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Dec 19, 2017 - methylammonium and formamidinium cations than analogous materials with ... Auger recombination of biexcitons is well-known in II−VI q...
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Letter Cite This: J. Phys. Chem. Lett. 2018, 9, 104−109

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Biexciton Auger Recombination Differs in Hybrid and Inorganic Halide Perovskite Quantum Dots Giles E. Eperon,*,†,‡ Erin Jedlicka,† and David S. Ginger*,† †

Department of Chemistry, University of Washington, Seattle, Washington 98105, United States Cavendish Laboratory, JJ Thomson Avenue, Cambridge CB3 0HE, United Kingdom

‡

S Supporting Information *

ABSTRACT: We use time-resolved photoluminescence measurements to determine the biexciton Auger recombination rate in both hybrid organic−inorganic and fully inorganic halide perovskite nanocrystals as a function of nanocrystal volume. We find that the volume scaling of the biexciton Auger rate in the hybrid perovskites, containing a polar organic A-site cation, is significantly shallower than in the fully inorganic Cs-based nanocrystals. As the nanocrystals become smaller, the Auger rate in the hybrid nanocrystals increases even less than expected, compared to the fully inorganic nanocrystals, which already show a shallower volume dependence than other material systems such as chalcogenide quantum dots. This finding suggests there may be differences in the strength of Coulombic interactions between the fully inorganic and hybrid perovskites, which may prove to be crucial in selecting materials to obtain the highest performing devices in the future, and hints that there could be something “special” about the hybrid materials.

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ultrafast time-resolved Kerr effect spectroscopy data that seem to provide evidence for more liquid-like dipolar screening motions on picosecond-time scales from perovskites with methylammonium and formamidinium cations than analogous materials with Cs+ cations. While these measurements have stimulated much theoretical work, the relative contributions of the organic cations in explaining the unusual photophysics of the lead halide perovskites remains an open question.12−14 Although the connections to device performance are even more speculative, the fact remains that, to date, the highest efficiency perovskite solar cells have all contained some fraction of organic cations on the A-site. Here, we use Auger recombination of biexcitons as a means to explore the role that organic cations may play in influencing Coulomb-mediated carrier dynamics in halide perovskites. Auger recombination of biexcitons is well-known in II−VI quantum dots, where the Auger rate increases rapidly with decreasing quantum dot size due to the relaxation of bulk momentum conservation rules, and increase in exciton−exciton Coulomb coupling as the nanocrystal volume is decreased.15 Recent experiments in all-inorganic CsPbBr3 quantum dots have reported Auger rates that are no slower than those in II− VI dots, although with an apparently weaker volume scaling term.16 In this work, we explore the possible role of the organic cations in screening Coulomb interactions in perovskites comparing Auger rates across size series for three different

alide perovskites, solution-processable semiconductors with an ABX3 lattice structure, have been the center of a great deal of research activity in recent years. This interest is due mainly to their rapid rise in solar cell power conversion efficiencies.1 The highest-performing perovskite solar cells, which have attained over 22% power conversion efficiency, incorporate organic A-site cations and inorganic B- and X-site metals and halides, respectively.2−5 In addition to their high efficiencies in photovoltaics, halide perovskites also exhibit a range of seemingly unusual transport and photophysical properties, ranging from the comparative ease at which samples with very low levels of nonradiative recombination can be prepared,6−8 to the slow intraband cooling of hot carriers photoexcited far above the band edge.9−11 Understanding the fundamental origins of these unusual properties is broadly important, not only for optimizing the performance of conventional lead halide perovskite solar cells, but for understanding the general design rules that might enable the synthesis of new materials with tailored control over their photophysical properties for application in hot carrier devices, photocatalysis, and nonlinear optics. One proposal put forward to explain the seemingly unusual hot carrier dynamics reported for halide perovskites is the formation of large polarons around charge carriers, which could result from both the soft lattice modes of the heavy B and X site ions, as well as the rapid reorientation of the dipolar A-site cations.9 Arguing for the importance of fast dynamics for dipolar organic A-site cations, Zhu and co-workers have used hot carrier photoluminescence to show that hot carriers cool more slowly in perovskites with dipolar A-site cations compared to those with Cs+ on the A site. They have also performed © XXXX American Chemical Society

Received: October 23, 2017 Accepted: December 15, 2017

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DOI: 10.1021/acs.jpclett.7b02805 J. Phys. Chem. Lett. 2018, 9, 104−109

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Figure 1. Fluence-dependent time-resolved PL for nanocrystals of 1000−2000 nm3 of the three compositions under study (a = MAPbI3, b = FAPbBr3, c = CsPbBr3). The samples are excited at 450 nm (a) or 365 nm (b,c) with 50 fs pulses.

Figure 2. Determination of biexciton lifetimes. (a) Long-time-normalized fluence dependent PL decays in MAPbI3 nanocrystals of 11 ± 4 nm diameter. (b) Isolated multiexciton component of the decays, obtained by subtracting the lowest pump fluence single-exciton dynamics normalized to the long-time PL at each fluence. Dashed lines show single-exponential fits to the data, for which the ⟨N⟩ < 1 decays are averaged to attain a biexciton lifetime, in this case 280 ± 50 ps. (c) Comparison of extracted multiexciton decays for similarly sized (∼1000 nm3) QDs of the three compositions under study, at fluence of ⟨N⟩ ∼0.5.

perovskite, and II−IV semiconductor quantum dots.16,19−21 Briefly, we measure the PL decays over the first 5 ns after excitation using a 10 ps-resolution streak camera, at excitation fluences over a range of approximately 1011−1015cm−3s−1. Each sample comprised a stirring dilute solution of nanocrystals in a sealed N2 atmosphere, and we excited them with a Ti:sapphire pulsed laser (50 fs pulses) tuned to an appropriate wavelength above the bandgap of the nanocrystal (365 nm for bromide perovskites, 450 nm for iodide perovskites). After determining the single-exciton decay rate at low fluence, we can then extract the excess early time decay rate associated with the multiexciton Auger processes and determine the Auger rate as a function of the average number of excitons excited per dot (⟨N⟩ ). Figure 1 shows typical fluence-dependent early time PL decays for 8−11 nm average diameter nanocrystals of the three compositions under study. The curves are labeled with the average number of excitons excited per quantum dot, ⟨N⟩ , using the absorption cross-section of the samples as described in the SI. First, we note that the decays for all three quantum dot compositions look qualitatively similar: at low fluences (⟨N⟩ ≪1), the decays follow the single-exponential behavior expected for an excitonic decay from a sample with high PLQY. The lifetime of these decays is long in comparison to the 5 ns time window measured here, consistent with literature reports of monoexponential lifetimes of 5−100 ns for perovskite quantum dots.16,22−24 When we increase the fluence to ⟨N⟩ ∼ 1 and higher, an additional fast (10s of ps) decay becomes evident in the PL dynamics, growing with increasing excitation

types of perovskite quantum dots: cesium lead bromide, formamidinium lead bromide, and methylammonium lead iodide (Figure 1A). We find that the organic-cation-containing hybrid perovskites exhibit a significantly weaker volume dependence of the biexciton Auger rate than Cs-based perovskites, which is consistent with the proposal that the organic cation may play a role in mediating carrier interactions on picosecond time scales. We find that for small enough nanocrystals, the Auger recombination rate is slower in the hybrid perovskite QDs compared to all-inorganic quantum dots. We fabricated size-controlled nanocrystal quantum dots of the inorganic halide perovskite CsPbBr3, and of the organiccontaining CH2(NH2)2PbBr3 (or FAPbBr3), and CH3NH3PbI3 (or MAPbI3), using literature methods or variations thereof, as described in the SI. For each cation, Cs, MA, and FA, we prepared a series of different sized particles, as confirmed by both photoluminescence (PL) and transmission electron microscopy (TEM) (SI Figures S1−3). The as-synthesized nanocrystals exhibited PLQEs of 50−90% (SI Table 1), consistent with previous reports.17,18 The QDs exhibit quantum confinement effects, consistent with exciton formation. More than one exciton can be excited in each QD, depending on the incident fluence and the decay time for each (multi)excitonic state. We extract the multiexciton Auger recombination rates by analyzing the early time PL dynamics as a function of excitation fluence, as has been commonly used in the literature for both 105

DOI: 10.1021/acs.jpclett.7b02805 J. Phys. Chem. Lett. 2018, 9, 104−109

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The Journal of Physical Chemistry Letters fluence, but collapsing back to the same monoexponential slope as the ⟨N⟩ ≪ 1 decays at long times. Such kinetics are consistent with a fast, multiexciton, nonradiative Auger recombination pathway, whereby one exciton decays by transferring its energy to (an)other excited carrier(s) in the QD.25 Since this is an exciton/exciton interaction, once the multiple excitons have decayed away via Auger processes, only a single exciton will remain, decaying with the same monoexpontial kinetics as for the < N > ≪1 fluences. To extract the component of the decays that is due to multiexciton interactions, we first subtract the single-exciton component off each decay to leave only the higher order excitonic contributions. To do this, we first normalize the decays to the long-time PL, as shown in Figure 2a. We observe that after completion of the short-time decays, the dynamics collapse to a single common decay curve, as expected for the long-lived single exciton component. The commonality of this long-time component allows us to subtract the normalized decay measured experimentally at the lowest fluence from the higher fluence decays, thus leaving the excess PL contribution that must be due to multiexciton decays. Figure 2b shows the isolated multiexciton components extracted in this manner. The data attained for fluences of ∼0.1 < ⟨N⟩ < 1, where some QDs are multiply excited and exhibit a biexciton component, fit a single exponential decay well, as shown by the fits (dashed lines) in Figure 2b. The fitted lifetime for these decays gives the biexciton lifetime (for fluences ∼0.1 < ⟨N⟩ < 1, it is effectively the same) at 280 ± 50 ps for the different excitation densities shown. At higher fluences, triexciton and higher order contributions begin to impact the multiexciton decays, which then exhibit a deviation from the biexciton decay rate (this can be seen beginning to take effect in the ⟨N⟩ = 1.05 plot in Figure 2b). We note that the magnitude of the biexciton signal should fit Poisson statistics, scaling as ⟨N⟩ 2; we verified that for ∼0.1 < ⟨N⟩ < ∼ 0.7 this is the case (see Figure S5). We can now compare biexciton lifetimes (τ2x) in the different nanocrystals studied. Figure 2c shows a comparison of biexciton decays at ⟨N⟩ ∼ 0.5 for nanocrystals of the three materials. It is immediately apparent that the Cs-based nanocrystals show a more rapid decay, with fits giving a biexciton lifetime (τ2x) of 74 ps, which stands in contrast to the organic-containing FAPbBr3 and MAPbI3 with τ2x = 227 and 198 ps, respectively. The value attained from the CsPbBr3 is in good agreement with the literature; the longer biexciton lifetime in the organic-containing QDs is noteworthy. The biexciton decay rate is well-known to increase with decreasing quantum dot volume.15 This dependence occurs both because the Auger process is mediated by carrier−carrier Coulomb interactions, which increase as the average distance between the carriers decreases like 1/R, and because of relaxation of momentum conservation requirements that manifests at smaller sizes, which scale like 1/R3. In chalcogenide QDs, the biexciton Auger rate dependence follows an almost linear volume scaling. However, in CsPbBr3 QDs, the scaling was shown to be shallower (less dependent on volume), following a τ2x proportional to V0.5 relation.16 Because the size-dependence of the Auger rate should depend on the Coulomb interactions between the excitons, and local symmetry, both of which can be affected by the organic cation, we next measured the size-dependence of the biexciton lifetime for each of the three quantum dot types studied herein

as a test of the hypothesized role of the organic cation on screening Coulomb interactions on fast time scales. In Figure 3, we show biexciton Auger lifetimes for all three materials as a function of average QD volume. Initially, we

Figure 3. Volume-dependent biexciton Auger lifetimes for CsPbBr3, FAPbBr3, and MAPbI3. Data from ref 16 is shown in gray, and the volume scaling of τ2xαV0.5 determined in that work is shown as a gray dashed line. Volume and its error bars are determined from the width of the PL peak as described in the SI, and for the lifetime errors are determined from the standard deviation of the decays at all suitable fluences (∼0.1 < ⟨N⟩ < ∼ 0.7). Dashed lines labeled VB(Br) and VB(I) represent the volume at which the radius of the nanoparticle is equal to the Bohr radius, for the Cs and FA lead bromide (VB(Br)), which have a similar reported Bohr radius, and MAPbI3 (VB(I)).

checked that our measurements on CsPbBr3 QDs were similar to those measured in the literature, and we find reasonable agreement with our data and that of Klimov and co-workers (plotted in gray) giving us confidence in our experimental method and analysis procedures. The volume scaling found by Klimov and co-workers, with which our data appears consistent, yields τ2x proportional to ∼V0.5, a shallower volume scaling than the “universal volume scaling” observed in other systems.15 This behavior is unusual, and the origin of it is unclear. Interestingly, Figure 3 shows that the size dependence for the MAPbI3 and FAPbBr3 dots both have a substantially weaker volume scaling than the purely inorganic CsPbBr3. While the trend for our CsPbBr3 dots may be slightly steeper than that reported by Klimov, if anything this only accentuates the difference in slopes. A result of this trend is that, at smaller sizes, the organic-containing perovskite quantum dots have much slower Auger rates, and at larger sizes, they approach similar rates as the Cs QDs. The measured biexciton lifetimes in QDs can be compared to the Auger coefficients in the bulk. Measurements of k3 for the bulk materials have been carried out using THz spectroscopy. k3 for MAPbI3 and FAPbBr3 have been measured as ∼1 × 10−28 cm6 s−1.26 An Auger coefficient for bulk CsPbBr3 has not been measured, but for bulk CsPbI3, k3 has been measured as ∼5 × 10−29 cm6 s−1, fairly similar to the organic-containing perovskites.27 This observation is consistent with our findings that the Auger rates in nanocrystals are similar in the hybrid and inorganic materials when confinement is less, with the discrepancy increasing with increased confinement. The effective k3 coefficient for an ensemble of QDs can be expressed as k3 = V2/8τ2x,16 if k3 is assumed to be volume independent. Extrapolating k3 for the nanocrystals gives k3 ∼ 10−29−10−30 cm6 s−1 for the larger nanocrystals of both 106

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induce high nonradiative recombination rates. Finally, the weak volume dependence of Auger rate in the organic-containing NCs could be evidence for the organic components forming a polaronic “screen”, mediated by rapid rotation of the polar organic, that attenuates the interactions of the excitons with each other, and with the particle surfaces.9 Elucidating the exact nature of the origin of this effect is beyond the scope of this study, but deserves further detailed investigation. The observation of a difference between inorganic and organic-containing perovskites, in properties not explored previously, provides one observation that there may be fundamental differences between the materials that are not yet understood, and that may somehow connect to the differences observed in device performances. Using time-resolved photoluminescence measurements, we have determined size-dependent biexciton Auger decay rates for organic-containing and all-inorganic perovskite nanoparticles. The inorganic perovskite nanocrystals show a shallower volume dependence than other previously explored materials, deviating from the common 1/V volume scaling, in agreement with previous reports, but we find that the organic-containing perovskite nanocrystals show an even shallower volume dependence, with Auger rate changing very little as the QDs become more confined. The implications of this shallow volume dependence are interesting. The fast Auger decay rates of the Cs-containing QDs may ultimately limit the efficiency of LEDs and lasers based on these materials, since in devices such as these that operate at high charge densities, Auger recombination becomes a key decay channel. The slower decay rates for the organiccontaining QDs at their smallest sizes, may mean that they could ultimately yield more efficient light-emitting devices under high excitation density conditions than conventional counterparts. Furthermore, this observation provides suggestive evidence, but does not prove that the organic components are playing a stronger role in slowing exciton−exciton interactions than the confinement is having on increasing the likelihood of such events. This finding demonstrates that there could be fundamental, and as yet not understood, differences between the inorganic and organic-containing perovskites that may go some way to rationalizing the discrepancies in their other properties, such as device performance.

inorganic and organic-containing, within an order of magnitude of the reported bulk rates.26 We highlight that, due to the weak volume scaling observed here, the Auger decay rate for even fairly small organic-cationcontaining perovskite nanocrystals is of a similar order as for the bulk, whereas for the Cs-containing nanocrystals, and indeed nanocrystals of other technologies, the rate is significantly higher. Previously, Padilha and co-workers showed that the volume scaling of the Auger rate showed a significant change above and below the Bohr radius.28 Here, all the nanocrystals measured have a radius greater than the Bohr radii extracted from literature,29,30 which we have plotted on the graph in Figure 3, and are thus all in the weak confinement regime, so we cannot attribute the differences in volume scaling between the different A-site cation nanocrystals to differences in Bohr radii. However, the weaker volume scaling we observe, if not the cation dependence, is broadly consistent with being in the weak confinement regime as pointed out by Padhila and coworkers.28 Yang and co-workers found that the Auger rates for bulk MAPbBr3 were ∼4× faster than for MAPbI3, and ascribed this result to differences in the exciton binding energy dominating over the expected reduction in Auger rate with an increasing bandgap. The absence of consensus regarding the true exciton binding energies in the literature makes it difficult to analyze our data with respect to this trend, but it seems unlikely that exciton binding energy would affect volume scaling so strongly, given that materials with different exciton binding energies exhibit similar volume scaling for metal chalcogenide quantum dots.30−32 We also note that in cases where binding energies have been reported for multiple perovskites, they are similar for materials with different A-site cations (and the same B and X site), so it appears unlikely to be able to explain the different volume scaling in different A-site materials.30 We thus consider additional explanations for the observation of a very shallow volume scaling in the organic-containing materials, all of which remain speculative at this time. First, the shallow volume scaling could arise due to a difference in band structure between the materials; however, it is known that the A site cation does not change band structure near the band-edge significantly, so this possibility seems unlikely.33 Second, there may, however, be some impact on the nature of allowed and disallowed transitions that occurs due to the breaking of symmetry when a dipolar organic is included in the lattice, which could change the strength of the biexciton Auger transitions, but one might expect such an effect to result in faster Auger rates for perovskites containing dipolar cations in the bulk, if the effect were purely due to the organic cation disorder/symmetry breaking. Third, differences in defect densities may dominate the volume-dependent dynamics.26 Since the Cs-based perovskites show a more volume-dependent Auger rate, this result may imply that there is a surface-based effect that impacts the Cs-based particles more; we speculate that this effect may be related to surface defect densities being greater in the Cs, or having a larger impact on Auger recombination. However, at present it is difficult to reconcile a defect-mediated picture with the high PLQEs of our samples. It has been suggested that transient localization of carriers could increase their interaction probability with an exciton, increasing the Auger rate.34 If this effect dominates, it could lead to high Auger rates with shallower volume dependence, such as we observe here, so this remains a possibility, if such traps did not

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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.jpclett.7b02805. Details of nanocrystal synthesis, experimental methods, nanocrystal characterization, and other supporting measurements (PDF)

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AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected] (G.E.E.). *E-mail: [email protected] (D.S.G.). ORCID

Giles E. Eperon: 0000-0001-9600-4847 David S. Ginger: 0000-0002-9759-5447 Notes

The authors declare no competing financial interest. 107

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ACKNOWLEDGMENTS G.E.E. is supported by the European Union’s Framework Programme for Research and Innovation Horizon 2020 (20142020) under the Marie Skłodowska-Curie Grant Agreement No. 699935. Part of this work was conducted at the Molecular Analysis Facility, a National Nanotechnology Coordinated Infrastructure site at the University of Washington, which is supported in part by the National Science Foundation (Grant ECC-1542101), the University of Washington, the Molecular Engineering & Sciences Institute, the Clean Energy Institute, and the National Institutes of Health. We thank Prof. Xiaosong Li, Hongbin Liu, and Mark Ziffer for helpful discussions, and Dr. Liam Bradshaw for assistance with the laser system.

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DOI: 10.1021/acs.jpclett.7b02805 J. Phys. Chem. Lett. 2018, 9, 104−109

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The Journal of Physical Chemistry Letters (30) Galkowski, K.; Mitioglu, A.; Miyata, A.; Plochocka, P.; Portugall, O.; Eperon, G. E.; Wang, J. T.-W.; Stergiopoulos, T.; Stranks, S. D.; Snaith, H. J.; et al. Determination of the Exciton Binding Energy and Effective Masses for Methylammonium and Formamidinium Lead TriHalide Perovskite Semiconductors. Energy Environ. Sci. 2016, 9, 962− 970. (31) Ziffer, M. E.; Mohammed, J. C.; Ginger, D. S. Electroabsorption Spectroscopy Measurements of the Exciton Binding Energy, Electron−Hole Reduced Effective Mass, and Band Gap in the Perovskite CH 3 NH 3 PbI 3. ACS Photonics 2016, 3, 1060−1068. (32) Protesescu, L.; Yakunin, S.; Bodnarchuk, M. I.; Krieg, F.; Caputo, R.; Hendon, C. H.; Yang, R. X.; Walsh, A.; Kovalenko, M. V. Nanocrystals of Cesium Lead Halide Perovskites (CsPbX 3, X = Cl, Br, and I): Novel Optoelectronic Materials Showing Bright Emission with Wide Color Gamut. Nano Lett. 2015, 15, 3692−3696. (33) Filip, M. R.; Eperon, G. E.; Snaith, H. J.; Giustino, F. Steric Engineering of Metal-Halide Perovskites with Tunable Optical Band Gaps. Nat. Commun. 2014, 5, 5757. (34) Cohn, A. W.; Schimpf, A. M.; Gunthardt, C. E.; Gamelin, D. R. Size-Dependent Trap-Assisted Auger Recombination in Semiconductor Nanocrystals. Nano Lett. 2013, 13, 1810−1815.

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DOI: 10.1021/acs.jpclett.7b02805 J. Phys. Chem. Lett. 2018, 9, 104−109