Fluorescence decay enhancement and FRET inhibition in self-assembled hybrid gold CdSe/CdS/CdZnS colloidal nanocrystals supraparticles

We report on the synthesis of hybrid light emitting particles with a diameter ranging between 100 and 500 nm, consisting in a compact semiconductor CdSe/CdS/CdZnS nanocrystal aggregate encapsulated by a controlled nanometric size silica and gold layers. We first characterize the Purcell decay rate enhancement corresponding to the addition of the gold nanoshell as a function of the particle size and find a good agreement with the predictions of numerical simulations. Then, we show that the contribution corresponding to F\"orster resonance energy transfer is inhibited.

Plasmonic structures enable to modify the photoluminescence properties of individual fluorophores for a wide range of applications such as quantum optics [1,2], optoelectronics [3] or the detection of molecules of chemical or biological interest [4]. When colloidal semiconductor nanocrystals (NCs) with a CdSe core are considered, many configurations involving plasmonic surfaces or nanoparticles were reported [5][6][7][8]. They allow to enhance the emission intensity, to control the emission pattern or to suppress the NC residual blinking.
From a general point of view, as an alternative to photonic structures, confinement of multiple emitters in a small volume offers the possibility to benefit from their interaction in order to enhance the emission through coherent dipole-dipole interactions leading to superradiance or superfluorescence [9]. Plasmonic devices and cooperative effects can be combined and hybrid metal/emitters structures were designed to develop SPASER for example [10].
Dipole-dipole interactions can also generate a non-reversible and incoherent energy transfer which corresponds to FRET (Förster resonance energy transfer), especially when condensed matter nanoemitters showing a large inhomogeneity of their spectral properties such as NCs are considered [11,12]. Widely used for the investigation of biological or chemical systems [13,14], FRET and its control through optical cavities is also the subject of numerous works in the field of optoelectronics for the development of devices such as LEDs or photovoltaic devices [15][16][17]. On a fundamental level, C. L. Cortes and Z. Jacob have shown that the fluorescence enhancement by the Purcell effect could be tuned independently of the increase or suppression of FRET [18].
In a recent paper, we have demonstrated the synthesis of NC aggregates surrounded by a silica shell, called supraparticles (SPs) in the following, which exhibit a perfectly stable emission intensity at room temperature [19]. This study also highlighted that the decay rate corresponding to FRET is of the order of the radiative decay rate. Here, we characterize the emission properties of similar structures when coupled to a nanoresonator consisting of a thin gold shell encapsulating the SPs. We first describe the synthesis of these nanoobjects and their elementary structural properties. Next, using several spectroscopic and/or complementary time resolved setups, we show the reduction of the FRET efficiency induced by the gold nanoshell.

I. CHEMICAL SYNTHESIS AND STRUCTURAL PROPERTIES OF GSPS
A multistep procedure was performed to prepare a hybrid structure containing few hundred NCs inside a gold nanoshell.

A. Superparticles synthesis
First, CdSe NCs were synthesized by a procedure slightly modified from Cao et al. [20] and shells of CdS/CdZnS were synthesized with continuous injection of shell precursors at high temperatures [21]. Typically, these reactions generate CdSe/CdS/CdZnS NCs of about 7.7 ± 1 nm in size with an emission centered at 645 nm (FWHM = 30 nm). These NCs are then assembled into spherical aggregates using a micro-emulsion/evaporation method [22]. Typically, 6 nmol of NCs were re-dispersed in 1 mL of chloroform and added to 1 mL of dodecyltrimethylammonium bromide solution (20 mg/mL in water). The solution was vortexed for 30 seconds to obtain a stable oil in water emulsion. The chloroform was evaporated by heating the solution at 70°C in an oil bath for 10 minutes. The obtained NC assemblies stabilized by DTAB are hereafter referred to as NC supraparticles, SPs.
They were purified by centrifugation at 6 000 g for 5 minutes and re-dispersed in 4 mL of ethanol. NC SPs were coated with a silica shell (20 nm in thickness to prevent thereafter the quenching by the gold nanoshell of the emission of the NCs located close to the surface of the SP) by hydrolysis and condensation of tetraorthoethylsilicate (TEOS) precursors. For a typical reaction, 1 mL of NC SP solution was first sonicated in 9 mL of ethanol and 1.5 mL of deionized water for 10 minutes. Then 0.5 mL of ammonia solution (NH4OH, 28 wt% in water) and 10 µL TEOS were added. The mixture was sonicated for 20 minutes to prevent aggregation [23]. The silica-coated NC SPs were purified by centrifugation and redispersed 1 mL of ethanol. Silica shells were functionalized by reaction with aminosilane precursors [24]. Typically, 500 µL of NC SPs coated with silica were added to a mixture of 500 µL of ethanol, 1 mL of water and 50 µL of aminopropyltriethoxysilane and reacted at 60°C for 2 hours. The solution was washed 3 times with ethanol and twice with water to remove excess silane and then re-dispersed in 1 mL of water. The growth of gold nanoshells was performed using a protocol derived from Halas and coworkers [25]. Gold seeds were prepared by the Duff method [26]. 100µL from the previous 1 mL functionalized NC SPs were mixed with 1 mL of gold seeds solution for 30 minutes. The NC SPs were purified by centrifugation in water and re-dispersed in 300 µL of water. 100 µL from this solution were then dispersed in 5 mL of gold growth solution [25] followed by the addition of 25 µL of formaldehyde and stirred for 2 h. The final gold-coated NC SPs (golden supraparticles, GSPs) were centrifuged in water and re-dispersed in 500 µL of water. The full description and characterization of the NC GSP synthesis at the different steps of the preparation are described in a separate report [27].

B. Gold nanoshell deposition
We follow the common synthesis route developed by Halas and coworkers [25]  remove excess of gold seeds in solution. Gold seeds immobilized onto the silica layer act as nucleation sites for electroless Au plating using an aqueous HAuCl 4 plating solution in the presence of formaldehyde [28,29]. This last stage consists of the growth and coalescence of gold seeds to form a continuous gold nanoshell onto SPs (see locate the individual particles with respect to the grid and measure their size so that the confocal experiments will be performed on supraparticles whose size are known. In order to carry out the optical measurements (see Fig. 3), a confocal microscope  various conditions: at 300 K in air or vacuum (low helium pressure ∼ 10 −3 mbar), or 4 K (same low helium pressure). In vacuum, thick shell CdSe/CdS NCs are well known to become ionized since no water or oxygen molecules can neutralize the emitter once it has been photoionized [31]. The photoluminescence (PL) lifetime then decreases since the trion recombines twice as fast as the exciton [32]. For the single CdSe/CdS/CdZnS NCs used to synthesize the SPs and GSPs, we measured a PL lifetime about 5.6 ns in vacuum. As a result, the increase of the PL decay rate of GSPs at 300 K when placed under vacuum compared to in air (Fig. 4) shows that NCs inside a GSP become ionized. Indeed, the porosity of the chemically synthesized silica and gold shells does not prevent the escape of the water or oxygen molecules from the SPs or GSPs. In the following, the experiments are performed at 4 K and we will consider that the NCs forming the aggregates are always ionized. in the aggregates [34]. We point out that this model can give information on Purcell effect but does not account for dipole-dipole interactions between NCs. Therefore, FRET is put 7 aside in this first analysis.
To model gold-coated aggregates, the roughness of the metallic layer is described by a homogeneous layer following the method of ref. [35]. The gold refractive index is defined thanks to a Drude model adjusted from ref. [36]. To account for the specific optical properties of gold obtained by chemical process, we followed ref. [35] where a fivefold increase of the optical losses and a slight adjustment of the plasma frequency is done on the Drude model. These high Joule losses result in plasmonic modes which show no resonances.
Using Mie theory, we expand the field emitted by a single dipole on a basis of spherical harmonics. We can then compute the power emiited by the dipole inside the supraparticle [37]. Transition rates of atoms near spherical surfaces] and average over all wavelengths and over the different positions of the dipole inside the aggregate. From the emitted power, we can derive the decay rate. In principle, we should also take into account the dielectric interface corresponding to the glass coverslip that modifies a dipole emission located at a distance lower than typically 0.1 λ = 60 nm [38][39][40]. However, calculations show that the interface only slightly modifies the radiated power, which is consistent with the size of the SPs (greater than 200 nm) and the shell thickness (20 nm for the SPs and 50 nm for the GSPs). Finally, to calculate the Purcell factor, we use a single dipole above a glass substrate as reference (the latest is obtained following [38]).
Experimentally, we first fitted the PL decay rates of single NCs at 4K under vacuum was first fitted by a bi-exponential function, the first component corresponding to the decay of the trion [31]. The luminescence decays of individual aggregates are fitted with a lognormal distribution with a central decay rate Γ LN [19] for the NC emission plus a monoexponential function to take into account a slow emission from traps [41]. We now turn to decay rates of gold-coated GSPs (Fig. 5.b). As expected, the emission enhancement is even more pronounced than for non-metallized aggregates, particularly for the smaller GSPs where accelerations of 8 compared to individual NCs have been obtained.
It should be noted that the good agreement between model predictions and measurements for GSPs and SPs was not obvious, given the FRET is not taken into account in our calculations. However, if the quantum efficiency and the radiative decay rate "blue" NCs (corresponding to the NCs with the shortest wavelength emission) are the same as the "red" ones, the FRET does not modify the overall luminescence decay time. Indeed, let us consider the basic situation of excited donor (D) and acceptor (A) emitters characterized by single fluorescence (k) and FRET (k F RET ) decay rates. This simplifed system can be depicted by the following rate equations: By summing the two equations, one finds that the total number of excited emitters that means that the overall decay rate is left unchanged. The generalization to multiple population classes is straightforward and leads to the same conclusion. The FRET only modifies the spectrum that is redshifted. This first analysis focused on Purcell effect, to compare FRET between NCs in the SPs and GSPs. In the next section, we turn into the measurements allowing spectrally-resolved measurements of the decay rates.

C. FRET
Aggregates of NCs are known to exhibit FRET [12][13][14]33]. In a SP, the energy transferred from a NC is all the greater as its wavelength emission is blueshifted, as a result of an increased overlap between its emission spectrum and the average absorption spectrum of its neighbours [19]. We now show that the gold nanocavity modifies the impact of FRET on the PL emission properties of the GSPs with respect to the SP ones. As already mentionned, the Fourier transform of the signal recorded by the SPAD at the ouput of the interferometer enables to plot a fluorescence map as a function of the detection wavelength and the time of photon detection τ (Fig. 6.a). From this data, we can plot the PL decay for a given Black curves correspond to the decay rates obtained by the numerical simulations. Crosses and circles are the decay rates of the log-normal distribution used to fit measurements. wavelength ( Fig. 6.b) or, alternatively, the evolution of the emission spectrum at a given time after the pulse excitation ( Fig. 6.d). Both data sets demonstrate the strong effect of FRET on non-metallized SPs. First, PL decays for shorter wavelengths are faster than for longer ones. FRET is also evidenced by the wavelength dependence of the delay between the pulse excitation and the PL signal peak. Due to energy transfer from the "blue" NCs to the "red" ones, the maximum emission of the "red" is delayed with respect to the "blue" one. Lastly, the normalized spectrum is redshifted over time (Fig. 6.d).
Simulations done on SPs show negligible variation of the Purcell-enhanced decay rates when the wavelength varies inside the NCs emission spectrum (not shown). Since the decay rate of the trion k does not depend on the NC emission wavelength [19], the variations of the decay rate with the wavelength can be entirely attributed to FRET. As a result, the decay rate k(λ) for NCs inside a GSP emitting at a wavelength λ writes: where k F RET (λ) is the decay rate due to FRET. The variations that we measure between the fast decay rates of the "blue" NCs and the slower "red" NCs comes from the FRET decay rate k F RET . In [19], we have also shown that the energy transferred by FRET from a given NC decreases with its wavelength emission and vanishes for the highest wavelength, that is λ = 647 nm. Fig. 7.a shows the value of k F RET deduced by the difference between the decay rates measured at 640 nm and at 615 nm. An average value of k F RET (λ = 615nm) = 0.45 ns −1 is obtained (spectral filtering reducing the number of counts used to plot the PL decay, we used a basic monoexponential fit). The variations between SPs can be due to the difficulty to adjust the weak luminescence decays at the edges of the emission spectrum.
In contrast with SPs, the effect of FRET is far less visible for the GSPs. The differences between the decay rates of "blue" NCs and "red" NCs are less marked (Fig. 8.c) than on SPs and even hardly visible on some GSPs (Fig. 8.a). This is explained by the enhancement of the emission by Purcell effect which dominates over the FRET rates. We also point out that the shift of the PL decay maximum (Fig. 6.c) with the wavelength is no more visible.
Simultaneously, the modification of the normalized spectrum over time is small (Fig. 8.b and Fig. 8.d, to be compared with Fig. 6.b and Fig. 6.d), and all the more so as the contribution of FRET is low. Fig. 7.a shows that we obtain comparable k F RET on GSPs than on SPs. As shown by C. L. Cortes and Z. Jacob in their detailed modeling [18], the effect of the gold plasmonic resonator on the FRET rate is not straightforward: it can either have no effect, increase or decrease the ratio between the total decay rate and the FRET rate in a way that depends strongly on the position of the donor-acceptor pair with respect to the photonic mode, independently of the evolution of the radiative rate.
In order to determine the probability that a NC decays by FRET rather than other recombination channels, we deduced from measurements the FRET efficiency which is defined as the ratio between k F RET and the decay rates measured at short wavelengths ( Fig. 7.b).
For the smallest structures (below 300 nm), the FRET efficiency of GSPs is reduced by a factor of 3 compared to non-metallized SPs, showing the strong impact of the metallic layer to reduce FRET of NCs inside SPs. We can also notice that FRET efficiencies become comparable for larger diameters, which was expected since the Purcell effect becomes similar for SPs and GSPs when the size increases.
The modification of the FRET efficiency is also confirmed by the shape of the emission spectrum integrated over 10 s. The FRET broadens the overall spectrum for the SP with respect to the GSP one (Fig. 9). In the case of SP, FRET favors the emission of the "red" NCs through their excitation by the "blue" ones. The result is a relative increase of  the "red" part of the emission spectrum and a relative decrease of the central peak height (the systematic asymmetry of the emission spectrum towards the red indicates that a small fraction of the NCs exhibit a slightly larger size).

III. CONCLUSION
In conclusion, we first have presented the synthesis of hybrid structures consisting in NCs aggregates surrounded by a gold nanoresonator. As expected, the PL decay rate is increased by the metallic structure. We have shown that the mean Purcell factor is well predicted by a model and depends on the particle size. In addition, through the study of the SPs with or without a gold shell, we have also analyzed in detail the influence of the metallic resonator on FRET. Especially, interferometric measurements providing time resolved fluorescence spectra show that the relative contribution of FRET decreases by a factor of 3 for the smallest GSPs. Beyond the fine structure of the PL temporal dynamics, we have also found that the overall spectrum of the GSPs is narrowed with respect to the SPs ones. In terms of applications, the GSPs are submicronic bright and photostable sources that could be used for example for lighting. More fundamentally, the inhibition of FRET, which is an incoherent energy transfer process, opens the possibility to achieve coherent interactions between NCs that could enable to achieve quantum collective emission regime such as superradiance.

IV. ACKNOWLEDGMENTS
This work is supported by the Agence in the framework of the GYN project (Grant No. ANR-17-CE24-0046).