Spectral and Dynamical Properties of Single Excitons, Biexcitons, and

Feb 16, 2016 - Enhanced Size Selection in Two-Photon Excitation for CsPbBr3 Perovskite Nanocrystals ..... Applied Surface Science 2018 455, 425-432 ...
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Spectral and Dynamical Properties of Single Excitons, Biexcitons, and Trions in Cesium−Lead-Halide Perovskite Quantum Dots Nikolay S. Makarov, Shaojun Guo, Oleksandr Isaienko, Wenyong Liu, István Robel, and Victor I. Klimov* Chemistry Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, United States

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S Supporting Information *

ABSTRACT: Organic−inorganic lead-halide perovskites have been the subject of recent intense interest due to their unusually strong photovoltaic performance. A new addition to the perovskite family is all-inorganic Cs−Pb-halide perovskite nanocrystals, or quantum dots, fabricated via a moderatetemperature colloidal synthesis. While being only recently introduced to the research community, these nanomaterials have already shown promise for a range of applications from color-converting phosphors and light-emitting diodes to lasers, and even room-temperature single-photon sources. Knowledge of the optical properties of perovskite quantum dots still remains vastly incomplete. Here we apply various timeresolved spectroscopic techniques to conduct a comprehensive study of spectral and dynamical characteristics of single- and multiexciton states in CsPbX3 nanocrystals with X being either Br, I, or their mixture. Specifically, we measure exciton radiative lifetimes, absorption cross-sections, and derive the degeneracies of the band-edge electron and hole states. We also characterize the rates of intraband cooling and nonradiative Auger recombination and evaluate the strength of exciton−exciton coupling. The overall conclusion of this work is that spectroscopic properties of Cs−Pb-halide quantum dots are largely similar to those of quantum dots of more traditional semiconductors such as CdSe and PbSe. At the same time, we observe some distinctions including, for example, an appreciable effect of the halide identity on radiative lifetimes, considerably shorter biexciton Auger lifetimes, and apparent deviation of their size dependence from the “universal volume scaling” previously observed for many traditional nanocrystal systems. The high efficiency of Auger decay in perovskite quantum dots is detrimental to their prospective applications in light-emitting devices and lasers. This points toward the need for the development of approaches for effective suppression of Auger recombination in these nanomaterials, using perhaps insights gained from previous studies of II−VI nanocrystals. KEYWORDS: Cs−Pb-halide perovskites, nanocrystal, quantum dot, radiative recombination, Auger recombination, absorption cross-section, band-edge-state degeneracy, intraband cooling, exciton−exciton interaction

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cubically shaped with a side length ranging from 4 to 15 nm. The emission was color tunable across the entire range of visible wavelengths (400−700 nm) by combining size and composition control. More recent works demonstrated a highly effective postsynthetic anion exchange, which resulted in the partial or complete replacement of ions of one halide with another.13,14 This interesting approach allowed for facile manipulation of emission color without modifying the QD dimensions. The initial reports on Cs-based QDs primarily focused on the chemistry of these novel materials and their basic spectroscopic properties such as absorption and photoluminescence (PL) spectra as well as PL efficiencies and lifetimes.12−14 These earlier measurements found surprisingly high emission efficiencies (∼50% and higher) for as-fabricated QDs

ybrid organic−inorganic perovskites CH3NH3MX3 (M is a metal, typically Pb, and X is a halide, typically Cl, Br, or I) exhibit large absorption coefficients, high emission efficiencies, and excellent charge transport characteristics.1−4 These properties make them attractive materials for applications across a range of technologies from solar energy conversion1,2,5 to light-emitting diodes (LEDs)6 and lasers.7 Especially impressive have been recent advances in the efficiency of perovskite solar cells that surged from 3.8%8 to 20.1% over the past several years.5,9,10 Recently, hybrid perovskites have been also synthesized as nanocrystal quantum dots (QDs) and studied in the context of their applications as color-tunable down-converting phosphors.11 The newest addition to the family of perovskite QDs is all-inorganic nanocrystals introduced by Kovalenko and coworkers.12 In these nanostructures, the organic CH3NH3 cations are replaced with Cs+, which results in the composition CsPbX3, where X is one of the three halides (Cl, Br, or I) or their binary mixture. The particles reported in ref 12 were © 2016 American Chemical Society

Received: December 11, 2015 Revised: February 1, 2016 Published: February 16, 2016 2349

DOI: 10.1021/acs.nanolett.5b05077 Nano Lett. 2016, 16, 2349−2362

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Figure 1. Transmission electron microscopy (TEM) images and optical spectra of perovskite QDs. (a) A large-area TEM image of CsPbI3 QDs indicates that they have cubic shapes, and the average side length is 11.2 ± 0.7 nm. Inset: A high-resolution TEM image of an individual CsPbI3 QD indicates that the {100} planes are spaced by 0.62 nm and aligned parallel with the cube side. (b) Absorption spectra (solid black lines) of the CsPbX3 QDs of various compositions (X = I, Br1.5I1.5, and Br) plotted together with the PL (blue lines) and PL excitation (red dashed lines) spectra. The spectra of different samples are displaced vertically for clarity. The vertical scale bar corresponds to the QD absorption cross-section of 5 × 10−14 cm2; it can be used to derive spectrally dependent absorption cross-sections based on the absorption spectra displayed in this figure. (c) The second derivative of the absorption spectra (black lines) plotted together with the PL spectra (red lines); the values of the apparent Stokes shift are inferred from the difference in the positions of the lowest-energy minimum in the second derivative of the absorption spectrum, α′′(hv), and the PL peak.

The purpose of the present study is to conduct a comprehensive spectroscopic characterization of Cs-based perovskite QDs with focus on energy relaxation and recombination processes. Specifically, using time-resolved PL and transient absorption (TA) spectroscopies, we evaluate the degeneracies of the band-edge states and quantify spectroscopic characteristics such as absorption cross-sections, radiative lifetimes, time constants of nonradiative Auger decay, exciton−exciton interaction energies, and intraband cooling rates. Our overall assessment is that the properties of perovskite QDs are in general similar to those of well-studied CdSe and PbSe QDs. Specifically, we observe extremely fast intraband relaxation, which occurs on subpicosecond-to-picosecond time scales, similar to those reported for CdSe17 and PbSe18 QDs. Our measurements also indicate fairly large exciton−exciton interaction energies of the order of 10 meV, again comparable to those in large-size CdSe QDs.19,20 Further, we find that multiexciton recombination is dominated not by radiative processes but by very fast Auger decay, which is in direct

suggesting their potential usability as, for example, colorconverting phosphors or active elements in LEDs. A demonstration of low-threshold, color-tunable amplified spontaneous emission (ASE) also suggested that this type of QDs could be explored in the context of lasing applications.15 Furthermore, recent single-dot measurements indicated the feasibility of using individual perovskite QDs as roomtemperature sources of single photons.16 While the conducted studies indicate considerable promise of these novel QDs for applications that rely on light emission, their practical utilization in light-emitting devices would benefit from a more complete understanding of spectral and dynamical properties of electronic excitations in these materials. More studies are also required to assess whether perovskite QDs can compete, and potentially outperform, more traditional visiblelight-emitting II−VI and III−V nanocrystals that have been successfully exploited in a range of applications including a commercialized display technology. 2350

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Nano Letters analogy to other nanocrystalline systems.21,22 In fact, the biexciton lifetimes measured for perovskite QDs are even shorter than those in CdSe and PbSe QDs of similar sizes, suggesting that Auger decay will represent a serious obstacle to the realization of practical lasing and LED devices, as in the case of other QD systems. This points toward the importance of developing effective approaches for suppressing Auger decay in novel perovskite QDs, perhaps, by taking advantage of a large amount of theoretical23 and experimental24−26 studies devoted to controlling Auger decay in II−VI nanocrystals. Quantum Dot Samples. Perovskite QDs of three compositions, CsPbBr3, CsPbI3, and CsPbBr1.5I1.5 (referred to as Br-QDs, I-QDs, and Br1.5I1.5-QDs, respectively) were synthesized following a procedure from ref 12 with some modifications (see Methods). The synthesized QDs are cubically shaped single crystals with a mean side length (L) of 6.3−11.2 nm and size dispersion of ∼10% (see Figure 1a and Figure S1 of Supporting Information, SI). High-resolution transmission electron microscopy (TEM) images (Figure 1a, inset) indicate that QD sides are parallel to the {100} lattice planes. The spacing between these planes is 0.62 nm for the IQDs (Figure S1b of SI), which is consistent with the cubic perovskite crystal structure of CsPbI3.12−14 According to calculations of ref 12, the Bohr exciton diameters (2a0) in bulk CsPbBr3 and CsPbI3 are 7 and 12 nm, respectively. On the basis of these values, in a mixed-halide sample, 2a0 is approximately 9.4 nm. For the QD sizes studied in the present work, the L/2a0 ratio is from ∼0.9 to ∼1.3. This situation corresponds to the regime of so-called “intermediate confinement” when the QD size is comparable to that of a bulk exciton. A similar regime is realized, for example, in large-size (8−10 nm diameter) CdSe QDs where the Bohr exciton diameter (2a0 = 9.6 nm) is close to that in Pb-halide perovskites. Optical Spectra, Photoluminescence Dynamics, and Radiative Lifetimes. In all optical measurements described in this work, perovskite QDs were dissolved in hexane and loaded into airtight optical cuvettes under argon atmoshere. All spectroscopic studies were conducted at room temperature. Figure 1b shows the absorption (α), PL, and PL excitation (PLE) spectra of the studied QD samples. We observe that the PLE spectra closely match the absorption spectra up to energies of ∼4 eV (instrument limit in these measurements), indicating that photoinjected “hot” carriers are efficiently funneled into the “emitting” band-edge states independent of excitation energy. The absorption spectra exhibit a relatively sharp steplike onset and a fairly narrow PL band (∼90 meV; determined in terms of a full width at half-maximum, FWHM). Since the absorption spectra lack a pronounced band-edge peak, to quantify the position of the lowest-energy “absorbing” transition, we analyze the second-derivative of α(hv), α′′(hv), an approach used previously for visualizing poorly resolved spectral features in QD samples (hv is the photon energy).27 Based on the position of the first minimum in the α′′(hv) spectrum (black lines in the Figure 1c) versus the PL peak, we infer that the apparent Stokes shift (ΔS) is of the order of 20− 30 meV, which is comparable to that in large-size CdSe QDs.28 As was reported previously,12 as-synthesized QDs exhibit high PL quantum yields (QYs) that are in the 40−50% range (see Table S1 of SI). Such high QYs are remarkable given that these QDs are synthesized at relatively low temperatures (130− 160 °C) and are not overcoated with a shell of a wider-band gap semiconductor usually required for obtaining high emission

efficiencies in II−VI or III−V QDs. We also do not detect any signatures of intragap emission, which is often present in coreonly CdSe QDs. These observations suggest a considerably lower abundance of intragap states in perovskite QDs compared to other studied QDs. Figure 2a shows PL dynamics for the perovskite QDs measured with a superconducting nanowire single-photon

Figure 2. Low-pump-intensity photoluminescence (PL) dynamics of perovskite QDs. (a) PL dynamics of the perovskite I-QDs (red line), Br-QDs (black line), and I1.5Br1.5-QDs (green line) measured with the SNSPD (time resolution 50 ps) using low-intensity (⟨N⟩ ≪ 1) pulsed excitation (220 fs pulse duration) at 3.6 eV exhibit multiexponential decay with lifetimes from ∼1 to ∼30 ns. Inset: Zoomed-in view of the early time PL dynamics in I-QDs from a higher temporal resolution (10 ps) streak-camera measurement (black line) does not show any additional fast components not resolvable in the SNSPD trace (red line). (b) The measured PL dynamics of the I-QDs (red line) are modeled as a sum of three single-exponential decays (black line) with time constants of 0.88, 8.6, and 33.3 ns (shown by blue dashed lines). The ratio of the area under the measured PL trace (gray shading) and the area under the trace for the ideal purely radiative decay (solid blue line) is equal to the PL quantum yield Q.

detector (SNSPD; temporal resolution Δtres = 50 ps)29 using pulsed excitation (220 fs pulse duration) at 3.6 eV, with a perpulse fluence of 3.5 × 1011 photons/cm2, which corresponds to the average QD excitonic occupancy, ⟨N⟩ ≪ 1, as estimated based on the absorption cross-section (σ) inferred from the time-resolved PL measurements (see below). For these excitation levels, a majority of the QDs in the photoexcited ensemble contain a single electron−hole pair, which we will refer to as a single-exciton state. Hence, the measured PL dynamics report on the single-exciton lifetime. In agreement with the observations of ref 12, the PL decay for the Br-QDs is faster than that for the I-QDs, while the mixed-anion sample shows dynamics that are intermediate 2351

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depends on QD size due to the size-dependent splitting of finestructure states. With all of these contributions the radiative rate in the QDs can be expressed as rr,X ∝ γ|f|2EgEp. Next, we will attempt to understand which of the factors are primarily responsible for the strong dependence of rr,X on anion identity observed experimentally. In CdSe QDs of large sizes, for example, the effects of exciton fine-structure at room temperature are insignificant, as the separation between the split-off states quickly decreases with increasing QD size. For QD diameters greater than 5−6 nm it is just a few meV, i.e., smaller than the thermal carrier energy (∼24 meV). One might expect that a similar situation is realized in large-size perovskite QDs studied here; i.e., even if the fine structure splitting exists in these materials (which is still not known), its role is probably insignificant, at least at room temperature. This conclusion is supported by the observation of fairly small Stokes shift values (on the order of the thermal energy) indicated by the measurements in Figure 1c. Thus, the factor of γ is unlikely to lead to large anion-dependent variations in rr,X. A somewhat different conclusion can be made for the factor Eg|f |2. The estimations of this product show that it changes by a factor of ∼2 between the I- and Br-based QDs, which is significant, but still smaller than the difference between lifetimes observed experimentally (factor of 5.6). This suggests that the remaining difference is likely accounted for by the Kane energy which seems to vary from one anion to another. This conclusion is somewhat unexpected given that in traditional II−VI, III−V, and group-IV semiconductors the Kane energy is almost insensitive to material’s composition and is ca. 20 eV34 for a wide range of semiconductors. This is a consequence of the close similarity between the wave functions of the conduction and valence band-edge states in these materials that have “pure” s- and p-type characters, respectively. The situation, however, is different in I−III−VI2 semiconductors. For example, in CuInS2, the band-edge state in the valence band has a considerable admixture of the d-type wave function, which leads to the reduction of the Kane energy by more than 60% compared to that in closely related II−VI semiconductors.35 It is known that in perovskites the lowest energy valence band state has also a mixed character and is contributed by the halide 5p and Pb 6s orbitals.12,36−38 The strength of the mixing is expected to be dependent upon the anion identity. This would lead to the anion-dependent Kane energy, which could explain the observed variations in the radiative decay rate. Based on our measurements, the ratio of Kane energies for the Br-QDs and I-QDs can be as large as ∼3. Transient-PL Signatures of Multiexcitons and Absorption Cross-Sections. To assess the properties of multiexciton states, we excite perovskite QDs with high intensity frequencydoubled, 50 fs pulses from an amplified Ti:sapphire laser (3.1 eV photon energy) or 200 fs pulses from an amplified Yb:KGW laser (3.6 eV photon energy) and time-resolve QD emission with either an SNSPD or a streak camera. Figure 3a shows an example of fluence-dependent decay traces obtained for the IQDs using SNSPD. At low excitation fluences (⟨N⟩ ≪ 1), the measured PL exhibits tens-of-ns decay typical of single-exciton recombination, as discussed in the previous section. With increasing excitation fluences (to ⟨N⟩ of ∼1 and higher), a much faster, tens-of-ps component emerges in the PL dynamics and quickly (superlinearly) grows with excitation fluence. This fast decay is a typical signature of multiexcitons generated via absorption of multiple photons from the same pulse (hence, nonlinear pump-intensity dependence) and then decaying via

between the two pure-anion QDs. The recorded traces exhibit multiexponential decay, with time constants from 670 ps to 33.3 ns. Higher temporal resolution streak-camera measurements (Δtres = 10 ps) (see inset of Figure 2a; black line) and an even faster femtosecond PL upconversion (uPL) experiment (Δtres = 300 fs) do not reveal any additional shorter-lived contributions to PL, indicating that the SNSPD technique provides an adequate resolution for capturing all PL relaxation components. Next, we will use the recorded PL transients along with the measured PL QY (Q) for deriving radiative lifetimes (τr,X; subscript “X” indicates that this quantity denotes a singleexciton lifetime) of our perovskite QD samples. In the analysis of PL dynamics, we assume that all QDs in the measured ensemble are characterized by the same radiative time constant, while the nonradiative lifetime may differ from dot to dot due, e.g., to the difference in the number and/or identity of centers for nonradiative recombination. In this case, τr,X = Q−1⟨τX⟩, where ⟨τX⟩ is the average exciton lifetime in the QD ensemble, which accounts for both radiative and nonradiative processes as well as sample heterogeneities in recombination dynamics (see Section 1 of SI). By examining the recorded PL dynamics, we find that they can be accurately fitted to the sum of three exponentials. Combining the results of the fits with the measured PL QYs, we calculate first the average and then the radiative time constants. This procedure is illustrated in Figure 2b for the I-QD sample, for which the measured PL trace is decomposed into the three individual exponential components ui(t) (i = 1, 2, or 3) with time constants (τiX) of 880 ps, 8.6 ns, and 33.3 ns and respective amplitudes (ki) of 0.24, 0.31, and 0.45, which yields ⟨τX⟩ = i ∑i=3 i=1kiτX = 17.8 ns. Based on this value and the measured PL QY of 41% (Q = 0.41), we obtain τr,X of 43.4 ns. A similar procedure has been applied to the Br- and Br1.5I1.5-QD samples, and the results for ⟨τX⟩ and τr,X are summarized in Table S1 of SI. The radiative lifetime obtained for the Br-QD sample is 7.8 ns, which is considerably shorter than that for the I-QD sample. As expected, the mixed-anion sample shows an intermediate radiative lifetime of 36.6 ns. For a simple dipole emitter, the radiative decay rate (rr,X = 1/τr,X) is expected to scale as a product of the energy of the emitting transition (Eem) and the square of the modulus of the matrix element of the momentum (p): rr,X ∝ Eem|p|2. In the case of semiconductor materials, Eem can be replaced with the band gap energy (Eg), while p with the matrix element of the conduction-to-valence band transition (p = pcv) calculated for the band-edge states. The latter can further be expressed in terms of the Kane energy, EP: |pcv|2 = m0Ep/2.30−33 For the QDs, the radiative rate is also influenced by dielectric screening which can be accounted for by introducing the factor |f|2 ≤ 1 into the expression for rr,X. In general, this factor depends on the shape of the particle and its orientation with respect to the electric field. For the situation of cubic perovskite QDs randomly oriented with regard to the field direction, it can be approximated by that of a sphere, for which f = 3εm/(εs + 2εm), where εm and εs are dielectric constants of, respectively, the semiconductor particle and the medium (both taken at the emission wavelength). Finally, in the QDs the emission process frequently involves not just a single-exciton state but a set of closely spaced fine-structure states, populated according to the thermal distribution (e.g., Boltzmann) function. This can be accounted for by the temperature- (T) dependent population redistribution factor γ(T) ≤ 1, which in addition to T also 2352

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nanocrystals, as following fast multiexciton recombination each photoexcited QD is populated with a single exciton independent of its initial occupancy. For the quantitative analysis of the late-time PL signal, we make a usual assumption of a Poisson distribution of early time QD occupancies, which is a direct result of Poisson statistics of photon absorption events.39 In this case, the probability of a QD to contain i excitons is given by pi = (⟨N⟩i/i!) exp(−⟨N⟩), where ⟨N⟩ is the average number of excitons per QD. The value of ⟨N⟩ can further be expressed in terms of the QD absorption crosssection and per-pulse photon fluence (jp): ⟨N⟩ = σjp. Following multiexciton recombination, each photoexcited QD contributes a single exciton to the PL signal and hence the late-time PL amplitude can be presented as IPL(t ≫ τm) ∝ (1 − p0) = (1 − e−⟨N⟩) = (1 − e−σjp), where τm is the lifetime of the initial fast decay of multiexcitons. Thus, the long-time PL intensity saturates with increasing pump fluence, and since the onset of this saturation is directly controlled by the QD absorption cross-section, it can be used to quantify σ. In Figure 3b, we display the fluence dependence of the latetime PL signal for perovskite QDs of different compositions (symbols) (additional measurements using a streak camera, uPL, and saturation data for time-integrated PL are shown in Figure S2a of SI). We observe that all of the measured dependences can be accurately fit to the Poisson expression (lines in Figure 3b), confirming that the short-lived, early time PL component is due to multiexcitons. As a result of the fitting procedure, we also obtain QD absorption cross-sections. Based on the fits in Figure 3b and additional measurements in Figure S2a of SI, the average values of the 3.1 eV cross-sections are (1.3 ± 0.6) × 10−14 cm2, (1.5 ± 0.5) × 10−14 cm2, and (1.3 ± 0.6) × 10−14 cm2 for the Br-QD, Br1.5I1.5-QD, and I-QD samples, respectively. We plot the derived values in Figure 3c as a function of QD volume (VQD) along with absorption crosssections of two more Br-QD samples of smaller sizes. All of these data are also included in Table S1 of SI. We observe that for Br-QDs of varied sizes σ scales linearly with the QD volume, which is a trend commonly seen for other colloidal nanocrystals excited well above the band edge.39 Further, we find that the measured absorption cross-sections are considerably smaller (by almost an order of magnitude) than those of CdSe QDs of the same volume. This conclusion is confirmed by side-by-side pump-intensity-dependent measurements of saturation of the late-time-PL signal in samples of CdSe and Br-QDs (Figure S2b of SI). Despite a large difference in QD volumes for these two samples (250 versus 47.7 nm3 for the perovskite and the CdSe QDs, respectively) both samples show essentially identical absorption cross-sections of 3.5 × 10−15 cm2 at 3.1 eV. The above results suggest that the absorption coefficient of bulk CsPbX3 perovskites is smaller than that of bulk CdSe. Indeed, the absorption cross-section of the QDs can be related to the bulk absorption coefficient by the following expression: σ = (nm/ns)|f |2αVQD, where ns and nm are refractive indices of the semiconductor material and the surrounding medium, respectively (all spectroscopic parameters are taken at the excitation wavelength). Based on this expression and the difference in the dielectric screening factors, we estimate that at 3.1 eV the absorption coefficient of bulk CsPbBr3 is approximately an order of magnitude smaller than that of bulk CdSe. It would be interesting to see if this assessment is confirmed by direct measurements of absorption coefficients of bulk CsPbX3 crystals. Such data, however, are not readily

Figure 3. Pump-fluence dependence of PL dynamics in perovskite QDs. (a) Fluence-dependent time-resolved PL of the I-QDs obtained using SNSPD; the sample is excited at 3.6 eV with 220 fs pulses. (b) The PL signal measured at time t = 1 ns when Auger recombination is completed as a function of QD average occupancy for I- (blue triangles), I1.5Br1.5- (red circles), and Br- (black squares) QDs; the data sets are offset vertically for clarity. Lines show fits to (1 − p0) calculated for the Poisson distribution of initial QD occupancies. These fits were used to determine QD absorption cross-sections, σ. (c) The 3.1 eV absorption cross-sections of a series of perovskite QDs (symbols) as a function of QD volume, VQD; the line corresponds to linear scaling of σ with VQD. Data points correspond to average values of the measurements obtained by different techniques including SNSPD, streak camera, uPL, and time-integrated PL saturation (see Figure S2 of SI for details).

the nonradiative Auger process, wherein the electron−hole recombination energy is not emitted as a photon but instead is transferred to the third carrier (an electron or a hole) residing in the same dot.21,22 Thus, these measurements indicate that in perovskite QDs, as in other types of colloidal nanocrystals, Auger recombination represents a dominant decay channel of multiexciton states. To validate the assignment of the fast decay component to multiexciton recombination, we first analyze the pump-intensity dependence of the late-time signal, which is detected immediately following the fast initial decay (Figure 3b). If the early time PL component is indeed due to multiexcitons, and further, if its time scale is much shorter than that of singleexciton decay, then the late-time amplitude should be directly proportional to the total number of the photoexcited 2353

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single-exciton recombination regime, which establishes following the multiexciton decay. Next, we subtract the contribution from single excitons obtained based on traces measured for ⟨N⟩ ≪ 1, from the traces measured for ⟨N⟩ ∼ 0.1 and higher, which allows us to isolate the contribution solely due to multiexcitons (Figure 4b).21 The extracted dynamics can be fit to a singleexponential decay, which yields τ2X = 93 ps for our example of I-QD. Very similar values of τ2X are also obtained with timeresolved techniques that have a higher temporal resolution. For example, according to the analysis of TA and uPL dynamics τ2X = 92 ps. By averaging results of all of these measurements, we obtain τ2X of 92 ± 1 ps. To prove that the observed fast lifetime is indeed due to biexcitons we have verified that the amplitude of the corresponding PL component has a proper scaling with pump fluence. The contribution of multiexcitons (M) to early time PL is obtained by subtracting the PL amplitude related to single excitons (B in Figure 4a) from the total early time PL signal (A in Figure 4a): M = A − B. Following established procedures, the value of B is derived from “tail-normalized” PL time-transients using the early time amplitude of the self-similar PL traces recorded at the lowest pump fluences (⟨N⟩ ≪ 1). While the complete description of the saturation behavior of the multiexcitonic PL component requires knowledge of the band-edge degeneracy (see our discussion below), here we can note that at moderate excitation levels (⟨N⟩ < 0.5), the amplitude of this component is proportional to the Poisson probability p2 or ⟨N⟩2, as in this case, the dominant multiexcitonic species are biexcitons. Figure 4c shows that, in the range of ⟨N⟩ from 0.05 to 0.5, the fast PL component indeed scales as ⟨N⟩2 (dashed line in Figure 4c) confirming that it is due to biexciton recombination. After establishing that the fast initial decay in Figure 4a is due to biexcitons, we analyze its mechanism and also evaluate its dependence on the QD composition and size. All of the measured values of τ2X (see summary in Figure 5 and Table S1 of SI) are shorter than 100 ps, which immediately excludes their explanation in terms of radiative decay. Indeed, based on a large amount of literature data for II−VI and IV−VI nanocrystals, the radiative lifetime of the N-exciton state (τr,NX) can be related to that of a single exciton by a so-called statistical scaling,41,42 for which τr,NX = N−2τr,X. Applying this scaling to a biexciton, we obtain that τr,2X = τr,X/4. Using measured single-exciton radiative lifetimes, we estimate that the expected values of τr,2X are from ∼2 to ∼11 ns, which is orders of magnitude longer than the measured τ2X. Hence, the observed fast sub-100 ps decay of biexcitons is almost purely due to nonradiative Auger recombination, that is, τ2X ≈ τA,2X. Based on our measurements, biexciton Auger lifetimes in the Cs−Pb-halide perovskite QDs vary from 20 to 100 ps depending on composition and size (open symbols in Figure 5). A trend usually observed in traditional QDs of many different compositions including II−VI, III−V, and IV−VI semiconductors is a nearly linear scaling of Auger lifetimes with QD volume.21,22 In Figure 5, this trend is illustrated using measurements for CdSe and PbSe QDs (solid symbols).22,43,44 Despite a significant difference in electronic structures between these two materials one of which is wide-gap (CdSe) while the other narrow-gap (PbSe), they exhibit a surprisingly similar QD-volume dependence. In fact, even absolute values of Auger lifetimes for these two materials are very similar and can be described by τA,2X = βVQD, where β = 1 ps/nm3. This expression is especially accurate for QDs of smaller sizes (VQD

available in the literature, as the majority of previous optical studies of perovskites have focused on hybrid organic− inorganic versions of these materials.36,40 Biexciton and Trion Auger Lifetimes. The pumpintensity dependent dynamics in Figure 3a can also be used to quantify the lifetime of doubly excited QDs, which is usually referred to as a biexciton lifetime (τ2X). For this purpose, we first normalize the PL traces in such a way as to match their late-time components (Figure 4a). In this representation the long-time dynamics appear to be self-similar, as expected for the

Figure 4. Auger recombination dynamics and biexciton lifetimes in perovskite QDs. (a) Pump-fluence-dependent PL dynamics of I-QDs from the same set of data as in Figure 3a but normalized to match the late-time tails that correspond to single-exciton recombination (characteristic time τX). This representation helps highlight the early time short-lived PL component due to biexcitons (characteristic time τ2X), which emerges at higher pump intensities. Symbols A and B denote the amplitudes of the total PL signal and its single-exciton component, while M = A − B denotes the amplitude of the multiexciton signal. (b) The multiexcitonic component is isolated from the single-exciton decay by subtracting the self-similar dynamics measured at the lowest pump fluences. It is fitted to single-exponential decay (dashed lines), which yields the biexciton lifetime τ2X = 93 ps. (c) Pump-fluence-dependence of the single-exciton PL amplitude (B; black squares) and the amplitude of the multiexcitonic component (M = A − B; red circles) follows the expected trends obtained assuming Poisson statistics of the initial QD occupancies (solid lines). At low pump fluences the multiexciton component follows the quadratic scaling, as expected for biexcitons (red dashed line). 2354

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ps at the charge carrier densities of ∼1019 cm−3.47 These values correspond to CA of ∼2 × 10−27 cm6/s, which is comparable to the effective Auger constants backed out from our measurements of the perovskite I-QDs. However, despite this similarity, Auger recombination in QDs is clearly not bulk-like. The bulksemiconductor scenario would suggest that CA is QD sizeindependent. In this case, the biexciton lifetime would scale as the square of the QD volume τA,2X = V2QD/(8CA). The actual size-dependence observed in our measurements (Figure 5) is considerably weaker (τA,2X ∝ V0.5QD), indicating that CA is a size-dependent quantity, which scales with the QD volume approximately as V1.5QD (for the sizes studied). This implies that, as in other QD systems, Auger decay in perovskite QDs is strongly affected by quantum confinement. In traditional semiconductor QDs, in addition to dominating recombination of neutral multiexcitons, Auger decay also dominates recombination dynamics of charged excitons. The latter can be generated, for example, through the effect of photoionization, a process whereby one of the charges of the photogenerated exciton (an electron or a hole) leaves the dot before the exciton recombines.48−50 Photocharging or charging in general is detrimental to many applications as it reduces the QD emission efficiency. It further underlines at least some of the regimes of PL intermittency (or PL blinking) typical of all studied QD systems including perovskite QDs.16 Finally, it can lead to artifacts in spectroscopic measurements including, for example, the studies of carrier multiplication wherein the signatures of charged excitons can be misinterpreted as those of neutral multiexcitons.51 To eliminate the effects of photocharging in spectroscopic measurements, QD solutions are either flowed or vigorously stirred in the optical cells to refresh the photoexcited sample volume between sequential photonabsorption events.48,49,52 Following approaches from previous studies,47,48 in order to quantify the lifetimes of charged excitons (known as trions), we have compared PL decays collected for stirred versus unstirred (static) samples of Br1.5I1.5-QDs (Figure 6a). As typically observed for photocharging, in the static sample the singleexciton long-lifetime component of the PL decay is reduced (only the subensemble of QDs with neutral single excitons is emitting) while the amplitude of the early time component is enhanced due to increasing rate of trion emission compared to that of a neutral exciton. In the case of statistical scaling of the radiative rate with the number of electrons (Ne) and holes (Ne) residing in a QD (1/τr ∝ NeNh), the radiative lifetime of a trion (τr,X*) is half that of a neutral exciton (τr,X* = τr,X/2), and hence, its radiative rate is twice as large.41,51 By isolating and fitting the difference between the normalized stirred and unstirred decay traces, we obtain the trion lifetime τX* of 235 ps (Figure 6b). The fact that this value is orders of magnitude shorter than the expected radiative lifetime of a trion (∼18 ns in the case of Br1.5I1.5-QDs) indicates that it is due to fast nonradiative Auger recombination, i.e., τX* ≈ τA,X*. It is instructive to compare the trion lifetime to that of a biexciton. In the case of statistical scaling, and the situation of identical rates of Auger channels mediated by re-excitation of an electron (negative trion pathway) and a hole (positive trion pathway), the Auger rate relates to the electron and hole occupancies of a QD by 1/τA ∝ NeNh(Ne + Nh − 2).41 This expression suggests that τA,X* = 4τA,2X. For the sample of Br1.5I1.5-QDs, Figure 6, τA,2X = 47 ps, which yields τA,X* of ca. 190 ps. This value is slightly shorter than that measured experimentally suggesting the asymmetry between the negative

Figure 5. Auger lifetimes in perovskite QDs in comparison to those in CdSe and PbSe QDs. Biexciton Auger lifetimes of perovskite QDs as a function of QD volume (open symbols) plotted together with the biexciton Auger lifetimes of CdSe (solid stars; from ref 22) and PbSe (solid circles; from refs 22, 43, 44) QDs together with the linear dependence (dashed line), which describes a “universal volume scaling”. The biexciton lifetimes of perovskite QDs are considerably shorter than those in PbSe and CdSe QDs and seem to deviate from the linear volume scaling. In the limited size range studied here, the observed volume dependence can be described by the sublinear scaling τ2X ∝ V0.5QD.

< 200 nm3). On the larger-size end, it becomes less accurate and in the case of PbSe QDs overestimates the measured values of τ2X. Perovskite QDs (open symbols in Figure 5), seem to deviate from this general trend. First, the biexciton lifetimes in this case are considerably shorter (by about an order of magnitude) than those in CdSe and PbSe QDs. Second, the scaling with volume is slower than linear (characterized by a log−log slope of approximately 0.5) at least for the Br-based family and in the range of QD sizes studied in the present work. We would like to point out that, among the three compositions studied here, the CsPbBr3 perovskite has the smallest exciton size (2a0 = 7 nm), and therefore, Br-based QDs are characterized by a fairly weak confinement (L/2a0 is up to 1.3), the regime where one might expect changes in the mechanism for Auger recombination resulting in distortion of the volume scaling seen for smaller QDs. One possible source of the distortion is a transition from three-particle Auger recombination of uncorrelated carriers to a two-particle process involving Coulombically bound excitons, as was previously observed for CdSe nanorods.45 The measured biexciton Auger lifetimes can be used to estimate an effective Auger constant (CA) used to characterize Auger recombination in bulk semiconductors. In bulk materials, the rate of Auger recombination is cubic in carrier concentration, n: dn/dt = −CAn3. For each n, one can introduce an instantaneous concentration-dependent Auger time constant τA,n = 1/(CAn2). In the case of a QD ensemble, τA,n can be related to the N-exciton Auger lifetime (τA,NX) by τA,n = τA,NX⟨N⟩|⟨N⟩=N, where n is defined as n = ⟨N⟩/VQD.22,46 Now, we can express the effective Auger constant of the QDs in terms of the biexciton lifetime as CA = V2QD/(8τA,2X). On the basis of the τA,2X measurements for the studied perovskite QDs, CA is in the range 3 × 10−28 to 4 × 10−27 cm6/s. Recent measurements of CH3NH3PbI3 films used as a PV active layer indicate the Auger recombination times of ca. 5 2355

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While being somewhat disappointing, this result is not unexpected. Lead-halide perovskites are characterized by nearly identical electron (me) and hole (mh) effective masses.12 In this case, due to optical selection rules, the photon energy in excess of the band gap is partitioned equally between a hot electron and a hot hole, which increases the CM threshold to ∼3Eg57 as is observed, e.g., in PbSe QDs,43,57 where me ≈ mh. Given these considerations, the CM threshold in the studied I-QDs is around 5.4 eV, which is considerably higher than the photon energy used in our measurements (4.81 eV). The projected CM threshold is also outside the PV-relevant region of the solar spectrum, and therefore, even if CM is observed at these high energies it will not be of practical importance. Future exploration of CM in perovskites QDs would greatly benefit from the development of nanostructures with a lower band gap energy. Degeneracy Factors of Band-Edge States. Our studies of multiexciton dynamics can help determine the degeneracy factors of band-edge electron (ge) and hole (gh) states in perovskite QDs. This is an important characteristic of the QDs, which defines the limit of the ultimate QD occupancy in the case of resonant or quasi-resonant excitation. It also strongly influences the scaling of multiexciton radiative and nonradiative Auger lifetimes41,46 and defines the onset for optical gain.58 For common CdSe and PbSe QDs, the band-edge state degeneracies have been extensively studied both theoretically59,60 and experimentally58,61,62 (see a brief survey of these studies in Section 3 of SI). On the basis of the literature results, the band-edge state degeneracy factors in CdSe QDs are ge = 2 and gh = 4, while for PbSe QDs, ge = gh = 8; these values do not account for fine-structure effects associated with electron−hole exchange interactions, shape anisotropy, intervalley splitting, etc.. Contrary to the II−VI and IV−VI materials, where the band extrema are, respectively, at Γ- or L-points of the Brillouin zone,59,60 the perovskites with a cubic lattice have band extrema at the R-points.36,38,63 Since the zone contains 8 R-points that are shared between 8 primitive cells (see Figure 7a), the multiplier in the degeneracy factor resulting from the apparent presence of multiple band extrema in the Brillouin zone is still one as in the case of the Γ-point. The situation, however, is complicated by a mixed 5p(halide)/ 6s(Pb) character of the valence band,12,36 and strong spin− orbit coupling (SOC).36−38 Calculations of the organometallic perovskites and similar compounds36−38,63 suggest that up to three degenerate bands with different effective masses might coexist at the conduction-band minimum if SOC is neglected. The SOC effects in perovskite compounds are, however, important and need to be properly accounted for. Several theoretical studies have been devoted to this topic (see, e.g., refs 36, 37, 63), however, with somewhat inconsistent outcomes with regard to the predicted band gap values and the final degeneracies of electron band-edge states that can be either 2 or 4 (Figure 7a; panel at right). Here, in order to determine the values of ge and gh in perovskite QDs, we conduct an analysis of fluence-dependent PL and TA signals.39 Figure 7b shows fluence-dependent multiexcitonic dynamics in the mixed Br1.5I1.5-QDs (streak camera measurements at the PL peak) obtained by subtracting a low-fluence single-exciton decay (practically constant on the time scale of these measurements) from the recorded traces, a procedure similar to that used earlier to generate data in Figure 4b. Interestingly, with excitation fluences up to ∼6 excitons per dot per pulse on average, we observe single-exponential

Figure 6. Effect of photocharging on PL dynamics and chargedexciton (trion) lifetime. (a) Time-resolved PL of the stirred (black) and static (red) solutions of the I1.5Br1.5-QDs used to extract a trion lifetime. The increase of the early time PL amplitude in the static versus the stirred sample, accompanied by the reduction of the latetime signal, are typical signatures of photocharging, indicating the presence of a subset of dots with a nonzero net charge. (b) PL dynamics in charged QDs obtained by subtracting the tail-normalized “stirred” trace from the “static” trace. The single-exponential fit yields the charged-exciton (trion) lifetime of 235 ps.

and positive trion pathways in perovskite QDs. Such asymmetry is commonly observed, for example, in CdSe QDs where the positive-trion pathway is faster than the negativetrion channel.41,53 Similar asymmetry likely also exists in perovskite QDs and potentially it can help determine the sign of the QDs produced by photocharging. While in the above studies of Auger recombination multiexcitons were generated via absorption of multiple photons from the same pump pulse, alternatively, they can be also created by a single high-energy photon via carrier multiplication (CM) or multiexciton generation (MEG).54,55 In addition to being fundamentally interesting, CM is also of practical significance as by boosting the photocurrent it could lead to increased PV efficiencies.56 Since CM can be interpreted as the time-inverse of Auger recombination, enhanced multiexciton recombination in the perovskite QDs is expected to lead to the enhanced CM efficiency. So far, however, CM has not been studied for either bulk or QD forms of perovskites. Here, we have attempted to detect CM in perovskite QDs using the sample with the smallest band gap (I-QDs with PL at 1.816 eV) and the shortest practical excitation wavelength of 258 nm (hv = 4.81 eV) available to us. The corresponding photon energy is 2.65Eg, which is above the fundamental 2Eg CM threshold, making CM potentially possible. However, a careful examination of PL traces measured with high (hv > 2Eg) and low (hv < 2Eg) energy photons has not reveled any signatures of CM, indicating that even if this effect is present it occurs at excitation energies higher than 2.65Eg (see Section 2 and Figure S3 of SI). 2356

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Figure 7. Degeneracy of the band-edge states in perovskite QDs. (a) Cubic crystal structure of MPbX3 perovskite compounds (top left) and the corresponding first Brillouin zone (bottom left). The conduction- and valence-band extrema are located at the eight identical R-points each of which is shared between eight adjacent unit cells. In this situation, the band structure does not lead to the additional increase in the degeneracy of the bandedge states. Possible scenarios of the band-edge level splitting upon inclusion of the spin−orbit coupling are shown on the right. The resulting splitting of the conduction-band-edge states can be either 2 (upper scheme) or 4 (lower scheme). (b) Fluence-dependent decay of multiexitonic PL component (obtained by subtracting self-similar single-exciton dynamics) in Br1.5I1.5-QDs measured at the peak of the PL band shows the presence of only biexciton decay even at the average QD occupancy as high as ∼6. This indicates that the band-edge states cannot accommodate more than two carriers suggesting that they are 2-fold degenerate. (c) The PL dynamics on the blue side of the PL peak show progressively faster relaxation with increasing the detection energy, which is indicative of the increasing contribution from short-lived muliexcitons of orders higher than 2. (d) Pump-intensity-dependence of the early time (A; black squares) and late-time (B; red circles) PL amplitudes is consistent with calculations conducted for the 2-fold degenerate states (solid lines) assuming Poisson statistics of QD initial occupancies. The dashed lines show the calculated dependences of A on ⟨N⟩ for band-edge-state degeneracy factors 2 and 4 (blue), or 4 and 4 (green).

the limit of high excitation levels. As was discussed earlier, it can be presented as B = ηr1(1 − p0), where r1 = rr,X = 1/τr,X is a single-exciton radiative rate, and η is a constant scaling factor, which is the same for both A and B signals.39 On the other hand, the saturation of the total PL amplitude does depend on both degeneracies ge and gh. Specifically, according to Poisson excitation statistics,39,51 A can be expressed in terms of Poisson probabilities pi (see our earlier discussion in this paper) as:

dynamics indicating that they are exclusively due to biexcitons without apparent features of higher-order multiexcitons. In a similar situation, PbSe QDs that can accommodate up to 8 carriers in the band-edge states, show an increasing contribution from triexcitons and other species of higher multiplicities.42 The behavior observed for perovskite QDs is a signature that both the electron and the hole band-edge states cannot accommodate more than 2 carriers. Therefore, independent of pump fluence the band-edge dynamics are dominated by biexcitons, while higher-order multiexcitons manifest in the emission from the higher-energy states. Indeed, the PL traces recorded at above-band-edge energies (Figure 7c) display considerably faster relaxation compared to biexciton decay, which is due to a rapid increase in the Auger decay rate with increasing the exciton multiplicity.46 This is also consistent with an asymmetric broadening of the PL spectrum on its blue side observed at high fluences (Figure S4 of SI). In addition to the PL data, the ultrafast TA measurements of the band-edge bleach for the same sample (Figure S5 of SI) confirm the absence of any relaxation component with lifetimes shorter than those of the biexciton. The 2-fold degeneracy of the band-edge states is further confirmed by comparing saturation levels of the total PL amplitude (A) and its single-exciton component (B). The saturation of the B amplitude is insensitive to the structure of the band-edge states and is defined by the total fraction of photoexcited QDs in the ensemble which approaches unity in

g min

A = ηr1(p1 +

g max

∑ i 2pi + gmin ∑ i=2

i = g min + 1

∞

ipi + gmingmax

∑

pi )

i = g max + 1

where gmin = min(ge, gh) and gmax = max(ge, gh).41,51 We use this expression to calculate the fluence dependence of A using ηr1 derived from the fit to the measured pump dependence of B. We further consider three different situations: gmin = gmax = 4, gmin = 2 and gmax = 4, and gmin = gmax = 2 (lines in Figure 7d shown, respectively, by dark green, blue and black). Next, we compare the results of the calculations to the pumpintensity-dependent measurements of A and B, which we have limited to ⟨N⟩ < 10 (symbols in Figure 7d). At higher fluences, the absorption changes were irrepressible indicating permanent photodamage of the sample. In the range of the studied pump fluences, both A and B exhibit saturation at higher ⟨N⟩. As expected, the onset of saturation of the B-amplitude is close to ⟨N⟩ = 1, while it occurs around ⟨N⟩ = 2 for A. In fact, the overall behavior of the A amplitude follows very closely the 2357

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Nano Letters dependence calculated for gmin = gmax = 2. This confirms our earlier assessment that both the band-edge electron and hole states in CsPbX3 QDs are 2-fold degenerate. Intraband Relaxation and Exciton−Exciton Interaction Energy. In addition to highly efficient Auger recombination, another universal feature of traditional colloidal QDs is extremely fast intraband relaxation, which occurs on subpicosecond-to-ps time scales independent of composition and size. When observed initially,17 these fast intraband dynamics were unexpected as they contradicted so-called “phonon-bottleneck” theories,64,65 according to which a wide spatial separation between QD electronic levels should inhibit phonon emission because of difficulties in meeting the energy-conservation requirement. While a universal opinion on the mechanism (or mechanisms) underlying fast intraband relaxation in QDs is still lacking, the overall agreement is that it is not bulk-like (i.e., not a cascaded phonon emission), but it relies on quantumconfined nature of electronic excitations in the QDs and their strong coupling to species at the QD surface. Processes such as electron−hole Auger type energy transfer,17,66 coupling to surface ligands,67,68 and multiphonon emission due to nonadiabatic electron−phonon coupling18 have been invoked to explain ultrafast cooling dynamics in the QDs. Recently, it has been suggested that in their bulk form perovskites can exhibit slower cooling dynamics than more traditional semiconductors (e.g., group-IV, III−VI, or II−VI materials), which was ascribed to a hot-phonon bottleneck69 or the reduced polaron-phonon scattering in crystals with a strongly ionic character.70 An interesting question is whether a QD form of perovskites also shows reduced intraband cooling rates compared to QDs studied previously. To answer this question, here we apply femtosecond TA to directly examine intraband carrier dynamics in perovskite QDs at near bandedge energies. Figure 8a shows a series of time-resolved TA spectra of the I-QDs taken at a low excitation level (⟨N⟩ = 0.1) with pulsed excitation at 3.1 eV (150 fs pulse duration, 1 kHz repetition rate). At early times after excitation, before carrier cooling is completed, the lowest-energy states are not filled yet (see schematic in Figure 8b). However, the band-edge signal is still nonzero, which is as a result of the Coulomb interaction of the high-energy “hot” exciton generated by the pump pulse and the band-edge exciton produced by the probe pulse. In fact, the early time TA spectra exhibit the typical signature of a Coulomb-interaction-induced red shift of the band edge transition (so-called “biexciton effect”19,71) observed as a derivative-like feature with photoinduced absorption (PA) at lower energies and bleaching at higher. At longer times, as carriers accumulate in the lowest-energy states, the PA signal eventually decays being replaced by strong band-edge bleaching due to state filling. The above measurements allow us to evaluate both the exciton−exciton interaction energy (ΔXX) and the rate of intraband cooling.17,19 In the case of a spectrally narrow bandedge transition when its width δ is smaller than ΔXX, the latter quantity can be simply determined from the energy separation between the bleach and the PA feature that would directly mark the positions of the original and the shifted transition, respectively. However, if ΔXX is comparable or smaller than δ, the separation between these features depends not only on the exciton−exciton interaction energy but also the transition line width. In this situation it is still possible to derive ΔXX using not the positions but the early time amplitude of the photoinduced feature (a) and the later-time amplitude of the

Figure 8. Early time carrier dynamics in perovskite QDs probed by transient absorption spectroscopy. (a) TA spectra of CsPbI3 QDs (L = 11.2 nm) show a transformation from a derivative-like feature due to the Coulomb-interaction-induced shift of the band-edge optical transition at early times after excitation (pump−probe delay Δt < 1 ps) to the band-edge bleach at longer times (Δt > 1 ps). (b) A schematic illustration of TA evolution in the course of carrier intraband relaxation. Without excitation (at left), optical transition energies “seen” by a probe pulse are defined by single-exciton energies (solid lines). After a high-energy “hot” exciton is injected into a QD (middle), the transition energies seen by the probe pulse are modified by the exciton−exciton interaction (dashed lines). In the case of exciton−exciton attraction (shown in this example), an energy required to introduce the second exciton into the QD is reduced compared to that of the single-excition state by the exciton−exciton interaction energy (ΔXX). This is a so-called “biexciton effect” manifested as a red shift of the band-edge transition observed in early time TA as a derivative like feature with a photoinduced absorption (PA) at the lower energy accompanied by a bleach at the higher energy. After carriers relax into the band-edge state (at right), the PA feature is overwhelmed by the bleach signal resulting from the state-filling effect. (c) Early time TA dynamics probed at the positions of the PA (1.76 eV) and the bleach (1.84 eV) features show complementary behaviors: the PA decay is accompanied by the bleach build-up. Both processes are characterized by the same time constant of 570 fs, which represents the relaxation time between the two lowestenergy quantized states.

bleach (b) measured after the intraband relaxation is finished.19,71 Specifically, as shown in refs 19, 71, the a/b ratio is a direct function of ΔXX/δ. It is also a function of the degeneracy of the band-edge states as the increase in the degeneracy enhances the relative strength of PA compared to the bleach. This is easy to understand if one accounts for the 2358

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absorption cross-sections of the perovskite QDs exhibit a linear scaling with nanocrystal volume as previously observed for more traditional colloidal nanostructures including, e.g., CdSe QDs. However, in absolute terms, the measured values of σ are lower by approximately a factor of 10 than in CdSe QDs of the same volume. Further, we evaluate the degeneracy factors of the band-edge states and conclude that both electron and hole band-edge levels are 2-fold degenerate. We also show that in perovskite QDs, as in more common colloidal nanocrystals, the decay of multiexcitons and charged excitons is dominated by very fast Auger recombination. Interestingly, the observed time scales of Auger decay (∼20−100 ps) are even faster (by a factor of 5 to 10) than in dots studied previously and seem to deviate from a “universal volume scaling” not only in a numerical prefactor but also in the type of scaling, which is sublinear in nanocrystal volume. As other types of nanocrystals, perovskite QDs are prone to photocharging, which leads to the formation of charged excitons (trions) decaying primarily via the Auger process. In addition to quantifying biexciton lifetimes, we also measure the biexciton binding energy, which is around 10 meV, a value comparable to that of larger-sized CdSe QDs. The studies of early time carrier dynamics reveal extremely fast intraband cooling with time constants of ∼360−570 fs, that again are comparable to those in more traditional QDs. Finally, the measurements of carrier dynamics with excitation at high spectral energies do not show any signs of CM up to hv = 2.65Eg. The lack of CM, however, is not surprising as the expected CM threshold in studied perovskite QDs is around 3Eg, which is a consequence of similar electron and hole effective masses in these materials. Methods. Chemicals and Materials. Oleic acid (OA, 90%), oleylamine (OAm, 80−90%), Cs 2 CO 3 (99%), hexane (99.99%), PbI2 (99.999%), and PbBr2 (99.999%) were purchased from Aldrich. All chemicals were used as received without any further purification. Synthesis of Cs-Oleate. 0.8 g of Cs2CO3 was loaded into a mixture of 30 mL of octadecene and 2.5 mL of oleic acid and then heated to 200 °C until the white powder was completely dissolved. Then, the mixture was kept at 130 °C for 1 h under vacuum. Note that, during the synthesis of perovskite QDs, the temperature of Cs−oleate mixture should be kept at least at 130 °C to avoid precipitation. Synthesis of the Perovskite QDs. For the synthesis of the IQDs, Br-QDs, or mixed Br/I-QDs, 0.092 g of PbI2, or 0.072 g of PbBr2, or 0.046 g of PbI2 and 0.036 g of PbBr2, respectively, were added into a mixture of 5 mL of octadecene, 0.5 mL of OAm, and 0.5 mL of OA, and then heated to 120 °C for 30 min under vacuum. The temperature was then raised to 180 °C, followed by the rapid injection of 0.45 mL of Cs-oleate solution, and then the solution was rapidly cooled by the water bath. In order to make CsPbBr3 QDs of smaller sizes (6.3 and 8.1 nm), the injection temperature was set at 132 and 162 °C instead of 180 °C, respectively. The composition of the mixed anion CsPbBr1.5I1.5 sample is deduced from the molar ratio of the reactants, which is expected to be close to the actual composition of the final QDs.13 Size Characterization. The sizes of the CsPbX3 (X = I, Br) QDs were characterized with a transmission electron microscope (TEM, JEOL JEM 2010) operating at an accelerating voltage of 200 kV equipped with an energy-dispersive X-ray (EDX) spectrometer (Bruker Quantax). Samples for TEM characterization were prepared by placing several drops of a dilute nanocrystal solution onto a carbon-coated copper grid.

fact that all degenerate band-edge transitions are affected by the exciton−exciton interaction and thus contribute to the PA feature. On the other hand, a state-filling induced bleach arises not from all but only occupied states, i.e., only one electron and/or one hole state in the regime of the single-exciton occupancy realized under the condition of ⟨N⟩ ≪ 1 used in these measurements. Using the measured TA spectra (Figure 8a) and dynamics (Figure 8c), we obtain a/b ≈ 0.3. Based on this value and following the formalism in ref 71 applied to the situation of the 2-fold-degenerate band-edge states, we obtain that in the IQDs, ΔXX = 12 meV. A similar approach yields essentially the same value (ΔXX = 11 meV) for the mixed Br1.5I1.5-QDs. Both of the derived values are comparable to those observed previously for large size (>6 nm) CdSe QDs.71 Since the early time band-edge PA feature is eventually replaced by bleaching as a result of the buildup of the population of the band-edge states, its decay (τPA) provides a quantitative measure of the characteristic intraband cooling time. In fact, as was demonstrated in ref 17, τPA is directly related to the relaxation (cooling) time (τcool) between two adjacent band-edge states (1S and 1P in spherical particles studied in ref 17). Based on the decay of the PA feature (Figure 8c), τcool = 570 fs, pointing toward extremely fast, subpicosecond carrier cooling. The same time constant describes well the buildup of the band-edge bleach, validating its assignment to intraband relaxation. The analysis of time transients recorded for mixed Br1.5I1.5-QDs indicates even faster relaxation with τcool = 360 fs. The observed time scales of carrier cooling in perovskite QDs are similar to those observed previously for large CdSe39 and PbSe18 QDs. Thus, the conclusion on slower intraband relaxation in bulk perovskites compared to more traditional semiconductors does not seem to apply to the QD form of these materials. The exact mechanism for very fast, subpicosecond intraband relaxation in perovskite QDs requires further investigations. While the studied QDs have fairly large sizes, carrier relaxation in these structures cannot be bulk-like. Because of small effective masses (within 0.1−0.2m0 for both electrons and holes;12 m0 is a free electron mass), the spacing between the two lowest band-edge electronic states in these dots is large (150−200 meV), and specifically, is much greater than phonon energies (up to 20−30 meV in lead-halide perovskites and related materials).63,72−74 Thus, usual bulk-type relaxation by sequential emission of single phonons is not possible, which should, in principle, lead to slowed intraband cooling due to “phonon bottleneck”64,65 mentioned earlier. The measured relaxation, however, is extremely fast (subpicosecond time scale), suggesting the involvement of the mechanisms specific to quantum-confined systems,17,18,66−68 as discussed in the beginning of this section. Conclusions. We have conducted a comprehensive spectroscopic characterization of cesium−lead-halide perovskite QDs. We quantify several characteristics of this new class of materials including radiative lifetimes and absorption crosssections. These measurements suggest a significant dependence of the Kane energy on the halide identity (I, Br or their mixture), which is likely a consequence of a mixed s−p character of the valence band of Pb-halide perovskites. This is in contrast to the situation realized in traditional semiconductors with a purely s-type conduction and purely p-type valence band (e.g., group-IV, II−VI, and III−V), where the Kane energy is nearly composition independent. The 2359

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Letter

Nano Letters

SNSPD measurements was typically done using several samples taken from the same batch and prepared with identical concentrations. For example, for the SNSPD measurements of I-QDs at per-pulse fluences greater than 4 × 10 13 photons/cm2 (this corresponded to ⟨N⟩ of more than 1) and the 200 kHz repetition rate, the acquisition time required to obtain a decay trace with an acceptable noise level was 25 min. Starting with a fresh sample, we could only conduct 2 or 3 measurements of this type without inducing photodamage. The streak camera measurements had the shortest acquisition times (∼100 s per trace) and allowed for complete characterization of fluence-dependent carrier dynamics with a single sample. Under the same experimental conditions, CdSe and PbSe QDs could be exposed to laser light for at least 10 h without noticeable changes in their optical properties.

The perovskite QDs are found to be cubic in shape (Figure S1 of SI). The size (length of the cube edge) of the CsPbI3 QDs is measured to be 11.2 ± 0.7 nm (Figure S1a of SI) whereas under identical synthesis condition, the sizes of CsPbI1.5Br1.5 and CsPbBr3 QDs are 10.7 ± 1.1 nm (Figure S1c of SI) and 9.3 ± 0.9 nm (Figure S1d of SI), respectively. Br-QDs synthesized at lower temperatures have sizes of 8.1 ± 1.1 nm (Figure S1e of SI) and 6.3 ± 0.5 nm (Figure S1f of SI). Time-Resolved Photoluminescence (PL) Measurements. Time-resolved PL was measured using three different techniques. Streak camera Hamamatsu C10910 with temporal resolution of 10 ps (defined by the instrument response function, IRF) was used for simultaneous measurements of spectrally- and temporally resolved PL. The PL was excited using 50 fs, 1 kHz repetition rate, 400 nm pulses of the second harmonic of the fundamental 800 nm output of the regenerative Ti:sapphire amplifier (Spectra-Physics Spitfire). The excited spot had a diameter of 130 μm at the 1/e2 intensity level. Superconducting nanowire single-photon detector (SNSPD) described previously29 (IRF ≈ 50 ps) was used to monitor decays on longer time scales. The PL was excited using third harmonic (343 nm) of the Yb:KGW amplified laser system (Light Conversion Pharos) at the 200 kHz repetition rate. The excited spot diameter was 140 μm. Fourth harmonic of the same laser (258 nm wavelength, 75 μm excited spot diameter) was used in the CM study. To achieve better temporal resolution, we also applied the technique of ultrafast PL upconversion (uPL), in which the sample PL was gated with a time-delayed ultrashort pulse in a nonlinear crystal (beta barium borate, BBO) and the upconverted PL was detected at the sum frequency of the PL and the gate pulses.75 By using the compressed pulse output from the high-repetition-rate regenerative Ti:sapphire amplifier (Coherent RegA-9000), we were able to achieve time resolution of 300−500 fs when the PL was collected in the transmission mode (to avoid lengthening of the IRF due to a difference in the travel times of the PL from the front and the back sample surfaces to the nonlinear crystal). In these measurements, the PL from perovskite QDs was excited using 250 kHz repetition rate, 390 nm pulses (second harmonic of the fundamental 780 nm output). The diameter of the excited spot at the 1/e2 level was 50 μm. Transient Absorption (TA) Measurements. TA spectra and dynamics were recorded using a LabView-controlled homebuild setup in a standard pump−probe configuration with 400 nm, ∼150 fs pump pulses at a 1 kHz repetition rate (second harmonic output of a Ti:sapphire regenerative amplifier; Spectra-Physics Spitfire) and a broad-band, white light supercontinuum probe. The excited spot diameter was 650 μm at the 1/e2 level. TA measurements were performed on QD solutions with the optical density (OD) below 1 at the excitation wavelength. All of the measurements were conducted under oxygen-free and moisture-free conditions using airtight quartz cuvettes. The organic solvents used were dry and stored under argon. Sample preparation was done in inert atmosphere in a glovebox. Stability of the Perovskite QDs. Synthesized perovskite QDs showed lower stability compared to more traditional QDs based, e.g., on CdSe or PbSe. Even though the measurements were carried out under oxygen-free and moisture-free conditions, significant degradation of the samples at high excitation fluences was observed. A complete characterization of pump-fluence-dependent dynamics using TA, uPL, or

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.nanolett.5b05077. Derivation of radiative lifetimes from measured photoluminescence traces, carrier dynamics for excitation with high-energy photons in relation to carrier multiplication, degeneracy factors of band-edge states in CdSe and PbSe quantum dots, transmission electron microscopy images of studied perovskite QDs, additional measurements of absorption cross-sections, excitation-fluence-dependent photoluminescence spectra, and TA biexciton dynamics. (PDF)

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS These studies were supported by the Chemical Sciences, Biosciences and Geosciences Division, Office of Basic Energy Sciences, Office of Science, U.S. Department of Energy. S.G. was supported by a LANL Oppenheimer Distinguished Postdoctoral Fellowship.

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REFERENCES

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