Photonic-based quantum networks have the potential to paradigmatically change information sciences.1 One essential element for photonic quantum networks is the quantum light source. CsPbX3 (X = Cl, Br, I) perovskite quantum dots (QDs) are promising light-emitting materials because of their high photoluminescence (PL) quantum yield (QY) and facile syntheses.2–4 Recent advances in the precise synthetic control over the size, shape, and composition5–7 of these perovskite QDs have catalysed the development of highly efficient LEDs8–10,lasers11 and quantum light sources.12, 13 Recently, single CsPbX3 QDs were intensively studied to demonstrate their single photon emissions14 with high brightness15 and photocoherence16. However, research on exciton dynamics in single CsPbX3 QDs to date has mainly focused on weakly confined nanocrystals because size-confined CsPbX3 QDs generally exhibit poor photostability. Particularly, perovskite QDs show severe PL intermittency (“blinking”) and photodegradation when their sizes are smaller than their exciton Bohr diameters.17–19 This convolutes their exciton properties with defect-related dynamics.20, 21 Therefore, improving the photostability of strongly confined perovskite QDs is vital to achieving reliable experimental determinations of size-dependent structural-optical relationships in perovskites, including exciton PL lifetime, exciton-lattice coupling, and many-body interactions. This knowledge is crucial to consolidating our current theoretical models of band-edge excitons in perovskites22–24 and guiding the design of high-fidelity QD-based quantum light emitters.
The insufficient photostability of small CsPbX3 QDs relates to their strong quantum confinement. Since the scales of exciton-surface lattice interactions are inversely proportional to the volume of the QD, the optical properties of small CsPbX3 QDs are more prone to surface defects. These surface defects can trap photo-generated charge carriers from excitons and leave the QD charged.25 Subsequently generated excitons in this charged QD will form trions that can undergo fast non-radiative Auger recombination and turn the PL of the QD “OFF”.26 This defect-induced QD charging is the primary blinking mechanism and relates to structural degradations in perovskite QDs.19, 27, 28
To improve the photostability of CsPbX3 QDs, their surface defects need to be well passivated. While coating a wide-bandgap semiconductor shell can suppress blinking and photodarkening in II-VI QDs, such as CdSe,29 a well-established shelling protocol for highly ionic CsPbX3 QDs has yet to be discovered. Instead of shelling, a nearly epitaxial ligand coverage is required for a defect-free QD surface. Unfortunately, traditional ligands on CsPbX3 QDs are under adverse solubilization equilibrium and thus only deliver sufficient surface coverages in concentrated QD colloids.30, 31 Consequently, when the colloidal QDs are diluted to ensure low QD density for single particle studies, the ligands will be stripped along with ions comprising the QD surfaces, creating surface defects. Ligands with enhanced binding affinities have been developed to mitigate QD surface disintegrations. For example, charge-neutral Zwitter-ionic molecules were applied to weakly confined CsPbBr3 QDs to mitigate the ionic metathesis during QD dilution.32–34 Additionally, surface treatments using didodecyldimethylammonium bromide (DDAB) or phosphonic acids can passivate exposed Pb cations and thus improve PLQY of CsPbBr3 QDs.35, 36 Nevertheless, small-sized CsPbX3 QDs still suffer from blinking and photodarkening,18, 37 suggesting that their surfaces are still under-passivated. While tolerated by weakly confined perovskite QDs, under-passivated surfaces can be detrimental to strongly confined QDs.9
Incomplete surface ligand coverage in solid-state single QDs
The cause of incomplete surface defect passivation lies in the intermolecular interaction in bulky ligands that cohered on QD surfaces in the solid state.38 These ligands contain long hydrocarbon tails that are required to impart sufficient miscibility of ionic QDs with non-polar solvents. Furthermore, designer ligands often adopt branched or multiple hydrocarbon ligand tails to entropically promote the colloidal stability of QDs.32, 39 However, the steric effect of bulky tails can negatively affect surface ligand coverage in the solid state. For example, DDA, which has two long-chain tails, is a well-established ligand for colloidal CsPbBr3 QDs. But fully passivating the (100) facet of CsPbBr3 using DDA would require an aliphatic chain density of ~ 5.7 chains·nm− 2, exceeding that of the crystalline aliphatic chain density (4.9 chains·nm− 2).40 Therefore, bulky aliphatic ligands stabilizing QDs in solution are unlikely to accommodate complete surface passivation of single CsPbBr3 QDs in the solid state.
To understand the incomplete surface ligand coverage of perovskite QDs in the solid state, we used density functional theory (DFT) to estimate the surface energies of a DDA (truncated to reduce computation cost) passivated 2×2×1 CsPbBr3 slab as a function of surface ligand coverages (Supplementary Note 1 and Supplementary Fig. 1–5). Considering that the bulky ligand tails in DDA will lose conformational freedom when being solidified, the intramolecular entropy reduction can significantly increase the surface energy (Supplementary Note 2). As shown in Fig. 1a and 1b, the lowest surface energy of the CsPbBr3 slab was achieved when 7 of the 8 Cs+ sites were filled by DDAs, and adding an additional DDA would increase the surface energy. This suggests that the ligand-to-ligand interactions can destabilize the surface passivation (Supplementary Note 3), which is in good agreement with previous studies.41 To better visualize the effect of intermolecular interactions, we investigated the differential in surface energy regarding the numbers of surface ligands (Fig. 1b and 1d) which represents the energy gain/loss of binding the Nth (N = 1–8) ligand onto the surface. It is seen that after the 4th DDA (50% surface coverage), additional DDA bindings were less energetically favoured, and the 8th DDA binding was energetically forbidden. Therefore, complete surface passivation is not favoured in solid state QD samples when bulky, entropic ligands are used.
Near-epitaxial QD surface passivation
This problem can be solved by reducing the size of ligand tails and functionalizing them with moieties featuring attractive intermolecular interactions. To assess the effect of such tail groups, we replaced truncated DDA cations with phenethylammonium (PEA) cations, a small ligand that can feature attractive intermolecular π-π stacking (Fig. 1c). First, the surface free energy reached the minimum when the surface is fully covered by PEAs (Fig. 1d). In addition, smaller ligand tails reduced the entropy penalty, and the surface free energy was much lower than that of the DDA-covered surface. Furthermore, the differential surface free energy of the PEA-covered QD slab indicated that increasing PEA coverage would always be favoured. This suggests that intermolecular π-π interaction between PEA cations can drive the near-epitaxial surface passivation of the QD surface, minimizing the probability of defect formations.
Our ligand design was then tested using strongly confined CsPbBr3 QDs synthesized following a previously reported method with modifications (Methods).5 The QDs have a cubical shape and expose mostly the (100) facets (Fig. 1e and Supplementary Fig. 6). The π-π interaction between the bound PEA ligands were investigated using nuclear magnetic resonance (NMR) Overhauser effect spectroscopy (NOESY). To prepare PEA-exchanged QD colloids for NMR measurements, a small amount of saturated PEA bromide (PEABr) N,N-dimethylformamide (DMF) solution was added into the QD colloids followed by purification (Methods). The 1H NMR spectrum showed that both PEA and oleylammonium cations (the original ligands) were bound to the QDs (Supplementary Figs. 7 and 8). The incomplete exchange was expected due to the limited solubility of PEABr in non-polar organic solvents. To investigate the intermolecular interaction between PEAs, the NOESY was used to monitor the coupling of protons on the surface-bound phenyl rings. To distinguish the nOe signals contributed by intermolecular π-π stacking from the intramolecular coupling, half of the PEAs used for the ligand exchange were labelled by a methyl group on the para position of their phenyl rings (MPEA). Figure 1e shows the expanded region of the NOESY spectrum of the ligand-exchanged CsPbBr3 QD colloids (full spectrum in Supplementary Fig. 9). Strong cross-peaks at 7.09, 7.13, and 7.32 ppm arose from the intermolecular correlations between the para-, meta-, and ortho-protons on the PEA phenyl rings and the para-methyl protons on the MPEA, respectively. This demonstrates the π-π stacking between the phenyl rings in surface bound PEA and MPEA.
An approach to address incomplete surface ligand exchange using solubility-incompatible ligands is solid-state ligand exchange, in which the QDs capped by original ligands were exposed to polar solutions of shorter ligands.42 To make QD samples for single-particle studies, we performed the solid-state exchange by casting diluted CsPbBr3 QDs onto a supersaturated PEABr solution in DMF on a spinning substrate (Methods). QD dilutions facilitate the detachment of original ligands, and the low QD concentration also increases the PEA-to-QD ratio, which is critical for thorough ligand exchanges.42 Furthermore, additional bromide introduced by PEABr can compensate the potential surface bromide loss during QD dilution, and the PEABr surface termination can support the intrinsic electronic structure of CsPbBr3, increasing the PLQY.35, 43 After the exchange, the sample was carefully annealed in a nitrogen glovebox to assist intermolecular stacking (Methods). Accordingly, the PEA-covered QDs were dispersed in a crystalized matrix formed by excess PEABr molecules, as demonstrated in X-ray diffraction patterns (Supplementary Fig. 10). NMR spectra of digested PEA-exchanged QDs show no signal from original ligands, suggesting the high efficiency of the solid-state ligand exchange approach (Supplementary Fig. 11). Also, QDs in the PEABr matrix retained their cubical shape, suggesting the integrity of QDs is preserved during the solid-state ligand exchange (Extended Fig. 1 and Supplementary Fig. 6).
Blinking behaviours of single CsPbBr3 QDs
We first studied the blinking behaviours of single CsPbBr3 QDs (~ 4.5 nm) passivated by long-chain ligands (DDA) and PEA. The OFF-state intensity threshold was determined by the QY of OFF states/trions, which were usually smaller than 20% in CsPbBr3 QDs.44, 45 Typically, PL emissions with intensities above the OFF threshold were all considered as the “ON” state. However, PL from this “ON” state cannot properly represent the pure excitonic emissions, since the frequent PL intensity fluctuation in CsPbBr3 QDs together with photodarkening can convolute PL with dimmer emissive states (e.g., grey states) with the PL from exciton states.46, 47 To better quantify the ON state fraction, the ON/OFF state threshold was raised to 50% of the maximum PL intensity. As shown in Fig. 2a and 2c, the DDA-covered CsPbBr3 QD exhibited severe PL blinking and was photodarkened only after 120 s of excitation. Typical ON/OFF intensity threshold would result in a 47.0% and 90.2% ON time fraction for measurement duration of 300 s and 60 s, respectively. Instead, our higher threshold yielded 16.5% and 55.4% ON time fraction, which better represented the blinking behaviour of DDA-covered CsPbBr3 QDs. Despite the aggressive threshold, the PEA-covered QD remained mostly in the ON state without photodarkening over 10 mins (Fig. 2b). Figure 2d shows a blinking trace in a 60 s time window. Specifically, the QD exhibited an ON fraction of 94.2% over 10 mins and 98.6% over 60 s, both much higher than that of the DDA-covered QD.
To better analyse the PL intensity trajectories of our PEA-covered CsPbBr3 QD, we also used the Mandel Q parameter to quantify the deviation of the PL intensity distribution from shot-noise limited, Poisson statistics (Supplementary Note 4).47, 48 The PL intensity distribution of a blinking-free QD should simultaneously have a high ON fraction and a close-to-zero Q parameter. Shown in Fig. 2c, DDA-covered QDs exhibited a broad and asymmetric PL intensity distribution histogram with a Q parameter of 7.3. In stark contrast, the PEA-covered QD exhibited a narrow PL intensity distribution with a Q parameter of 0.3. The ON time fraction and Mandel Q parameter of the PEA-covered QD remained consistent when a shorter bin time was used (Extended Fig. 2). These suggest that the PL emissions from the PEA-covered QD were dominated by exciton radiative recombination and were not influenced by stochastic QD charging or environmental charge redistributions.
Another consequence of charging-induced PL blinking is spectral diffusion, which has been frequently reported in long-chain ligands covered CsPbBr3 QDs.16, 32 Such PL energy jumping is detrimental to the performance of QDs as quantum emitters. Our PEA-covered QD shows a spectrally stable PL. As shown in Fig. 2e, no spectral diffusion was detected, which was consistent with the nearly non-blinking behaviour. In comparison, the DDA-covered QD show clear spectral diffusion in the first 10 s of the measurement (Supplementary Fig. 12). The high single photon purity of the PEA-covered QD with a g(2)(0) value of 0.013 was also expected, given its strong size confinement (Fig. 2f). This is also one of the lowest g(2)(0) values reported for perovskite QDs.
This significantly improved single QD optical performance was echoed by the statistics of the ON and OFF durations extracted from blinking traces of 60 PEA-covered CsPbBr3 QDs, as shown in Fig. 2g. The probability distributions for the duration (t) of the ON and OFF events, PON/OFF, were fitted to a power law distribution \(P\propto {t}^{-{k}_{\text{O}\text{N}/\text{O}\text{F}\text{F}}}\), where kON/OFF were set as the power law exponents that describe the statistics of the ON/OFF events. For instance, a smaller kOFF (a steeper slope in the log-log plot) means long-duration OFF events were less likely to happen. In typical QDs, both kON and kOFF values are ~ 1.5.49 Our QDs showed an average kON of 2.0 and kOFF value of 1.0, comparable to one of the best non-blinking core-shell II-VI and III-V QDs reported.29, 50 This implies that our CsPbBr3 QDs are almost defect-free.
The nearly complete passivation of PEA-covered QDs benefit from the attractive intermolecular interactions between PEA cations. To demonstrate the necessity of this, we applied another low-steric ligand without π-π stacking effects, iso-propylammonium (IPA) bromide, to cover the same CsPbBr3 QDs used in Fig. 2 (4.5 nm). IPA-covered QDs still showed suppressed blinking with an ON time fraction of 83% (Extended Fig. 3). This was potentially due to the absence of strong intermolecular steric repulsion in IPA compared to DDA. However, a clear OFF fraction distribution was observed, implying the existence of surface defects due to incomplete passivation in IPA-covered QDs.
Stability of PEA-covered CsPbBr QDs
Similar to PL blinking, rapid photodegradation of CsPbBr3 QDs has been a long-standing obstacle to investigations of their excitonic properties at the single particle level. Strongly confined CsPbBr3 QDs are reported to experience spectral blue-shifting due to size shrinking within a short time of laser excitation.13, 51, 52 According to the DFT modelling, QD surface can be significantly stabilized when it is fully-covered by PEAs. This would be manifested as resistance to photodegradation. Indeed, the single strongly confined CsPbBr3 QD showed no spectral diffusion and size shrinking-induced blue-shifting during 30 mins of laser irradiation (Fig. 3a and 3b), and the PL spectra before and after operation were nearly identical (Fig. 3c).
CsPbBr3 QDs are notoriously prone to photodarkening. This occurs when light irradiation creates new surface defects on QDs and intensifies their PL blinking. To explore the surface structural stability of strongly confined PEA-covered CsPbBr3 QDs at an ensemble level, a collection of isolated QDs was illuminated at the same time. Their PL intensity stayed constant over the course of the measurement (> 10 h). In comparison, the PL intensity of the same QDs covered by DDA dispersed in polystyrene decreased since the first minute of laser exposure and became nearly completely dark after ~ 10 min (Fig. 3d). Notably, the PEA-covered QD remained nearly non-blinking with a 98% ON fraction beyond 12 hours of continuous operation (Fig. 3e and 3f). We also tested the PEA-covered single QDs at high excitation rates using a pulsed laser with tuneable laser pulse energy. During the test, QDs remained nearly non-blinking when the excitation density (average number of excitons created per pulse) was increased to 0.21 (Extended Fig. 4 and Supplementary Note 5). In addition, PEA-covered QD stayed blinking-free for about a month of storage at ambient condition (Supplementary Fig. 13). To the best of our knowledge, this is comparable to some of the most photostable non-blinking CdSe QDs with CdS shells.29
PL performance of CsPbBr QDs with various sizes
We then explored our ligand design on single CsPbBr3 QDs with various sizes. The extent of quantum confinement in QDs increases with decreasing size, making the QD more sensitive to surface defects. Rarely can a surface passivation method work effectively for QDs with different sizes. Figure 4a – 4d show blinking traces of four different single CsPbBr3 QDs covered by PEA with their sizes determined by their PL spectra (Fig. 4e) with an empirical sizing curve.6 All CsPbBr3 QDs were nearly blinking-free with ~ 98% ON fractions and shot noise-limited PL intensity distributions, suggesting that PEA epitaxially passivated CsPbBr3 QD surfaces (additional single QD measurements are shown in Supplementary Fig. 14). Notably, weakly confined CsPbBr3 QDs can also benefit from the high surface PEA coverage: a single CsPbBr3 QD with the size of 9 nm was nearly blinking free and maintained a 94.1% ON time fraction over 30 minutes; no spectral diffusion nor size-shrinking were detected during 1 hour of laser irradiation (Extended Fig. 5).
These QDs were then examined to study their biexciton dynamics (Fig. 4f). The fast biexciton Auger recombination of strongly confined CsPbBr3 QDs was also echoed by a low average g(2)(0) value (0.054) from the statistics built using 60 strongly confined QDs (Extended Fig. 6). We noted that the variations of g(2)(0) values of non-blinking QDs were smaller than QDs exhibiting PL intensity fluctuations (Supplementary Fig. 15).13 The larger g(2)(0) value variations in blinking QDs can be partially attributed to the attenuated single exciton emissions from other non-radiative channels. Non-blinking QDs are thus particularly useful for studying the biexciton recombination mechanisms since their g(2)(0) values can better represent the biexciton emission QY.53
Determining the size-dependent exciton properties at the single QD level
Size-dependent exciton properties are fundamentally important for unravelling the PL emission mechanism and exciton-lattice interaction in QDs. Experimental determination of PL properties in single QDs exclude the interferences of ensemble inhomogeneity. However, blinking and photodarkening can change exciton dynamics and PL line shapes. The nearly non-blinking CsPbBr3 QDs with significantly improved photostability are therefore ideal to studying the intrinsic effects of quantum confinement on excitons.54, 55
Exciton recombination dynamics were then studied using our single CsPbBr3 QDs. They show mono-exponential PL intensity decay (Fig. 5a) due to the absence of dimmer emissive states. We extracted the PL lifetimes from 81 QDs with sizes ranging from 3.6 nm to 14 nm (Fig. 5b). Interestingly, the size-radiative rate correlation was not monotonic: the exciton radiative rate increased with reducing sizes and then decreased when the size was smaller than 4.5 nm. The initial increase of the radiative rates can be attributed to the increase of the optical band gap induced by quantum confinement.56, 57 When the QD is more confined, thermal mixing of bright and dark exciton states will take over and reduce the radiative rate due to larger exciton fine structure splitting.55, 56
Not only do our PEA-covered QDs reveal the exciton radiative rates, but they also exhibit intrinsic PL linewidths to help understand the size-dependence on exciton-lattice interaction in QDs. We discovered that the PL spectra were asymmetric for all CsPbBr3 QDs even without spectral diffusion and shifting (Fig. 5c). We employed two Voigt functions with a common peak position to fit the single QD PL spectra. The half-width half-maximums (HWHMs) of both functions were extracted for 81 non-blinking QDs (Fig. 5d). In the weakly confined region, our QDs showed similar or narrower PL peaks compared to reported values from other literature (Supplementary Fig. 16). With decreasing QD size, the PL linewidths increase monotonically, which agreed well with previous studies.58 However, the low-energy tail of the PL experienced a stronger dependence on the QD size compared to the high-energy part.
The low energy tail in PL spectrum of CsPbBr3 QD ensembles was frequently observed but rarely studied. Bright band tail states were proposed to explain the asymmetric PL.59 However, this would imply the existence of multiple dimmer emissive states compared to the exciton state and was inconsistent with the mono-exponential PL decay observed in our nearly non-blinking QDs. Asymmetric PL spectra have also been discovered in CsPbBr3 polycrystalline films and have been attributed to the Cs+ relocation.60 However, this effect should not be evident at room temperatures. The strong size dependence of the low energy tail infers that the surface lattices of the QDs may induce the PL asymmetry. Thus, the intrinsic PL asymmetry can be related to the optical phonon sideband61 or momentarily trapped exciton-polarons formed by exciton-surface lattice interactions, which were also found in 2D perovskite nanoplates.62 This is supported by the spectrally independent PL decay dynamics of PEA-covered CsPbBr3 QDs (Supplementary Fig. 17). Our study suggests that even for defect-free QDs, the size can still substantially affect exciton-lattice interactions.