Long-Lived Hot Carriers in Formamidinium Lead Iodide Nanocrystals

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Long-Lived Hot Carriers in Formamidinium Lead Iodide Nanocrystals Paris Papagiorgis, Loredana Protesescu, Maksym V. Kovalenko, Andreas Othonos, and Grigorios Itskos J. Phys. Chem. C, Just Accepted Manuscript • Publication Date (Web): 15 May 2017 Downloaded from http://pubs.acs.org on May 17, 2017

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The Journal of Physical Chemistry

Long-Lived Hot Carriers in Formamidinium Lead Iodide Nanocrystals Paris Papagiorgis†, Loredana Protesescu‡,#, Maksym V. Kovalenko‡,#, Andreas Othonos‖ and Grigorios Itskos†,* †

Department of Physics, Experimental Condensed Matter Physics Laboratory, University of

Cyprus, Nicosia 1678, Cyprus ‡

Institute of Inorganic Chemistry, Department of Chemistry and Applied Biosciences, ETH

Zürich, CH-8093 Zürich, Switzerland #

Laboratory for Thin Films and Photovoltaics, Empa – Swiss Federal Laboratories for Materials

Science and Technology, Überlandstrasse 129, CH-8600 Dübendorf, Switzerland ‖

Department of Physics, Laboratory of Ultrafast Science, University of Cyprus, Nicosia 1678,

Cyprus

1 Environment ACS Paragon Plus


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ABSTRACT

The efficient harvesting of hot carrier energy in semiconductors is typically inhibited by their ultrafast thermalization process. Recently, highly promising experiments reported on the slowdown of the intraband relaxation in hybrid metal halide perovskites. In this work, we report on the presence of long-lived hot carriers in weakly-confined colloidal nanocrystals (NC) of formamidinium lead iodide perovskite (FAPbI3). The effect is apparent from the excitationdependent lengthening of the rise time and broadening of the high-energy tail of the transient absorption bleaching signal, yielding a retardation of the carrier relaxation by two orders of magnitude compared to typical timescales in colloidal semiconductor NCs. Three distinct cooling stages are observed, occurring at sub-ps, ~5 ps and ~40 ps timescales, which we attribute to scattering from LO-phonons, contribution from a hot phonon bottleneck effect and Auger heating, respectively. Thermalization appears also influenced by the FAPbI3 NCs purity, with trapping at unreacted precursor impurities further reducing the carrier energy loss rate.


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INTRODUCTION The performance of semiconductor photonic devices can be greatly improved by harvesting the excess kinetic energy of hot carriers and converting it into useful electrical work 1-3. Maintaining a substantial population of hot carriers for extended time, to allow for such an energy conversion to take place, requires the efficient retardation of thermalization processes that occur via interactions with phonons, other carriers and defects.4 Recently, an efficient slowdown of the hot carrier cooling has been reported in thin films of hybrid lead halide perovskites (APbI3), where A is either methylammonium, (MA), or formamidinium, (FA)

5-7

and attributed to a hot phonon

bottleneck effect that results in carrier re-heating by re-absorption of the optical phonons. Such a phenomenon is present in polar semiconductors such as GaAs

8-10

and appears significantly

pronounced in hybrid perovskites. Combined with their outstanding optoelectronic properties and defect-tolerant electronic structure

11-13

hybrid perovskites emerge as highly promising

materials for hot carrier absorber and emitter applications. The carrier relaxation can potentially be further prolonged in nanosized crystals of perovskites due to the absence of the continuum of electronic states that results in reduced carrier-phonon coupling.4,

14-15

Such high-quality quantum-sized perovskite NCs were recently produced via

colloidal chemistry routes. Fully inorganic CsPbX3 NCs (X=Cl, Br, I and combination thereof) received much attention owing to their outstanding light emitting properties.16-21 However, preliminary studies on NC colloids indicate a fast intraband relaxation18, due to efficient Auger dissipation of the carrier excess energy, similar to that previously reported for other colloidal NCs.22,23 The result is consistent with a recent study reporting on an order of magnitude slower carrier cooling in bulk crystals of hybrid perovskites compared to their inorganic counterparts.7 During the writing of this manuscript, the higher potential of hybrid perovskite NCs for hot



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carrier photonics, as compared to their fully inorganic cousins, was confirmed in a publication reporting on two orders of magnitude slower hot-carrier relaxation in MAPbBr3 NC films compared to their bulk-crystal film counterparts.24 Importantly the authors demonstrate that a significant fraction of the generated hot electrons can be efficiently extracted via fast transfer to an electron acceptor material, providing an avenue towards hot-carrier solar cells. Recently the facile synthesis of FAPbI3 NCs was demonstrated.25 Such NCs exhibit a lower energy gap in the red and near-infrared region and higher crystal chemical durability compared to the MA-based counterparts, making them ideal candidates for hot solar cell applications. In this work, we report transient absorption pump-probe experiments on FAPbI3 NCs and present spectral and temporal signatures of a long-lived hot carrier population. Furthermore, we provide experimental evidence that the slow carrier cooling is not solely a solid-state property of perovskite bulk5-7 or nanoscaled crystals24 but appears also in the colloidal state of such materials.

EXPERIMENTAL METHODS Chemicals used: PbI2 (Aldrich, 99%), octadecene (ODE, Aldrich, 90%), oleic acid (OA, Aldrich, 90%), oleylamine (OLA, Acros Organics, 80-90%), formamidinium acetate (Aldrich, 99%), hexamethyldisilazane (Aldrich, 99.9%), toluene (Aldrich, 99.9%), acetonitrile (SigmaAldrich, 99.9%). Synthesis of FAPbI3 NCs: PbI2 (0.172 g, 0.374 mmol) and ODE (10 mL) were added to a 25-mL round-bottom flask, dried for 1 h at 120 °C and mixed with OA (2 mL, vacuum-dried at 120 °C) and OLA (1 mL, vacuum-dried at 120 °C). When the PbI2 was fully dissolved and the mixture was cooled to 80 °C, the preheated FA-oleate precursor (4 mL, c=0.25 M of FA+) was injected. After 60 s of stirring, the solution was cooled to RT in a water bath. The crude solution was


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centrifuged for 5 min at 12100 rpm, the supernatant solution was discarded and the precipitate was redispersed in toluene (named unwashed NCs). Next, NCs were precipitated and redispersed by adding acetonitrile (volume ratio of toluene:acetonitrile=3:1) to destabilize the colloids, followed by centrifuging and dispersing the NCs in toluene again. Finally, the NCs were redispersed in toluene for characterization and film deposition. The Formamidinium oleate (FAoleate) precursor was prepared using formamidinium acetate (FA-acetate, 0.521 g, 5 mmol), dried octadecene (ODE, 16 mL) and OA (11.3 mmol, 4 mL) in a 50-mL round-bottom flask. This mixture was degassed for 10 min at RT and then heated under nitrogen to 130 °C, which yielded a clear solution. After drying for 30 min at 50 °C under vacuum, the FA-oleate was heated to 100 °C before use because it often precipitates when cooled to RT. Film deposition: Films were processed in ambient conditions, out of colloidal FAPbI3 NC solutions with concentration of ~25g/l in toluene. They were spin coated multiple times (up to 6 times) at 1000 rpm on quartz substrates, pre-treated by hexamethyldisilazane resulting in uniform films of ~150-200 nm thickness. Transient pump-probe absorption (TA): Measurements were carried out using two ultrafast amplifier systems generating pulses with FWHM of ~60 fs at 800 nm: (i) a mode-locked Ti:Sapphire amplifier (Spectra-Physics Spitfire) with repetition rate of 1 kHz and output energy of 1.3 mJ per pulse, or (ii) a high repetition rate Ti:Sapphire Amplifier (RegA 9050 – Coherent) running at 250kHz with an energy of 80nJ per pulse. Qualitatively similar results were obtained with each of the two systems, with better signal-to-noise ratio attained using the high repetition amplifier at the expense of a small sample heating effect, discussed in the manuscript text. A non-linear β-barium borate (BBO) crystal was used to frequency-double the amplifiers output at 400 nm (3.1 eV). A fraction of the fundamental beam was used to generate a super continuum



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light for probing in the 600-900 nm (~2.07-1.38 eV) range. After dispersion at the optical elements of the setup, the two systems exhibit an estimated temporal resolution of ~100-120 fs. Measurements were carried out using a typical pump-probe optical setup in a non collinear configuration where differential transmission was measured as a function of optical delay between the pump and the probe pulses. All measurements were performed in an inert nitrogen atmosphere. Absorption: Measurements were carried out in a Perkin Elmer Lamda 1050 spectrophotometer equipped with a three-detector module covering the 300-3000 nm spectral range. Photoluminescence: Steady-state photoluminescence (PL) was performed on a FluoroLog FL3 Horiba Jobin Yvon spectrofluorimeter. Excitation PL (PLE) experiments were carried out in the same setup, using the monochromator-filtered output of a 450W ozone-free Xe lamp. Timeresolved photoluminescence (TR-PL) was based on a time-correlated single photon counting (TCSPC) method and excited by a 375 nm NanoLED or a 633nm DeltaDiode laser diode operating at 100 KHz. All data were acquired with samples placed in vacuum (ca.10-5 mbar). Calculation of the average carrier occupancy per nanocrystal :

.

For films: < N > = . =

For solutions: < N > =

!" ∙$%&%'&() * +," / -.) ∙0∙345) 623

!" ∙$%&%'&() * +," / -.) ∙0 123


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with Einc the incident energy per laser pulse, Al the absorbance at the laser excitation energy, Eexc the energy of one laser photon, Rl the laser’s spot radius, d the film or vial thickness, Csol the solution concentration, mNC the average mass and VNC the average volume of one nanocrystal.

RESULTS AND DISCUSSION We have studied FAPbI3 NCs, ~10 nm in average size and nearly cubic in morphology [Figure 1(a)], synthesized as reported in our recent publication.25

Figure 1. (a) TEM image of the ~10 nm, nearly cubic FAPbI3 NCs under study. (b) Normalized PL, PLE and absorption spectra of spin-casted films of FAPbI3 NCs. The second derivative of the absorption is also displayed. (c) Time resolved PL spectra under 375nm (non-resonant) and 633nm (resonant) excitation and the average PL lifetime extracted from triple-exponential fits, in logarithmic scale.



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Absorption, photoluminescence emission (PL) and excitation (PLE) spectra of a spin-casted FAPbI3 NC film are displayed in Figure 1(b). The NC band-edge is estimated by the second derivative of the absorbance obtaining a value of ~765 nm (~1.62 eV), blue-shifted due to confinement by ~140 meV (~76 nm) compared to the bulk FAPbI3 (at 1.48 eV/838 nm).26 The bright luminescence, close resemblance of the absorption and PLE spectra, small Stokes shift of ~35 meV, and the long PL lifetime of ~65 ns, recorded under both quasi-resonant and nonresonant excitation, overall confirm the defect-tolerant and high quality of the synthesized FAPbI3 NCs [Figure 1(c)]. Carrier dynamics in such FAPbI3 NC films, were investigated by transient absorption (TA) pump-probe spectroscopy, using excitation at 3.1 eV while probing in the 1.4-2 eV range. Typical TA spectra at pump fluences of 80 µJ cm-2 and 10 µJ cm-2 that result in an average carrier occupancy per nanocrystal of ~2 (carrier density n~1.1*1018 cm3) and ~0.25 (n~1.4*1017 cm3), respectively are displayed in Figures 2(a) and 2(b). The spectra are dominated by a broad bleaching feature attributed to band edge state filling. At all excitation fluences, the bleaching feature shows a small time-dependent red-shift of ~35 meV. The source of the shift is unknown, however its insensitivity to the photoexcited carrier concentration, excludes bandgap renormalization as its origin. Importantly, the TA signal exhibits a fluence-dependent, high energy tail, characteristic of state filling by carriers with kinetic energies higher than the lattice temperature.5-7, 24 The high energy broadening persists at times equal or longer than 100 ps after the pump pulse, indicating a slowdown of the hot carrier relaxation by order(s) of magnitude compared to typical sub-ps cooling times measured in colloidal NCs.22-23, 27-28


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Figure 2. Transient absorption spectra at (a) high pump fluence (N~2) (b) low pump fluence (N~0.25). The steady-state absorption of the film is also displayed. (c) Extracted carrier temperatures versus delay time for different carrier densities.

Quantitative analysis is performed under the assumption that a quasi-equilibrium characterized by a Fermi-Dirac distribution is established soon after carrier excitation. The distribution of hot carriers with energies substantially larger than the quasi-Fermi EF level can be approximated by a Maxwell-Boltzmann function. The approximation is commonly used to extract the hot carrier temperatures in semiconductors with a continuum of energy states. For the weakly-confined NCs of our study, the validity of such an approach is justified by the small energy level spacing compared to the thermal energy kT, as extensively discussed by Mingjie L. et al 24 for perovskite NCs in a similar confinement regime. The establishment of this quasi-equilibrium in semiconductors such as GaAs occurs fast at timescales as short as 10 fs.29 In the NC films, the bleaching tail assumes a single-exponential form within 200 fs from the pump pulse, which



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defines the approximate time for the quasi-equilibrium formation. For longer times, the normalized TA signals are fitted by the following Maxwell-Boltzmann function: 789: = 7; ∗ =

&> ?@ AB

+ 7DEF

(1)

With I0 the tail point in which the bleaching intensity assumes half of its maximum value i.e. I0 = 0.5, and fitting parameters the carrier temperature Tc and the background IPIA that accounts for photoinduced absorption (PIA) appearing at energies higher than 1.8 eV. Model (1) produces good fits of all TA signals in the 0.2-530 ps range, shown superimposed to the raw data in Figures 2(a) and (b). The fits and the extracted temperatures appear weakly sensitive on the choice of I0 within a reasonable 0.6-0.3 range. On the other hand, a minimum fitted tail length of 0.2 eV is required to produce good single-exponential fits. Such observations agree with those produced via a thorough statistical analysis on similar fits on the TA data of bulk FAPbI3 crystals.5 The time-dependent temperatures are displayed in Figure 2(c) for NC carrier occupancies of ~0.25, 0.5 and 2, yielding values at 200 fs of ~1430 K, ~1740 K and ~2320 K, respectively. Carriers exhibit much higher temperatures at earlier times of 200 fs however the TA tails in such case acquire a non-exponential shape which indicate the inadequacy of model (1) fits to extract such values. All three curves are described by triple-exponentials of the following form: GH 8I: = G; + JK =

L

M N%

+ JO =

L

M N/

+ JP =

L

M NQ

(2)

The term T0 accounts for the background carrier temperature at a pump-probe delay of 530 ps. The output parameters of the fits are presented in Table S1. Interestingly the fits yield lifetimes that are nearly independent of pump intensity, with τ1 in the 0.25-0.5 ps range, τ2 of ~5 ps and τ3


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of ~40 ps, essentially defining three distinct cooling stages of the hot carriers. The relative weight of the three decays is fluence dependent as observed in Table S1, resulting in average cooling times of ~6, ~14 and ~16 ps for ~0.25, 0.5 and 2, respectively. At the lowest pump energy, carrier cooling is dominated by the sub-ps τ1 channel, with a fraction of the excess energy i.e. ~30%, dissipated via the substantially longer channels τ2 and τ3 effectively prolonging the cooling time by one order of magnitude. At higher pump intensities, the fast cooling stage rapidly quenches in favor of the decays τ2 and τ3, resulting in a further slow-down of the thermalization time by a factor of ~3. The background temperature T0 yielded by the fits, also increases with fluence, reaching a value as high as ~385 K at ~2. This increase of T0 above the lattice temperature is attributed to a small lattice heating by the pump pulses. Such heating was estimated to be in the 15-20 K range in pump probe experiments performed using similar pump energies in hybrid perovskite films 5 ; in our case a higher effect is observed due to the higher repetition of the pump laser used. The average cooling rate per carrier, J can be calculated as shown by Mingjie L. et al 24, by: W

P

P

R8GS , < U >: = − WX $O YZ GS * = − O YZ

W[B WX

(3)

The derived cooling rates versus Tc are graphed in Figure 3(a). Representative values at different temperatures for the three excitation regimes are also displayed in Table S2. At carrier excess energies higher than 70 meV (~800 K), the loss rate at ~0.25 assume values more than an order of magnitude larger to those produced at higher fluencies, as evidenced in Table S2, confirming the strong-dependence of the relaxation times on the carrier concentration. At lower carrier temperatures, the cooling rates rapidly quench, as typically observed in semiconductors,



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and become less sensitive to fluence, with the ~0.25 and 0.5 curves exhibiting comparable values, smaller by a factor of 3 to 4 compared to those of the ~2 regime.

Figure 3. (a) Average cooling rate per carrier versus carrier temperature, for three NC excitation regimes. (b) Normalized ground state bleaching TA curves and single exponential fits at early times, from FAPbI3 NC and CdSe NC spin-casted films. (c) Carrier density-dependence of the bleaching rise time from the two films, fitted by the allometric functions displayed in the graph.

The slow population build-up of the ground state core NC states, results in a characteristically long and power-dependent rise of the band-edge bleaching signal, as seen in Figure 3(b). The rise time, extracted by single exponential fits of the TA signal, provides another quantitative measure of the carrier cooling time. At low pump of ~0.25, the rise time assumes a value of ~250 fs that monotonically increases with power, and doubles at value of ~495 fs at ~2, as seen in Figure 3(c). Interestingly the derived relaxation times, closely match the time constants of the fast relaxation channel τ1 yielded by the Boltzmann fits of the TA high energy tail. The


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fluence dependence of the rise time is approximated by an empirical allometric function with an exponent of ~0.37. The graph, also contains bleaching rise times from a spin-casted film of weakly-confined CdSe NCs, measured under identical experimental conditions. Compared to the FAPbI3 NCs, significantly smaller rise times and a much weaker fluence dependence i.e. a fit exponent of ~0.14, is obtained, in accordance with the fast intraband relaxation reported in such NCs.22, 28 An even slower build-up of the bleaching signal is observed in solutions of FAPbI3 NCs, as seen in Figure 4. Purified solutions, were imposed to filtering and acetonitrile/toluene washing followed by redispersion in toluene that removes unreacted precursor products. The same processing step was employed before deposition of all studied films. For such NC solutions, the fluence-dependence of the bleaching rise time, displayed in Figure 4(c) is almost identical to that observed in Figure 3(c) for films, as quantified by the similar exponent of the power law fits. On the other hand, solutions that were intentionally not purified, were found to exhibit a consistently slower build-up of the TA signal and a systematic departure from the power law dependence at high pump energies.



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Figure 4. Early times bleaching signals for purified and unpurified FAPbI3 NC solutions at low (a) ~0.5 and (b) high ~4 carrier densities. Exponential fits of the rise signals are also displayed. (c) Rise times as a function of NC carrier population. The data are fitted by power law functions yielding the exponents displayed.

Based on the presented data, plausible interpretations for the origin of the three carrier cooling stages that effectively slow-down carrier thermalization in FAPbI3 NCs can be deduced. The initial cooling via the sub-ps τ1 channel, is attributed to early interactions of carriers with LOphonons that dominates carrier cooling in hybrid perovskites.5-7, 30 The spectral and temporal fits


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in Figures 1(c), 2(b) and 3(c) consistently indicate a 2-fold retardation of this relaxation channel, upon increasing the NC carrier density by a factor of ~8. The slow-down indicates the formation of an early hot quasi-equilibrium between the LO–phonons and the excited carriers. Channel τ2, that retards relaxation at timescales of ~5 ps, for excitations of ~0.5 or larger, is assigned to a buildup of a hot phonon population at later times, similar to that observed in bulk FAPbI3 crystals and attributed to a high phonon emission rate5 or upconversion of low energy acoustical phonons.7 The third cooling stage, occurs at significantly longer timescales of ~40 ps, and increases monotonically with power. The dynamics and fluence-dependence exactly match the Auger decay τ1 via which the TA bleaching signal is recovered. The TA kinetics are displayed in Figure S1 and discussed in Note S1 with the interpretation supported by recent work from references 18, 24, 33. Based on such evidence, the slow-down via the ~40 ps relaxation channels is attributed to Auger heating

31

of the NC carriers, in agreement with recent findings in

MAPbBr3 NC films.24 A fourth retardation channel, present in intentionally non-purified FAPbI3 solutions is assigned to hot carrier trapping at states above the NC gap, associated with unreacted precursor products. Carrier trapping can slow-down exciton cooling by order(s) of magnitude in colloidal NCs.32 Evidence for the presence of trap states is provided in Figure S2. Impure FAPbI3 NCs exhibit dissimilar absorption and PLE spectra at high energies and large Stokes shifts as displayed in Figure S2(a), which in combination with the long build-up of the PL transient signal and significantly longer PL lifetimes under non-resonant excitation, shown in Figure S2(c), indicate the presence of significant trapping during carrier relaxation to the band-edge states, unlike the case of purified material, where such trapping evidence is absent, as evidenced by Figures S2(b), (d).



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CONCLUSIONS Our studies indicate that depending on the excitation regime and material purity, carrier-lattice, carrier-carrier and carrier-defect interactions effectively slow down intraband relaxation by order(s) of magnitude in FAPbI3 NCs in both the solid and the colloidal state. Combined with the structural integrity, strong absorption and red-to-IR bandgap, FAPbI3 colloidal nanocrystals appear as highly promising candidates for applications in hot solar cells. Towards such goal, further studies are required to assess the potential of hot24 and thermalized34 carrier extraction from FAPbI3 NCs to appropriately engineered electron or hole acceptor materials.

ASSOCIATED CONTENT Supporting Information Table with extracted carrier cooling times, Table with average cooling rate per carrier, estimation of Auger recombination lifetime, and optical data comparison between purified and non-purified solutions of FAPbI3 NCs. AUTHOR INFORMATION Corresponding Author *E-mail: [email protected] Notes The authors declare no competing ﬁnancial interest.


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ACKNOWLEDGEMENTS M.V.K. acknowledges financial support from the European Union through the FP7 (ERC Starting Grant NANOSOLID, GA No. 306733) and from the Swiss Federal Commission for Technology and Innovation (CTI-No. 18614.1 PFNM-NM).

REFERENCES (1) Shah, J. Hot Carriers in Semiconductor Nanostructures, Physics and Applications. Academic Press, Inc, 1992. (2) Conibeer, G.; Guillemoles, J.; Yu, F.; Levard, H.. Advanced Concepts in Photovoltaics. Royal Society of Chemistry, 2014. 12. 379–424. (3) Ross, R., T; Nozik, A., J. Efficiency of Hot-Carrier Solar-Energy Converters. J. Appl. Phys. . 1982, 53, 3813–3818. (4) Nozik, A. J. Spectroscopy and Hot Electron Relaxation Dynamics in Semiconductor Quantum Wells and Quantum Dots. Annu. Rev. Phys. Chem. 2001, 52, 193-231. (5) Yang, Y.; Ostrowski, D. P.; France, R. M.; Zhu, K.; van de Lagemaat, J.; Luther, J. M.; Beard, M. C. Observation of a Hot-phonon Bottleneck in Lead-iodide Perovskites. Nat. Photonics. 2016 , 10, 53. (6) Price, M. B.; Butkus, J.; Jellicoe, T. C.; Sadhanala, A.; Briane, A.; Halpert, J. E.; Broch, K.; Hodgkiss, J. M.; Friend, R. H.; Deschler, F;. Hot-carrier Cooling and Photoinduced Refractive Index Changes in Organic–Inorganic Lead Halide Perovskites. Nat. Comm. 2015, 6, 8420. (7) Yang, J.; Wen, X; Xia, H.; Sheng, R.; Ma, O.; Kim, J.; Tapping, R; Harada, T; Kee, T. W.; Huang, F.; et al. Acoustic-Optical Phonon Up-Conversion and Hot-Phonon Bottleneck in LeadHalide Perovskites. Nat. Comm. 2017, 8, 14120. (8) Potz, W. Hot-Phonon Effects in Bulk GaAs. Phys. Rev. B. 1987, 36, 5016–5019. (9) Joshi, R. P.; Ferry, D. K. Hot-Phonon Effects and Interband Relaxation Processes in Photoexcited GaAs Quantum Wells. Phys. Rev. B. 1989, 39, 1180–1187. (10) Murdin, B.; Heiss, W.; Langerak, C.; Lee, S. Direct Observation of the LO Phonon Bottleneck in Wide GaAs/AlxGa1-xAs Quantum Wells. Phys. Rev. B. 1997, 55, 5171–5176. (11) Manser, J. S.; Christians, J. A.; Kamat, P. V. Intriguing Optoelectronic Properties of Metal Halide Perovskites. Chem. Rev. 2016, 116, 12956–13008.



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TOC GRAPHIC


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Figure 1. (a) TEM image of the ~10 nm, nearly cubic FAPbI3 NCs under study. (b) Normalized PL, PLE and absorption spectra of spin-casted films of FAPbI3 NCs. The second derivative of the absorption is also displayed. (c) Time resolved PL spectra under 375nm (non-resonant) and 633nm (resonant) excitation and the average PL lifetime extracted from triple-exponential fits, in logarithmic scale. 177x69mm (300 x 300 DPI)

ACS Paragon Plus Environment

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Figure 2. Transient absorption spectra at (a) high pump fluence (N~2) (b) low pump fluence (N~0.25). The steady-state absorption of the film is also displayed. (c) Extracted carrier temperatures versus delay time for different carrier densities. 177x80mm (300 x 300 DPI)



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Figure 3. (a) Average cooling rate per carrier versus carrier temperature, for three NC excitation regimes. (b) Normalized ground state bleaching TA curves and single exponential fits at early times, from FAPbI3 NC and CdSe NC spin-casted films. (c) Carrier density-dependence of the bleaching rise time from the two films, fitted by the allometric functions displayed in the graph. 177x62mm (300 x 300 DPI)


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Figure 4. Early times bleaching signals for purified and unpurified FAPbI3 NC solutions at low (a) ~0.5 and (b) high ~4 carrier densities. Exponential fits of the rise signals are also displayed. (c) Rise times as a function of NC carrier population. The data are fitted by power law functions yielding the exponents displayed. 177x136mm (300 x 300 DPI)



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TOC schematic 61x44mm (150 x 150 DPI)


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Long-Lived Hot Carriers in Formamidinium Lead Iodide Nanocrystals

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