Ferroelectric Domains May Lead to Two-Dimensional Confinement of

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Ferroelectric Domains May Lead to 2-D Confinement of Holes but Not of Electrons in CHNHPbI Perovskite 3

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Ana Lilian Montero-Alejo, Eduardo Ariel Menendez Proupin, Pablo Palacios, Perla Wahnon, and José Carlos Conesa J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.7b09625 • Publication Date (Web): 07 Nov 2017 Downloaded from http://pubs.acs.org on November 9, 2017

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The Journal of Physical Chemistry

Ferroelectric Domains May Lead to 2-D Confinement of Holes but Not of Electrons in CH3NH3PbI3 Perovskite Ana L. Montero-Alejo,∗,† E. Menéndez-Proupin,‡ P. Palacios,¶ P. Wahnón,§ and J. C. Conesak Group of Materials Modeling, Departamento de Física, Facultad de Ciencias, Universidad de Chile, Las Palmeras 3425, 780-0003 Ñuñoa, Santiago, Chile, Departamento de Física, Facultad de Ciencias, Universidad de Chile, Las Palmeras 3425, 780-0003 Ñuñoa, Santiago, Chile, Instituto de Energía Solar and Dept. FAIAN, ETSIAE Aeronáutica y del Espacio, Universidad Politécnica de Madrid, Spain, Instituto de Energía Solar and Dept. TFB, E.T.S.I. Telecomunicación, Universidad Politécnica de Madrid, Spain, and Instituto de Catálisis y Petroleoquímica, CSIC, Marie Curie 2, 28049 Madrid, Spain E-mail: [email protected]

To whom correspondence should be addressed Group of Materials Modeling, Departamento de Física, Facultad de Ciencias, Universidad de Chile, Las Palmeras 3425, 780-0003 Ñuñoa, Santiago, Chile ‡ Departamento de Física, Facultad de Ciencias, Universidad de Chile, Las Palmeras 3425, 780-0003 Ñuñoa, Santiago, Chile ¶ Instituto de Energía Solar and Dept. FAIAN, ETSIAE Aeronáutica y del Espacio, Universidad Politécnica de Madrid, Spain § Instituto de Energía Solar and Dept. TFB, E.T.S.I. Telecomunicación, Universidad Politécnica de Madrid, Spain k Instituto de Catálisis y Petroleoquímica, CSIC, Marie Curie 2, 28049 Madrid, Spain ∗ †

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Abstract We investigate the possibility that formation of ferroelectric domains in CH3 NH3 PbI3 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 the solar cells of hybrid perovskites. We find that a two-dimensional hole confinement in CH3 NH3 PbI3 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 by varying the strength of the ordered dipoles. The confinement of holes is favored by the 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 the electrons.

Introduction Photovoltaic (PV) research has been shaken by the introduction of the metal-organic perovskite CH3 NH3 PbI3 . The solar cells based on this material are expected to be even more efficient and commercially competitive with other energy source in the coming years. 1 Presumably, the hybrid nature of this semiconductor provides the most suitable properties within the PV materials, i.e. broad sun light-harvesting and an efficient separation of photo-carriers. Latest feature seems to be a consequence of the experimentally determined long carrier lifetime (giving high photo-luminescence quantum yield), 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 carries, especially for the 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 the recombination 14,15 (see Figure 1). These diffusion paths would be located at the walls of ferroelectric 2


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nano-domains that could be formed within the crystal. Spontaneous polarization within the structure can be caused by the alignment and displacement of the CH3 NH+ 3 (MA) cations, as well as displacement of Pb off the centers of the PbI6 octahedra. All these possibilities are justified by the well-known structurally “soft” nature, i.e. the dynamic symmetry breaking in the room temperature phases of this material. 14–20 The ferroelectric behavior of CH3 NH3 PbI3 remains an important topic of discussion, since this property appears as 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

Figure 1: Proposition of a multidomain ferroelectric thin-film in hybrid perovskites (adapted from ref. 14 with permission from American Chemical Society). 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. Prior theoretical studies have already supported the idea of the charge localization in CH3 NH3 PbI3 due to the 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 the inorganic framework distortions. 26,28–31 The structural dynamics of the system makes difficult to 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 degree 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 the two-dimensional pathways for photo-carriers and identify planes in the CH3 NH3 PbI3 crystal where the alignment of MA cation dipoles may 3



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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 only revealed 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 in the picosecond time scale of the organic cation, two-dimensional conduction paths of the holes at the valence band could be expected. Our models provide insights for a better understanding of the complex charge carrier transport properties in the metal-organic perovskites.

Models and Computational Methods The existing crystallographic models of the room temperature CH3 NH3 PbI3 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 CH3 NH3 PbI3 39 in which the partial disorder of organic cations is suppressed lowering the

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lattice symmetry to monoclinic (space group P 21 /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 (SI)). 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 which are oriented in the same direction 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 couple of opposed short arrows that represent the dipoles of the two consecutive MA layers (see Figure 2).

Figure 2: a) Crystal structure of the CH3 NH3 PbI3 base unit cell (tetragonal phase model). Each layer of two MA (CH3 NH+ 3 ) is schematized by a short arrow. A couple of opposed short arrows within a box represent the unit cell. b) Symbols of different models of polarized nanodomains in CH3 NH3 PbI3 for tetragonal-derived (M1, M2, M3a, M3b, M3c and M3d) 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). The colored lines represent the possible localization sites of electrons (blue) and holes (red). If in each of the two layers parallel to the ab plane of the base unit cell the C and N atoms are exchanged in one of the two MA, retaining the inversion symmetry (triclinic space group P¯1), one obtains a cell in which no layer of MA ions has a net dipole moment. In this way, 5



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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 nano-domains 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 the CH3 NH+ 3 ) in each layer to obtain different arrangements of net dipole layers. A couple 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. The red and blue marks represent the regions where holes and electrons could be expected to localize if the above 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 low temperature phase (Mort) of CH3 NH3 PbI3 , used in our previous work, 40 is also added. In this case, a couple of short horizontal arrows represent the MA dipoles which are oriented parallel to the ab−plane. We have performed on these models DFT calculations with the 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 and charged states (q=0, 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. The k-point grid was automatically generated requiring that the maximum space between adjacent k-points is smaller than 0.3 Å−1 (mesh of 3 × 3 × 1 for all supercell models). The state occupation numbers were fixed manually to ensure that the electron (q=−1) at the lowest conduction band (LCB) or the hole (q=+1) at the highest valence band (HVB) are

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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. The electron density distributions and the band structures were obtained considering spin-orbit coupling, as it is crucial to describe the structure of the conduction band states 40,44 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 to 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-Dresselhauss splitting. 45 The visualization of the structures and the isosurfaces were achieved with the help of VESTA 46 and VMD 47 packages.

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 CH3 NH3 PbI3 tetragonal phase (see model structures in Fig. S1 of SI). 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 SI, Table S1). The relaxed structure of the unpolarized cell, named Unpol model, is the most stable configuration within the tetragonal models. The formation of the polarized tetragonal cell models is energetically feasible, since they are close in energy with respect to the reference (Unpol) cell (∆E ≤ 7.3 meV/atom). 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

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as it was proposed. 14,15 The charge density profile along the c−axis, right-hand side of the Figure 3, quantify the localization of the VBM wave function at 83 % for M1 (90 % for the equivalent area in 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, either in distorted or undistorted inorganic frameworks, breaks the inter-plane symmetry and pushes the hole into a favored plane. In Unpol model the VBM is homogeneously distributed across all PbI2 planes parallel to the ab−plane.

Figure 3: At left, electron density distributions of the VBM and CBM of base unit cell, relaxed M1 and unpolarized (Unpol) models. At right, the corresponding electron density profiles along the c−axis. The transparent filled regions represent the calculated percentage of localization of the M1 (VBM in red) and base unit cell (CBM in blue) wave functions. Analogously, one would expect in the base unit cell and model M1 that the CBM wave function be localized at the PbI2 plane in the center of the cell, where the MA cations head the positive part (NH+ 3 group). However, as seen in Fig. 3 (top), this is only observed in the undistorted structure (base cell with 72 % of 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 form mainly the conduction state. The CBM wave function of the relaxed M1 structure, on the contrary, is delocalized on the whole 8


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cell, i.e. it is equally shared by all PbI2 planes, similar to the Unpol model. This means that the structural relaxation or the distortions of inorganic framework drives the system to maintain an equivalent contribution of all PbI2 planes to the lowest unoccupied wavefunction 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 PBE-only and van der Waals-including 48 density functional approaches. When the base cell relaxes to the M1 model, as average the nitrogen atoms are closer to iodine atoms than the carbon atoms (see Figure 4 and the pair distribution functions analysis, Figure S2 in SI). This configuration favors the hydrogen bond interactions between the NH+ 3 groups and the nearby iodines, as have been reported. 19,26,49–51 Note that the hydrogen bonds presented in the base cell are only with the PbI2 plane facing the NH+ 3 groups. However, M1 model relax to a configuration in which the hydrogen bonds involves iodine atoms of both PbI2 planes and the intermediates. These interactions deform the inorganic structure, tilting the octahedra and breaking the symmetry among the geometry of the PbI2 planes. In this case, the Pb-I distance significantly increases in the layer facing NH+ 3 groups, while remaining 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 confine electrons and holes, as seen in Ref. 24, 25 and 27. In the distorted structure, the adapted cuboctahedral (MA)I12 cavity, because of the 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

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the effect the oriented dipoles on the inequivalence between the lead atoms which form mainly the conduction band. This highlights the importance of considering the effect of the 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 the MA cations.

Figure 4: Cuboctahedral (MA)I12 cavity (bottom) and how it looks inside the surrounding lead atoms (MA)Pb4 I12 (top) in the base unit cell (left) and in M1 model (right). Pb-I bond distances are highlighted (black dashed lines) in each case. The possible hydrogen bond interactions [N-H· · ·I]; with H-I distance equal or less than 3.0 Å, are represented with sticks. Results from the larger models with double and triple cells are shown in Fig. 5 (see the corresponding electron density isosurfaces in Fig. S4 and S5 of the SI). 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 10


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Å, but not in the plane at c ≈ 12.5 Å as could be expected. The result of all models leads us to conclude in any case that two single layers of MA dipoles pointing outward are enough to cause hole confinement in PbI2 planes. M3a

M2

M3b

q= 0 q=−1

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Figure 5: Charge density profile along the c−axis of the VBM (bottom) and CBM (top) for M2, M3a, M3b, M3c and M3d models. Graphics include the density profile of neutral (lines) and charged (dot line for q= +1, dashed line for q= −1) models. The data of the CBM were increased (x4) to improve the visual representation. The transparent filled regions represent the zones of localization with the indicated percentage. 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) are reduced in comparison with the equivalent distortions in other planes (see Fig. S1 and related text of the SI). It is known that the octahedral distortion in these type of structures is due to the 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 are relatively less 11



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stabilized. The result of this model evidences the effect of the lattice distortions induced by the orientation of the molecular dipoles to guide the 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 significantly this behavior. M3a, M3c and M3d models show a slight increase of the CBM charge density in some planes respect to others within the supercell. Notice that, unlike the VBM localization, the regions with an increased CBM density sometimes include the PbI2 plane where the electron localization could be expected, and some other PbI2 planes close to it (Figure 5). But these effects are slight; if one considers an uniform distribution of the 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 variations, but is still weaker than that obtained for holes. These results are in agreement with the above interpretation of the frontier states of M1 model compared with the states of base cell. That is, although a larger dipole vector due to the orientation of many layers of organic cations might be formed, the relaxation of the 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 the MA cations (see Figure S3 of the SI). Under this condition, at least, there isn’t 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 and Figure S6 in SI for M1 and Unpol models). Note that the dispersion is significantly reduced along the Zdirection, i.e. 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 in SI) support the confinement behavior discussed above. In contrast, the bands are rather isotropic for the

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lowest conduction bands. These results are in agreement with the localization/delocalization patterns found in the real space analysis. M2

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Figure 6: Band diagrams of the M2, M3a, M3b, M3c and M3d models computed along the X-Γ-Z direction. The VBM (Fermi energy) is indicated with a dotted line. 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 the trifluorinated ones (CF3 NH+ 3 ). 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 the localization of the frontier states does not significantly change for smaller molecular dipole, as it is for the (CH3 PH+ 3 ). In fact, the latter result is more similar to that obtained with (CF3 NH+ 3 ), than that found for (CH3 NH+ 3 ), 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. 13



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Figure 7: Charge density profile along the c−axis of the VBM in red (bottom) and CBM in + blue (top) for M1 (lines), (CF3 NH+ 3 )PbI3 (dot lines) and (CH3 PH3 )PbI3 (dot dashed lines) models. The density profiles correspond to the neutral systems. The confinement of holes is favored by both, the MA orientations and the distortion of the inorganic framework. The iodine cuboctahedron is then asymmetrically deformed due to the interactions with the cations. We have tested this idea performing a calculation of the M1 structure 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 Pb and I structure of this model). In the latter case, the charge density profile was obtained with (CsPbI3 ) and without ([Cs]PbI3 ) relaxing the position of Cs atoms. Similarly, corresponding models were obtained from the base cell. If the Cs atoms are in place of the ammonium cation 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 ap14


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pears either in distorted (M1 model) or undistorted (base cell) inorganic framework, but the confinement of electrons is only observed in the base cell. This result reveals the importance of the asymmetric interaction of the positive charge, i.e. of any cation, within the iodine cuboctahedron for the confinement of the wave functions in the 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 ), i.e. by removing the cation. Overall, we can conclude that the non-spherical 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 of the electron-hole asymmetry.

CH3NH3PbI3

[PbI3]−1

[Cs]PbI3

CsPbI3

hole electron

hole electron

hole electron

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12.8

6.4 3.2 0.0 0.0 0.2 0.4 0.6 0.8 1.0

0.0 0.2 0.4 0.6 0.8 1.0

0.0 0.2 0.4 0.6 0.8 1.0

0.0 0.2 0.4 0.6 0.8 1.0

12.8

hole electron

hole electron

hole electron

hole electron

9.6

base

Z vector (Å)

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6.4 3.2 0.0 0.0 0.2 0.4 0.6 0.8 1.0

Ψ2 (a.u.)

0.0 0.2 0.4 0.6 0.8 1.0

0.0 0.2 0.4 0.6 0.8 1.0

Ψ2 (a.u.)

Ψ2 (a.u.)

0.0 0.2 0.4 0.6 0.8 1.0

Ψ2 (a.u.)

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), the 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 ).

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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 the cation rotation. Hence, these hole confinement planes may provide carrier diffusion pathways in the high-temperature phases of this perovskite. In contrast, model Mort, which has been considered as reference of the orthorhombic phase, does not show a localizing effect of the frontier states (see Figure S4 of the SI). The studied CH3 NH3 PbI3 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.

Conclusions In summary, if the CH3 NH3 PbI3 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), the charge densities of the frontier bands are distributed homogeneously along all PbI2 planes. However, it seems that two single layers of CH3 NH+ 3 dipoles outward oriented are enough to cause hole confinement in tetragonal phase models. Layers with opposite polarization along the unique axis may cause a 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 NH+ 3 groups. The modification of the organic cations by the manipulation of their intrinsic dipole magnitude cannot change this behavior. That is probably because the hybrid structure evolves in the way to shield the charges avoiding the formation of the proposed electric potential. Our finding highlights the importance of inorganic framework polarizability in perovskites as a guide of their carrier transport behavior.

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Acknowledgement This research has been supported by FONDECYT Grants No. 3150174 and 1171807 (Chile), by the Comunidad de Madrid project MADRID-PV (S2013/MAE/2780) and by the Ministerio de Economía y Competitividad through the project SEHTOP-QC (ENE2016-77798C4-4-R) (Spain). Powered@NLHPC: This research was partially supported by the supercomputing infrastructure of the NLHPC (ECM-02) at Universidad de Chile. The authors acknowledge the computer resources and technical assistance provided by the Centro de Supercomputación and Visualización de Madrid (CESVIMA).

Supporting Information Available The following files are available free of charge. 1: Models: Cell dimensions and atomic positions of the base unit cell, Unpol, M1, M2, M3a, M3b, M3c, M3d and Mort models. 2: Analysis: Structural parameters of all models. Isosurfaces of the consistent electron density associated to the wave functions of the VBM and the CBM for each model, band diagrams of M1 and Unpol models, effective masses and widths of the top valence band of each model. This material is available free of charge via the Internet at http://pubs.acs.org/.

References (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

17



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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 Solution-Grown CH3 NH3 PbI3 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 Trap-State 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. Nature Physics 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-Organic-Inorganic 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 ExcitonPhonon Coupling in CH3 NH3 PbI3 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 Car18


Page 18 of 25

Page 19 of 25

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


rier Diffusion in n-Type and p-Type CH3 NH3 PbI3 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, 1700405. (13) Munson, K. T.; Grieco, C.; Kennehan, E. R.; Stewart, R. J.; Asbury, J. B. TimeResolved Infrared Spectroscopy Directly Probes Free and Trapped Carriers in OrganoHalide 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 Organic-Inorganic Perovskites. Chem. Mater. 2008, 20, 1272–1277.

19



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

(17) Frost, J. M.; Butler, K. T.; Walsh, A. Molecular Ferroelectric Contributions to Anomalous Hysteresis in Hybrid Perovskite Solar Cells. APL Mater. 2014, 2, 081506. (18) Quarti, C.; Mosconi, E.; De Angelis, F. Interplay of Orientational Order and Electronic Structure in Methylammonium Lead Iodide: Implications for Solar Cells Operation. Chem. Mater. 2014, 26, 6557–6569. (19) Montero-Alejo, A. L.; Menéndez-Proupin, E.; Hidalgo-Rojas, D.; Palacios, P.; Wahnón, P.; Conesa, J. C. Modeling of Thermal Effect on the Electronic Properties of Photovoltaic Perovskite CH3 NH3 PbI3 : The Case of Tetragonal Phase. J. Phys. Chem. C 2016, 120, 7976–7986. (20) Beecher, A. N.; Semonin, O. E.; Skelton, J. M.; Frost, J. M.; Terban, M. W.; Zhai, H.; Alatas, A.; Owen, J. S.; Walsh, A.; Billinge, S. J. L. Direct Observation of Dynamic Symmetry Breaking above Room Temperature in Methylammonium Lead Iodide Perovskite. ACS Energy Lett. 2016, 1, 880–887. (21) Kutes, Y.; Ye, L.; Zhou, Y.; Pang, S.; Huey, B. D.; Padture, N. P. Direct Observation of Ferroelectric Domains in Solution-Processed CH3 NH3 PbI3 Perovskite Thin Films. J. Phys. Chem. Lett. 2014, 5, 3335–3339. (22) Hoque, M. N. F.; Yang, M.; Li, Z.; Islam, N.; Pan, X.; Zhu, K.; Fan, Z. Polarization and Dielectric Study of Methylammonium Lead Iodide Thin Film to Reveal its Nonferroelectric Nature under Solar Cell Operating Conditions. ACS Energy Lett. 2016, 1, 142–149. (23) Rohm, H.; Leonhard, T.; Hoffmann, M. J.; Colsmann, A. Ferroelectric Domains in Methylammonium Lead Iodide Perovskite Thin-Films. Energy Environ. Sci. 2017, 10, 950–955. (24) Ma, J.; Wang, L.-W. Nanoscale Charge Localization Induced by Random Orientations of Organic Molecules in Hybrid Perovskite CH3 NH3 PbI3 . Nano Lett. 2015, 15, 248–253. 20


Page 20 of 25

Page 21 of 25

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(25) Liu, S.; Zheng, F.; Koocher, N. Z.; Takenaka, H.; Wang, F.; Rappe, A. M. Ferroelectric Domain Wall Induced Band-Gap Reduction and Charge Separation in Organometal Halide Perovskites. J. Phys. Chem. Lett. 2015, 6, 693–699. (26) Quarti, C.; Mosconi, E.; De Angelis, F. Structural and Electronic Properties of OrganoHalide Hybrid Perovskites from Ab Initio Molecular Dynamics. Phys. Chem. Chem. Phys. 2015, 17, 9394–9409. (27) Pecchia, A.; Gentilini, D.; Rossi, D.; der Maur, M.; Di Carlo, A. Role of Ferroelectric Nanodomains in the Transport Properties of Perovskite Solar Cells. Nano Lett. 2016, 16, 988–992. (28) Hakamata, T.; Shimamura, K.; Shimojo, F.; Kalia, R. K.; Nakano, A.; Vashishta, P. The Nature of Free-Carrier Transport in Organometal Halide Perovskites. Sci. Rep. 2016, 6, 19599. (29) Neukirch, A. J.; Nie, W.; Blancon, J.-C.; Appavoo, K.; Tsai, H.; Sfeir, M. Y.; Katan, C.; Pedesseau, L.; Even, J.; Crochet, J. J. et al. Polaron Stabilization by Cooperative Lattice Distortion and Cation Rotations in Hybrid Perovskite Materials. Nano Lett. 2016, 16, 3809–3816. (30) Zhang, X.; Zhang, M.; Lu, G. Charge Stripe Formation in Molecular Ferroelectric Organohalide Perovskites for Efficient Charge Separation. J. Phys. Chem. C 2016, 120, 23969–23975. (31) Kang, B.; Biswas, K. Preferential CH3 NH+ 3 Alignment and Octahedral Tilting Affect Charge Localization in Cubic Phase CH3 NH3 PbI3 . J. Phys. Chem. C 2017, 121, 8319– 8326. (32) Ma, J.; Wang, L.-W. The Nature of Electron Mobility in Hybrid Perovskite CH3 NH3 PbI3 . Nano Lett. 2017, 17, 3646–3654.

21



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

(33) Lindblad, R.; Bi, D.; Park, B.-w.; Oscarsson, J.; Gorgoi, M.; Siegbahn, H.; Odelius, M.; Johansson, E. M. J.; Rensmo, H. Electronic Structure of TiO2 /CH3 NH3 PbI3 Perovskite Solar Cell Interfaces. J. Phys. Chem. Lett. 2014, 5, 648–653. (34) Mosconi, E.; Quarti, C.; Ivanovska, T.; Ruani, G.; De Angelis, F. Structure and Electronic Properties of Organo-Halide Lead Perovskites: a Combined IR-Spectroscopy and Ab-Initio Molecular Dynamics Investigation. Phys. Chem. Chem. Phys. 2014, 16, 16137–16144. (35) Carignano, M. A.; Kachmar, A.; Hutter, J. Thermal Effects on CH3 NH3 PbI3 Perovskite from Ab Initio Molecular Dynamics Simulations. J. Phys. Chem. C 2015, 119, 8991– 8997. (36) Goehry, C.; Nemnes, G. A.; Manolescu, A. Collective Behavior of Molecular Dipoles in CH3 NH3 PbI3 . J. Phys. Chem. C 2015, 119, 19674–19680. (37) Mattoni, A.; Filippetti, A.; Saba, M. I.; Delugas, P. Methylammonium Rotational Dynamics in Lead Halide Perovskite by Classical Molecular Dynamics: The Role of Temperature. J. Phys. Chem. C 2015, 119, 17421–17428. (38) Mattoni, A.; Filippetti, A.; Saba, M. I.; Caddeo, C.; Delugas, P. Temperature Evolution of Methylammonium Trihalide Vibrations at the Atomic Scale. J. Phys. Chem. Lett. 2016, 7, 529–535. (39) Kawamura, Y.; Mashiyama, H.; Hasebe, K. Structural Study on Cubic-Tetragonal Transition of CH3 NH3 PbI3 . J. Phys. Soc. Jpn. 2002, 71, 1694–1697. (40) Menéndez-Proupin, E.; Palacios, P.; Wahnón, P.; Conesa, J. C. Self-Consistent Relativistic Band Structure of the CH3 NH3 PbI3 Perovskite. Phys. Rev. B 2014, 90, 045207. (41) Kresse, G.; Furthmüller, J. Efficient Iterative Schemes for Ab Initio Total-Energy Calculations Using a Plane-Wave Basis Set. Phys. Rev. B 1996, 54, 11169–11186. 22


Page 22 of 25

Page 23 of 25

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(42) Blöchl, P. E. Projector Augmented-Wave Method. Phys. Rev. B 1994, 50, 17953–17979. (43) Kresse, G.; Joubert, D. From Ultrasoft Pseudopotentials to the Projector AugmentedWave Method. Phys. Rev. B 1999, 59, 1758–1775. (44) Even, J.; Pedesseau, L.; Jancu, J.-M.; Katan, C. Importance of Spin-Orbit Coupling in Hybrid Organic/Inorganic Perovskites for Photovoltaic Applications. J. Phys. Chem. Lett. 2013, 4, 2999–3005. (45) Amat, A.; Mosconi, E.; Ronca, E.; Quarti, C.; Umari, P.; Nazeeruddin, M. K.; Grätzel, M.; De Angelis, F. Cation-Induced Band-Gap Tuning in Organohalide Perovskites: Interplay of Spin-Orbit Coupling and Octahedra Tilting. Nano Lett. 2014, 14, 3608–3616. (46) Momma, K.; Izumi, F. VESTA 3 for Three-Dimensional Visualization of Crystal, Volumetric and Morphology Data. J. Appl. Crystallogr. 2011, 44, 1272–1276. (47) Humphrey, W.; Dalke, A.; Schulten, K. {VMD} – {V}isual {M}olecular {D}ynamics. J. Mol. Graphics 1996, 14, 33–38. (48) Klimeš, J.; Bowler, D. R.; Michaelides, A. Van der Waals Density Functionals Applied to Solids. Phys. Rev. B 2011, 83, 195131. (49) Quarti, C.; Grancini, G.; Mosconi, E.; Bruno, P.; Ball, J. M.; Lee, M. M.; Snaith, H. J.; Petrozza, A.; De Angelis, F. The Raman Spectrum of the CH3 NH3 PbI3 Hybrid Perovskite: Interplay of Theory and Experiment. J. Phys. Chem. Lett. 2014, 5, 279–284. (50) Weller, M. T.; Weber, O. J.; Henry, P. F.; Di Pumpo, A. M.; Hansen, T. C. Complete Structure and Cation Orientation in the Perovskite Photovoltaic Methylammonium Lead Iodide between 100 and 352 K. Chem. Commun. 2015, 51, 4180–4183. (51) Egger, D. A.; Kronik, L. Role of Dispersive Interactions in Determining Structural

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Properties of Organic-Inorganic Halide Perovskites: Insights from First-Principles Calculations. J. Phys. Chem. Lett. 2014, 5, 2728–2733. (52) Walsh, A.; Payne, D. J.; Egdell, R. G.; Watson, G. W. Stereochemistry of PostTransition Metal Oxides: Revision of the Classical Lone Pair Model. Chem. Soc. Rev. 2011, 40, 4455–4463.

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Table of Contents Graphic

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Ferroelectric Domains May Lead to Two-Dimensional Confinement of

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