Ferroelectric Domains May Lead to Two-Dimensional Confinement of

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Ferroelectric Domains May Lead to Two-Dimensional Confinement of Holes, but not of Electrons, in CH3NH3PbI3 Perovskite Ana L. Montero-Alejo,*,† E. Menéndez-Proupin,† P. Palacios,§ P. Wahnón,∥ and J. C. Conesa⊥ †

Group of Materials Modeling, Departamento de Física, Facultad de Ciencias, Universidad de Chile, Las Palmeras 3425, 780-0003 Ñ uñoa, Santiago Chile § Instituto de Energía Solar and Departamento de Física Aplicada a las Ingenierías Aeronáutica y Naval, Escuela Técnica Superior de Ingeniería Aeronáutica y del Espacio, and ∥Instituto de Energía Solar and Departamento de Tecnología Fotónica y Bioingeniería, Escuela Técnica Superior de Ingeniería Telecomunicación, Universidad Politécnica de Madrid, 28040 Madrid, Spain ⊥ Instituto de Catálisis y Petroleoquímica, Consejo Superior de Investigaciones Científicas, Marie Curie 2, 28049 Madrid, Spain S Supporting Information *

ABSTRACT: We investigate the possibility that formation of ferroelectric domains in CH3NH3PbI3 can separate the diffusion pathways of electrons and holes. This hypothesis has been proposed to explain the large recombination time and the remarkable performance of solar cells of hybrid perovskites. We find that a twodimensional hole confinement in CH3NH3PbI3 is possible under room-temperature conditions. Our models of the tetragonal phase show that the alignment of dipole layers of organic cations induces the confinement of holes but not of electrons. This behavior does not change even when the strength of the ordered dipoles is varied. The confinement of holes is favored by asymmetric deformation of the inorganic framework triggered by its interaction with the organic cations. However, the lattice distortions counteract the effect of the oriented organic dipoles, preventing the localization of electrons.

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INTRODUCTION Photovoltaic (PV) research has been shaken by the introduction of the metal−organic perovskite CH3NH3PbI3. Solar cells based on this material are expected to be even more efficient and commercially competitive with other energy sources in the coming years.1 Presumably, the hybrid nature of this semiconductor provides the most suitable properties within the PV materials, that is, broad sunlight harvesting and an efficient separation of photocarriers. The latter feature seems to be a consequence of the experimentally determined long carrier lifetime (giving high photoluminescence quantum yields), long carrier diffusion lengths,2−4 and weakly bound excitons at room temperature.5 There is still a discussion to explain this behavior despite the low mobility measured for charge carriers, especially for electrons, in relation to other PV materials.6−13 One of the mechanisms proposed to explain the high carrier diffusion lengths is the existence of separated diffusion paths for holes and electrons that can reduce recombination14,15 (see Figure 1). These diffusion paths would be located at the walls of ferroelectric nanodomains that could be formed within the crystal. Spontaneous polarization within the structure can be caused by the alignment and displacement of the CH3NH3+ (MA) cations, as well as displacement of Pb from the centers of PbI6 octahedra. All these possibilities are justified by the wellknown structurally soft nature, that is, the dynamic symmetrybreaking in the room-temperature phases of this material.14−20 The ferroelectric behavior of CH3NH3PbI3 remains an important topic of discussion, since this property appears to © 2017 American Chemical Society

Figure 1. Proposition of a multidomain ferroelectric thin film in hybrid perovskites. In this scheme, the electrons move along potential minima located at some domain interfaces, while holes move along maxima located at other interfaces, forming the two-dimensional separated pathways. Adapted with permission from ref 14. Copyright 2014 American Chemical Society.

be dependent on the experimental sample types and their manufacturing techniques.21−23 Even so, stable ferroelectric domains at room temperature have recently been observed in thin films, which are the form commonly used in solar cells.23 Prior theoretical studies have already supported the idea of charge localization in CH3NH3PbI3 due to fluctuation in the potential induced by MA dipoles.18,24−32 The more comprehensive models show that this electric potential is modified by the screening effect of inorganic framework distortions.26,28−31 The structural dynamics of the system makes it difficult to Received: September 28, 2017 Revised: November 7, 2017 Published: November 7, 2017 26698

DOI: 10.1021/acs.jpcc.7b09625 J. Phys. Chem. C 2017, 121, 26698−26705

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The Journal of Physical Chemistry C rationalize this phenomenon. For a specific phase, the polarization due to the global positions and orientations of the organic cations may be boosted or shielded by this screening.10 In fact, the resulting models have displayed different sites and degrees of localization of the charge carriers. This scenario seems to be an effect of the polarizability of the inorganic framework in perovskites. In this paper, we revisit the idea of two-dimensional pathways for photocarriers and identify planes in the CH3NH3PbI3 crystal where the alignment of MA cation dipoles may cause a confinement of holes. It seems that the presence of two single layers of oppositely oriented MA dipoles leads to hole confinement in tetragonal-phase models. In contrast, the same models show that electrons remain mainly delocalized throughout all the PbI2 planes. The localization of holes appears in both distorted (relaxed) and undistorted (unrelaxed) inorganic frameworks. In contrast, electron localization is revealed only when two layers of MA dipoles are head-oriented on the PbI2 plane in an undistorted inorganic lattice. Moreover, this behavior does not change if the net dipole magnitude of the organic cation varies. These results suggest that, under room-temperature conditions, the polarizable medium of iodide ions deforms asymmetrically to shield the enclosed molecular dipole. Consequently, it affects the electrical potential generated by the ordered dipole of organic cations, and the separate diffusion paths for holes and electrons cannot be explained under this condition. However, according to the significant structural fluctuations in perovskites,14−20,26,28,30 guided by the large movement on the picosecond time scale of the organic cation, two-dimensional conduction paths of holes at the valence band could be expected. Our models provide insights for a better understanding of the complex charge-carrier transport properties in metal−organic perovskites.

Figure 2. (a) Crystal structure of CH3NH3PbI3 base unit cell (tetragonal-phase model). Each layer of two MA (CH3NH3+) is schematized by a short arrow. A pair of opposed short arrows within a box represents the unit cell. (b) Symbols of different models of polarized nanodomains in CH3NH3PbI3 for tetragonal-derived (M1, M2, and M3a−d) and orthorhombic (Mort) phases. M1 is the structure resulting from relaxation of the base unit cell. The lengths and orientations of the arrows symbolize the layers of MA dipoles within the cells (see text). Colored lines represent the possible localization sites of electrons (blue) and holes (red).

P1)̅ , then one obtains a cell in which no layer of MA ions has a net dipole moment. In this way, we get a fully unpolarized cell to use as reference unit cell. The relaxed structures of base unit cell and the unpolarized cell correspond to the M1 and Unpol models, respectively. In addition, to obtain a variety of polarized nanodomains and their boundaries, we have replicated the base unit cell along the c-axis, obtaining supercell models with double and triple unit cells. Thereafter, we conveniently invert dipoles (exchanging C and N atoms of CH3NH3+) in each layer to obtain different arrangements of net dipole layers. A pair of consecutive layers with the same dipole orientation is represented here by a large arrow within the unit cell. Figure 2 shows the different models that we have considered for arranging the layer dipoles along the c-axis. Red and blue lines represent the regions where holes and electrons could be expected to localize if the mentioned hypothesis of separated diffusion paths were realized. According to the proposed ferroelectric multidomain scheme (Figure 1), one expects that electrons and holes will be located preferentially at the minimum and maximum crystal potentials, respectively. Finally, a model of the orthorhombic lowtemperature phase (Mort) of CH3NH3PbI3, used in our previous work,40 is also added. In this case, a pair of short horizontal arrows represent the MA dipoles that are oriented parallel to the ab plane. We have performed on these models density functional theory (DFT) calculations with the Perdew−Burke-Ernzerhof (PBE) exchange−correlation functional, as implemented in the Vienna Ab initio Simulation Package (VASP) code.41 All model structures, except the base unit cell, were relaxed to minimal energy (forces ≤0.01 eV/Å), including neutral (q = 0) and charged states (q = ±1; here q = +1 means that there is one electron less). The core−valence interaction is included through the projector-augmented waves approximation.42,43 The wave functions were expanded in plane waves with a kinetic energy cutoff of 364 eV.

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MODELS AND COMPUTATIONAL METHODS Existing crystallographic models of the room-temperature CH3NH3PbI3 phase describe average structures of an ensemble of configurations differing in the orientations of the MA cations. Configurational ensembles have been obtained by means of molecular dynamics (MD) simulations.17−19,26,33−38 The electronic properties can be obtained for a MD ensemble,19,26 although this approach has a very high computational cost. Here, we follow the low-cost route of using a single structure derived from the tetragonal unit cell (i.e., the symmetry occurring at near-ambient temperature) reported for CH3NH3PbI339 in which the partial disorder of organic cations is suppressed, lowering the lattice symmetry to monoclinic (space group P21/a). The model retains the inversion symmetry and therefore the cell has no net dipole moment, even though the MA cations are oblique to all three cell axes. Then, we locate conveniently the H atoms and relax their positions (see structure in Supporting Information). We name this structure the base unit cell (48 atoms). It has two layers of MA perpendicular to the c-axis, and each layer contains two MA ions that are oriented in the same direction with respect to the c-axis. Hence, the layers are polarized in opposite directions along the tetragonal unique axis. This base unit cell is here schematized by a pair of opposed short arrows that represent the dipoles of the two consecutive MA layers (see Figure 2). In each of the two layers parallel to the ab plane of the base unit cell, if the C and N atoms are exchanged in one of the two MA, retaining the inversion symmetry (triclinic space group 26699


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Figure 3. (Left) Electron-density distributions of VBM and CBM of base unit cell, relaxed M1, and unpolarized (Unpol) models. (Right) Corresponding electron-density profiles along the c-axis. Shaded regions represent the calculated percentage of localization of M1 (VBM in red) and base unit cell (CBM in blue) wave functions.

The k-point grid was automatically generated with the requirement that the maximum space between adjacent kpoints is smaller than 0.3 Å−1 (mesh of 3 × 3 × 1 for all supercell models). The state occupation numbers were fixed manually when modeling charged states to ensure that the electron (q = −1) at the lowest conduction band (LCB) or the hole (q = +1) at the highest valence band (HVB) is at Γ point. Hence, the effective number of added or removed electrons per unit cell is 1/9, and the calculation is equivalent to having one electron or hole in a 3 × 3 × 1 supercell. Electron-density distributions and band structures were obtained by considering spin−orbit coupling, as it is crucial to describe the structure of the conduction-band states40,44 Calculations at the hybrid DFT or GW higher theory levels were not undertaken, since they only affect to the separation between conduction and valence bands. The isosurfaces associated with the wave functions of the valence band maximum (VBM) and the conduction band minimum (CBM) drawn below correspond to 0.005 isovalue (Å−3). We consider the VBM and CBM at Γ point, neglecting the Rashba−Dresselhaus splitting.45 Visualization of structures and isosurfaces was achieved with the help of VESTA46 and VMD47 packages.

The VBM wave function of the base unit cell and M1 model is localized in the region of change of polarization in the cell boundary, where the MA dipoles are arranged outward (Figure 3, bottom). Here, the MA cations head their negative or less positive parts (CH3 groups) toward this region, which might become a potential well for positive charge carriers, as was proposed.14,15 The charge-density profile along the c-axis (Figure 3, right) quantifies the localization of the VBM wave function at 83% for M1 (90% for the equivalent area in the base cell). This wave function is large near the PbI2 planes of this region, as it is composed of mainly I (5p) and Pb (6s) orbitals. The dipole orientation, in either distorted or undistorted inorganic frameworks, breaks the interplane symmetry and pushes the hole into a favored plane. In the Unpol model, the VBM is homogeneously distributed across all PbI2 planes parallel to the ab plane. Analogously, one would expect in the base unit cell and model M1 that the CBM wave function would be localized at the PbI2 plane in the center of the cell, where the MA cations head the positive part (NH3+ group). However, as seen in Figure 3, top, this is observed only in the undistorted structure (base cell with 72% localization). The localization is here somewhat lower than in the VBM case, probably because the MA cation interacts less directly with the Pb ions, the orbitals of which mainly form the conduction state. The CBM wave function of the relaxed M1 structure, on the contrary, is delocalized on the whole cell; that is, it is equally shared by all PbI2 planes, similar to the Unpol model. This means that the structural relaxation or distortion of the inorganic framework drives the system to maintain an equivalent contribution of all PbI2 planes to the lowest unoccupied wave function despite the orientation of the organic cations. Consequently, the minimum in the electrostatic potential under this condition is avoided. These patterns do not change when a net charge ±1 is imposed to the M1 system. We may mention that the charge densities of this model remain unchanged (data not shown) in both PBEonly and van der Waals-including48 density functional approaches.

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RESULTS AND DISCUSSION The relaxed structures (T = 0 K) reasonably reproduce both the configuration of the inorganic framework and the MA orientations corresponding to the CH3NH3PbI3 tetragonal phase (see model structures in Figure S1). There are distortions with respect to the initial (ideal) symmetry structure, as expected. However, the distortions are similar to those obtained within the configurational ensembles of this phase that include the thermal effects (see details in Table S1). The relaxed structure of the unpolarized cell, named Unpol model, is the most stable configuration within the tetragonal models. Formation of the polarized tetragonal cell models is energetically feasible, since they are close in energy with respect to the reference (Unpol) cell (ΔE ≤ 7.3 meV/atom). 26700


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symmetry in the geometry of the PbI2 planes. In this case, the Pb−I distance significantly increases in the layer facing NH3+ groups, while it remains almost unchanged with respect to the base cell in the other plane (see Figure 4). In this way, the inorganic framework tends to shield the positive charge centers, reducing the molecular dipole effect on the crystal potential. In other words, the local polarization environment around each organic cation partially compensates the polarized domains of the MA dipole moments. In the undistorted structure (base cell) the orientation of molecular dipoles provides the electric potential that confines electrons and holes, as seen in refs 24, 25, and 27. In the distorted structure, the adapted cuboctahedral (MA)I12 cavity, because of favorable interactions with MA cations, keeps the inequivalence between the iodines in the VBM state, so that holes become localized on only some of them. However, the same distortion screens the effect of oriented dipoles on the inequivalence between the lead atoms, which mainly form the conduction band. This highlights the importance of considering the effect of flexible inorganic structure on the electronic properties of perovskites. The delocalized distribution of the VBM state of Unpol model suggests that the confinement of holes within only one of the PbI2 planes requires layers with an appropriate orientation of MA cations. Results from the larger models with double and triple cells are shown in Figure 5 (see corresponding electron-density isosurfaces in Figures S4 and S5). These models consider the possible formation of larger or wider polarized domains due to the orientation of MA cations by layers. Leaving aside the result of model M3b, the VBM wave function (and its potential for hole confinement) appears localized always at the expected PbI2 planes. Notice that the contributions of other PbI2 planes to the VBM state are negligible. On the other hand, model M3b does shows a strong hole confinement at the PbI2 plane around c = 32.5 Å, but not in the plane at c ≈ 12.5 Å as could be expected. The results of all models lead us to conclude in any

When the base cell relaxes to the M1 model, on average the nitrogen atoms are closer to iodine atoms than carbon atoms (see Figure 4 and the pair distribution function analysis in

Figure 4. Cuboctahedral (MA)I12 cavity (bottom) and how it looks inside the surrounding lead atoms (MA)Pb4I12 (top) in the base unit cell (left) and in M1 model (right). Pb−I bond distances are highlighted (black dashed lines) in each case. Possible hydrogen-bond interactions [N−H···I]; with H−I distance equal to or less than 3.0 Å, are represented with sticks.

Figure S2). This configuration favors hydrogen-bond interactions between NH3+ groups and nearby iodines, as has been reported.19,26,49−51 Note that the hydrogen bonds presented in the base cell are only with the PbI2 plane facing the NH3+ groups. However, the M1 model relaxes to a configuration in which the hydrogen bonds involve iodine atoms of both PbI2 planes and intermediates. These interactions deform the inorganic structure, tilting the octahedra and breaking the

Figure 5. Charge-density profiles along the c-axis of the VBM (bottom) and CBM (top) for M2 and M3a−d models. Graphics include the density profile of neutral models (lines) and charged models (dotted line for q = +1, dashed line for q = −1). Data for the CBM were increased (×4) to improve the visual representation. Shaded regions represent zones of localization with the indicated percentages. 26701


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Figure 6. Band diagrams of M2 and M3a−d models computed along the X-Γ-Z direction. The VBM (Fermi energy) is indicated with a dotted line.

vector due to the orientation of many layers of organic cations might be formed, the relaxation of iodine cavities tends to polarize the environment of the positive charge centers within the supercell. The strength of the octahedral Pb−I bonds weakens regularly in the PbI2 planes that face the positive charge of MA cations (see Figure S3). Under this condition, at least, there is not an effective molecular dipole to provide the electric potential within the lattice. The band structure shows, in all polarized models, a clear anisotropy in the dispersion of the top of valence bands along the X-Γ-Z direction (see Figure 6 for M2 and M3a−d models and Figure S6 for M1 and Unpol models). Note that the dispersion is significantly reduced along the Z-direction, that is, perpendicularly to the PbI2 planes where the hole is confined. The effective masses and the widths of the top valence band of all models (Table S2) support the confinement behavior discussed above. In contrast, the bands are rather isotropic for the lowest conduction bands. These results are in agreement with the localization/delocalization patterns found in the realspace analysis. Can the cuboctahedral cavity shield stronger molecular dipoles? We assessed this effect by a simple test in which model M1 was constructed by replacing MA cations with trifluorinated ones (CF3NH3+). The dipole moment is triplicated, according to the estimation in vacuum conditions.14 The confinement of the hole remains, in this case, almost unchanged compared to M1 (see Figure 7), and the localization of the CBM wave function is still modest (∼6%). Moreover, Figure 7 also shows that localization of the frontier states does not significantly change for smaller molecular dipole, as for CH3PH3+. In fact, the latter result is more similar to that obtained with CF3NH3+ than that found for CH3NH3+, suggesting that maybe this effect is more dependent on the size of the cation, and their influence over the lattice distortions, than on its dipole moment strength. This outcome suggests that the magnitude of the cation dipole might not be determinant to confine electrons or holes in the hybrid perovskites.

case that two single layers of MA dipoles pointing outward are enough to cause hole confinement in PbI2 planes. However, the orientation of molecular dipoles does not appear to be the only determinant factor to define the hole location within a particular plane. Model M3b relaxed to a configuration where the I and Pb atoms involved in VBM state are almost in the same plane. That is, the tilting of the octahedra around the c-axis (in the plane at c ≈ 32.5 Å) is reduced in comparison with the equivalent distortions in other planes (see Figure S1 and related text). It is known that octahedral distortion in these types of structures is due to electronic stabilization caused by the allowed hybridization between Pb and I atomic orbitals.15,52 The minor distortion in this plane within the supercell is a response to the reduction of this hybridization, and consequently the occupied state is relatively less stabilized. The results of this model demonstrate the effect of lattice distortions induced by the orientation of the molecular dipoles to guide localization of the electronic states. The electron-density picture at the CBM appears in all these cases mainly delocalized over all PbI2 planes in the supercell models (see Figure 5), similar to the corresponding state in M1 and Unpol models. The addition of one electron (q = −1) does not change this behavior significantly. M3a, M3c, and M3d models show a slight increase of CBM charge density in some planes respect to others within the supercell. Notice that, unlike VBM localization, the regions with increased CBM density sometimes include the PbI2 plane where electron localization could be expected, and some other PbI2 planes close to it (Figure 5). But these effects are slight; if one considers a uniform distribution of CBM electron density over the PbI2 planes, the augmentation due to the MA polarized domains is around 3% for M3a and M3d models and 6% for M3c model. Hence, these models show that the localization of electrons at the CBM has some variation but is still weaker than that obtained for holes. These results are in agreement with the previous interpretation of the frontier states of M1 model compared with the states of base cell. That is, although a larger dipole 26702


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Pb and I structure of this model). In the latter case, the chargedensity profile was obtained with (CsPbI3) and without ([Cs]PbI3) relaxation of the position of Cs atoms. Similarly, corresponding models were obtained from the base cell. If the Cs atoms are in place of the ammonium cations without relaxation (i.e., the structures [Cs]PbI3, in which the position of Cs atoms approaches the position of the positive end of the MA ion), the confinement of holes and electrons is almost equivalent to that found for the original M1 and base cells (see Figure 8). That is, a significant confinement of the holes appears in either distorted (M1 model) or undistorted (base cell) inorganic framework, but the confinement of electrons is observed only in the base cell. This result reveals the importance of asymmetric interaction of the positive charge (that is, of any cation) within the iodine cuboctahedron for confinement of the wave functions in perovskites. Conversely, by relaxing the Cs atoms (CsPbI3) they tend to the center of the iodine cuboctahedron to form a similar interaction with all anions. In this case, the charge densities of the frontier bands tend to be distributed almost homogeneously along all PbI2 planes. The situation is almost equivalent to the model in which the negative charge of the inorganic network was fixed (PbI3]−1), that is, by removing the cation. Overall, we can conclude that the nonspherical nature of the organic cation, with its positive charge at location driven by its interaction with the polarizable network of iodine atoms, regardless of the strength of cation dipole, is responsible for the electron−hole asymmetry. Two-dimensional hole confinement within a PbI2 plane seems to require at least two single layers of the dipole cation with opposite orientations. This configuration could appear, maybe as a transient state, because of the considerable thermally activated motion of the lattice and the picosecond time scale of cation rotation. Hence, these hole confinement planes may provide carrier diffusion pathways in the hightemperature phases of this perovskite. In contrast, model Mort, which has been considered as a reference for the orthorhombic

Figure 7. Charge-density profiles along the c-axis of the VBM (red, bottom) and CBM (blue, top) for M1 (lines), (CF3NH3+)PbI3 (dotted lines), and (CH3PH3+)PbI3 (dotted−dashed lines) models. The density profiles correspond to the neutral systems.

The confinement of holes is favored by both MA orientations and distortion of the inorganic framework. The iodine cuboctahedron is then asymmetrically deformed due to interactions with the cations. We have tested this idea by performing a calculation of the M1 structure and removing the MA cations. That is, we are considering the [PbI3]−1 network (with the negative charge fixed), keeping the Pb and I positions fixed as in the full M1 structure. In addition, we place cesium (Cs) atoms at the position of the nitrogen atoms of the corresponding methylammonium in M1 model (i.e., using the

Figure 8. Charge-density profiles along the c-axis (VBM in red and CBM in blue): from left to right, base unit cell (bottom) and M1 model (top); inorganic framework ([PbI3]−1 without MA cations) of the corresponding model; cesium (Cs) in place of nitrogen (N) atoms of the corresponding methylammonium without relaxation ([Cs]PbI3); and Cs atoms relaxed within the inorganic framework of the corresponding model (CsPbI3). 26703


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assistance provided by the Centro de Supercomputación and Visualización de Madrid (CESVIMA).

phase, does not show a localizing effect of the frontier states (see Figure S4). The studied CH3NH3PbI3 models show that neither the molecular dipole nor the inorganic framework distortion alone can provide significant two-dimensional conduction electron localization; a cooperation of different factors may be required for this.

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(1) Green, M. A.; Ho-Baillie, A. Perovskite Solar Cells: The Birth of a New Era in Photovoltaics. ACS Energy Lett. 2017, 2, 822−830. (2) Stranks, S. D.; Eperon, G. E.; Grancini, G.; Menelaou, C.; Alcocer, M. J. P.; Leijtens, T.; Herz, L. M.; Petrozza, A.; Snaith, H. J. Electron-Hole Diffusion Lengths Exceeding 1 Micrometer in an Organometal Trihalide Perovskite Absorber. Science 2013, 342, 341− 344. (3) Dong, Q.; Fang, Y.; Shao, Y.; Mulligan, P.; Qiu, J.; Cao, L.; Huang, J. Electron-Hole Diffusion Lengths > 175 μm in SolutionGrown CH3NH3PbI3 Single Crystals. Science 2015, 347, 967−970. (4) Shi, D.; Adinolfi, V.; Comin, R.; Yuan, M.; Alarousu, E.; Buin, A.; Chen, Y.; Hoogland, S.; Rothenberger, A.; Katsiev, K.; et al. Low TrapState Density and Long Carrier Diffusion in Organolead Trihalide Perovskite Single Crystals. Science 2015, 347, 519−522. (5) Miyata, A.; Mitioglu, A.; Plochocka, P.; Portugall, O.; Wang, J. T.W.; Stranks, S. D.; Snaith, H. J.; Nicholas, R. J. Direct Measurement of the Exciton Binding Energy and Effective Masses for Charge Carriers in Organic-Inorganic Tri-Halide Perovskites. Nat. Phys. 2015, 11, 582−587. (6) Brenner, T. M.; Egger, D. A.; Rappe, A. M.; Kronik, L.; Hodes, G.; Cahen, D. Are Mobilities in Hybrid Organic-Inorganic Halide Perovskites Actually “High”? J. Phys. Chem. Lett. 2015, 6, 4754−4757. (7) Zhu, X.-Y.; Podzorov, V. Charge Carriers in Hybrid-OrganicInorganic Lead-Halide Perovskites Might Be Protected as Large Polarons. J. Phys. Chem. Lett. 2015, 6, 4758−4761. (8) Phuong, L. Q.; Nakaike, Y.; Wakamiya, A.; Kanemitsu, Y. Free Excitons and Exciton-Phonon Coupling in CH3NH3PbI3 Single Crystals Revealed by Photocurrent and Photoluminescence Measurements at Low Temperatures. J. Phys. Chem. Lett. 2016, 7, 4905−4910. (9) Semonin, O. E.; Elbaz, G. A.; Straus, D. B.; Hull, T. D.; Paley, D. W.; van der Zande, A. M.; Hone, J. C.; Kymissis, I.; Kagan, C. R.; Roy, X.; et al. Limits of Carrier Diffusion in n-Type and p-Type CH3NH3PbI3 Perovskite Single Crystals. J. Phys. Chem. Lett. 2016, 7, 3510−3518. (10) Zhu, H.; Miyata, K.; Fu, Y.; Wang, J.; Joshi, P. P.; Niesner, D.; Williams, K. W.; Jin, S.; Zhu, X.-Y. Screening in Crystalline Liquids Protects Energetic Carriers in Hybrid Perovskites. Science 2016, 353, 1409−1413. (11) Yang, X.; Yan, X.; Wang, Y.; Chen, W.; Wang, R.; Wang, W.; Li, H.; Ma, W.; Sheng, C. Photoluminescence in Organometal Halide Perovskites: Free Carrier Versus Exciton. IEEE Journal of Photovoltaics 2017, 7, 513−517. (12) Augulis, R.; Franckevičius, M.; Abramavičius, V.; Abramavičius, D.; Zakeeruddin, S. M.; Grätzel, M.; Gulbinas, V. Multistep Photoluminescence Decay Reveals Dissociation of Geminate Charge Pairs in Organolead Trihalide Perovskites. Adv. Energy Mater. 2017, 7, No. 1700405. (13) Munson, K. T.; Grieco, C.; Kennehan, E. R.; Stewart, R. J.; Asbury, J. B. Time-Resolved Infrared Spectroscopy Directly Probes Free and Trapped Carriers in Organo-Halide Perovskites. ACS Energy Lett. 2017, 2, 651−658. (14) Frost, J. M.; Butler, K. T.; Brivio, F.; Hendon, C. H.; van Schilfgaarde, M.; Walsh, A. Atomistic Origins of High-Performance in Hybrid Halide Perovskite Solar Cells. Nano Lett. 2014, 14, 2584− 2590. (15) Frost, J. M.; Walsh, A. What Is Moving in Hybrid Halide Perovskite Solar Cells? Acc. Chem. Res. 2016, 49, 528−535. (16) Worhatch, R. J.; Kim, H. J.; Swainson, I. P.; Yonkeu, A. L.; Billinge, S. J. L. Study of Local Structure in Selected Cubic OrganicInorganic Perovskites. Chem. Mater. 2008, 20, 1272−1277. (17) Frost, J. M.; Butler, K. T.; Walsh, A. Molecular Ferroelectric Contributions to Anomalous Hysteresis in Hybrid Perovskite Solar Cells. APL Mater. 2014, 2, No. 081506. (18) Quarti, C.; Mosconi, E.; De Angelis, F. Interplay of Orientational Order and Electronic Structure in Methylammonium

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CONCLUSIONS In summary, if the CH3NH3PbI3 structure presents an order of organic cations that provides not only a null global dipole but also no organization of dipole heads in any particular direction (such as happens in the Unpol model presented here), then the charge densities of the frontier bands are distributed homogeneously along all PbI2 planes. However, it seems that two single layers of CH3NH3+ dipoles oriented outward are enough to cause hole confinement in tetragonal-phase models. Layers with opposite polarization along the unique axis may cause symmetry breaking, with the effect of localizing the VBM and hole in the PbI2 layer that gets in touch with CH3 groups. In contrast, a very weak localization is found for electrons in the CBM near the NH3+ groups. Modification of the organic cations by manipulation of their intrinsic dipole magnitude cannot change this behavior. That is probably because the hybrid structure evolves in a way to shield the charges, avoiding formation of the proposed electric potential. Our finding highlights the importance of inorganic framework polarizability in perovskites as a guide to their carrier- transport behavior.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcc.7b09625. Cell dimensions and atomic positions of the base unit cell, Unpol, M1, M2, M3a−d, and Mort models (TXT) Additional text, six figures, and two tables with structural parameters of all models, isosurfaces of consistent electron density associated with wave functions of VBM and CBM for each model, band diagrams of M1 and Unpol models, and effective masses and widths of the top valence band of each model (PDF)

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REFERENCES

AUTHOR INFORMATION

Corresponding Author

*E-mail [email protected]; phone +56 2 2978 7439. ORCID

Ana L. Montero-Alejo: 0000-0003-1675-0546 J. C. Conesa: 0000-0001-9906-8520 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This research was supported by FONDECYT Grants 3150174 and 1171807 (Chile), by the Comunidad de Madrid Project MADRID-PV (S2013/MAE/2780), and by the Ministerio de Economı ́a y Competitividad through Project SEHTOP-QC (ENE2016-77798-C4-4-R) (Spain). Powered@NLHPC: This research was partially supported by the supercomputing infrastructure of the NLHPC (ECM-02) at Universidad de Chile. We acknowledge the computer resources and technical 26704


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