Termination Dependence of Tetragonal ... - ACS Publications

Letter pubs.acs.org/JPCL

Termination Dependence of Tetragonal CH3NH3PbI3 Surfaces for Perovskite Solar Cells Jun Haruyama,†,‡ Keitaro Sodeyama,†,§ Liyuan Han,∥,⊥ and Yoshitaka Tateyama*,†,§,⊥ †

International Center for Materials Nanoarchitectonics (WPI-MANA) and ‡Global Research Center for Environmental and Energy Nanoscience (GREEN), National Institute for Materials Science (NIMS), 1-1 Namiki, Tsukuba, Ibaraki 305-0044, Japan § Elements Strategy Initiative for Catalysts and Batteries, Kyoto University, Goryo-Ohara, Nishikyo-ku, Kyoto 615-8245, Japan ∥ Photovoltaic Materials Unit, National Institute for Materials Science (NIMS), 1-2-1 Sengen, Tsukuba, Ibaraki 305-0047, Japan ⊥ PRESTO and CREST, Japan Science and Technology Agency (JST), 4-1-8 Honcho, Kawaguchi, Saitama 333-0012, Japan S Supporting Information *

ABSTRACT: We investigated the termination dependence of structural stability and electronic states of the representative (110), (001), (100), and (101) surfaces of tetragonal CH3NH3PbI3 (MAPbI3), the main component of a perovskite solar cell (PSC), by density functional theory calculations. By examining various types of PbIx polyhedron terminations, we found that a vacant termination is more stable than flat termination on all of the surfaces, under thermodynamic equilibrium conditions of bulk MAPbI3. More interestingly, both terminations can coexist especially on the more probable (110) and (001) surfaces. The electronic structures of the stable vacant and PbI2-rich flat terminations on these two surfaces largely maintain the characteristics of bulk MAPbI3 without midgap states. Thus, these surfaces can contribute to the long carrier lifetime actually observed for the PSCs. Furthermore, the shallow surface states on the (110) and (001) flat terminations can be efficient intermediates of hole transfer. Consequently, the formation of the flat terminations under the PbI2-rich condition will be beneficial for the improvement of PSC performance. SECTION: Surfaces, Interfaces, Porous Materials, and Catalysis of equimolar MAI and PbI2 in γ-butyrolactone onto a TiO2 film, was first introduced for this synthesis.1,18 Later, Grätzel and co-workers introduced a seemingly more effective two-step method.2 In this method, PbI2 is first introduced from solution onto a mesoporous TiO2 film and subsequently transformed into the MAPbI3 by the exposition of a solution containing MAI. It is suggested that the use of such a high PbI2 concentration is critical to obtain a high loading on the mesoporous TiO2 films to fabricate solar cells with higher performance. The experimental results indicate that the PbI2rich growth condition modifies the MAPbI3 surface and TiO2/ MAPbI3 interface in such a way that photoexcited carrier transport is improved. In this Letter, we have investigated the structural and electronic properties of various terminations of the tetragonal MAPbI3 surfaces under different chemical potential conditions by using density functional theory (DFT) calculations. In particular, we discuss the interfaces with the hole-transport molecular materials (HTMs) such as spiro-OMeTAD (2,2′,7,7′-tetrakis(N,N-di-p-methoxyphenylamine)-9,9′-bifluor-

P

erovskite solar cells (PSCs)1−3 have attracted considerable attention because of their high performance for conversion of sunlight into electrical power.4,5 Since the seminal work by Miyasaka and co-workers,1 the photoconversion efficiencies (PCEs) of the PSCs have been rapidly increasing from 3.8 to near 20% only in the past few years.2,3,6−9 PSCs are often compared with dye-sensitized solar cells (DSCs)10,11 because of similarities in their device compositions; mesoporous n-type TiO2 is sensitized by light-absorbing components and placed into a medium containing charge-transfer mediators. However, there are some characteristic differences as well. Compared with typical DSCs, the perovskite sensitizers, for example, CH3NH3PbI3 (MAPbI3), MAPbBr3, and MAPbI3−xClx, have higher absorption coefficients to enable greater light absorption in thinner layers.12,13 In addition, the perovskite materials have long diffusion lengths of up to 100 nm14 or exceeding 1 μm15,16 for both holes and electrons. These characteristics make the perovskite sensitizers more appropriate for solar cells with high efficiency.17 Another important characteristic is the availability of solution processes such as spin or dip coating for deposition of the perovskite components onto the mesoporous and compact TiO2 electrode. This allows a sufficiently low cost of fabrication.18 A one-step method, dropping a precursor solution © XXXX American Chemical Society

Received: July 18, 2014 Accepted: August 7, 2014

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dx.doi.org/10.1021/jz501510v | J. Phys. Chem. Lett. 2014, 5, 2903−2909

The Journal of Physical Chemistry Letters

Letter

necessary for tetragonal (100) and (101). In fact, X-ray diffraction measurements reveal the (110) peak in planar heterojunction PSCs (MAPbI3−xClx)3 and (110) and (001) peaks on mesoporous-TiO2 films (MAPbI3).20 Therefore, after the structural stability analysis, we focused on the probable (110) and (001) surfaces in the investigation of the electronic states. Here, we examined a variety of defective terminations of the four target surfaces as well as for the flat termination. Polarization emerging with defect formation or polar-layer alternation often causes failures of the DFT supercell calculations with periodic boundary condition. To avoid this situation, that is, net dipole appearance in the supercell, we introduced the same composition of the terminations on both surfaces of the MAPbI3 slab. Recently, Frost and co-workers showed that ferroelectric domains of MAPbI3 cause separation of photoexcited electron and hole pairs.21 The surface polarization may contribute to a certain extent, although we will not discuss such effects here, and it will be the subject of future work. In this study, we have focused on the outermost PbI6 octahedron layer (B plane in the conventional perovskite notation ABX3). The surfaces targeted here have two or four PbI6 octahedrons due to the tetragonal phase. We therefore used the components of the outermost Pb polyhedrons as the label of the termination. For instance, the flat nonpolar and the (PbI2)2-vacancy terminations of the (110) surfaces are labeled as -(PbI5)4 and -(PbI5)(PbI3), respectively. All of the terminations investigated here are summarized in Figure S3 and Table S2 in the Supporting Information. Note that we have not considered the MA plane terminations except for the apical I atoms, relying on the observation of a small understoichiometry in I and N atoms for the two-step synthesis of the TiO2/MAPbI3 interface reported by Lindblad et al.22 The initial MA configuration is determined by reference to the previous study by Mosconi et al.23 We also adjusted the surface polarization to interchange the C and N atoms in a symmetric fashion, similar to Roiati et al.,24 to avoid unreasonable large dipole in the supercell. To compare the structural stabilities of different stoichiometries, PbαIβ(MAPbI3)γ,25,26 we used the grand potential Ω approach as follows

ene) because the present vacuum surfaces can make reasonable interface models due to weak interactions with the HTMs. With the resultant stable surface terminations and their electronic states, we finally suggest the desired properties for good PSC performance. We carried out DFT calculations of the representative (110), (001), (100), and (101) surfaces of tetragonal MAPbI3, which is the stable phase at room temperature. The unit cell of the bulk tetragonal phase (Figure 1a) can be expressed as a √2 ×

Figure 1. (a) Unit cell of tetragonal MAPbI3. The H, C, N, I, and Pb atoms are depicted as white, brown, light blue, purple, and black spheres, respectively. Black octahedrons represent the PbI6 unit. Red dashed lines indicate the (110), (100), (101), and (001) planes. (b) Relationship between the present tetragonal cell with the conventional perovskite notation. (c) The range of Pb and I chemical potentials. The only red region is the thermodynamic stable range for equilibrium growth of MAPbI3.

Ω(ΔμPb , ΔμI , Δμ MAPbI ) ≈ Etot[Pbα Iβ(MAPbI3)γ ] 3

bulk − αμPb

β bulk − μIgas − γμ MAPbI − αΔμPb − β ΔμI 3 2 2

− γ Δμ MAPbI

(1)

3

√2 × 2 perovskite ABX3 unit cell, where A, B, and X correspond to MA, Pb, and I, respectively, in the present material. Note that the VESTA package was used to visualize the crystal structure clearly throughout this Letter.19 The [110], [001], [100], and [101] directions in the tetragonal phase correspond to the [010], [001], [110], and [111], respectively, in the conventional perovskite (Figure 1b). Thus, the tetragonal (110) and (001) are flat nonpolar surfaces, which consist of alternate stacking of the neutral [MAI]0 and [PbI2]0 planes. The tetragonal (100) surface is constructed with stacking of the [MAPbI]2+ and [I2]2− layers, while the [MAI3]2− and [Pb]2+ layers compose the tetragonal (101). Thus, the tetragonal (110) and (001) surfaces are expected to be stable as they are, while large reconstructions or defect formation may be

bulk ΔμPb = μPb − μPb

ΔμI = μI −

bulk Δμ MAPbI = μ MAPbI − μ MAPbI 3

3

3

1 gas μ 2 I2 (2)

The details of the grand potential components are described in the Computational Details section. Assuming that ΔμMAPbI3 = 0 and the system is under equilibrium for Pb, I2, MAI, and PbI2 phases, the thermodynamic stable range of ΔμPb and ΔμI for equilibrium growth of MAPbI3 is represented as ΔHform[MAPbI3] ≤ ΔμPb ≤ 0 2904

ΔHform[MAPbI3] ≤ ΔμI ≤ 0 (3)



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Here, we analyze the slab size dependence employing the (110) stable vacant and PbI2-rich flat terminations. The relaxed structures are shown in Figure S8, and convergence data are listed in Table S4 in the Supporting Information. The absolute values of Ω/S are converged at the 7 Pb layer slab, whereas the differences between Ω/S are almost converged about 0.3 eV/ nm2 at the 5 Pb layer slab. Therefore, we expect that the phase diagrams obtained from the 5 Pb layer slab can hold in the larger slabs, qualitatively. Taking the molecular nature of MA into account,29 we also re-examined the surface termination diagrams (Figure S4 in the Supporting Information) using a van der Waals density functional (vdW-DF) recently proposed for both molecules and solids.30 Consequently, the phase diagrams do not vary depending on the functionals, indicating that the present result is qualitatively robust. The relaxed structures of the stable vacant and PbI2-rich flat terminations are shown in Figure 3. Note that the relaxed

ΔHform[MAPbI3] − ΔHform[MAI] ≤ ΔμPb + 2ΔμI ≤ ΔHform[PbI 2]

(4)

where ΔHform is the heat of formation. We summarize Etot and ΔHform of the solid and gas phases in Table S3 in the Supporting Information. The chemical potential range satisfying eqs 3 and 4 for bulk MAPbI3 is shown in Figure 1c and is consistent with recent results by Yin et al.27 The thermodynamic stable range for the equilibrium growth is very narrow, indicating that the tetragonal MAPbI3 compound easily decomposes into PbI2 and MAI. The right upper and left lower lines represent the borders to the PbI2- and MAI-rich conditions, respectively. Note that the PbI2-rich condition actually depends on the reference PbI2 polymorph, which has a large variety.28 However, our results using ΔμPb and ΔμI will not be sensitive to the uncertainty of the PbI2-rich condition. We then calculated the grand potential Ω of the surface with the total energies of the relaxed slab structures and depicted the surface termination diagrams of the four target surfaces, as in Figure 2. All diagrams consist mainly of the (MAPbI3)γ and

Figure 2. Surface termination diagrams at different MAPbI3 growth conditions: (a) (110), (b) (001), (c) (100), and (d) (101) surfaces. The dark and light blue regions indicate vacant and PbI2-rich flat terminations, respectively. The red region is the thermodynamic stable range represented by eqs 3 and 4.

(PbI2)α(MAPbI3)γ regions illustrated as the dark and light blue areas, respectively. That is, the terminations are basically classified as stable vacant termination for the dark blue area and the PbI2-rich flat termination for the light blue area. The thermodynamically stable range for the equilibrium MAPbI3 is located mostly on the vacant termination region, implying the predominance of this type of surface in PSCs. On the other hand, the flat termination region is also close to the thermodynamically stable range. In fact, the grand potentials per unit area Ω/S at ΔμPb = 0, ΔμI = −1.19 eV indicate that the surface energy differences between the two major terminations on the (110), (001), and (101) surfaces are within 0.3 eV/nm2. Therefore, we conclude that the stable vacant and PbI2-rich flat terminations coexist on various MAPbI3 surfaces, and the latter can be dominant under the PbI2-rich condition. Note that data of all of the terminations are summarized in Table S2 in the Supporting Information.

Figure 3. Relaxed surface terminations on (a) (110), (b) (001), (c) (100), and (d) (101) surfaces. The left and right structures indicate a stable vacant and the PbI2-rich flat terminations, respectively. The surface terminations are characterized by the outermost Pb polyhedrons that are magnified as well. On the (110) and (001) surfaces, the flat termination with -(PbI5)4 corresponds to a nonpolar BX2 plane in terms of the conventional perovskite notation ABX3.

structure of the (110) -PbI5PbI3 termination forms PbI4 tetrahedrons at the outermost layers (see Figure S5 in the Supporting Information), while the other terminations keep their initial outermost Pb polyhedrons. In the stable vacant terminations, incompleteness of the outermost layer leads to significant symmetry breaking, especially on the (110) and 2905



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(001) surfaces. On the other hand, all of the PbI2-rich flat terminations can almost keep the crystal phase structures. The difference in the termination structures can affect their energy gaps as well, as shown in Table 1. Compared to the Table 1. Calculated Energy Gaps of the Stable Vacant and PbI2-Rich Flat Terminations of the Outermost Pb Polyhedron Layers (in eV) (110) (001) (100) (101)

stable vacant

PbI2-rich flat

1.91 1.83 1.87 1.87

1.63 1.56 1.77 1.77

PbI2-rich flat terminations, the stable vacant types have larger energy gaps by ∼0.2 eV, which is attributed to a wide range of PbI6 octahedron distortions (e.g., change of the Pb−I distance) in the bulk part, induced by the surface PbI4 polyhedrons in these terminations. We consider that such a structure with lower symmetry leads to a larger energy gap. This idea can also be used to explain the increase of MAPbI3 energy gaps after the transition from the tetragonal to orthorhombic phase.31 A similar discussion was applied for three- and two-dimensional MAPbI3 crystals by Umebayashi et al.32 We also carried out DFT calculations of the orthorhombic phase or cell optimized structure and found increases in the band gaps (see Table S1 in the Supporting Information). The slab size dependence of the energy gaps listed in Table S4 in the Supporting Information also supports the current scenario. In the stable vacant case, the energy gap convergence toward the bulk value as the slab thickness increases is rather slow, indicating that the PbI6 octahedron distortions are reached in the middle region. In the PbI2-rich flat terminations, on the other hand, the octahedron distortion is already small at the subsurface region, and the energy gap is converged at a smaller slab thickness. Nevertheless, we confirmed that the electronic properties obtained in the present condition are not altered qualitatively compared to the larger slab cases. For analysis of electronic states, we focus on the stable vacant and the PbI2-rich flat terminations of the probable (110) and (001) surfaces. Figure 4 shows the projected density of states (PDOS) of those four surfaces. All of the surfaces have very similar characteristics as the bulk tetragonal phase; the valence and conduction bands consist mostly of I-5p and Pb-6p orbitals, respectively. Previous studies reported that the Pb-6p bands are modified by the inclusion of a spin−orbit coupling (SOC).33−35 Thus, it is also expected that the surface energy gaps decrease by the splitting of the conduction bands as well. Note that the (100) and (101) surfaces have very similar PDOS as well (see Figure S6 in the Supporting Information). We emphasize that there are no midgap surface states on the PDOS in Figure 4. This indicates that the hole−electron recombination hardly occurs even at the surfaces, and thus, the observed long lifetimes of the photoexcited carriers can be realized.14−16 A similar situation exists in the case of bulk defects.27,36 This is explained that these characteristics arise from the ionic bonding from organic−inorganic hybridization. Figure 5 shows the highest occupied molecular orbitals (HOMOs) of the four surfaces selected in Figure 4. The HOMOs of the stable vacant terminations are distributed inside of the surface slab, while the PbI2-rich flat terminations have the HOMOs well localized at the outermost layers. The surface-

Figure 4. PDOS of the MAPbI3 surfaces with (a) vacant (110), (b) flat (110), (c) vacant (001), and (d) flat (001) terminations. Black, green, red, orange, and blue lines represent the PDOS of the total, I 5s, I 5p, Pb 6s, and Pb 6p, respectively. The tops of the valence bands are set to the energy origin.

Figure 5. Charge distribution of the HOMOs of (a) (110) and (b) (001) surfaces. The left and right figures correspond to stable vacant and PbI2-rich flat terminations, respectively.

localized HOMOs in the latter case have the advantage of enhanced transfer of the photoexcited holes to the adjacent HTMs through those states. In contrast, the HOMOs inside of the bulk are less effective in this role. These characteristics can affect the incident-photon-to-current conversion efficiency (IPCE) properties. Moreover, the energy levels of the surface states are located just above the top of the valence bands in the bulk MAPbI3, indicating that the energy loss through the charge transfer via the surface states is expected to be considerably small. Here, we discuss the surface states of the (110) stable vacant and PbI2-rich flat terminations (see Figure S9 in the Supporting Information). The surface states of both terminations have mixed character of I-5p and Pb-6s orbitals and show strong antibonding coupling, similar to the argument in ref 27 for the bulk valence band. In the stable vacant terminations, the antibonding character is weakened with the decrease of the number of Pb−I bonds. Therefore, their surface states are stabilized compared with those in the PbI2-rich flat case and are located at 0.2 eV below the HOMO level. 2906



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In conclusion, we have investigated the termination dependence of the structural stability and electronic states of the representative (110), (001), (100), and (101) surfaces of tetragonal MAPbI3 by using DFT calculations. By examining various types of PbIx polyhedron terminations, we found that a vacant termination is more stable than the PbI2-rich flat one on all the surfaces, under thermodynamic equilibrium growth conditions of bulk MAPbI 3 . More interestingly, both terminations can coexist especially on the more probable (110) and (001) surfaces. Their electronic structures substantially maintain the characteristics of the tetragonal MAPbI3 bulk phase without a midgap surface state. Thus, these surfaces can contribute to the long carrier lifetime actually observed in PSCs. Furthermore, flat terminations on the (110) and (001) surfaces have surface states just above the bulk valence band, which can attract hole carriers photogenerated in MAPbI3. These states can thus be efficient intermediates of hole transfer to the adjacent HTMs with smaller energy loss. Consequently, we suggest that increased availability of the flat termination under PbI2-rich conditions will be of great benefit for the further improvement of PSC performance.

Now, we briefly examine the SOC effect. Figure 6 shows the PDOS and the lowest unoccupied molecular orbitals (LUMOs)

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COMPUTATIONAL DETAILS DFT calculations were carried out within the plane wave basis and pseudopotential framework as implemented in the QUANTUM-ESPRESSO package.37 The PBE exchange− correlation functional38 within the spin-unpolarized scheme was adopted. The core−valence interactions were represented through the ultrasoft pseudopotentials.39,40 The electronic configurations are 1s1 for H, 2s22p2 for C with nonlinear core correction (NCC),41 2s22p3 for N with NCC, 5s25p5 for I with NCC, and 5d106s26p2 for Pb with NCC. The cutoffs of the plane wave basis are set to 40 and 320 Ry for the smooth part of the wave functions and the augmented charge, respectively. Convergent k-point sampling was adopted for the bulk and surface systems. The atomic positions were relaxed until the residual forces became less than 0.001 Ry/bohr. In the surface calculations, the slab thicknesses were selected as 2−3 nm, and a vacuum region of 1.5 nm was always added to the supercell. The calculated cell parameters were fixed to the experimental values (a = 8.8009 Å, c = 12.6857 Å).42 We checked the quantities in the supercell with the computationally optimized lateral parameters using some representative systems and confirmed that the conclusions do not change. Regarding the surface treatment, we made both surfaces of the slab active and their terminations symmetric to avoid a possible artificial net dipole in the supercell as well as estimate the surface termination stability more precisely. To examine the effect of van der Waals interaction, we also used the rev-vdW-DF functional30,43−46 for the check calculations. For the PDOS calculations, we conducted non-self-consistent-field calculation with convergent k-point meshes. The occupation number was determined by the Gaussian smearing technique with a smearing parameter of 0.01 Ry. The SOC coupling was included by solving nonrelativistic Kohn−Sham equations with pseudopotentials tailored to reproduce the solutions of fully relativistic atomic Dirac-like equations.47−49 The SOC-DFT was only applied for the PDOS calculation, and we did not optimize the atomic coordinate. The details of the components in the grand potential, eqs 1 and 2, are expressed as follows. Etot[PbαIβ(MAPbI3)γ] is the DFT total energy of the surface slab containing α Pb atoms, β I atoms, and γ MAPbI3 complexes. μPb, μI, and μMAPbI3 are the

Figure 6. PDOS (left) and LUMOs (right) of the flat terminations (-(PbI5)4) of the (a) (110) and (b) (001) surfaces, including SOC.

for the PbI2-rich flat termination of the (110) and (001) surfaces. The energies of the LUMOs decrease by about 1 eV in both surfaces, while the occupied states are nearly unaffected. The band gaps are 0.68 and 0.76 eV, respectively. Compared with the LUMOs without SOC (Figure S7, Supporting Information), those distributions with SOC spread to entire slabs. These behaviors are the same as those previously reported for bulk MAPbI3.33,34 Because the large SOC effects are due to the Pb-6p character of conduction bands, we obtained the energy shifts regardless of the surface terminations and orientations. Finally, we will discuss the relationship between the two major terminations in this work and the experimental results. We suppose that the stable vacant termination is mainly formed by the one-step methods because this type of termination covers the most parts of the thermodynamically stable range of MAPbI3 growth. The characteristics of their HOMOs have disadvantages for the ability of the hole transfer to the HTM. In addition, they possess characteristics of slightly larger energy gaps; reducing the bulk reduces the IPCE near the band gap wavelength, ∼800 nm region. On the other hand, the PbI2-rich flat termination surfaces are partly formed by the two-step method because of the intrinsic PbI2-rich condition. This enables the photoexcited carriers to transfer to the HTM smoothly without significant energy loss. Note that the composition ratios of the flat termination surface are consistent with the I atom understoichiometry observed only in the twostep method.22 However, we expect that the coverage of the PbI2-rich flat termination surfaces is not so large because the most stable surfaces in the thermodynamic range correspond to the stable vacant terminations. Therefore, we propose that the realization of the larger area of the PbI2-rich flat termination surface significantly contributes to an increase in IPCE and further improvements of PSC for photovoltaic applications. 2907



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gas bulk chemical potentials of Pb, I, and MAPbI3. μbulk Pb , μI2 , and μMAPbI3 are the chemical potentials in the Pb bulk, I2 gas, and MAPbI3 bulk phases, respectively, which are approximated by the DFT total energy per unit. Δμ is the chemical potential variations from those references, representing the environmental conditions. Following the conventional surface DFT study,26 we ignored the entropy terms in eq 1. ΔHform in eqs 3 and 4 is the heat of formation and is calculated as the difference between the DFT total energy of the compounds and the composition-weighted sum of their constituents as ΔHform[AB] = Etot[AB] − Etot[A] − Etot[B].

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(6) Im, J. H.; Lee, C. R.; Lee, J. W.; Park, S. W.; Park, N. G. 6.5% Efficient Perovskite Quantum-Dot-Sensitized by Lead-Halide Compounds. Nanoscale 2011, 3, 4088−4093. (7) Kim, H. S.; Lee, C. R.; Im, J. H.; Lee, K. B.; Moehl, T.; Marchioro, A.; Moon, S. J.; Humphry-Baker, R.; Yum, J. H.; Moser, J. E.; Grätzel, M.; Park, N. G. Lead Iodide Perovskite Sensitized AllSolid-State Submicron Thin Film Mesoscopic Solar Cell with Efficiency Exceeding 9%. Sci. Rep. 2012, 2, 591. (8) Lee, M. M.; Teuscher, J.; Miyasaka, T.; Murakami, T. N.; Snaith, H. J. Efficient Hybrid Solar Cells Based on Meso-Superstructured Organometal Halide Perovskite. Science 2012, 338, 643−647. (9) Liu, D.; Kelly, T. L. Perovskite Solar Cells with a Planar Heterojunction Structure Prepared Using Room-Temperature Solution Processing Techniques. Nat. Photonics 2014, 8, 133−138. (10) O’Regan, B.; Grätzel, M. A Low-Cost, High-Efficiency Solar Cell Based on Dye-Sensitized Colloidal TiO2 Films. Nature 1991, 353, 737−740. (11) Zhang, S.; Yang, X.; Numata, Y.; Han, L. Highly Efficient DyeSensitized Solar Cells: Progress and Future Challenges. Energy Environ. Sci. 2013, 6, 1443−1464. (12) Snaith, H. J. Perovskites: The Emergence of a New Era for LowCost, High-Efficiency Solar Cells. J. Phys. Chem. Lett. 2013, 4, 3623− 3630. (13) 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) Xing, G.; Mathews, N.; Sun, S.; Lim, S. S.; Lam, Y. M.; Grätzel, M.; Mhaisalkar, S.; Sum, T. C. Long-Range Balanced Electron- and Hole-Transport Lengths in Organic-Inorganic CH3NH3PbI3. Science 2013, 342, 344−347. (15) 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. (16) Wehrenfennig, C.; Eperon, G. E.; Johnston, M. B.; Snaith, H. J.; Herz, L. M. High Charge Carrier Mobilities and Lifetimes in Organolead Trihalide Perovskites. Adv. Mater. 2014, 26, 1584−1589. (17) Loi, M. A.; Hummelen, J. C. Perovskite under the Sun. Nat. Mater. 2013, 12, 1087−1089. (18) Etgar, L.; Gao, P.; Xue, Z.; Peng, Q.; Chandiran, A. K.; Liu, B.; Nazeeruddin, M. K.; Grätzel, M. Mesoscopic CH3NH3PbI3/TiO2 Heterojunction Solar Cells. J. Am. Chem. Soc. 2012, 134, 17396− 17399. (19) Momma, K.; Izumi, F. VESTA: A Three-Dimensional Visualization System for Electronic and Structural Analysis. J. Appl. Crystallogr. 2008, 41, 653−658. (20) Heo, J. H.; Im, S. H.; Noh, J. H.; Mandal, T. N.; Lim, C.-S.; Chang, J. A.; Lee, Y. H.; Kim, H.-J.; Sarkar, A.; Nazeeruddin, M. K.; Grätzel, M.; Seok, S. I. Efficient Inorganic−Organic Hybrid Heterojunction Solar Cells Containing Perovskite Compound and Polymeric Hole Conductors. Nat. Photonics 2013, 7, 486−491. (21) Frost, J. M.; Butler, K. T.; Brivio, F.; Hendon, H.; van Schilfgaarde, M. Walsh, Atomistic Origins of High-Performance in Hybrid Halide Perovskite Solar Cells. Nano Lett. 2014, 14, 2584− 2590. (22) 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/CH3NH3PbI3 Perovskite Solar Cell Interfaces. J. Phys. Chem. Lett. 2014, 5, 648−653. (23) Mosconi, E.; Amat, A.; Nazeeruddin, M. K.; Grätzel, M.; De Angelis, F. First-Principles Modeling of Mixed Halide Organometal Perovskites for Photovoltaic Applications. J. Phys. Chem. C 2013, 117, 13902−13913. (24) Roiati, V.; Mosconi; Listorti, A.; Colella, S.; Gigli, G.; De Angelis, F. Stark Effect in Perovskite/TiO2 Solar Cells: Evidence of Local Interfacial Order. Nano Lett. 2014, 14, 2168−2174.

ASSOCIATED CONTENT

S Supporting Information *

DFT calculation data of the tetragonal and orthorhombic MAPbI3 bulk, comprehensive data of the surface terminations investigated here, total energies of the reference systems, the surface termination diagrams within the vdw-DF functional, the outermost Pb polyhedron structures of (110) -PbI5PbI3 and (001) -(PbI3)2 terminations, the projected density of states of the (100) and (101) surfaces, the charge densities obtained in the DFT calculations with the spin−orbit coupling effect, the relaxed structures and electronic properties for the (110) terminations calculated with different numbers of Pb layers, and the partial charge densities of the (110) surface states. This material is available free of charge via the Internet at http:// pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors thank Dr. Jonathan Hill for his proof-reading. Y.T. and K.S. were partially supported by KAKENHI (No. 23340089). This work was also supported by the Strategic Programs for Innovative Research (SPIRE), MEXT and the Computational Materials Science Initiative (CMSI), Japan. The calculations in this work were carried out on the supercomputers in NIMS, Institute for Solid State Physics, The University of Tokyo, as well as the supercomputers in the Information Technology Center, The University of Tokyo and Research Institute for Information Technology, Kyushu University through the HPCI Systems Research Project (Proposal Number hp140179 and hp140110).

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REFERENCES

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