciton lifetimes of QDs on glass and near Au NPs at three excitation wavelengths. The data points corresponding to QDs on glass distribute closely around point (1, 1) in Fig. 6(d), indicating that the values of exciton lifetimes of QDs on glass at three excitation wavelengths are almost identical, which is again expected. Exciton lifetimes of QDs near Au NPs are appreciably shorter than those of QDs on glass, as seen in Fig. 6(c). However, although the data points corresponding to QDs near Au NPs are more scattered compared to those corresponding to QDs on glass in Fig. 6(d), they still seem to distribute around point (1, 1), suggesting no apparent difference in exciton lifetime across three excitation wavelengths. To assess if there is truly no statistically significant change in the exciton lifetime, we performed one-way repeated measures analysis of variance on the exciton lifetimes of QDs near Au NPs at three excitation wavelengths (see details in Sec. 6 of the supplementary material). The results from this analysis confirmed that across the three wavelengths, there is no statistically significant change in the exciton lifetime of QDs near Au NPs.

The exciton lifetime τ_X derived from the bright intensity state of a QD near Au NPs is determined by the rates of radiative exciton recombination γ_R, energy transfer γ_EnT, and other non-radiative processes γ_NR [illustrated in Fig. 7(a)],

We ruled out the possibility of electron transfer from QDs to Au NPs because of the relative thick insulating layer of alumina. The first component γ_R is the radiative exciton recombination of QDs in the presence of Au NPs. It has been demonstrated that the radiative rate of exciton in QDs is enhanced when they are placed near plasmonic nanostructures due to the increased density of optical states.^24–26 However, γ_R should not be excitation wavelength-dependent if we consider the timescales of the processes [see Fig. 7(b)]. Once the QDs are excited, the recombination of excitons happens on the nanosecond timescale after excitation. Meanwhile, the dephasing time of plasmons of Au NPs is on the order of femtoseconds,^27,28 much faster than the exciton recombination, which implies that plasmons would have decayed completely before exciton recombines. Thus, γ_R is not impacted by the excitation process. The second term that determines the exciton lifetime is the rate γ_EnT of the energy transfer from QDs to nearby Au NPs. γ_EnT is determined by the size and shapes of Au NPs and QDs, the separating distance, the spectral overlap of the PL peak of QDs and the LSPR peak of Au NPs, etc.^29,30 These factors were fixed in the study, so γ_EnT is not excitation wavelength-dependent either. Finally, for a QD near Au NPs in its bright intensity state, there may be some non-radiative pathways related to surface effect, thermal effect, etc., which could contribute to γ_NR. Nevertheless, these processes are probably outcompeted by fastened radiative exciton recombination; otherwise, the PL intensity of the bright state would have been much lower and excluded by trimmed clustering. Thus, whether they have excitation wavelength dependence will not substantially affect the overall excitation wavelength dependence of exciton lifetime. From the experimental observations and the above discussion, we concluded that the exciton lifetime of a QD near Au NPs is not significantly excitation wavelength-dependent.

In summary, we studied the excitation wavelength dependence of PL decays of single CdSe/CdS core/shell QDs near plasmonic Au NPs under mild excitation conditions. By applying multiple statistical methods at the single QD level, we verified rigorously in an integrative perspective that the PL decay of a single QD near Au NPs is generally excitation wavelength-dependent: it is faster when the excitation wavelength is close to the LSPR peak of Au NPs. We also elucidated the cause of the excitation wavelength dependence by decoupling the possible factors. Although Au NPs modify the exciton annihilation of a nearby QD in various ways, the exciton lifetime is not excitation wavelength-dependent. Instead, the excitation wavelength dependence of the PL decay is mainly the result of excitation wavelength-dependent proportion of photons from biexciton emission relative to all the emitted photons. The biexciton emission proportion varies when tuning the excitation wavelength because the local electric field enhancement from LSPR is dependent on excitation. We hope that the results of this work will provide guidance for rationally designing and manipulating QD-related hybrid nanosystems that require certain PL decay characteristics.

See the supplementary material for the synthetic and analytical details.

J.Z. acknowledges the financial support from the National Science Foundation CAREER Award (Grant No. CHE-1554800).

The authors have no conflicts to disclose.

Y.S. and J.Z. conceived the project. H.Z. and N.J. synthesized QDs under O.C.’s supervision. Y.W. synthesized Au NPs and prepared and characterized Au NP substrates. A.M. performed atomic layer deposition of alumina under N.B.’s supervision. Y.S. performed spectroscopic measurements. Y.S., K.C., and J.Z. analyzed the data. Y.S. and J.Z. wrote the manuscript. All the authors contributed to the discussion. All the authors have given approval to the final version of the manuscript.

The data that support the findings of this study are available within the article and its supplementary material.