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Collective Behavior of Molecular Dipoles in CHNHPbI Charles Goehry, George Alexandru Nemnes, and Andrei Manolescu

J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.5b05823 • Publication Date (Web): 07 Aug 2015 Downloaded from http://pubs.acs.org on August 12, 2015

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The Journal of Physical Chemistry

Collective behavior of molecular dipoles in CH3NH3PbI3 C. Goehry,† G. A. Nemnes,‡,¶ and A. Manolescu† †School of Science and Engineering, Reykjavik University, Menntavegur 1, IS-101, Reykjavik, Iceland ‡Horia Hulubei National Institute for Physics and Nuclear Engineering, 077126 Magurele, Ilfov, Romania ¶University of Bucharest, Faculty of Physics, Materials and Devices for Electronics and Optoelectronics Research Center, 077125 Magurele, Ilfov, Romania

Abstract

Keywords: Organohalide perovskites, atomistic simulations, dipole moments, correlation functions.

Using ab-initio molecular dynamics, we report a detailed exploration of the thermal motion occurring in perovskite crystals of formula CH3 NH3 PbI3 . We exploit the data generated to obtain estimates of the rotational relaxation time of the cation CH3 NH3+ . We examine the tetragonal and cubic phase, as both may be present under operational conditions. Influenced by each other, and by the tilting of PbI6 octahedra, cations undergo collective motion as their contribution to polarization does not vanish. We thereby qualitatively describe the modus operandi of formation of microscopic ferroelectric domains.

Introduction Organohalide lead perovskite is regarded as a promising candidate material in the array of solutions explored to answer modern global energetic challenges. The efficiency of the bestperforming solar cells based on MAPbI3 (MA stands for methylammonium CH3 NH3+ , the inorganic cage bearing a net negative charge PbI3− ) have seen a dramatic increase in the past few years, recently reaching up to 20.1 %. 1 Research on this type of cell is currently intense. 2–10 However, some aspects of the operating mode are still under debate. Researchers obtained a dynamic response (hysteresis) under working conditions, that makes unambiguous characterization of electric properties of hybrid perovskite solar cells efficiency problematic. 11–13 This anomalous behavior has been partly associated to microscopic ferroelectric domains, 14 but the ferroelectric character of the material has not been demonstrated. 15 Other possible factors, like charge trapping or ion migration within the perovskite layer are also involved. 16 X-ray diffraction techniques are unable to

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fully characterize the structure of MAPbI3 , 17 since the MA dipole and the inorganic PbI3− cage undergo permanent reorientation. 18–20 Only mean positions are shown in the crystal structures. MA dipoles are not directly involved in the band gap of this type of perovskites. 21 However, they create a local electric field and may participate in separating and diffusing efficiently electrons and holes generated by photons within the absorber material. 22–25 This is in contrast with p-n junctions where a macroscopic electric field spans over a region of several hundreds of nanometers. Precisely describing the motion of the dipoles could therefore help to explain the efficiency of perovskite solar cell and also the hysteresis of the material. Recently, various theoretical models were proposed, placing the focus on the behavior of those dipoles. 26–29 In this paper we propose to computationally describe the rotational motion of the dipoles within the inorganic cages in the absence of a bias voltage. We explore what factors are affecting their motion and whether collective behavior is to be expected in an ideal MAPbI3 crystal. The behavior of the dipoles in the presence of a bias voltage is also tested.

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perimental data. 17,33 Structural relaxations are performed using a 100 Ry mesh cut-off accounting for the grid in the real space, until the ˚ Van der Waals forces are less than 0.04 eV/A. pairwise corrections have not been considered here, as they have been shown on the same system to have a limited influence on atomic positions and relative energies. 15 Unless specified otherwise, a total 100 ps of molecular dynamics are performed on the canonical ensemble (NVT) using a Nose thermostat and a 2.0 fs time step at 298.15 K. All dynamics presented here start from the fully relaxed available crystallographic structures. In order to account better for the randomness of atomic motions, each of the molecular dynamics simulations listed thereafter are run 11 times in parallel. Each run uses random initial atomic forces. As the system is heated from 20.0K to 298.15 K, 1.0 ps is singled-out in our analysis. Setting aside calibration and various tests, the data presented in this paper consumed about 150.000 CPU hours on Intel Xeon E5649 2.53 GHz machines. A typical calculation ran on 9 nodes in parallel. The tetragonal to cubic transition temperature is located at 327.4 K 17 (about 54 ◦ C). Encountering both phases is therefore likely, depending on the operating conditions of a perovskite-based solar cell. Tetragonal (T) and cubic (C) phases are here tested in two distinct sets. The T1 model is made of a tetragonal unit ˚ c=12.5 A), ˚ that cell (lattice parameters: a=8.8 A, contains four initially aligned dipoles. Models T2 and T3 are identical to T1 except that the dipoles are set to point at each other at the beginning of the simulations, respectively on the [110] and [001] axes. In Figure 1 the structure of a MAPbI3 crystal is shown in the a) tetragonal and b) cubic phase. Computational investigations allow us to test hypothetical situations, even if they are somewhat unrealistic. The analyzed systems, labeled by T1 to T4 and C1 to C7, are schematically represented in Figure 2. The tetragonal systems T1, T2 and T3 contain 4 dipoles in the unit cell, while for a more detailed dipole-

Methods Computational details Ab initio DFT calculations are performed using the SIESTA package, 30 which allows a linear scaling of the computational time with the system size by employing a set of strictly localized numerical atomic orbitals as basis set. Our calculations are performed using the Ceperley-Alder 31,32 correlation functional, within the LDA approximation. A standard split norm of 0.15 was considered in the splitvalence scheme to obtain the double-zeta basis set. The sampling of the Brillouin zone was performed using a 3x3x3 k-grid scheme. Core electrons are accounted for using norm conserving Troullier-Martins pseudopotentials. Finally, the initial structures are taken from ex-


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Figure 1: Representation of the structure of a MAPbI3 crystal in the a) tetragonal and b) cubic (right) phase. Grey = lead, purple = iodine, blue = nitrogen, beige = carbon, white = hydrogen. The unit cells are delimited in black. Notice that a single cubic cell does not allow the same deformations as for the tetragonal cell.

Figure 2: Schematic two-dimensional representations of the sets T1 to T4 and C1 to C7. Blue arrows represent the orientation of CH3 NH3+ dipoles. A “+” symbol stands for the nonpolar NH4+ , see text. For both series, the axes are shown on the first set only for clarity, and for C7 the orientation of the depth added.

correlation analysis we also consider the fictitious T4 model, where only one dipole is contained in the tetragonal cell. The other three dipoles of the cell are replaced by smaller and rather spherical, non-polar NH4+ molecules. This will provide us some insights on the influence of neighbors on the motion of dipoles. The C1 model is made of a single cubic cell ˚ which is depicted (lattice parameter: a=6.3 A), Figure 1 b) and contains only one dipole. For the C2 set, the temperature is set at 330K. The optimal number of primitive cubic cells to include in a model is assessed with C3, C4, C5, C6 and C7 models. To do so, we build respectively the 2x1x1, 3x1x1, 2x2x1, 2x2x1 and 2x2x2 sets. In C5, all dipoles are aligned, while in C6 and C7, neighboring dipoles are oriented 90 degrees to each other. Previous work 15 pleads in favor of a superior stability when neighboring dipoles have perpendicular orientations. In order to clarify the differences inside and between the sets T1 to T4 and C1 to C7, we propose in Figure 2 their schematic representations.

Correlation functions Auto-correlation From all the trajectories, we extract the position of the dipoles at each time step and compute the auto-correlation functions in each of the sets T1 to T4 and C1 to C7. The auto-correlation function is defined as: auto − corr (τ ) =

< Φi ( t ) · Φi ( t + τ ) > (1) < d2 >

In equation (1), Φ is the C-N vector of the CH3 NH3+ cation. As we normalize Φ, < d2 > can be ignored. t represents the reference time and t + τ represents the time at which we wish to calculate the correlation. Index i stands for a given dipole. We use all available values of τ and t and repeat the calculation for all available dipoles, over the 11 trajectories of each set. Finally, we perform the corresponding averages over t and the trajectories. Note that the auto-correlation is a function of τ, while t has a sampling role, see Figure S2.


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Rotational relaxation time The rotational relaxation time indicates how long it takes for a dipole to lose memory of its initial orientation. In other words, after t = τr , initial orientational information gets lost, statistically speaking. To obtain an estimate of the rotational relaxation time of each set least-square fitting is performed assuming an exponential decay of the form −τ

f (τ ) = e τr ,

(2)

where τr is the rotational relaxation time. The relaxation time τr is experimentally accessible quantity. From a computational point of view it is expected that the intermediary estimated values using partial data sets asymptotically converge as the data grows in size and becomes statistically balanced: lim τi (ts ) = τr .

Figure 3: a) Rotational correlation data and fitting lines for sets T1 to T4. b) Convergence of the rotational relaxation time calculated for sets T1 to T4 respect to increasing simulated time.

(3)

ts →∞

In equation (3) ts is the total simulated time and τi (ts ) is the intermediary value of τr calculated within the time ts . In this paper, the largest value of τ considered in the fits to an exponential decay is the half of its maximum possible value. The reason is that smaller values of τ correspond to statistically more dense regions of the correlation data.

tional relaxation times using the first n (n = 5, 10, 20, 30, ..., 100) picoseconds of our simulations, using a maximum value for τ of n/2. Incrementally increasing the size of the subsets the rotational relaxation times we calculate tend to converge in an acceptable fashion on the simulated time scale (100 ps). Of course, one could increase convergence and therefore precision by extending the simulation times, on the expense of larger CPU time use. The values obtained for τi to be considered our best estimates for τr are presented Table 1. τi(T1) (22.6 ps) is found smaller than τi(T2) (32.7 ps) and τi(T3) (also 32.7 ps). The convergence of τi(T1) respect to simulated time is somewhat questionable. As τi(T1) is not as well converged and also significantly below τi(T2) and τi(T3) , we extended our calculations for T1 to reach 150.0 ps. With this extra data, τi(T1) increases to 27.5 ps. While the difference between the set T1 and the sets T2 and T3 may still be related to insufficient sampling, it is quite significant and rather demonstrates the influence of neighboring dipoles on each other. The value ob-

Results and discussion Relaxation time Our first results concern the rotational correlation functions associated to the sets T1 to T4, which we report in Figure 3 a). The vertical axis is shown with a logarithmic scale, so fitting decay functions come out as straight lines. It appears that the decays obtained by the means of molecular dynamics are fairly close to exponential, except in the far right region of the graph. The convergence of the different values obtained for τi with respect to simulated time is presented Figure 3 b). We re-calculated for this purpose rota-


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tained for τi(T4) (25.0 ps) weighs in favor of this hypothesis. In the T4 set, only one dipole is present and relaxation process is faster than τi(T2) and τi(T3) . Given the data presented it is likely that τi(T1) , τi(T2) , and τi(T3) will asymptotically converge to reach the same value if the simulated time would be extended. Table 1: Rotational relaxation times obtained for sets T1 to T4 and C1 to C7. Set T1 T2 T3 T4

τi (ps) 22.6 32.7 32.7 25.0

Set C1 C2 C3 C4 C5 C6 C7

τi (ps) 7.9 5.7 24.7 25.8 22.0 20.4 15.2

Figure 4: a) Rotational correlation data and fitting lines for sets C1 to C7. b) Convergence of the rotational relaxation time of sets C1 to C7 respect to simulated time.

With a smaller unit cell (12 atoms), the cubic phase allows us more flexibility in our study than the tetragonal cell (48 atoms). It is therefore a good candidate to repeat calculations using various supercells. The correlation data obtained for the sets C1 to C7 are indicated in Figure 4 and summarized in Table 1. The values obtained for τi(C1) (7.9 ps) and τi(C2) (5.7 ps) demonstrate a temperature induced enhanced dipole motion. A change of about 33 degrees decreases the rotational relaxation by almost 30%. Comparing τi(C1) to τi(C3) (24.7 ps), τi(C4) (25.8 ps), τi(C5 ) (22.0 ps), τi(C6 ) (20.4 ps) and τi(C7 ) (15.2 ps) demonstrates again the effects induced by neighbors in the rotational motion of molecular dipoles. In the cubic phase all directions are equivalent and this serves quite well our purpose here. A supercell expansion in any direction would be equivalent, e.g. 2x1x1 and 1x2x1. Figure 4 b) shows the convergence of the values of τi with respect to the size of the simulation subset. The size of the cell also influences the convergence of τi : a large cell contains more dipoles and provides more statistical weight (albeit with a higher computational cost). Despite this fact, convergence is more complete with C1 and C2, which likely means

more complex phenomena are taking place for the other representatives of the cubic phase. τi(C3) , τi(C4) , τi(C5) , τi(C6) , and τi(C7) may keep increasing if we increase the simulated time to 150 or more picoseconds, as we illustrated Figure 3 a) for T1. Nevertheless, it appears that our values can provide a good estimate.

Tilting of the inorganic cages It was previously demonstrated that the fluctuations of the inorganic cages play a role in the rotational dynamics of the dipoles. 29 Also, it was observed that PbI6 cage has a greater thermal vibration in the cubic phase. 34 To explore the influence of the immediate environment of the MA molecules we look at selected I-I (iodine-iodine) distances in the cell and monitor them. The two I atoms are located on two non adjacent edges of the same face of a cube formed by the lead trihalide cage, see Figure 6 a). As previously studied, 27 we looked at the distribution of rotation angles, see Figures 5 for a) set T2, b) C7, and S4 for all the sets. The choice of the unit cell strongly influences the


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sets of favored angles.

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see Figure 6 b) (more data in Figure S6). It is therefore reasonable to think that the orientational disorder of the dipoles is constrained in sets C1 to C6. Under these circumstances, in the case of the cubic phase, any cell smaller than C7 (2x2x2 cubic supercell) seems insufficient to produce accurate results. The tetragonal cell seems more adapted to this purpose since it allows three dimensional tilting of cages.

Figure 5: Distribution of rotation angle obtained in our simulations, for the sets a) T2 and b) C7.

Collective motion of dipoles It would be very interesting to know more about the collective motion of dipoles, which if present could shed some light on the hysteresis observed in measurements and the non-ferro electric character of the material as opposed to the observation of microscopic ferroelectric domains. As a mean to estimate the amplitude or absence of collective behavior we calculate −→ −→ ∑ (CN ) pol MA = , (4) #dipoles

−→ pol MA being an estimate of the instantaneous contribution of the orientation of dipoles to the polarization of the perovskite crystal. It −→ is a normalized vector sum of the CN vectors. C and N refer to the relative Cartesian coordinates of the C and N atoms of the MA dipole. A value of 0 (or 1) at a given time would indicate cancelling (or additive) sum of vectors, in other words dipoles pointing at each other (or aligned). We show in Figure 7 the time evolution averaged over the trajectories and normalized by dividing our results by the number of dipoles present in each cell. For a good equilibration 10 to 20 ps are needed, which is also the case for crosscorrelation functions (see Figure S3). In all −→ cases pol MA significantly differs from 0 and stabilizes at values between 0.4-0.8. Sets C1 and C2 are not shown since we would invariably obtain a value of exactly 1. With increasing cell size we observe an incremental de−→ crease of pol MA . This indicates two things: (i)

Figure 6: a) Snapshot taken from C5 (2x2x1 cubic cell), viewed from the [001] axis. The unit cell is shown with a black line. Dotted (dashed) line: typical “short” (“long”) I-I distance. b) Time evolution of selected I-I distance, for 11 trajectories of the set C5 (thin red lines) and C7 (bold blue lines). An animated video of a molecular dynamics trajectory is available in the supplementary material. Following structural relaxations a tilting of the inorganic cages is obtained. When a PbI6 cage tilts, its neighbors tend to tilt in an opposite way. No reversibility of the tilting is observed in the set C5 on the simulated timescale,


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Table 2: Rotational relaxation times of the normalized sum of CN vectors obtained for sets T1 to T3 and C3 to C5. Set T1 T2 T3

τi (ps) 12.3 29.8 27.3

Set C3 C4 C5 C6 C7

τi (ps) 31.6 35.7 42.6 28.1 20.5

Figure 7: Time evolution of the contribution of the orientation of MA to the polarization of the cells a) T1 to T3 and b) C3 to C7. we probably did not reach complete convergence in terms of cell size and (ii) we observe steady microscopic ferroelectric domains on the simulated time. Does this estimate converge to zero as the size of the supercell increases? This question is difficult to answer, but it is however likely that a non-zero value remains until a critical size is met, which corresponds to the ferroelectric domain size (experimentally estimated around 100 nanometers, 14 or about 150 unit cells). This is unfortunately computationally out of reach using the present method, but what we establish here is essentially an intrinsic polarization of the cells which is an important effect in the understanding of the microscopic polarization of MAPbI3 . Going one step further, one can study the −→ relaxation time of pol MA , just as we did for molecular dipoles. The results are presented Figure 8 and Table 2. In the sets T1, T2 and T3, the correlation functions properly decay. We get values of in the range 12.3-29.8 ps, which appear fairly short. In the case of T1 the erratic behavior at large values of τi is corrected if we take into account the simulations up to 150 ps used earlier for our convergence tests.

Figure 8: Rotational correlation of the normalized sum of CN vectors. a) Sets T1 to T3. b) Sets C3 to C6. The sets C3, C4, C5, and C6, with relaxation times in the range 28.1-42.6 ps, appear distinct from the set C7 (20.5 ps), see Table 2. We −→ demonstrate the stability of k pol MA k, while −→ the orientation of pol MA is clearly not stable on the timescale of tens of picoseconds in all cases.

Estimated effects of a bias voltage Under operating conditions a bias voltage is being applied to the solar cell, typically of the order of 1 V. For a perovskite layer of 200 nm the corresponding electric field is about ˚ 27 Such a field is rather weak 5 × 10−4 V/A. compared to the internal (molecular) fields


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that govern the dipole movement at a given temperature. In order to test the behavior of the dipoles in the presence of the external electric field we used the model C4 (Fig. 2), this time as a slab with the electric field in the vertical z direction. We carried additional (single test) simulations on this selected model, at 50 K and at room temperature. These tests ˚ showed that for a field of magnitude 0.2 V/A or lower, there is no observable response of the dipoles within a time of 20 ps which is comparable to our relaxation times obtained in the absence of the field. Such an electric field had some influence on the cage, but the effect on the dipoles should be observable only on a much longer time scale, which is unreachable by our simulations. We could obtain a fast alignment of the dipoles, within 10 ps, only with a much stronger, although unrealistic, test ˚ However, a systematic study field of 1 V/A. of the dipole dynamics in the presence of an applied voltage is a much more demanding task and it is beyond the scope of our present work. For example, the reorientation of the dipoles may occur at domain walls, where the dipoles can be less stable. 35

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several favored positions was experimentally determined around 14 ps at room temperature, 35 which comforts our study and conclusions. In summary, we performed first-principles molecular dynamics to simulate the behavior of a CH3 NH3 PbI3 perovskite crystal in the tetragonal and cubic phases. The main conclusions of this work are the following: (i) We calculated the rotational relaxation time in the tetragonal and cubic phases: respectively 32.7 and 15.2 ps. The results are only rough estimates that require further refinements, notably concerning unit (super) cell size and extended simulation times. (ii) We described the collective behavior of the CH3 NH3+ cation both in terms of alignment of neighbors and geometric environment, especially in correlation with the tilting of the PbI6 cages. (iii) A 1x1x1 cubic cell is not adapted to the study of the motion of molecular dipoles in MAPbI3 . In crystallographic models, the average position of C and N are superimposed due to molecular disorder. Our findings may help crystallographers to improve their models. (iv) We have the first ab-initio evidence of microscopic ferroelectricity in MAPbI3 that can elegantly explain the lack of macroscopic ferroelectricity, while microscopic domains are experimentally observed.

Conclusions Hybrid perovskites are challenging from the computational point of view due to their peculiar properties, in particular due to the relaxation processes involving dipole motion. We investigated here thermal effects by means of ab initio molecular dynamics calculations, within the DFT framework. A thermal “exploration” such as proposed in this work can reveal the inner complexity of the system. On one hand dipoles influence each others and, on the other hand, continuous tilting of the inorganic cage influences their motion as well. The relaxation times calculated here (best value for the cubic phase at room temperature: 15.2 ps) is above an experimental value of 5.37 ps at 300K. 19 However, those authors commented that this value was “rather short” and was probed with an electric field. Recently, the residence time of MA dipoles in one of the

Acknowledgments The research leading to these results has received funding from EEA Financial Mechanism 2009 - 2014 under the project contract no 8SEE/30.06.2014. We are very thankful to Ioana Pintilie, Lucian Pintilie, Lucian Ion, Neculai Plugaru, Halldor Svavarsson, and Sigurdur Erlingsson for instructive discussions. The computer simulations were performed on resources provided by the Nordic High Performance Computing (NHPC).


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References

(10) Motta, C.; El-Mellouhi, F.; Kais, S.; Tabet, N.; Alharbi, F. Sanvito, S. Revealing the role of organic cations in hybrid halide perovskite CH3NH3PbI3. Nat Commun 2015, 6.

(1) http://www.nrel.gov/ncpv/images/ efficiency_chart.jpg. (2) Liu, M.; Johnston, M. B.; Snaith, H. J. Efficient planar heterojunction perovskite solar cells by vapour deposition. Nature 2013, 501, 395–398.

(11) Wei, J.; Zhao, Y.; Li, H.; Li, G.; Pan, J.; Xu, D.; Zhao, Q.; Yu, D. Hysteresis Analysis Based on the Ferroelectric Effect in Hybrid Perovskite Solar Cells. J. Phys. Chem. Lett. 2014, 5, 3937–3945.

(3) Snaith, H. J. Perovskites: The Emergence of a New Era for Low-Cost, HighEfficiency Solar Cells. J. Phys. Chem. Lett. 2013, 4, 3623–3630.

(12) Snaith, H. J.; Abate, A.; Ball, J. M.; Eperon, G. E.; Leijtens, T.; Noel, N. K.; Stranks, S. D.; Wang, J. T.-W.; Wojciechowski, K.; Zhang, W. Anomalous Hysteresis in Perovskite Solar Cells. J. Phys. Chem. Lett. 2014, 5, 1511–1515.

(4) Boix, P. P.; Nonomura, K.; Mathews, N.; Mhaisalkar, S. G. Current progress and future perspectives for organic/inorganic perovskite solar cells. Mater. Today 2014, 17, 16–23.

(13) Sanchez, R. S.; Gonzalez-Pedro, V.; Lee, J.W.; Park, N.-G.; Kang, Y. S.; Mora-Sero, I.; Bisquert, J. Slow Dynamic Processes in Lead Halide Perovskite Solar Cells. Characteristic Times and Hysteresis. J. Phys. Chem. Lett. 2014, 5, 2357–2363.

(5) Park, N.-G. Organometal Perovskite Light Absorbers Toward a 20% Efficiency Low-Cost Solid-State Mesoscopic Solar Cell. J. Phys. Chem. Lett. 2013, 4, 2423– 2429.

(14) Kutes, Y.; Ye, L.; Zhou, Y.; Pang, S.; Huey, B. D.; Padture, N. P. Direct Observation of Ferroelectric Domains in SolutionProcessed CH3NH3PbI3 Perovskite Thin Films. J. Phys. Chem. Lett. 2014, 5, 3335– 3339.

(6) Grätzel, M. The light and shade of perovskite solar cells. Nat. Mater. 2014, 13, 838–842. (7) Edri, E.; Kirmayer, S.; Mukhopadhyay, S.; Gartsman, K.; Hodes, G.; Cahen, D. Elucidating the charge carrier separation and working mechanism of CH3NH3PbI3xClx perovskite solar cells. Nat. Commun. 2014, 5, 3461 .

(15) Fan, Z.; Xiao, J.; Sun, K.; Chen, L.; Hu, Y.; Ouyang, J.; Ong, K. P.; Zeng, K.; Wang, J. Ferroelectricity of CH3NH3PbI3 Perovskite. J. Phys. Chem. Lett. 2015, 6, 1155–1161.

(8) Even, J.; Pedesseau, L.; Katan, C. Analysis of Multivalley and Multibandgap Absorption and Enhancement of Free Carriers Related to Exciton Screening in Hybrid Perovskites. J. Phys. Chem. C 2014, 118, 11566–11572.

(16) Green, M. A.; Bein, T. Perovskite cells charge forward. Nat. Mater. 2015, 14, 559561. (17) Baikie, T.; Fang, Y.; Kadro, J. M.; Schreyer, M.; Wei, F.; Mhaisalkar, S. G.; Graetzel, M.; White, T. J. Synthesis and crystal chemistry of the hybrid perovskite (CH3NH3)PbI3 for solid-state sensitised solar cell applications. J. Mater. Chem. A 2013, 1, 5628–5641.

(9) Yin, W.-J.; Shi, T.; Yan, Y. Unique Properties of Halide Perovskites as Possible Origins of the Superior Solar Cell Performance. Advanced Materials 2014, 26, 4653– 4658.


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(18) Wasylishen, R.; Knop, O.; Macdonald, J. Cation rotation in methylammonium lead halides. Solid State Commun. 1985, 56, 581– 582.

Page 10 of 11

(26) Frost, J. M.; Butler, K. T.; Brivio, F.; Hendon, C. H.; van Schilfgaarde, M.; Walsh, A. Atomistic Origins of HighPerformance in Hybrid Halide Perovskite Solar Cells. Nano Lett. 2014, 14, 2584–2590, PMID: 24684284.

(19) Poglitsch, A.; Weber, D. Dynamic disorder in methylammoniumtrihalogenoplumbates (II) observed by millimeterwave spectroscopy. J. Chem. Phys 1987, 87, 6373–6378.

(27) Frost, J. M.; Butler, K. T.; Walsh, A. Molecular ferroelectric contributions to anomalous hysteresis in hybrid perovskite solar cells. APL Mat. 2014, 2, 081506.

(20) Knop, O.; Wasylishen, R. E.; White, M. A.; Cameron, T. S.; Oort, M. J. M. V. Alkylammonium lead halides. Part 2. CH3NH3PbX3 (X = Cl, Br, I) perovskites: cuboctahedral halide cages with isotropic cation reorientation. Can. J. Chem. 1990, 68, 412–422.

(28) Ma, J.; Wang, L.-W. Nanoscale Charge Localization Induced by Random Orientations of Organic Molecules in Hybrid Perovskite CH3NH3PbI3. Nano Lett. 2015, 15, 248–253, PMID: 25493911. (29) Mosconi, E.; Quarti, C.; Ivanovska, T.; Ruani, G.; De Angelis, F. Structural 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.

(21) Filippetti, A.; Mattoni, A. Hybrid perovskites for photovoltaics: Insights from first principles. Phys. Rev. B 2014, 89, 125203. (22) Xing, G.; Mathews, N.; Sun, S.; Lim, S. S.; Lam, Y. M.; Grätzel, M.; Mhaisalkar, S.; Sum, T. C. Long-Range Balanced Electronand Hole-Transport Lengths in OrganicInorganic CH3NH3PbI3. Science 2013, 342, 344–347.

(30) Soler, J. M.; Artacho, E.; Gale, J. D.; ´ P.; Garc´ıa, A.; Junquera, J.; Ordejon, Sánchez-Portal, D. The SIESTA method for ab initio order- N materials simulation. J. Phys. Condens. Matter 2002, 14, 2745.

(23) 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.

(31) Ceperley, D. M.; Alder, B. J. Ground State of the Electron Gas by a Stochastic Method. Phys. Rev. Lett. 1980, 45, 566–569. (32) Perdew, J. P.; Zunger, A. Self-interaction correction to density-functional approximations for many-electron systems. Phys. Rev. B 1981, 23, 5048–5079.

(24) Zhao, Y.; Nardes, A. M.; Zhu, K. Solid-State Mesostructured Perovskite CH3NH3PbI3 Solar Cells: Charge Transport, Recombination, and Diffusion Length. J. Phys. Chem. Lett. 2014, 5, 490– 494.

(33) 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.

(25) Dong, Q.; Fang, Y.; Shao, Y.; Mulligan, P.; Qiu, J.; Cao, L.; Huang, J. Electronhole diffusion lengths ¿175 m in solution grown CH3NH3PbI3 single crystals. Science 2015,

Mashiyama, H.; (34) Kawamura, Y.; Hasebe, K. Structural Study on Cubic– Tetragonal Transition of CH3NH3PbI3.


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Journal of the Physical Society of Japan 2002, 71, 1694–1697. (35) Leguy, A. M. A.; Frost, J. M.; McMahon, A. P.; Sakai, V. G.; Kochelmann, W.; Law, C.- H.; Li, X.;Foglia, F.; Walsh, A.; O’Regan, B. C.; Nelson, J.; Cabral, J. T.; Barnes, P. R. F. The dynamics of methylammonium ions in hybrid organicinorganic perovskite solar cells. Nat. Commun. 2015, 6, 7124.


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