Vibrational Probe of the Structural Origins of Slow Recombination in

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Vibrational Probe of the Structural Origins of Slow Recombination in Halide Perovskites Kyle T. Munson, Grayson S. Doucette, Eric R. Kennehan, John R. Swartzfager, and John B. Asbury J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.9b00555 • Publication Date (Web): 06 Mar 2019 Downloaded from http://pubs.acs.org on March 6, 2019

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The Journal of Physical Chemistry

Vibrational Probe of the Structural Origins of Slow Recombination in Halide Perovskites Kyle T. Munson,1 Grayson S. Doucette,2,3 Eric R. Kennehan,1 John R. Swartzfager,1 and John B. Asbury1,2* 1. Department of Chemistry, The Pennsylvania State University, University Park, PA 16802, USA. 2. Intercollege Materials Science and Engineering Program, The Pennsylvania State University, University Park, PA 16802, USA. 3. Department of Materials Science and Engineering, The Pennsylvania State University, University Park, PA 16802, USA.

*Corresponding Author: [email protected] Abstract We use time-resolved vibrational spectroscopy to probe the structural origins of the remarkably long charge recombination lifetimes of halide perovskites. The N-H bend vibrational mode of CH3NH3+ organic cations is coupled to the inorganic perovskite lattice and provides a means to examine the structural fluctuations of the crystalline lattice of CH3NH3PbI3 films. In the excited electronic state, the photogeneration of charge carriers causes the N-H bend vibrational dephasing dynamics to become very sensitive to temperature, revealing large changes in amplitude of the structural motions of the lattice within a narrow 150 to 300 K temperature range of the tetragonal phase. The larger amplitude fluctuations of the lattice at elevated temperatures inhibit delocalization of photogenerated charges, causing them to self-trap into large polarons with delocalization lengths that decrease more than 30% as the temperature increases from 150 to 300 K. This self-trapping into large polarons introduces energetic barriers that decrease the capture cross section for electron/hole recombination by an order of magnitude at elevated temperatures. These findings indicate that the slow charge recombination kinetics of halide perovskites underpinning many of their remarkable properties are traced to the formation of energetic barriers that hinder wavefunction overlap of oppositely charged carriers in large polaron states. The findings also suggest that substitution of different sized ions in halide perovskites can be used to tune the balance of charge transport versus charge recombination for photovoltaic or light emitting applications because ions influence the structural flexibility and therefore the selftrapping of charge carriers into large polarons.

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Introduction Halide perovskite solar cells have emerged as leading candidates to replace existing photovoltaic technologies due to their high photovoltaic performance (~ 23 %),1 and potential for lost-cost, high-throughput production.2-4 The remarkable properties of halide perovskites have also led to research focusing on light-emitting diodes,5 lasers,6-8 and photodetectors.9 The high photovoltaic performance of perovskite-based devices is mainly due to halide perovskites having long carrier diffusion lengths,10-12 small exciton binding energies,13 and high absorption coefficients. Despite rapid progress made in halide perovskite-based devices, a complete understanding of the material’s photo-excitation dynamics and the corresponding role of structural dynamics is still lacking.14-18 Furthermore, most of the lead-halide perovskites used to make stateof-the-art devices lack long-term stability,19-20 hindering their ability to be used in durable outdoor applications. Therefore, development of design rules about how the electronic properties of perovskites depend on their composition and structure are needed to facilitate the search for new materials that exhibit greater thermodynamic and chemical stability while still retaining the desirable characteristics of current state of the art materials. Many of the exciting properties of halide perovskites can be traced to their large charge carrier diffusion lengths,10-12 which are related to their long carrier lifetimes. For example, in the archetypal organo-halide perovskite, methylammonium lead iodide (CH3NH3PbI3), reported carrier recombination rates are comparable to traditional single-crystalline semiconductors despite CH3NH3PbI3 being processed from solution.21-23 Conversely, carrier mobilities in CH3NH3PbI3 are modest (~50-100 cm2/Vs) in comparison to single-crystalline semiconductors.2426

Materials with low to moderate charge-carrier mobilities are often compared to the Langevin

model.27 This model, which describes the recombination of freely diffusing charges in a


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continuous medium, assumes that charge carriers recombine with unit probability when they enter each other’s joint capture radius defined by the dielectric permittivity of the medium. Despite the simplicity of this model, many high performance photovoltaic materials deviate significantly from this behavior.28-36 Bimolecular recombination rates in CH3NH3PbI3 thin films have also been reported to be orders of magnitude slower than those predicted by the Langevin model.37-39 Several studies have suggested that charge carriers in CH3NH3PbI3 self-trap into spatially localized states known as polarons,40-46 which may explain this non-Langevin behavior. Furthermore, recent theoretical work has suggested that lattice distortions causing self-trapping into polarons may generate repulsive interactions between oppositely charged carriers that can produce energetic barriers to recombination.47 The connection between self-trapping of charge carriers into polarons and charge recombination has led to investigations of phonon dynamics in lead-halide perovskites because polarons arise from electron-phonon coupling. For example, Raman spectroscopy and neutron diffraction measurements have been used to show that the perovskite crystal lattice is highly anharmonic and undergoes large amplitude fluctuations at room temperature.48-50 Recent studies have revealed that low frequency phonon modes of the halide perovskite lattice are coupled to photogenerated charge carriers.41,

44,

51-53

In parallel, two-dimensional infrared (2DIR)

measurements have shown that organic cations are able to reorient within the inorganic framework.54-56 These observations suggest that electron-phonon coupling is strong in this class of material, in agreement with temperature-dependent carrier transport and photoluminescence linewidth measurements.15, 57-58 Being motivated by the need to investigate polaron formation in lead-halide perovskites as the putative origin of energetic barriers that slow charge recombination,47 we examined the structural dynamics of the perovskite lattice following photoexcitation using temperature dependent timeresolved infrared (TRIR) spectroscopy. Time-resolved infrared spectroscopy provides the opportunity to examine phonon and electronic dynamics in materials ranging from molecular 3 ACS Paragon Plus Environment


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solids59-61 and glasses62-64 to liquids65-68 and proteins.69-73 In systems where vibrational lineshapes are dynamically broadened, structural dynamics can be examined through temperature dependent measurements of the vibrational line widths. For example, structural dynamics in a supercooled chalcogenide glass were examined through temperature dependent measurements of the linewidths of the phonon modes.62 Temperature dependent broadening of the vibrational line shapes of OH stretch and bend modes were also used to examine phonon dynamics in crystalline formic acid as the temperature approached the melting point.61 Here, we report the ability to probe phonon dynamics in halide perovskites using TRIR spectroscopy and use the technique to identify the structural origins of large polaron formation in this class of material. This work builds on our initial publication,74 which focused on the role that large polarons have on the photoluminescence, charge transport and charge recombination properties of halide perovskites. We found that at elevated temperatures near 300 K, photogenerated charge carriers relax into large polaron states in CH3NH3PbI3 films with lower radiative quantum yields but longer recombination lifetimes. Conversely, at lower temperatures around 150 K we demonstrated that charge carriers exist predominately in delocalized free-carrier states with corresponding higher radiative quantum yields but faster recombination kinetics. In this work, we focus on the structural origins of the lattice fluctuations that give rise to these behaviors. We report temperature-dependent infrared absorption spectra of the N-H bend vibrational modes of CH3NH3PbI3 films and find that they vary little with temperature in their ground electronic states. However, in the presence of photogenerated charge carriers, these vibrational features exhibit significant temperature sensitivity, indicating substantial changes in the structural dynamics of the perovskite lattice in the presence of charge carriers as the temperature varies within a narrow range of the tetragonal phase of CH3NH3PbI3.75 The ability to probe structural dynamics through the vibrational modes of the perovskite allows us to investigate the role that lattice fluctuations have on large polaron formation. We demonstrate that lattice fluctuations inhibit charge carrier delocalization, which causes them to self-trap into large polarons preferentially at 4 ACS Paragon Plus Environment

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elevated temperatures. This self-trapping creates energetic barriers that reduce the capture cross-section for bimolecular charge recombination, leading to recombination rates that deviate from the Langevin limit by as much as five orders of magnitude at room temperature. The connection between temperature dependent lattice fluctuations and large polaron formation suggests that the interplay between carrier transport and charge recombination in halide perovskites may be optimized for specific photovoltaic or light emitting applications by substitution of ions that influence the underlying phonon dynamics and structural flexibility of the lattice.76

Experimental Methods Sample Preparation. For all FTIR and TRIR measurements, we prepared CaF2/mesoporous alumina substrates by spin-coating a 5 wt % solution of Al2O3 nanoparticles in isopropyl alcohol (6000 rpm, 30 sec) unto oxygen plasma cleaned CaF2. The resulting Al2O3/CaF2 films were then annealed at 450 oC for 1 hr. Before perovskite films were deposited, the substrates were again treated with oxygen plasma for 4 min to ensure complete removal of organic materials remaining from the nanoparticle solution. Perovskite films were prepared via a two-step deposition method previously described.1-2 In brief, a 0.75 M solution of PbCl2/DMSO was deposited onto the plasmacleaned Al2O3/CaF2 substrates by spin-coating at 3000 rpm for 20 sec. The resulting PbCl2 film was then annealed for 3 min at 40 oC and then 5 min at 100 oC. After the PbCl2 films were cooled to room temperature, they were flooded with a 0.08 M solution of methylammonium iodide in isopropyl alcohol for 20 sec before spinning at 4000 rpm for 20 sec. The resulting perovskite film was then annealed at 100 oC for 5 min. The perovskite films were then treated with a 5 mM solution of TPPO dissolved in chlorobenzene in order to remove surface defects. Photoluminescence and Visible Absorption Measurements. Photoluminescence (PL) measurements were performed with a visible to near-infrared transient absorption system (enVISion) from NanoSpec Instruments (State College, PA) in which the probe light source was blocked. The instrument consisted of a nanosecond pulsed Nd:YAG laser as the excitation 5 ACS Paragon Plus Environment


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source. After excitation at 532 nm and 500 nJ/cm2 excitation density per pulse, PL was collected and dispersed into a monochromator with lenses. The output was then focused onto a silicon photodiode, and the signal was captured with a digital oscilloscope. UV-Vis absorption spectra were collected with a Beckman DU 520 UV/Vis spectrometer. The spectra were background subtracted by the CaF2/Al2O3 substrate absorption. FTIR and TRIR Measurements. FTIR absorption spectra were acquired with a Digilab Varian FTS 7000 Series FTIR spectrometer equipped with a liquid N2 cooled MCT detector. All spectra were the average of 1000 scans between the spectral range of 1300-3500 cm-1. The spectra were background subtracted by the CaF2/Al2O3 substrate absorption and baseline corrected using a third order polynomial. TRIR spectroscopy experiments were performed using a mid-IR transient absorption spectrometer (inspIRe) from NanoSpec Instruments (State College, PA). The instrument consisted of a nanosecond Nd:YAG laser with second harmonic generation (532 nm), which was used to excite the perovskite films. The pulse energy density used for all TRIR experiments was 500 nJ/cm2 per pulse. The infrared probe light was generated with a MoSi2 infrared element. The resulting continuous-wave infrared probe radiation was focused on the sample, overlapped with the laser pulse, and then dispersed into a monochromator. The transient absorption signal was collected with a liquid N2 cooled mercury cadmium telluride photovoltaic detector. To perform temperature-dependent measurements, perovskite films were loaded into a gas-tight cryostat, which was evacuated for 10–15 min before the sample was exposed to the excitation source. Scanning Electron Microscopy. Scanning electron micrographs were acquired with an FEI Nova NanoSEM 630 Field emission scanning electron microscope with a landing energy of 4.00 keV. To determine the pathlength, b, of our perovskite films, we used cross-sectional SEM. For cross sectional images, perovskite films were deposited onto glass-mesoporous alumina substrates using identical procedures as those used for the CaF2 substrates. Samples were cooled to 77 K and cleaved across the center of the substrate. 6 ACS Paragon Plus Environment

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Results and Discussion Halide perovskite semiconductors used to fabricate state of the art devices are salts consisting of an inorganic framework (PbX3-) and a sublattice of A+ cations such as CH3NH3+, (CH)N2H4+, or Cs+.18 The inset of Figure 1A shows a representation of the unit cell for a typical 3D perovskite, methylammonium lead-iodide (CH3NH3PbI3). Unlike classical semiconductors such as Si and GaAs, the perovskite lattice is soft and polarizable.77 As a result, distortions of the inorganic framework (PbX3-) coupled with the movement of the A+ cations are thought to have a strong effect on the excited state dynamics of the material.40-44,

78-81

For example, many of the

microscopic properties observed in lead-halide perovskites such as ion migration45, 82-83 and defect tolerance,40, 84 are thought to arise from the material’s underlying structural dynamics. The electronic structure near the band edges of lead-halide perovskites such as CH3NH3PbI3 arises exclusively from the hybridization of the iodine and lead orbitals of the inorganic framework (PbI3-) with no contribution from the organic cation.17, 85-90 This hybridization causes CH3NH3PbI3 to be a direct bandgap semiconductor with a bandgap energy of ~ 1.65 eV (750 nm). The main panel of Figure 1A displays the band-edge optical absorption and photoluminescence spectra of a CH3NH3PbI3 film. The A+ cation serves primarily as a counterion for charge balance and stabilization of the 3D perovskite structure.91 However, organic A+ cations such as methylammonium (CH3NH3+) and formamidinium ((CH)N2H4+) can interact with the surrounding inorganic framework mainly via hydrogen bonding and ion-dipole interactions.92-93 As a result, it has been hypothesized that interactions between the A+ cation and the inorganic framework can have a strong effect on the electronic properties of the material.44-45, 76, 94 Figure 1B shows the formula of the methylammonium cation as well as the IR absorption spectrum of CH3NH3PbI3 from 1300-3500 cm-1. The main vibrational features observed in the



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Figure 1. (A) Visible absorption and photoluminescence spectra of a CH3NH3PbI3 film. The inset depicts the structure of PbI3– octahedral with a CH3NH3+ cation occupying the A-site of the lattice. (B) FTIR spectrum of a CH3NH3PbI3 film highlighting the vibrational features of the CH3NH3+ cation.

spectrum correspond to the symmetric and antisymmetric N-H bend modes (~1470 and 1591 cm1

) and the symmetric and antisymmetric N-H stretch modes (~3156 and 3200 cm-1) of the

molecular cation.92, 95 Polarization-resolved 2DIR spectroscopy has been used to examine the reorientation dynamics of the CH3NH3+ cation by monitoring the dynamics of the symmetric N-H bend mode at 1470 cm-1.56, 96-97 Here, the authors took advantage of the alignment of the transition dipole moment of this vibration with the C-N axis of the molecule. A similar method was recently applied to the C-N stretching mode of formadinium cations in lead iodide perovskites. 54 In both cases, the results suggest that at room temperature, the interactions between the inorganic 8 ACS Paragon Plus Environment

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framework and A+ sublattice are not strong enough to immobilize the organic cations, allowing them to rotate within the perovskite lattice on fast time scales. We note other studies investigating the rotational dynamics of organic cations in the perovskite lattice98-100 and a recent perspective in which these results have been discussed.97 With rare exception, the vibrational dynamics of organic cations reported in these studies were examined in the ground electronic state of the materials wherein no photogenerated charge carriers were present. In the excited state, theoretical calculations have shown that the local environment experienced by the organic cation differs significantly if the cation resides near a charge carrier.46, 78, 101 Thus, it remains unclear how to extrapolate the ground state dynamics obtained from such vibrational studies to understand the structural dynamics that give rise to large polaron formation, which involve the presence of charge carriers. To address this shortcoming, we photoexcited the bandgap of a prototypical halide perovskite film composed of CH3NH3PbI3 and examined the corresponding vibrational dynamics of CH3NH3+ cations in the excited electronic state of the material.74, 102 Figure 2A illustrates the absorption processes that occur in the ground and excited electronic states of a CH3NH3PbI3 film observed in the Fourier transform infrared (FTIR) absorption spectra and the excited state TRIR transient absorption measurements of the CH3NH3PbI3 films. The lower panel of Figure 2B depicts the FTIR spectrum of the symmetric N-H bend mode of CH3NH3+ cations in the film in its ground electronic state. The upper panel represents a TRIR transient absorption spectrum of the CH3NH3PbI3 film in the same spectral region that was measured 40  20 ns following pulsed optical excitation of the perovskite film at 532 nm. An excitation intensity of 500 nJ/cm2 with a corresponding carrier density of ~31016 cm–3 was used in these and all other TRIR measurements described in this report. The transient absorption spectrum represents an average of several time points between 20 and 60 ns time delay.



Figure 2. (A) Cartoon depiction of the absorption processes observed in ground state IR and TRIR spectroscopy. (B) TRIR spectrum of the excited state N-H bend vibration of a CH3NH3PbI3 film following 532 nm excitation. The vibration is superimposed on a large polaron absorption. (C) TRIR spectrum spanning the mid-IR spectral region that was collected at 30 ns following pulsed excitation at 532 nm. The spectra reveal the distinct absorption of large polarons. The gray shaded box highlights the N-H bend regions of CH3NH3+ ions in the film. The inset presents a 2D frequency-time surface plot that highlights the rapid time evolution of the broad polaron absorption feature. (D) Schematic diagram depicting the photoionization of large polarons to free-carrier continuum states. Arrows indicate the transitions appearing in the TRIR spectra. (Adapted from ref 126).

Excitation of the bandgap of a perovskite film produces excitons that have very small binding 10 ACS Paragon Plus Environment

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energies,13 leading to fast and efficient photogeneration of charge carriers. The resulting TRIR transient absorption spectrum measured on the nanosecond time scale reports the transient vibrational features of CH3NH3+ ions in the presence of the photogenerated charge carriers. The origins of the vibrational features and their associated electronic states are indicated by lines connecting the features in Figure 2B with the corresponding transitions in Figure 2A. The N-H bend vibrational feature depicted in Figure 2B is superimposed on a broad electronic transition, which spans the mid-infrared spectral region as depicted in the TRIR transient absorption spectrum in Figure 2C. This spectrum was measured at a 30  8 ns time delay following 532 nm excitation. The grey shaded box highlights the spectral region depicted in Figure 2B for comparison. The inset of Figure 2C presents a two-dimensional frequency-time surface plot of the TRIR transient absorption spectra in the region of the N-H bend vibrational mode. The decay of the vibrational feature synchronously with the broad electronic absorption is evident, which is in detail in the Supporting Information. In our initial report, we assigned the broad electronic transition to that of large polarons that form due to the presence of photogenerated charges.74 Emin developed a description of large polarons in which nuclear distortions create polarization clouds that self-trap the carriers.103 If the polarization clouds are much larger than the lattice spacing of the crystal, then the self-trapped carriers are considered large polarons. As we show below, this is the case for polarons that form in halide perovskites. The self-trapping energy of a large polaron –Ep = TC + UC + UN is a result of several interactions that are described by a hydrogenic model. According to Emin,103 localization of the carrier into a large polaron increases its kinetic energy by an amount TC = Ep and increases the potential energy of the nuclei by an amount UN = 2Ep. The attraction of the charge carrier with its oppositely charged polarization cloud is described as UC = –4Ep so that the total self-trapping energy is –Ep. Figure 2D illustrates the potential energy well in which charge carriers become self-trapped in large polarons. Charge carriers in large polarons states can absorb photons, causing them to 11 ACS Paragon Plus Environment


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be photoionized back into band states of the material. The abrupt increase of the density of states at the band edge creates a sharp absorption onset at a transition energy E = 3Ep as illustrated by the dotted red vertical arrow in Figure 2C.74 The transition occurs at three times the selftrapping energy because the interaction of the electronic and nuclear coordinates during the transition is described by the Franck-Condon principle. This is because photoionization of trapped carriers by absorption of mid-IR photons occurs on time scales that are faster than nuclear motion. Therefore, both the self-trapping energy Ep and the potential energy of the nuclear distortions UN = 2Ep must be overcome103 during the optical transition that photoionizes charge carriers from large polarons. The absorption maximum at ~1200 cm-1 (~0.15 eV) in Figure 2C indicates that large polarons have self-trapping energy around 0.05 eV in CH3NH3PbI3 films. A Drude-like absorption tail is observed at higher transition energies. This absorption tail results from photoionization of self-trapped carriers into high energy band states as illustrated by the solid vertical arrow in Figure 2D. The decrease of the transient absorption amplitude at higher transition energies results from the need to involve more phonons in the optical transition in order to maintain energy and momentum conservation through the process.103 We note that the vibrational feature depicted in the TRIR spectrum in Figure 2B arises from perturbations of the symmetric N-H bend mode caused by the presence of photogenerated charge carriers in the perovskite film rather than from a ground state bleach signal. Ground state bleach signals were also not observed in TRIR measurements of the CN stretch mode54 of (CH)N2H4PbI3 and the N-H stretch mode of CH3NH3PbI3.102 Ground state bleaching refers to the decrease in absorption of CH3NH3+ cations in the ground electronic state of the material due to photoexcitation of charge carriers as indicated in Figure 2A. As such, a ground state bleach signal would report the behavior of the ground state of the material and would carry a negative sign in the TRIR transient absorption spectrum. From the excitation intensity used for the TRIR measurements (500 nJ/cm2 at 532 nm) and the FTIR spectra of the N-H bend mode, the ground state bleach signal should have an amplitude of ~200 nanoO.D., which is near the limit of detection of the TRIR 12 ACS Paragon Plus Environment

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spectrometer used in this work. In comparison, the transient absorption feature of the N-H bend in the electronic excited state is more than two orders of magnitude larger (~30 μO.D.) than the bleach signal. This coupling of nuclear motion of the perovskite lattice and vibrational modes of the organic cations suggested the opportunity to probe the structural origins of large polaron formation in the CH3NH3PbI3 halide perovskite films through the vibrational modes of CH3NH3+ cations. Control of temperature provides a facile way to tune the occupation of phonons in crystalline solids. Therefore, we undertook a temperature dependent study of the vibrational features of CH3NH3+ cations in both the ground and excited electronic states of the CH3NH3PbI3 halide perovskite films within the temperature range of the tetragonal phase of the material.75 Figure 3A depicts ground state FTIR absorption spectra of a CH3NH3PbI3 film measured at different temperatures in the region of the N-H bend vibrational mode. The data reveal little change in vibrational frequency or line width within the 190 – 310 K temperature range, indicating that changes in the occupation of phonon modes within this temperature window had little effect on the vibrational modes or their dephasing dynamics in the ground electronic state. For comparison, TRIR transient absorption spectra measured at the same temperatures and 30  8 ns following optical excitation of a CH3NH3PbI3 film at 532 nm are depicted in Figure 3B in the region of the N-H bend vibrational mode. The transient vibrational features are superimposed on the large polaron electronic transition as illustrated in Figure 2C. The spectra have not been offset nor have they been normalized. The amplitude of the broad absorption offset varies significantly with temperature, which has been discussed previously.74 This absorption offset arises from the temperature-dependent localization of charge carriers as described below. Unlike the FTIR spectra of the ground electronic state, both the center frequency and line width of the N-H bend vibrational mode change markedly with temperature in the TRIR spectra of the CH3NH3PbI3 film in the presence of charge carriers. This indicates that changes in phonon



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Figure 3. Comparison of (A) FTIR spectra and (B) TRIR spectra of a CH3NH3PbI3 perovskite film measured at a variety of temperatures in the region of the N-H bend vibrational mode 30  8 ns following 532 nm excitation. The FTIR spectra reflect the electronic ground state of the halide perovskite and demonstrate negligible influence of temperature on the electronic and vibrational properties of the film. In contrast, the TRIR spectra reveal significant changes in vibrational frequency and line width of the N-H bend as the thermal occupation of phonons changes with temperature within the tetragonal phase.

occupation at different temperatures has a pronounced impact on the electronic and vibrational coordinates of the material in its excited electronic state that are not reflected in the properties of the ground electronic state. Comparison of the center frequencies of the N-H bend vibrational features in the ground state FTIR and in the TRIR transient absorption spectra in Figure 3A and Figure 3B reveals that the


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N-H bend shifts to higher frequency by ~10 cm-1 in the presence of photogenerated charge carriers. We recall that the CH3NH3+ cations interact with the inorganic framework mainly via ionion, hydrogen bonding and ion-dipole interactions and that the band edge states have no contribution from the organic cations.17,

85-90

When these hydrogen bonding and ion-dipole

interactions weaken, the symmetric N-H bend mode shifts to higher frequency.92-93 Therefore, the blue-shift of the N-H bend mode suggests a weakening of the interactions between CH3NH3+ and the inorganic framework in the presence of charge carriers. Prior work also observed similar vibrational dynamics in the N-H stretch region (~ 3200 cm-1), which were thought to originate from fluctuations of the perovskite lattice in the presence of charge carriers.102 Additionally, TRIR spectroscopy was used to observe vibrational dynamics of formamidinium ions in a (CH)N2H4PbI3 film by probing the CN stretch mode of the (CH)N2H4+ cations.54 Those results also showed that the excited state mode of the formamidinium cation is blue-shifted relative to the ground state vibration, implying that both methylammonium and foramidinium cations respond to the presence of charge carriers in a similar manner. In addition to interactions between the methylammonium cation and the inorganic framework of the perovskite lattice, it is possible that internal electric fields associated with the presence of photogenerated charge carriers could cause a Stark shift the NH bend. While such Stark effects do not typically result in orders of magnitude enhancements of the transition dipole moment, it would be interesting to explore this possibility using mid-Infrared electro-absorption measurements. Figure 4A represents transient vibrational spectra of the N-H bend of CH3NH3+ cations in the electronic excited state of a CH3NH3PbI3 film that were obtained by subtracting the best fit of the broad absorption offsets from the TRIR transient absorption spectra appearing in Figure 3B. Transient vibrational spectra measured at 310 and 190 K are compared to the ground state infrared absorption spectrum reproduced from the 190 K spectrum appearing in Figure 3A. The data highlight the temperature dependence of the center frequency of the N-H bend in the excited electronic state. Furthermore, the transient vibrational features were fit with Lorentzian functions 15 ACS Paragon Plus Environment


Figure 4. (A) Baseline-corrected TRIR spectra for a CH3NH3PbI3 film collected at 310 and 190 K measured 30  8 ns following 532 nm excitation. The smooth curves through the data represent the Lorentzian functions used to quantify the center frequency and full width at half maximum of the vibrational features. The FTIR spectrum of the CH3NH3PbI3 film measured at 190 K is included for reference. (B) TRIR spectra of large polarons measured in a CH3NH3PbI3 film at different temperatures and at 30  8 ns time delay after photoexcitation. The spectra have been normalized to facilitate comparison of their shapes. The curves through the data represent best fits using the large polaron model developed by Emin. (C) The delocalization lengths of large polarons obtained from fitting the TRIR spectra are compared with the vibrational dephasing times of the N-H bend vibrations measured at different temperatures.

to quantify the changes in the line width of the N-H bend. The data demonstrate a 50% increase 16 ACS Paragon Plus Environment

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of the line width from 27 to nearly 41 cm-1 in the electronic excited state as the temperature increased from 190 to 310 K. An uncertainty limit in the full width at half maximum of 2 cm-1 is estimated from analysis of the data. The temperature dependence of the N-H bend vibrational line width in the electronic excited state is not a result of increased static heterogeneity of the perovskite, for such changes would be reflected in the spectra of the ground electronic state (Figure 3A). Instead, the transient vibrational spectra indicate faster vibrational dephasing of the N-H bend at elevated temperatures in the excited electronic state. Because the N-H vibrational mode is coupled to the nuclear coordinates of the inorganic lattice via hydrogen bonding and iondipole interactions,92-93 the faster vibrational dephasing dynamics reveal larger amplitude and possibly higher frequency structural fluctuations of the perovskite lattice at higher temperatures in the presence of photogenerated charge carriers. We considered the nature of the coupling that leads to enhancement of the N-H bend and the corresponding temperature dependence vibrational dephasing dynamics. In materials with strong electron-phonon coupling, vibrational features can be strongly coupled to the electronic and vibronic states involved in polaron formation.104-106 The transient vibrational spectra reveal that it is the symmetric bend at 1470 cm-1 that is selectively enhanced by coupling to the electronic transition, but the antisymmetric bend at 1590 cm-1 is not enhanced. This indicates that the nature of the coupling is highly directional. The symmetric bend transition dipole moment is directed along the C-N bond axis, while that of the antisymmetric bend is perpendicular to it. The hydrogen bonding interactions between the methylammonium groups and the surrounding inorganic lattice are more directional in comparison to the ion-dipole or ion-ion interactions. Consequently, we believe it is the ability of the methylammonium groups to hydrogen bond that leads to the strong coupling and oscillator strength borrowing. Furthermore, we note that the symmetric N-H bend should be most strongly coupled to elongation of the Pb-I bonds in the lattice, and preferential coupling of this mode to the lattice is consistent with the pronounced weakening of the Pb-I bonds



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that is indicated by the strong temperature dependence of the dephasing dynamics of the N-H bend. We note that the enhancement of the N-H stretch (3200 cm-1) oscillator strength is smaller in comparison to the enhancement of the bend (1470 cm-1). It is likely that both have similar wavefunction overlap with the electronic and vibronic states involved in polaron formation. But, the energy difference between the stretch and polaron absorption peak (1200 cm-1) is ten-fold larger in comparison to the bend. This leads to reduced coupling, which is observed as reduced enhancement of the stretch mode We correlated the structural fluctuations of the perovskite lattice reported by the vibrational dephasing dynamics of the N-H bend mode with the delocalization length of large polarons that form in the CH3NH3PbI3 perovskite film as a function of temperature. We could do this because the shapes of the large polaron absorption spectra provide information about their delocalization lengths.103 Referring to Figure 2D, the wavevector k of the band state accessed by photoionization of a self-trapped charge carrier back into the band by a photon with energy ħ𝜔 that is greater than three times the self-trapping energy 3Ep is given by the expression103

𝑘 = √(2𝑚(ħ𝜔 − 3𝐸𝑝 )/ ħ

(1)

where m is the effective mass of the charge carrier. In his development of the large polaron model, Emin used hydrogenic wavefunctions to describe the large polaron states and considered the electronic overlap of these states with free carrier states in the bands.103 This led to an expression for the frequency dependent absorption coefficient  for a given density of large polarons np

 𝑛𝑝

=

128𝜋𝑒 2

3𝑚𝜔𝑐

+

(𝑘𝑅)3 [1+(𝑘𝑅)2 ]4

(2)

In this expression, c is the speed of light and e the elementary charge. The wavevector k of the final band state accessed by absorption of a photon and the delocalization length of the original large polaron R determine the shape of the large polaron spectrum above the absorption onset


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at transition energies E > 3Ep. Therefore, Equations 1 and 2 can be used to fit the experimental large polaron spectra at different temperatures to extract their corresponding delocalization lengths. Figure 4B represents TRIR transient infrared absorption spectra of a CH3NH3PbI3 perovskite film measured at different temperatures and 30 ± 8 ns time delay following optical excitation at 532 nm. The spectra were normalized to facilitate quantitative comparison of their shapes at frequencies greater than the absorption maximum. Equations 1 and 2 were used to fit the transient spectra to extract the delocalization length of the large polarons at each temperature. The smooth curves overlaid on the data (circles) indicate the best fit curves. The corresponding best fit parameters appear in Table 1. To quantify the delocalization lengths of the large polarons, it is necessary to have an estimate of the effective masses of the charge carriers. Recent computations have suggested a value of of ~0.2 me,41 which we used to estimate the variation in large radii over this temperature range. Figure 4C depicts the variation of delocalization lengths we obtained from the best fits of the large polaron absorption spectra plotted versus the temperature at which the measurements were made. We find a variation of delocalization length from ~13 nm at 150 K to ~ 9 nm at 310 K. The error bars in Figure 4C are determined from the uncertainty limits of the least squares routine used to fit the data using Equations 1 and 2. Furthermore, we compared the variation of the vibrational dephasing dynamics with the large polaron delocalization lengths to establish whether the structural dynamics that cause charge carriers to localize into large polarons are correlated with the vibrational dynamics of the organic cations. Figure 4C compares the temperature dependence of the polaron delocalization lengths with the corresponding variation of the vibrational dephasing times obtained from the inverse of the line widths of the N-H bend vibrational modes in the excited electronic state of the CH3NH3PbI3 film. The quantitative correlation between the vibrational dynamics and polaron delocalization



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suggests that the larger amplitude and possibly higher frequency fluctuations of the ionic lattice causing faster dephasing also cause the decreased the delocalization lengths of large polarons.

Table 1. TRIR spectra line width fitting parameters. List of the fitting parameters for the spectral fits in Figure 4 in the main text. Temperature (K) 150 190 230 270 310

Delocalization Length (nm) 13.2 ± 0.8 11.7 ± 0.4 10.6 ± 0.2 9.4 ± 0.1 9.1 ± 0.2

Dephasing Time (ps) N/A 1.24 ± 0.9 1.05 ± 0.7 0.90 ± 0.5 0.82 ± 0.5

We next investigated the influence that increased lattice fluctuations and localization of charge carriers have on recombination processes in CH3NH3PbI3 perovskite films. The large polaron absorption signal can be used to measure charge recombination kinetics because its intensity is proportional to the density of photogenerated charge carriers in the perovskite film. Following their formation, charge carriers diffuse through the material until they relax to the ground state via charge recombination. The recombination of two oppositely charged polarons is a bimolecular process that depends on their capture cross section and their diffusivity through the material.31-32 Consequently, the polaron recombination process should depend sensitively on the delocalization length of polarons, the structural fluctuations of the perovskite lattice and the mobility of charge carriers. To determine the bimolecular recombination coefficient of charge carriers within our perovskite film, we adapted a method used to describe other bimolecular annihilation processes.107-112 In brief, the recombination of two oppositely charged polarons can be approximated using a simplified 2nd order bimolecular rate expression adapted to include the Beer-Lambert law: 𝛼𝑏 ∆𝐴

=

𝛼𝑏 ∆𝐴0

+ 𝑘𝑏𝑖 𝑒𝑥𝑝 𝑡

(3) 20

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where ∆A is the large polaron absorption signal, ΔA0 is the large polaron absorption signal at the time origin, t is time delay following the excitation pulse, kbiexp is the bimolecular recombination coefficient,  is the molar extinction coefficient of the polaron absorption, and b is pathlength.111 This expression differs slightly from the form used to fit triplet-triplet annihilation kinetics in pentacene derivatives.111-112 This is because triplet-triplet annihilation often leaves one triplet remaining after the annihilation event, while electron-hole recombination eliminates both carriers. From this expression, the bimolecular recombination coefficient of polarons within our perovskite film can be determined directly from the slope of a linear fit to the transient absorption data plotted as b/ΔA vs. t. We note that the pathlength of our sample was found to be ~ 300 nm using crosssectional SEM imaging (Figure S1). Additionally, we estimated the relative extinction coefficient of the large polaron absorption signal using excitation density-dependent TRIR measurements (Figure S4). A detailed description of the methodology used to determine the relative extinction coefficient is given in the Supporting Information. Figure 5A depicts infrared transient absorption spectra measured in a CH3NH3PbI3 film at 300 K at several time delays between 30 ns and 1 s following pulsed excitation at 532 nm using the same 500 nJ/cm2 excitation intensity as described above. The inset of Figure 5A represents the polaron absorption decay kinetics measured at 190 and 300 K and plotted as b/ΔA versus time t. In this representation, bimolecular decay processes exhibit a linear dependence on time, as indicated by Equation 3. To determine kbiexp for each temperature, we fit the data with linear functions. The slopes of these functions directly provide the bimolecular recombination coefficients, which are tabulated in Table 2. From the fitting procedure, we obtained bimolecular recombination rate constants varying between 5.2 X 10-9 cm3s-1 and 1.6 X 10-10 cm3s-1 at 190 and 300 K respectively. Uncertainty limits of ± 10% were determined from the fitting procedures Figure 5B summarizes the variation of bimolecular recombination coefficients obtained from the linear fits versus the corresponding temperatures of the measurements. We note that the



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Figure 5. (A) Infrared transient absorption spectra of a CH3NH3PbI3 film measured at 300 K at several time delays from 30 ns to 1 s. Inset: Plot of b/ΔA versus time t for polaron decay kinetics measured at 190 and 300 K, highlighting the bimolecular behavior of polarons within the CH 3NH3PbI3 film. The grey shaded region in the main panel indicates the frequency region of the spectra that was integrated to obtain the kinetics traces. (B) Experimentally determined bimolecular recombination coefficients obtained from analysis of the polaron absorption decay kinetics. The line at the top of the figure indicates the factor of two change in recombination coefficient expected from the temperature dependence of the carrier mobility. The blue dotted line serves as a guide to the eye. (C) Depiction of the influence of carrier localization into large polarons on charge recombination at higher temperatures. Fluctuations of the perovskite lattice localize charge carriers into large polarons, which introduces energetic barriers and reduces electron-hole wavefunction overlap, both of which slow charge recombination.

coefficients are independent of excitation density because the model properly accounts for the 22 ACS Paragon Plus Environment

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bimolecular recombination process (see Supporting Information). This is because the bimolecular rate law describes the rate of decay as proportional to the square of the carrier population, which accounts for the influence that differences in carrier population have on the observed decay of the signal. Therefore, the recombination coefficients obtained from analysis of the data using a bimolecular rate law are independent of the initial carrier concentration. None the less, we used the same excitation intensities across the range of temperatures to eliminate the potential for experimental artifacts that might complicate the analysis. Therefore, the recombination coefficients measured at different temperatures can be compared quantitatively. The comparison reveals more than an order of magnitude decrease of the charge recombination coefficient of the CH3NH3PbI3 perovskite film as the temperature increased from 190 to 300 K. We note that this increase is slightly greater than the 8-fold change we reported earlier.74 This is because our earlier report approximated the recombination kinetics using biexponential decay functions that did not fully describe the longer-time behavior of the recombination process. Modeling the data using Equation 3 allowed us to more precisely capture the time dependence of the recombination process, revealing a 30-fold change in the recombination coefficients as the temperature increased from 190 to 300 K. The decrease of the bimolecular recombination coefficient with increasing temperature observed here could arise from the temperature dependence of charge-carrier mobility or from Table 2. TRIR decay kinetics fitting parameters. List of the fitting parameters for the biexponential fits in Figure 5A. Temperature (K)

kbiexp (cm3s-1)

kbiLangevin (cm3s-1)

Predicted μ (cm2s-1)

300

(1.6 ± .2) X 10-10

2.8 X 10-5

100

270

(2.9 ± .1) X 10-10

3.0 X 10-5

110

240

(1.1 ± .1) X 10-9

3.3 X 10-5

120

210

(3.4 ± .3) X 10-9

3.6 X 10-5

130

190

(5.2 ± .4) X 10-9

4.0 X 10-5

140



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changes of the carrier capture cross-section describing the probability that electrons and holes will recombine at each bimolecular encounter. A recent theoretical model developed by Frost113 can be used to predict the temperature dependent variation of polaron mobilities for CH3NH3PbI3 films in the 190 to 290 K temperature range. Included in the top of Figure 5B is a guide to the eye, which indicates the relative change in recombination coefficient that would be predicted from the temperature dependence of the polaron mobility and the Langevin model. The calculated mobility of large polarons in lead halide perovskites is predicted to decrease by a factor of 1.5 as the temperature increases from 190 to 300 K.113 This prediction is consistent with experimentally obtained mobilities from Hall effect measurements and microwave conductivity studies. 15, 26, 43 From these comparisons, we can account for only a factor of 1.5 decrease in recombination coefficient from changes in mobility using the Langevin model. However, a factor of 30 change in coefficient is observed. The data reveal that the probability of electron and hole recombination at each encounter decreases significantly as the temperature increases. The spatial band diagram model represented in Figure 5C reflects the localization of charge carriers into large polarons that gives rise to the order of magnitude decrease of the bimolecular recombination coefficient beyond what would be predicted from changes in carrier mobility. At elevated temperatures, we demonstrated in our previous report74 that essentially all charge carriers in CH3NH3PbI3 films self-trap into large polarons states with radii of approximately 9 nm at 300 K. The nuclear distortions associated with this carrier localization cause faster structural fluctuations of the perovskite lattice that are reported in the faster dephasing dynamics of the N-H bend vibrational mode (Figure 4). This localization also produces polarization clouds that create energetic barriers to charge recombination47 and decrease the recombination probability of electrons and holes at each encounter. These together account for the slower recombination rates than those predicted from the temperature dependent changes in polaron mobility.


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It is instructive to compare the observed bimolecular recombination processes in halide perovskites with predictions from Langevin theory. We recall that the Langevin model27 provides a simple relationship of the recombination coefficient of charge carriers with their average mobility

 and the dielectric permittivity  of the material according to kbiLangevin = µe(ε)-1, where e is the elementary charge. We considered the temperature-dependent variation of polaron mobilities predicted by Frost113 and the value of the dielectric function at optical frequencies (ε ~ 6.5),114 which is appropriate for describing electronic processes such as charge transport and recombination. These allowed us to determine the temperature-dependent variation in kbiLangevin predicted from the Langevin model that appear in Table 2. Across all temperatures, the experimentally measured bimolecular recombination coefficients are four to five orders of magnitude lower than predicted values obtained from the Langevin model. The Langevin model does not take into account charge screening or repulsive interactions that arise from polarization clouds around oppositely charged large polarons. These effects are most pronounced at elevated temperatures, where charge carriers are more localized. However, the measured recombination coefficient is four orders of magnitude smaller than that predicted from the Langevin model even at 190 K, where the majority of charge carriers reside in delocalized states.74 We conclude that the soft anharmonic lattice of halide perovskites48-50 appears to screen charge carriers from each other and reduce their recombination cross section even without the influence of energetic barriers47 due to repulsions of polarization clouds.40-46 This charge screening behavior of the anharmonic lattice figures prominently in the remarkably long charge recombination lifetime of halide perovskites that underpin many of their exceptional properties.

Conclusions We used time-resolved infrared transient absorption spectroscopy to examine the structural origins of long charge recombination lifetimes of halide perovskite materials. The N-H bend mode of CH3NH3+ is coupled to the inorganic perovskite lattice, leading to enhancement of the oscillator 25 ACS Paragon Plus Environment


Page 26 of 35

strength of the vibrational mode in the excited electronic state. Furthermore, structural fluctuations of the inorganic lattice in the presence of photogenerated charge carriers cause changes in the vibrational dephasing time of the N-H bend. This coupling provides a means to directly probe the temperature dependent lattice dynamics that lead to large polaron formation. Time-resolved infrared spectroscopy also provides the opportunity to directly probe the localization of charge carriers into large polarons in halide perovskites because their spatial extent influences the shape of their transient absorption spectra that span the mid-IR spectral region. The temperature dependent dynamics that lead to faster dephasing of the N-H bend of CH3NH3+ cations also increase the localization of large polarons at higher temperatures. This localization introduces nuclear distortions around the charge carriers, which create energetic barriers to charge recombination. The rate of charge recombination in the CH3NH3PbI3 perovskite film slows more than an order of magnitude over the 150 to 300 K temperature range within the tetragonal crystalline phase. This change in recombination rate results from two effects, a change in mobility of the polarons and a change of the capture cross section at each encounter of electrons and holes. The change of mobility over this range is much smaller than the observed change in recombination rate, indicating that the change in capture cross section is the dominant origin for greatly slowed charge recombination at higher temperatures. These measurements highlight the influence that large polaron formation has on the capture cross sections through the introduction of energetic barriers to charge recombination. More generally, the effects of nuclear distortions of the anharmonic perovskite lattice that form around charge carriers in both free carrier and large polaron states underpin many of the exceptional properties of halide perovskites through the influence on their charge recombination process. Because substitution of ions of different sizes can influence the structural flexibility of halide perovskites,76 this approach may be used to tune the balance of charge transport versus charge recombination for specific applications in photovoltaic or light emitting applications. 26 ACS Paragon Plus Environment

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Furthermore, the formation of 2D Ruddlesden-Popper perovskites may also provide a means to tune the structural flexibility and large polaron formation that underpin charge transport and recombination processes in the materials.

Associated Content Supporting Information Scanning electron micrographs, detailed discussion of TRIR spectra, kinetics and their modeling. This material is available free of charge via the Internet at http://pubs.acs.org.

Author Information Corresponding Author J.B.A.: [email protected]

Acknowledgements The authors KTM and JBA are grateful for support of this work from the U.S. National Science Foundation under Grant Number CHE-1464735. KTM is grateful for support from the National Science Foundation Graduate Research Fellowship Program under Grant No. DGE1255832. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.

DECLARATION OF INTERESTS



Page 28 of 35

E.R.K. and J.B.A. own equity in NanoSpec Instruments, LLC, which has an interest in this project. Their ownership in this company has been reviewed by the Pennsylvania State University’s Individual Conflict of Interest Committee and is currently being managed by the University.

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