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# Chemical nature of ferroelastic twin domains in CH3NH3PbI3 perovskite

## Abstract

The extraordinary optoelectronic performance of hybrid organic–inorganic perovskites has resulted in extensive efforts to unravel their properties. Recently, observations of ferroic twin domains in methylammonium lead triiodide drew significant attention as a possible explanation for the current–voltage hysteretic behaviour in these materials. However, the properties of the twin domains, their local chemistry and the chemical impact on optoelectronic performance remain unclear. Here, using multimodal chemical and functional imaging methods, we unveil the mechanical origin of the twin domain contrast observed with piezoresponse force microscopy in methylammonium lead triiodide. By combining experimental results with first principles simulations we reveal an inherent coupling between ferroelastic twin domains and chemical segregation. These results reveal an interplay of ferroic properties and chemical segregation on the optoelectronic performance of hybrid organic–inorganic perovskites, and offer an exploratory path to improving functional devices.

## Main

Methylammonium lead triiodide (CH3NH3PbI3 or MAPbI3) and related hybrid organic–inorganic perovskites (HOIPs), have shown great potential for optoelectronic applications1,2,3,4. However, the intrinsic physical properties of these materials, which are critical to understand perovskites’ photophysics and to improve optoelectronic device longevity and performance, have yet to be dissected fully.

Underpinning many of the desirable optoelectronic properties is the potential role of ferroelectricity, which may dictate band alignment as well as the generation and transport of charge carriers5,6,7. However, the presence of ferroelectricity in MAPbI3 perovskites is debated. In part, this lack of clarity is related to the experimental challenges in separating ferroic behaviour from a mix of the spatial, mechanical and chemical signals present in these perovskite films. Traditional polarization–electric field measurements have hinted at both ferroelectric8 and non-ferroelectric behaviour9,10, and ionic conductivity along with dielectric relaxation have accounted for this disparity. A variety of characterization techniques, which include piezoresponse force microscopy (PFM)11,12,13,14,15, transmission electron microscopy16 and photothermal induced resonance12, revealed twin domains in HOIPs, which can be a signature of different spontaneous polarization (ferroelectricity)17, but can also be due to different orientation states in spontaneous strain (ferroelasticity)18 or to chemical heterogeneity19. Specifically, PFM, a technique known to be sensitive to the electromechanical response, has been used often to study these twin domains11,12,13,14,15. It is known, however, that PFM measurements are prone to artefacts, particularly in materials with a weak electromechanical response20. Indeed, other factors, such as topography changes, electrostatic contributions and local ion dynamics, as well as tip–sample contact stiffness, may also influence the PFM response. In addition, MAPbI3 twin domain studies have focused mainly on the ferroic properties, and so should be extended to chemistry, which can be expected to play an important role and is often reported in other systems such as Cu–Ni (ref. 19) and BiSbTe (ref. 21). In fact, in ferroelectric and ferroelastic domains, local variation of ion distribution—and therefore measurable differences in chemical composition—may occur due to the disparity in local defect densities and potentials22.

In this work, we explore how the chemical variation correlates with ferroelastic twin domains in MAPbI3 thin films using multimodal imaging techniques sensitive to a variety of local mechanical, electromechanical and chemical phenomena. Using advanced atomic force microscopy (AFM) techniques, we demonstrated that previously reported piezoelectric contrast is mechanical rather than electromechanical in nature, supported by significant elastic differences between the domains. Combining scanning electron microscopy (SEM), helium ion microscopy (HIM) coupled with secondary ion mass spectrometry (HIM–SIMS) and nanoscale infrared spectroscopy (namely, AFM-IR), we reveal ion segregation that correlates with the observed twin domain structures. Polarization-resolved two-photon total internal reflection fluorescence microscopy (TIRFM) studies reveal variations in the orientation of optical transition dipole moments, which are linked to changes in the local ordering in the film and suggests different crystallographic orientations of the domains. Finally, density functional theory (DFT) calculations offer a cohesive physical picture that describes the strain, chemical segregation and ferroelasticity. The structural–chemical interplay revealed in this work provides a roadmap to measure, interpret and understand the optoelectronic performance of related HOIPs.

MAPbI3 films were synthesized using a modified sequential deposition method1. A solution of lead iodide (PbI2) in dimethylformamide was spin coated onto an indium tin oxide (ITO)-coated glass substrate, followed by spin coating of the methylammonium iodide (MAI) solution in ethanol and annealing at 100 °C, which converted the PbI2–MAI bilayer into CH3NH3PbI3 perovskite. The resulting MAPbI3 films offer power conversion efficiencies of 10.23% in solar cells (Supplementary Fig. 1a). Supplementary Fig. 1b shows the MAPbI3 X-ray diffraction (XRD) spectrum at room temperature. Five peaks between 10° and 30° (2θ) correspond to the (110), (020), (211), (022) and (220) orientations of the MAPbI3 tetragonal phase23. XRD was also used to test sample stability in conditions that mimicked those used during other reported characterization modalities. The XRD diffractograms taken after three hours of exposure to ambient conditions (humidity ~35%) showed little change when compared to a freshly prepared sample. Topography images acquired after AFM measurements in air for one hour also revealed no signs of degradation (Supplementary Fig. 2). However, after 16 hours in ambient conditions, the degradation of MAPbI3 became apparent in a small peak that corresponded to the (001) orientation of PbI2. Supplementary Fig. 1c shows the ultraviolet–visible absorption and photoluminescence spectra of the sample, which are similar to the absorption and photoluminescence of the single crystal23 and suggest a film of good quality.

The striped twin domains were studied with both single-frequency PFM and band excitation (BE)-PFM. We note that the vast majority of previously reported PFM studies, except one15, relied on single-frequency PFM and took advantage of the cantilever resonance enhancement by closely matching the a.c. frequency to the contact resonance frequency. This is explained in Supplementary Fig. 3, which illustrates that the twin domain contrast is detected if the a.c. signal is set close to the resonance frequency (within 5–15 kHz), and disappears far from the resonance frequency (>15 kHz). It is necessary to operate close to the resonance frequency to detect the electromechanical effects in materials with a weak piezoelectric coefficient, but this makes single-frequency PFM measurements susceptible to misinterpretation24. For instance, in single-frequency PFM, shifts in the resonance frequency, which may originate from changes in the mechanical properties of the sample that induce changes in the tip–sample contact stiffness, can be easily mislabelled as purely piezoelectric.

BE-PFM provides additional cantilever dynamics information that helps to decipher the precise imaging mechanism. Compared to single-frequency PFM, BE-PFM suppresses the topographic cross-talk and tracks resonance frequency. Access to the wide frequency band response curve at each spatial point can be independently fitted to a model that produces a frequency distribution image, which provides a more complete picture of the tip–sample interaction25,26,27. The BE-PFM results are shown in Supplementary Fig. 4. Twin domains observed in single-frequency PFM (Supplementary Fig. 3) are also visible in BE-PFM amplitude (Supplementary Fig. 4b) and phase images (Supplementary Fig. 4c). Notably, the twin domain contrast in the phase image is not related to the typical ferroelectric domain signal seen in tetragonal systems (90° or 180°). Interestingly, corresponding twin domains are also observed in the frequency image (Supplementary Fig. 4d), which implies that different domains have different resonances, which is indicative of local elastic property variation28.

To verify this hypothesis, we performed BE-AFM, which is commonly used to measure local elastic properties9,29. This approach does not require biasing the cantilever, and hence can be used to isolate electromechanical from mechanical behaviour. The results are shown in Fig. 1. The frequency contrasts in both BE-PFM (Fig. 1b) and BE-AFM (Fig. 1c) show the same twin domain features. The absence of a similar contrast in topography (Fig. 1a) indicates that this behaviour is purely due to changes in the elastic modulus, where domains with a higher resonance frequency are stiffer than domains with a lower resonance frequency.

Additional confirmation was obtained via a laser Doppler vibrometer (LDV) detection system in our AFM. Unlike traditional optical beam deflection (OBD), LDV can be used to determine the precise tip–surface displacement in units of length (as opposed to voltage on the AFM detector). The effect of the cantilever geometry (or resonance effects) can be excluded when the laser spot is positioned directly above the tip, and included when the laser spot is far from the tip30. When the LDV laser is positioned directly above the tip (Fig. 2a), the resonance response is nearly flat (Supplementary Fig. 5), which indicates that the signal is not influenced by cantilever dynamics. The LDV–PFM amplitude and phase images measured in this configuration are shown in Fig. 2b,c, respectively. Interestingly, neither shows twin domains, which represents the lack of a detectable tip–sample displacement from an electromechanical response. When the LDV laser spot was positioned away from the tip (Fig. 2d) so that the measured signal included dynamic cantilever contributions, the twin domains were clearly visible in the LDV–PFM amplitude (Fig. 2e) and phase (Fig. 2f) images. The observed twin domains are identical to those observed in OBD-PFM (the traditional configuration used in the single-frequency PFM experiments in Supplementary Fig. 3, and the BE-PFM experiments in Supplementary Fig. 4). These results suggest that the detected piezoelectric response in OBD-PFM is not electromechanical, but is due to the coupling of the sample stiffness and stray dynamic behaviour, which implies a dependence on the elastic difference between the twin domains in the MAPbI3 film. An additional confirmation of the mechanical property significance in the detected ‘piezoelectric-like’ response is given by LDV–PFM measurements, performed far from the mechanical resonance conditions (Supplementary Fig. 6). In this case, twin domains were not detectable either with the laser located above the tip, or away from it.

When imaging the MAPbI3 thin films with SEM, both twin domain contrast and grain contrast (bright grains and dark grains) were observed. In Fig. 3a, the SEM image shows grains of varying shapes and sizes that range from 0.1 to 4 μm. Detailed analysis of the SEM images revealed a twin domain structure within the grains, as shown in Fig. 3b. The twin domains are periodic, 100 to 400 nm in width, in good agreement with the domain size observed with PFM. In a previous report, differences in the crystallographic orientation of the twin domains were observed with transmission electron microscopy, but were not sufficient to induce a contrast in SEM16. Therefore, the crystallographic orientation alone cannot explain the twin domain contrast in SEM; we believe the culprit is dissimilar chemical compositions, which result in different local electronic band structures and conductivities31.

To confirm this hypothesis, we used HIM–SIMS with Ne+ as the primary beam. The combination of the high-resolution imaging (<0.25 nm) of HIM and the chemical sensitivity of SIMS allows us to detect the ion distribution with a spatial resolution of ~10 nm (refs 32,33), and was recently used to explore the chemical composition of HOIPs34,35. Figure 4a shows the HIM–SIMS chemical maps for CH3NH3+, in which the grains and grain boundaries are clearly visible. The CH3NH3+ concentration varies between grains, consistent with the dark and bright grains in the SEM images in Fig. 3. Interestingly, the CH3NH3+ chemical map also shows twin domains, consistent with the SEM images. As illustrated in the enlarged images, Fig. 4b,c grains with both a high (Fig. 4b) and a low (Fig. 4c) CH3NH3+ concentration are observed with twin domains of comparable widths to those observed in PFM. This suggests a difference in chemical composition between the twin domains in our sample, in contrast with Rothmann et al.16 in which the lack of twin domains in the SEM probably indicates no ion segregation. Notably, our samples are ~5 times thicker (500 nm) than those used in Rothmann et al.16 (100 nm) and have bigger grains, which suggests a larger strain energy in our samples. The release of the strain energy may induce ion motion and thus a variation in CH3NH3+ concentration. DFT molecular dynamics (MD) simulations of MAPbI3 with a low-energy stoichiometric surface were performed to test the hypothesis that elastic strain can induce CH3NH3+ motion. The elemental mean squared displacement (m.s.d.) (Supplementary Fig. 7a) shows redistributions of C, N and H under a 1% biaxial lattice strain, which corresponds to an enrichment of CH3NH3+. The redistribution also correlates well with the m.s.d. for I. The quantitative difference in chemical distribution between the strained and the unstrained cases was shown by the fraction of CH3NH3I located at the surface of a slice of the CH3NH3PbI3 model (Supplementary Fig. 7b,c), which indicates a twofold increase in the sample with a 1% biaxial lattice strain. The process of CH3NH3+ motion and redistribution is given in Supplementary Fig. 7. It is notable that no redistribution was observed for Pb in either the strained or unstrained scenarios, consistent with HIM–SIMS, where Pb is uniformly distributed (Supplementary Fig. 8a).

AFM-IR was used to confirm qualitatively the difference in the local CH3NH3+ density in the twin domains. AFM-IR yields chemical composition maps by using an AFM probe to detect the local thermal expansion induced by infrared radiation. The sample was irradiated with an infrared laser at 1,400 cm–1, which corresponds to methylammonium deformation (the CH3–NH3+ rock)36. The CH3NH3+ chemical map is shown in Fig. 5b, and the simultaneously obtained topography is shown in Fig. 5a. The chemical image clearly shows twin domains with widths that match previous results. Control experiments (Supplementary Fig. 9) show that the twinning contrast is not visible without the infrared laser, which indicates that AFM-IR measurements are not sensitive to elastic variations between domains. These results confirm that the twin domain contrast in the chemical map (Fig. 5b) originates from the difference in chemical composition, which suggests chemical gradients in CH3NH3+ in the twin domains.

The CH3NH3+ segregation, which is induced by strain, is periodically ordered, which indicates that the strain is periodically distributed. This begs the question whether the ferroelastic nature of these twin domains can induce a periodically ordered strain tensor. To relate the above findings to the optical response of these materials, we show the results from polarization-resolved two-photon TIRFM. The experimental details and sample geometry are given in Methods and Supplementary Information. Note that the evanescent field exponentially decays on the sample side of the cover slip (Supplementary Fig. 10a). The distance of the perovskite from the cover slip surface determines the magnitude of the field (hence the excitation intensity) seen by the sample, and thus impacts the absolute photoluminescence intensity37. However, this distance dependence cancels out in the ratio of pixel intensity calculated for the polarization data. The obtained polarization image offers information on the optical transition dipole moments. Figure 5d shows these results as a two-photon polarization map, in which the colour scheme encodes the average relative orientation of the transition dipole moments. Notably, in regions of the sample where twin domains were observed, we found alternating red/white stripes, as expanded in Fig. 5e, with an average width of 363 nm, in good agreement with the domain size observed in other measurements. This indicates that different domains may show different orientations of the transition dipole moments, which is related to the crystallographic orientation, as revealed earlier38. CH3NH3+ rotation is known to distort crystal structure39, and thus the CH3NH3+ segregation may also affect the transition dipole moment. However, this distortion is dynamic and thus disordered due to the uncertainty and spatial variation of the CH3NH3+ direction. Therefore, TIRFM does show twin domains that have different crystallographic orientations even if CH3NH3+ segregation affects the transition dipole moment.

Evidence of crystallographic twin domains—in agreement with previous transmission electron microscopy studies16 that show domains with atomic level detail—is a signature of ferroelastic behaviour. Although previous reports drew similar conclusions on the ferroelasticity of twin domains11,16, mechanical cross-talk prevented the attribution of the behaviour to chemistry, as revealed by the multimodal imaging approaches used in this work. Given the difficulty in separating the contributions from crystallographic orientation and CH3NH3+ segregation to changes in the transition dipole moment identified with TIRFM, the ability to quantify specific domain orientation angles is limited. Regardless, TIRFM shows that the twin domains do significantly alter the interaction of the material with light, which is important for light harvesting and emission applications.

To summarize, the twin domains appear to be ferroelastic, not ferroelectric, at room temperature. The domains are under different strain conditions, which results in a redistribution of mobile ions and thus forms the stripes of chemical segregation. The combined difference in the crystallographic ordering and the chemical segregation causes an elastic variation between domains, which results in the twin domain contrast seen by BE-PFM and BE-AFM frequency images. Furthermore, as the applied bias couples to the elastic variation, this results in the ‘piezoelectric-like’ contrast observed in PFM. We verified the presence of elastic variation as well as the absence of electromechanical effects by combining BE-PFM, BE-AFM and LDV–PFM. Thus, the ‘piezoelectric-like’ contrast in PFM is due to the combined effect of the applied bias and the elastic variation, rather than to true piezoelectricity, which indicates that these twin domains are not ferroelectric domains.

Although the twin domains in MAPbI3 are not ferroelectric, two considerations remain. First, a transition to a ‘ferroelectric-like’ phase in one type of domain may occur due to a chemical composition shift or a strain change. In fact, domains with alternating polar and non-polar order have been proposed15, and this requires further studies to determine whether the resultant phase is truly ferroelectric or characterized by strain-induced birefringence and polar moment40,41. A second alternative may be that the domains are classically ferroelectric–ferroelastic42, but act differently due to the polarization conditions of the domains that cause variations in the coupling with surface charge.

Ferroelectric polarization was thought to facilitate the dissociation of photoinduced electron–hole pairs, which enhances the photovoltaic performance. However, our results point to the absence of ferroelectricity. Instead, the discovery of a periodic chemical composition difference offers the following new insights into this fascinating system (beyond ferroic behaviour): (1) ion segregation may lead to band bending at the domain walls due to different chemical composition, which facilitates charge separation and is beneficial for the photovoltaic action; (2) on the contrary, the achievable performance of HOIP solar cells might be limited by low-conductivity domains. To date, reports of photovoltaic performance of MAPbI3 with twin domains are controversial, as they range from a power conversion efficiency of 8.78% (ref. 43) (which is similar to our results) to 14% (ref. 13) and 17.6% (ref. 14). As we show here, the coupling between ion segregation and elastic energy provides an efficient avenue to design and control this nanoscale structure to investigate and optimize systematically the optoelectronic performance.

In conclusion, we present a systematic study of the MAPbI3 films with twin domains by using a multitude of analytical methods to explore their mechanical, chemical and ferroic properties. By using multimodal imaging methods to study twin domains, we demonstrate the interaction of phenomena such as ferroelasticity, chemical segregation and elastic variation. Our results clarify that previous claims on ferroelectricity13 are, in fact, misguided by the elastic variation between the domains, rather than by true piezoelectric (electromechanical) effects, which suggests the twin domains are non-ferroelectric. In addition to their ferroelastic nature, we reveal the underlying chemical segregation and elastic variation effects, which were ignored in previous studies11,12,13,14,15,16. Finally, and most relevantly for the optical applications of HOIPs, we have demonstrated that the physical variations in the material affect their interaction with light. This work offers insight into the fundamental behaviour of MAPbI3 thin films that exhibit twin domains, as well as a new line of investigative thought in these fascinating materials.

## Methods

### Film preparation

The pristine PbI2 and MAI precursors were prepared by dissolving 275 mg PbI2 (ultradry (Alfa)) in 0.5 ml dimethylformamide (Sigma) and 70 mg MAI (one material) in 1 ml ethanol (99.5% (Alfa)), respectively. Prior to film spin-casting, ITO-coated glass substrates were ultrasonically cleaned with deionized water and isopropanol, twice for 30 min. After drying with N2, the cleaned substrates were treated with ultraviolet/ozone for 30 min. The perovskite films were fabricated by spin-coating a hot PbI2 solution onto ITO, followed by spin-coating of room-temperature MAI solution to the cooled PbI2 in an N2-filled glovebox. The obtained bilayer films were transferred on a hotplate and annealed at 100 °C for 2 h.

### Device fabrication and characterization

Poly(3,4-ethylenedioxythiophene) polystyrene sulfonate (Clevios Al4083) was coated on cleaned ITO/glass by spin-casting at 4,000 r.p.m. for 60 s and annealing at 150 °C for 20 min. Then, the MAPbI3 was processed as discussed above and followed by spin-casting a (6,6)-phenyl-C61-butyric acid methyl ester layer at 2,000 r.p.m. for 60 s. Finally, an 80 nm thick Ag film was thermally deposited as the electrode with an effective area of 0.06 cm2. The current density–voltage (JV) curves were measured in a N2-filled glovebox at room temperature using a Keithley 2612 source meter under AM 1.5 G 1 sun (100 mW cm–2) illumination from a solar simulator (Thermal Oriel 96000). The light intensity of the solar simulator was calibrated with a Si reference cell certified by National Institute of Standards and Technology. The JV curves were measured by both reverse and forward sweeping with a scan speed of 0.1 V s–1, no delay time and no pretreatment.

### XRD

XRD patterns were recorded with a Panalytical X’Pert MPD Pro diffractometer (45 kV, 40 mA) using Cu Kα1 radiation (λ = 0.154 nm) with a step size of 0.0167° over the angular range 10–30°.

### Ultraviolet–visible absorption and photoluminescence

The ultraviolet–visible spectrum was collected at the normal incidence. The photoluminescence spectrum was collected using a 400 nm excitation incident on the sample at a 45° angle. The emitted light was double filtered to remove reflected excitation light, spectrally resolved in a monochromator and detected with a water-cooled photomultiplier tube.

### AFM

PFM, BE-PFM, LDV–PFM and BE-AFM were measured on a commercial AFM system (Cypher (Asylum Research and Oxford Instruments Co.)) equipped with a band-excitation generator at room temperature in ambient conditions. A Pt/Ir coated AFM tip (ElectriMulti75-G (Budget Sensors)) with a nominal stiffness of 3 N m–1 was used. Single-frequency OBD-PFM measurements were conducted by applying an a.c. bias of 1.0 V with 335 kHz and 300 kHz for resonance enhancement and non-resonance enhancement, respectively. The resonance frequency was around 340 kHz. LDV–PFM measurements were carried out by applying an a.c. bias of 1.0 V with 335 kHz and 300 kHz for resonance enhancement and non-resonance enhancement, respectively; the LDV laser spot was positioned at different positions. For band excitation, a band of frequencies near the resonant frequency was used to perturb the sample, and the response of the cantilever was measured by an external data-acquisition system that yielded amplitude, phase and frequency at each coordinate via Fourier transformation. BE-PFM measurements were performed by applying an a.c. bias of 1.0 V with a centre frequency of 340 kHz and band width of 100 kHz. In the case of BE-AFM, the cantilever and tip were driven by a blue laser, band excitation was performed with a centre frequency of 335 kHz and a band width of 100 kHz. Noteworthy, although the above measurements were taken at ambient conditions, we claim that the sample degradation is negligible during the measurements. As shown in Supplementary Fig. 2, this topography is acquired after all the measurements conducted at an identical region (Fig. 2 and Supplementary Figs. 3, 4 and 6) and, as there is no obvious change in the topography, the degradation during measurements is negligible. AFM-IR measurements yield a bulk chemical composition map by using an AFM probe to detect local volume change that results from the absorption of infrared radiation, which provides chemical compositional images with, simultaneously, the spatial resolution of AFM and the chemical analysis capability of infrared spectroscopy. AFM-IR experiments were carried out in a nitrogen atmosphere using Anasys Instruments, which include AFM-IR imaging. Both the height image and chemical image were recorded in contact mode. The chemical image was recorded by illuminating the MAPbI3 sample with a 1,400 cm-1 laser during scanning and probes the bulk concentration of the target chemical (here it is CH3NH3+).

### HIM–SIMS

A helium ion microscope (Zeiss Orion Nanofab) coupled to a secondary ion mass spectrometer (HIM–SIMS) was utilized for the mass-selected chemical imaging of perovskite samples as well as the identification of chemical species by spectrum collection. A HIM uses two gas field ionization sources (He+ and Ne+) for the high-resolution topographic imaging of materials of less than ~0.5 nm with secondary electrons. A dynamic SIMS is coupled to the HIM to measure the surface chemical information with a high surface sensitivity that analyses to a few nanometres in depth, a high mass resolution (MM, 500~1,000) and a high lateral resolution down to ~10 nm (refs 32,44). As the sputtering gun, a focused Ne+ beam with an acceleration voltage of 25 kV was irradiated over a 25 × 25 μm2 area and a 30 × 30 μm2 area of perovskite samples for chemical imaging and spectrum collection, respectively. A beam current for chemical imaging was measured as ~1.37 pA (ion dose of ~8.3 × 107 ions per pixel) at a beam spot size of 4 μm and a 40 μm aperture, and a 70 μm aperture was used to collect a spectrum with a higher current of ~120 pA. A +495 V sample bias was applied to extract the positive secondary ions generated, which included CH3NH3+ (m/z, ~32) and Pb+ (m/z, ~208). In both the chemical imaging and the spectrum collection, the Ne+ beam was focused on an area far away from the analysis areas to minimize sample damage by Ne+ exposure before the chemical analysis. Then, SIMS measurements were started on the randomly selected analysis areas simultaneously at the beam opening. The spectrum collection was done under the given magnetic field strength (magnetic sector) of 500 mT by moving three detectors with a step of 80 μm and with a sampling time of ~400 ms, which can detect atomic or molecular fragments with a mass range from ~12 to ~250 amu. Chemical imaging was done for 1 ms per pixel over 1,024 × 1,024 pixels. The HIM–SIMS chemical images in Fig. 4 and Supplementary Fig. 8a are Gaussian filtered to remove background noise.

### Polarization-resolved two-photon TIRFM

TIRFM images were collected on a custom two-photon total internal reflection fluorescence microscope and data were analysed using custom LabVIEW code, as described previously37. Briefly, the excitation light at 800 nm was produced by a femtosecond mode-locked Ti:sapphire laser (Tsunami (Spectra Physics)) and set to a known polarization with a Glan–Taylor polarizer and half-waveplate before being introduced into 1.49 NA/×100 objective (Nikon). The approximate maximum field of view for this microscope is ~80 μm, with a resolution dictated by the emission wavelength of the light. For all of the TIRFM experiments, the perovskite film was covered with a coverslip (No. 1 thickness) and inverted onto the microscope such that the oil from the oil-immersion objective was in contact with the coverslip. Due to the topology of the film, a thin layer of air existed between the coverslip and the film which provided the necessary index of refraction mismatch for a total internal reflection of the excitation light to occur. This creates an evanescent excitation field that exponentially decays in the z direction or towards the sample film surface. A photograph of a representative perovskite sample is given in Supplementary Fig. 10c. To prepare the sample, the perovskite solution was first coated onto an ITO glass substrate inside a N2-filled glovebox. The sample was then inverted such that the perovskite sample faced down and was gently set on top of a larger-area coverslip. No additional pressure was applied beyond the weight of the sample itself. The edges of the sample were then encased by poly(methyl methacrylate) (PMMA). Specifically, the PMMA solution (20 mg ml–1 in chloroform) was distributed along the edges of the sample to form a sealed N2-filled gap between the coverslip and sample slide. The sample was then left in the glovebox to harden for 2 h before removal for the TIRFM experiments. The experimental/sample geometry is shown in Supplementary Fig. 10.

The fluorescence signal below 725 nm was collected by the same objective and polarization resolved before being detected with a micro channel plate-equipped charge-coupled device camera. The transition dipole moment orientations were obtained by calculating the ratio of fluorescence emission intensity that corresponded to the variable excitation polarization:

$$P = \frac{{I_{\it{\parallel }} - I_ \bot }}{{I_{\it{\parallel }} + I_ \bot }}$$

where $$I_{\it{\parallel }}$$ is the fluorescence measured using p-polarized light (excitation parallel to the plane of incidence), which probes the out-of-plane dipole moments, and $$I_ \bot$$ is the fluorescence measured using s-polarized light (excitation perpendicular to the plane of incidence), which probes the in-plane dipole moments, as illustrated in Supplementary Fig. 10. In tetragonal CH3NH3PbI3, the photoluminescence polarization is caused by the lowest optical transition along the apical direction of the crystal structure38, which indicates the correlation of the transition dipole moment and the crystallographic orientation. CH3NH3+ segregation may also affect the transition dipole moment through distorting the PbI6 octahedra. However, this effect cannot result in large-scale ordering of the transition dipole moment because it is dynamic (CH3NH3 rotation) and thus disordered. Uncertainty in the polarization state used in the experiments is on the order of 1°, which would not impact the results in a meaningful way. The excitation laser power was kept very low to avoid sample degradation. This results in lower overall counts, which limits the quality of the images obtained and represents the largest source of uncertainty in these measurements.

### Scanning electron microscopy

The scanning electron microscope image was acquired with the inlens and secondary electron mode, line-average scanning with a work distance of 7.2 mm, magnification of 10.0 kx and gun voltage of 1.00 kV on a Zeiss Merlin scanning electron microscope.

### DFT

MD simulations based on DFT were performed using the Vienna Ab Initio Simulation Package 5.4.1 (refs 45,46,47) using the projector-augmented wave (PAW) method48,49. The electron–ion interactions were described using standard PAW potentials, with valence electron configurations of 5d106s26p2 for Pb, 5s25p5 for I, 3s23p5 for Cl, 2s22p2 for C, 2s22p3 for N and 1s1 for H. To account for the weak van der Waals (vdW) interactions, the vdW density functional method implemented by Dion et al. and modified by Klimeš et al. was employed50,51. To reduce the computational cost, the Brillouin zone integrations were performed on a Γ-centred 1 × 1 × 1 k-point grid, the kinetic energy cutoff for the plane waves was set to the default value of 400 eV and the ‘normal’ precision setting was adopted. The convergence criterion for the electronic self-consistent loop was set to 10–4 eV. The MD simulations were performed in a canonical NVT ensemble with the three lattice vectors constrained while all the atoms were allowed to move. The temperature of the simulations was maintained by a Nose–Hoover thermostat at 300 K. Each simulation was carried out at a time step of 1 fs, with the velocities of all the atoms initialized randomly according to the Maxwell–Boltzmann distribution. MD simulations for 2 ps were used to thermalize the energy and then additional 25 ps MD simulations were evaluated to analyse the motion of the ions. Supercell models of low-energy stoichiometric (100) and two (110) surfaces (one flat and the other corrugated) that contained five Pb layers52 were constructed using the experimental X-ray structure of CH3NH3PbI3 in a room-temperature tetragonal phase53. After a full optimization of these models, the relative mobilities of the different ions were estimated by monitoring the m.s.d. during the MD simulations performed at room temperature.

### Reporting summary

Further information on research design is available in the Nature Research Reporting Summary linked to this article.

### Data availability

All the data that support the findings of this study are available from the authors upon request.

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## Acknowledgements

This research was supported by the Laboratory Directed Research and Development Program of Oak Ridge National Laboratory, managed by UT-Battelle, LLC, for the US Department of Energy (Y.L., A.I., B.D. and O.S.O.). The research was partially sponsored by the Air Force Office of Scientific Research (AFOSR) under grant no. FA 9550-15-1-0064, AOARD (FA2386-15-1-4104), and the National Science Foundation CBET-1438181 (M.A. and B.H.) and supported by the University of Tennessee, Knoxville (B.R.W. and T.R.C.). This research was conducted at the Center for Nanophase Materials Sciences, which is a DOE Office of Science User Facility.

## Author information

### Affiliations

1. #### Center for Nanophase Materials Sciences, Oak Ridge National Laboratory, Oak Ridge, TN, USA

• Yongtao Liu
• , Liam Collins
• , Songkil Kim
• , Anton V. Ievlev
• , Stephen Jesse
• , Scott T. Retterer
• , Alex Belianinov
• , Kai Xiao
• , Jingsong Huang
• , Bobby G. Sumpter
• , Sergei V. Kalinin
•  & Olga S. Ovchinnikova
2. #### Department of Materials Science and Engineering, University of Tennessee, Knoxville, TN, USA

• Yongtao Liu
•  & Bin Hu
3. #### Asylum Research an Oxford Instruments Company, Santa Barbara, CA, USA

• Roger Proksch
4. #### School of Mechanical Engineering, Pusan National University, Busan, South Korea

• Songkil Kim
5. #### Department of Chemistry, University of Tennessee, Knoxville, TN, USA

• Brianna R. Watson
•  & Tessa R. Calhoun
6. #### Chemical Sciences Division, Oak Ridge National Laboratory, Oak Ridge, TN, USA

• Benjamin Doughty
7. #### Computational Sciences & Engineering Division, Oak Ridge National Laboratory, Oak Ridge, TN, USA

• Jingsong Huang
•  & Bobby G. Sumpter

### Contributions

O.S.O., S.V.K., B.H., S.T.R, K.X., M.A., L.C. and Y.L. conceived the project and O.S.O. directed the experiments. Y.L. prepared the samples and performed the SEM measurements. Y.L. performed the scanning probe microscopy measurements with help from L.C. and the NSIR measurements with help from S.K. and A.I. R.P. developed the LDV–PFM and S.J. developed the band excitation scanning probe microscopy and analysis tools. S.K. performed the HIM–SIMS measurements with help from A.B. B.D. performed the TIRFM measurements and T.R.C. and B.R.W. helped to develop the TIRFM technique. J.H. and B.G.S. performed the DFT simulations. Y.L., L.C. and O.S.O. wrote the manuscript. All the authors contributed to the discussions.

### Competing interests

The authors declare no competing financial interests.

### Corresponding author

Correspondence to Olga S. Ovchinnikova.

## Supplementary Information

1. ### Supplementary Information

Supplementary Figures 1–10