Cation Role in Structural and Electronic Properties of 3D Organic

May 16, 2014 - We found good agreement with previous experimental works, but at the same time we observed that the bare inorganic network [PbX3]− do...
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Cation Role in Structural and Electronic Properties of 3D Organic− Inorganic Halide Perovskites: A DFT Analysis Giacomo Giorgi,*,† Jun-Ichi Fujisawa,‡,§ Hiroshi Segawa,‡ and Koichi Yamashita*,† †

Department of Chemical System Engineering, School of Engineering, The University of Tokyo, 7-3-1, Hongo, Bunkyo-ku, 113-8656 Tokyo, Japan ‡ Research Center for Advanced Science and Technology (RCAST), The University of Tokyo, 4-6-1, Komaba, Meguro-ku, 153-8904 Tokyo, Japan § Japan Science and Technology Agency (JST), Precursory Research for Embryonic Science and Technology (PRESTO), 4-1-8 Honcho Kawaguchi, Saitama 332-0012, Japan ABSTRACT: Moving from a general revise of the structural and electronic properties of the 3D methylammoniumtrihalogenoplumbates (MAPbX3, X = Cl, Br, I) class of halide organic−inorganic perovskites, we have focused our attention on the organic cation and studied the role it plays in the electronic/optical features of this class of compounds, paying attention mainly to the iodide compound. We found good agreement with previous experimental works, but at the same time we observed that the bare inorganic network [PbX3]− does not fully take into account the electronic properties of 3D systems. A comparison is performed between the electronic properties of MAPbI3 organic−inorganic perovskite and those of the purely inorganic CsPbI3. Furthermore, we show that hybrid methods applied on top of the spin−orbit calculated structures are not able to open the bandgap sufficiently to reproduce the experimental value, revealing the need of further and more computationally demanding procedures to get improved agreement.

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The proper knowledge of the polymorphism7,12 of such a class of compounds represents the first step toward a full understanding of their role in perovskite-based solar cells. In their research Poglitsch and Weber7 reported the experimental order of stability of such 3D lead halide perovskite polymorphs, revealing striking relationships between the stability of the phase and the halide ion. It is interesting that the cubic phase (Pm3m) is the most stable one at ordinary temperature for MAPbCl3 and MAPbBr3, while for the iodide-based compound the same cubic polymorph becomes stable at a Tc > 327.4 K, the tetragonal phase (I4/mcm) being the most stable at ordinary conditions for such a MAPbI3 compound.13 More recently, still for the 3D systems Stoumpos et al.11 have deeply investigated both tin and lead iodide organic perovskites considering both methylammonium and formanidinium (HC(NH2)2+) as organic cations. By means of several experimental techniques (photoluminescence measurements, FT-IR, Seebeck coefficient, and Hall effect measurement), this paper gives a very interesting overview on the possible phase transitions that experimentally occur in these crystals, showing an overall marked tendency for Sn compounds to oxidize, forming p-type Sn4+-doped semiconductors characterized by metal-like conductivity. On the other hand, the 2D material counterparts already received attention in the past two decades: modifications due to

INTRODUCTION In the last few months, several papers have appeared in the literature reporting the enhanced photoconversion efficiency (PCE) up to 15%1 of organic−inorganic solar cells containing sandwiches of perovskite compounds, i.e., the light harvester, mesoporous TiO22−4 (alternatively alumina in the so-called meso-superstructured solar cells (MSSCs))5 and a polymeric hole conductor. Such novel photovoltaic architecture stems from the pioneering work of Miyasaka et al.6 where initial bromide and iodide cells were reported to have PCEs of 3.8 and 3.1%, respectively. The interest toward these materials is associated with the extremely appealing and not yet completely disclosed role that such mixed organic−inorganic perovskites play in the cell. 3D methylammoniumtrihalogenoplumbates(II) (MAPbX3)7,8 and stannates(II) (MASnX3)9,10 (MA = CH3NH3+; X = Cl−, Br−, I−) are characterized by high chemical stability and good transport characteristics once in contact with the mesoporous oxide when used in assembling the organic−inorganic solar devices. Recent experimental results have shown11 that this class of compounds can act as both n-type or p-type semiconductors (ambipolar behavior) depending on the synthetic preparation method, with the former ones obtained from solution and characterized by the lowest carrier concentration and the latter synthesized through solid state reactions, increasing the need of further investigations to better uncover the properties of these intriguing materials.11 © XXXX American Chemical Society

Received: May 16, 2014

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RESULTS AND DISCUSSION In the case of our cubic cell (Pm3m, Z = 1) we have considered and optimized several initial positions, finding the one with the C−N bond oriented along the (111) direction as the most stable structure. Indeed, the highly mobile organic cation leads to a large uncertainty in the prediction of the thermodynamic phase stability for these halides, inducing several possible thermodynamic metastable states. We tested two potentials for Pb (6s26p2 and 5d106s26p2) in the neutral and in the negatively charged state of the semiconductor skeleton (PbI3). All the main conclusions of this work are drawn based on the 5d106s26p2 Pb PAW potential usage. In Figure 1 the optimized structure of the MAPbI3 (hereafter also called (a) structure) is reported, together with the structure of the two other halides, MAPbCl3 and MAPbBr3, while the main optimized structural parameters for these three MAPbX3 organic−inorganic perovskites are reported in Table 1. Highly symmetric cubic structure is predicted only for X = Cl, Br. In fact, for X = I, a pseudocubic one is the most stable characteristic given by the presence of the bulky iodine atoms. Such a pseudocubic structure for the MAPbI3 compound we theoretically predict is in agreement with the very recent experimental refined data that appeared in the literature, where a high-temperature (T = 400 K) tetragonal structure (P4 mm, Z = 1) is observed via single-crystal X-ray diffraction analysis.11 The other two theoretically calculated structures considered in the paper are reported, together with the previously introduced (a) structure, in Figure 2. In detail, the (b) structure represents the fully optimized (lattice and ionic positions) inorganic network skeleton [PbI3]−, while the (c) structure represents the geometry of the MAPbI3 perovskite without MA, i.e., the single-point calculation of the [PbI3]− network keeping frozen the lattice parameter and ionic positions of the (a) structure. The calculated bandgap for the MAPbI3 perovskite crystals is 1.64 eV. It is direct on the R point (0.5, 0.5, 0.5) and in good agreement with the reported experimental value.17,26 The band structure of the initially optimized MAPbI3 (a) structure is reported in Figure 3(a). A detailed analysis of the frontier orbitals clearly reveals that the valence band maximum (VBM) on R point is constituted by the antibonding combination of Pb 6s orbitals and 5p ones of I. The same trend also holds for the other two halides (Cl and Br), increasing the localization on Pb 6s orbitals with the reduced size of the halide. On the other hand, the conduction band minimum (CBM) is formed by Pb 6p orbitals plus a residual contribution given by 5s (3s, 4s) ones of I (Cl, Br). From a closer analysis of the band population of the two systems we find a null contribution, regardless of its orientation, of CH3NH3+ to the frontier orbitals at the minimum gap point (R), confirming the scarce electronic coupling between the barrier and the semiconductor on the R point.8 In particular, in the case of MAPbI3, the first quantitative contribution ascribed to the methylammonium molecule is 5.00 eV below the VBM of the system and is constituted by 27% of C 2p. On the other hand, the first contribution in the conduction region is 2.78 eV above the CBM and consists of 3% C s and 4% N s orbitals. Qualitatively similar results hold for the other two MAPbX3 systems. Our results reveal general agreement with previous predictions26 mainly focused on the electronic structure for

the introduction of a long-chain organic cation have been investigated by the work of Mitzi who focused mainly on the possible optoelectronic oriented applications of such lowdimensional compounds.14−16 2D crystals seem to be anyway less attractive than 3D ones concerning the usage of such hybrid perovskites in the novel photovoltaics architecture: for the latter ones, indeed, low-energy bands are characterized by lower excitonic bonding energies, making them better performing as light harvesting materials.17 Still concerning the 3D crystals further experiments supported by DFT calculations have been performed very recently in the work by Baikie et al.18 where optical properties of MAPbCl3 obtained by UV−vis spectroscopy were compared to calculate the density of states and band structure and also in the paper of Mosconi et al.19 where the 2D/3D electronic properties of CH3NH3PbX3 and mixed halide CH3NH3PbI2X (X = Cl, Br, I) are deeply investigated. Also, we theoretically calculated the effective mass of the photocarriers in MAPbI3, confirming the experimentally reported ambipolar nature of such an organic−inorganic compound.20 Astonishingly, the theoretical knowledge of such materials with so much promising potential applicability in photovoltaics is still at its infancy. In this respect, two points stimulated our research, i.e., the fact that spin−orbit coupling (SOC) contribution is always speculated but to the best of our knowledge only very few recent papers have appeared including such an effect in the description of electronic/optical properties of such materials20,21 and, not secondarily, the role that the organic cation plays has been too much overlooked by modellizations that assign electronic, optical, and excitonic properties only to the semiconductor inorganic network region. Motivated by this lack of information, after a general introduction about MAPbX3 (X = Cl, Br, I) systems, we here intend to study the electronic properties of the MAPbI3 halide, focusing on the frontier orbital nature and on their band structure analysis, the impact of SOC, and how hybrid functionals can improve the band gap description of these 3D organic−inorganic perovskite materials. Finally, we demonstrate how a complete study of optical, electronic, and excitonic properties of 3D crystals requires the inclusion of the organic cation part (i.e., the “barrier”)8 and that such properties cannot only be ascribed simply to the inorganic network (i.e., the “semiconductor”).8

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COMPUTATIONAL DETAILS Spin-polarized DFT calculations have been performed with the generalized gradient approximation as implemented in the VASP code22 by means of the electron exchange-correlation functional proposed by Perdew−Burke−Ernzerhof (PBE). The electron−ion interaction is described by the projector augmented wave method (PAW).23 Also, still concerning the PAW potential, both a 6s26p2 and a 5d106s26p2 valence electron potential were tested for the Pb atom.24 A plane-wave basis set energy cutoff of 500 eV was used. For the structural optimization a 6 × 6 × 6 (corresponding to 216 points) Γcentered k-point sampling of the Brillouin zone was used (8 × 8 × 8 for the bulk modulus calculation), while for the study of electronic properties denser meshes have been used. Furthermore, SOC calculations are performed ,and also the HSE0625 hybrid functional is used on top of the DFT+SOC calculations to compare the predicted results with the experimentally reported ones. B

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In particular, we found the effective mass of the hole to be mh* = 0.36m0 and that for the electron me* = 0.32m0. The close similarity between the effective masses of the two carriers clearly confirms the ambipolar behavior reported at experimental level.27 MAPbI3 is indeed found to behave at the same time as a good electron5 and a good hole transport material when used in perovskite-based solar cells.28 Of course, we are aware that DFT is a theory which exactly predicts the properties of the fundamental ground state, and in this sense we know that the calculation of the effective mass of the electron can be an approximation of the real value, due to the inaccuracy of the description of the conduction region. Nevertheless, the perfect agreement with the experimental behavior makes us firmly believe in the reliability of our results. Even if, as we showed before, the states associated with methylammonium are quite deep in both the conduction and valence region at the at gap minimum point (R), it seems reasonable to further investigate the role, even indirect, that they can play in the band edge positioning of the final organic− inorganic MAPbI3 perovskite along the whole Brillouin zone. We have thus removed the MA cation from the cell, and properly compensating the extra charge, we have fully reoptimized and recalculated the band structure for the pure inorganic network ((b) structure in Figure 2). The most macroscopic structural effect that the MA removal has on the final geometry of the inorganic network is the recovered cubic symmetry with a subsequent expansion of the volume of the cell. This effect is clearly due to the fact that the cation removal reduces the long-range interactions between ammonium hydrogen atoms and the halide (H···I) that differently tend to shrink the MAPbI3 structure.19 Also, the enhanced symmetry induces the Pb−I bond lengths to be identical (3.50 Å), causing a bandgap reduction from 1.64 to 1.54 eV. We remark that the Jahn−Teller effect in solids29 is considered responsible in the 2D case for the bandwidth narrowing and for the energetic stabilization of the bandedges.26 In our case, the dimensionality (3D) and the reduced size of our cells do not enable us to properly define a reference to get the absolute meaning of eigenvalues. Similarly, the energy level of deep and flat states in the valence region and their relative difference slightly oscillate, making a comparison between the 2D and the 3D not doable. What we can clearly state is that the absence of the MA cation has another striking impact on the electronic properties of the ideal crystal: it drastically modifies the shape and the nature of the VBM as shown in Figure 3(b). In detail, while the CBM preserves its shape and population as in the MAPbI3 case, similarly to what is reported for the 2D case,26 clearly one can see that the shape of the VBM on R is manifestly changed. Now, indeed the VBM is constituted by the 5p orbitals of I atoms, while the Pb 6s ones (still mixed with 5p orbitals of I) are shifted down about 0.25 eV below the new VBM. Indeed, in the 3D case the removal/addition of MA induces a larger distortion of the cell: this finding impacts the final bandedge population: in the (b) structure the energy rise of I 5p orbitals that form the new VBM is due to the fact that their overlap is only slightly affected by the cell size increase. At variance, the antibonding overlap between localized Pb 6s and I 5p orbitals is highly reduced by the cell size increase with a subsequent energetic lowering of such a band inside the valence region.

Figure 1. Optimized structure of the (a) pseudocubic cell of MAPbI3, (b) the cubic cell of MAPbCl3, and (c) the cubic cell of MAPbBr3 organic−inorganic perovskite. [Large dark gray, lead; purple, iodine; green, chlorine; orange, bromine; brown, carbon; small light gray, nitrogen; white, hydrogen.]

lead iodide based low-dimensional systems that anyway neglect the contribution of the organic cation. In our previous paper,20 by means of the parabolic approximation, we estimated at DFT level the effective mass (m*) of carriers existing around the bottom of the conduction band or the top of the valence band. C

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Table 1. Calculated Main Structural Parameters for the Three Organic−Inorganic Halide Perovskites MAPbX3 (X = Cl) cubic

dPb−Cl a

a = 5.810 Å (a = 5.675a) B = 45.75 GPa = 2.831/2.986 Å, dC−N = 1.487 Å

(X = Br) cubic

dPb−Br

(X = I) pseudocubic

a = 6.08 Å (a = 5.90a) B = 20.59 GPa =3.132/2.962 Å, dC−N =1.491 Å

dPb−I

a = c = 6.45 Å b = 6.48 Å B = 15.60 GPa = 3.292/3.150/3.340/3.17 Å, dC−N = 1.492 Å

Ref 7.

Figure 2. (a) Structure: Optimized structure for the MAPbI3 organic−inorganic halide perovskite. (b) Structure: Optimized structure for the [PbI3]− inorganic network. (c) Structure: Single-point calculation on the geometry of (a) structure after the MA organic cation removal. Lattice parameters and ionic positions of the inorganic network of (a) and (c) are consequently identical. [Large dark gray, lead; purple, iodine; brown, carbon; small light blue, nitrogen; white, hydrogen.]

revealing (clearly, a direct transition on Γ is anyway unlikely to occur according to the very large EG) another interesting feature in the electronic properties of the 3D organic−inorganic perovskites still associated with the presence of the MA cation. Focusing more in detail on the bandgap value, as stated, the initial calculation of the MAPbI3 system ((a) structure) has led to a value on R, EG = 1.64 eV, that apparently is in very good agreement with the experimental data (1.55 eV, 1.70 eV).6,26 Other theoretical values ranging between 1.4526 and 1.57 eV (on Γ)19 are similarly reported, and we ascribe the slight difference between our and other theoretical data to a different computational setup, mainly to a different pseudopotential used for the lead atom and to the exchange-correlation potential employed. Concerning the quantitatively excellent agreement between theoretical and experimental values, it is straightforward that a basic knowledge of DFT shortcomings (incorrect treatment of the electron self-interaction) in predicting the bandgap of many materials manifestly points out the inconsistency between the two values. This contradiction is clearly solved once the spin−orbit coupling (SOC) contribution is included in the calculations.20,21 The inclusion of SOC on the previously optimized MAPbI3 (a) structure reveals on one side its dramatic effect on the conduction region with a huge reduction of the bandgap and on the other one that the agreement between previously calculated theoretical values and the experimental bandgap is purely coincidental. The band structure for the (a) structure including SOC is reported in Figure 3(d). Now the EG calculated including the SOC contribution is 0.52 eV, about one-third of the experimental value, and perfectly consistent with the DFT bandgap predictive capabilities. The physical picture that emerges from the inclusion of SOC is the splitting of the CBM 6p lead orbitals

The appealing electronic feature also experimentally detected, i.e., the ambipolarity,27 is clearly provided by the presence of the MA organic cation: its removal corresponds, as still observable in Figure 3(b), to the flattening of the [PbI3]− network ((b) structure) valence region with subsequent asymmetrization of the bandedges that confers to the inorganic network an electron conductive nature. We have further compared the results for this ideal inorganic network, cubic and highly symmetric ((b) structure), with those of the real one still without the MA organic cation ((c) structure in Figure 2) calculated, as stated before, keeping frozen both lattice parameters and ionic positions to those of the initially optimized MAPbI3. It is interesting to observe from the band structure of this latter case that the VBM order is restored to the initial MAPbI3 case ((a) structure), in tight similarity with results reported for the low-dimensional crystals,26 as observable in Figure 3(c). One aspect previously not discussed should be here reconsidered; indeed, our electronic property analysis for the case of the initial MAPbI3 ((a) structure) simply focused on the orbital population at the R point, i.e., at the minimum direct EG point. The rigorous comparison among the orbital population of (a) and (c) structures reveals that at the R point they are characterized by exactly the same electronic distribution. The noticeable difference is observed when we move toward the center of the Brillouin zone, at the Γ point, where the VBM of the inorganic network [PbI3]− ((c) structure) is still constituted by I 5p orbitals (mixed with some traces of Pb 6p orbitals), while the CBM is only populated by I 5s orbitals. Surprisingly, regardless of the fact that the band edges are formally identical (see and compare Figures 3(a) and 3(c)), in the case of MAPbI3 ((a) structure), at variance, the CBM main contribution is given by C and N 2s orbitals (about 8%), thus D

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Figure 3. Band structure of: (a) MAPbI3 crystal ((a) structure); (b) the bare fully optimized [PbI3]− network ((b) structure); and (c) the bare [PbI3]− network ((c) structure, same lattice parameter of the initially optimized MAPbI3 ((a) structure) here used). (d) DFT+SOC calculated band structure of the optimized (a) structure, MAPbI3. The cubic symmetry points are used (R = 0.5, 0.5, 0.5; Γ = 0, 0, 0; M = 0.5, 0.5, 0; X = 0.5, 0, 0).

in a 2-fold degenerate state |1/2, ± 1/2⟩, and in a 4-fold degenerate |3/2, ± 3/2⟩, |3/2, ± 1/2⟩ one, with a lightelectron/heavy-electron spin−orbit gap, ΔO, on R that is 1.41 eV.20 On top of the DFT+SOC calculated band structure we have applied the HSE0630 hybrid functional to correct the gap, finding anyway that on the R point such calculation leads to a new bandgap that is EG = 0.96 eV, a value still far from the experimentally reported one. For sake of comparison, we have applied this last procedure (1. DFT; 2. DFT+SOC; 3. DFT+SOC+HSE calculation) to the most studied full inorganic perovskite, i.e., the cubic polymorph of CsPbI3 (c-CsPbI3). At variance with MAPbI3 in this case the optimized structure is perfectly cubic (a = 6.41 Å), consistent with previous theoretical (a = 6.18 Å;31 a = 6.05 Å32at LDA level of calculation) and experimental (a = 6.29 Å33) findings. Despite the lack of experimental results concerning the bandgap for c-CsPbI3, our DFT level calculated value of 1.48 eV is in good agreement with the previously calculated data (1.321,31 and 1.1 eV32). Results from the comparison between the full inorganic and the mixed organic−inorganic are reported in Table 2. Concerning the nature of the bandedges of cCsPbI3, quantitative similarity is observed with those of the organic−inorganic counterpart MAPbI3: no contribution from the Cs ion (as in the case of methylammonium) is indeed

Table 2. Comparison of the Structural and Electronic Properties between the Cubic Fully Inorganic (c-CsPbI3) and the Organic−Inorganic (Pseudo) Cubic Iodide (MAPbI3) Perovskite optimized lattice parameter (Å, PAW/PBE) EG (eV, PAW/PBE) EG (eV, PAW/PBE+SOC) EG (eV, PAW/PBE+SOC+HSE06)

c-CsPbI3

(pseudo) c-MAPbI3

a = 6.41

a = c = 6.45, b = 6.48

1.48 0.32 0.75

1.64 0.52 0.96

detected on the two frontier orbitals at the bandgap minimum point (R), while exactly the same orbital composition is found for the VBM and CBM (Pb 6s orbitals combined in an antibonding fashion with I 5p orbitals for the former and mainly Pb 6p orbitals combined still in an antibonding fashion with traces of I 5s ones for the latter). As in the case of the organic cation, Cs 6s orbitals represent the main contribution (∼4%) of the conduction band on the Γ point. The correction given by the inclusion of SOC effects in this case (as in the case of MAPbI3) of ∼1.1 eV is perfectly consistent with the results reported, at LDA level of calculation, by Even et al.21 Still for c-CsPbI3, we estimate at the DFT level the effective mass (m*) of carriers existing around the bottom of the conduction band or the top of the valence band as a result of E

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the fitting of the dispersion relation. We obtain that the effective mass of the hole is mh* = 0.32m0, and that for the electron is me* = 0.42m0, along the R−Γ direction. The comparison with the same values calculated for MAPbI3 reveals the reduced ambipolarity for the case of the c-CsPbI3. Qualitatitive/quantitative agreement is found with the results of Even and Pedesseu et al., who calculated at the DFT (LDA) + SOC level the effective mass of the hole.34,35 The value they obtain is slightly smaller (mh* = 0.12m0) but consistent with the fact that introducing the SOC effects induces a quantitative reduction of the effective mass of the carriers in such perovskite systems as a consequence of the impact played by the bandgap reduction, as we also previously demonstrated.20 Additionally, the comparison at the DFT level between the bandedges of the two perovskites reveals that the reduction in the gap for CsPbI3 is due to a larger extent to the VBM upward shift of CsPbI3. To check the origin of this behavior, we considered two deep and flat levels belonging to the PbI3 network (common to the two perovskites, 5d Pb and 5s I orbitals) and calculated their difference for the two cases ((a) and (b) in Figure 4) finding an almost constant value (5.12 vs

overlap is observed with subsequent rise of the VBM energy. The CBM will be at variance influenced to a lesser extent since in this case the presence of iodine orbitals is residual, and thus the ΔECBM between the two cases will be smaller than ΔEVBM, due to a reduced impact of the shrinking on the orbital overlap. We can thus affirm that it is the lattice shrinking, and not the symmetry enhancement, that is mainly responsible for the bandgap difference and for the different band alignment between the fully inorganic (CsPbI3) and the organic− inorganic (MAPbI3) perovskite. According to our findings, we thus can clearly state that (i) the presence of methylammonium is the main cause of the ambipolarity of MAPbI3: its removal indeed induces the bandedge reordering with a subsequent VBM flattening, (ii) whatever the nature of the cation, the CBM at Γ is always mainly constituted by the cation orbitals, and (iii) due to the almost identical orbital contribution to the band edges, the bandgap reduction observed for the CsPbI3 inorganic perovskite has to be ascribed completely to the lattice shrinking of such a compound that makes c-CsPbI3 a better hole transporter, as previously found for the case of the other fully inorganic lead perovskite, i.e., CsSnI3.34 In particular, the experimental measurement of several properties (thermoelectric power and Hall effect) of this latter species has led to a calculated resistivity and mobility of 0.9 Ω cm and 585 cm2 V−1 s−1, representing one of the highest mobility values for ptype semiconductors characterized by a similar bandgap.36 Additionally, (iv) still regardless of the nature of the cation (organic or inorganic) the DFT+SOC+HSE calculation procedure is not sufficient to properly “open” the bandgap to reproduce the experimental value.

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CONCLUSIONS In this paper we have analyzed the properties of the pseudocubic polymorph of the organic−inorganic perovskite iodide, MAPbI3. The contribution of the organic part previously only marginally considered and mostly in the low-dimensional 2D case has been here analyzed, determining the impact that it has on the band structure of MAPbI3. The interesting feature related to the role of the MA cation resides in its ability to substantially change the shape and the nature and the orbital composition of the band edges, being responsible for the widely reported ambipolarity of such class of compounds. For the dramatic impact they have on the conduction band region of lead halide perovskites, we confirmed the relevance of spin−orbit coupling effects in the improvement of band structure prediction. We compared the electronic properties of MAPbI3 with those of the most studied fully inorganic counterpart, i.e., CsPbI3, finding that the bandgap reduction observed for the latter species is mainly ascribable to the lattice parameter shrinkage and also that CsPbI3 has a more marked hole conductive behavior compared to the more ambipolar MAPbI3. Finally, we combined the use of the HSE06 hybrid functional on top of the DFT+SOC calculated band structure, finding such a computational procedure not sufficient to “open” the bandgap to reproduce the experimental value. This last finding clearly reveals that further investigations by means of more computationally demanding methodologies (GW)37,38 are thus required to improve the agreement between experimentally reported and calculated bandgaps.

Figure 4. Bandedge alignment at the R point between: (a) optimized MAPbI3, (b) optimized CsPbI3, (c) CsPbI3 with lattice parameter, a = 6.45 Å, (d) CsPbI3 with lattice parameter, a = 6.48 Å. The ΔE between the deep 5d Pb and 5s I orbital is also reported as a reference.

5.14 eV). We have thus aligned VBM and CBM with respect to the deep (and flat) Pb 5d orbitals. This clearly confirms what was stated before concerning the slightly larger contribution to the ΔEG between the two halides that resides in the valence maximum (ΔEVBM = 0.68 eV; ΔECBM = 0.53 eV). Furthermore, we did try to figure out which parameter mainly influences this trend, the lattice shrinking or the symmetry enhancement that characterize CsPbI3; a not cumbersome and still meaningful procedure is to apply to CsPbI3 the lattice parameters of MAPbI3 and, by means of the same procedure previously described, calculate the band structure and consistently align the bandedges. We thus found that progressively increasing the lattice parameters of CsPbI3 leads to a sensitive approach toward MAPbI3 bandedge energy; in particular, at a = 6.48 Å, the CBM of CsPbI3 lies at energies comparable to MAPbI3, with the VBM still slightly differing between the two perovskites. This result is consistent with the fact that the VBM of both the perovskites is formed by the antibonding combination of Pb 6s and I 5p orbitals, both orbitals present in quite large amount. In the case of CsPbI3, whose optimized lattice parameter (a = 6.41 Å) is smaller than MAPbI3 (a = c = 6.45, b = 6.48 Å), a larger F

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AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected] *E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This research is supported by the Japan Society for the Promotion of Science (JSPS) through its “Fundamental Program for World-Leading Innovative R&D on Science and Technology (FIRST Program)”. GG wants to thank Mr. H. Kawai of the Department of Chemical System Engineering, School of Engineering, The University of Tokyo, for the always very useful and stimulating scientific discussions.

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