Supporting Information for: Discovery of Pb-Free Perovskite Solar Cells via. High-Throughput Simulation on the K Computer

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1 Supporting Information for: Discovery of Pb-Free Perovskite Solar Cells via High-Throughput Simulation on the K Computer Takahito Nakajima* and Keisuke Sawada Computational Molecular Science Research Team, RIKEN Advanced Institute for Computational Science, Minatojima-minami, Cyuo-ku, Kobe, Hyogo , Japan * nakajima@riken.jp. S1

2 COMPUTATIONAL DETAILS All first-principles calculations were performed with the Vienna Ab initio Simulation Package (VASP). 1 The periodic structures of the materials were obtained by geometry and cell optimizations using the planewave DFT method with the projector-augmented wave (PAW) potentials, which were obtained from the PAW library of VASP. The default values contained in the potential files in VASP were adopted as the kinetic energy cutoff. The centered grid was used for Brillouin zone integration for structure optimization. Further, the van der Waals correction 2 was added to the DFT calculation. In this study, the electronic structure calculations were restricted to non-magnetic calculations. The band structures and the projected density of states (PDOS) were obtained by PBE 3 calculation, which includes the spin orbit (SO) effects, with k-point grids. The band dispersions were depicted via the specific path, X (0.5, 0.0, 0.0) (0.0, 0.0, 0.0) M (0.5, 0.5, 0.0) R (0.5, 0.5, 0.5). All calculations were performed using the K computer. DETAILS OF HIGH-THOROUGHPUT COMPUTATION High-throughput computational simulation was systematically performed for all the possible compositions of organic inorganic halide compounds. In this study, we did not consider the total charge neutrality condition, in which the typical oxidation numbers of a metal atom were adopted. Although the charge neutrality condition is available to reduce the number of possible combinations, it may overlook the novel candidates. Thus, the limitations on the total charge neutrality were relaxed, which allowed a much broader choice of metal cations. Four ABX3 or two A2BBʹX6, that is, A4B4X12 or A4B2Bʹ2X12, were included in the unit cell to avoid band calculation for odd S2

3 electron systems. There are three different configurations for A4B2Bʹ2X12. The configuration where the components B and Bʹ were alternatively repeated was adopted in this study because the previous computational study 4 for MA2PbSnI6 concluded that the three different configurations show essentially the same stability with less than 0.01 ev. The computational results were compiled as a materials database to select the novel candidate materials for organic inorganic halide perovskite solar cells at a later stage. The details to construct the library for the hybrid metal halide compounds are as follows: 1. The geometry and cell optimizations for all compositions of ABX3 and A2BBʹX6 were performed by scalar relativistic (SR) PBE functional with the width of the Gaussian smearing. The geometry and cell optimizations for these kinds of compounds are sensitive to the initial structure. Thus, after three and four different initial structures were optimized for ABX3 and A2BBʹX6, respectively, the optimized structure with the most stable total energy was selected. For ABX3, the structures were first optimized by starting with a distorted orthorhombic structure. Then, two sets of initial structures were obtained from the optimized structures with different X. For A2BBʹX6, one set of initial structure was obtained by replacing the four Pb atoms of the optimized A4Pb4X12 structure with two B and Bʹ atoms, and another set was obtained by averaging the optimized ABX3 and ABʹX3 structures. After the optimizations were complete for the second set, two other initial sets were prepared from the optimized structures with different X for the second set. After all the optimized structures with the most stable total energies were obtained, the metallic systems were excluded from the subsequent calculations. The partial occupation numbers in the bands were used to determine S3

4 whether a system was metallic or not. The system wherein the occupation number of the valence band was below 0.72 or that of the conduction band was over 0.07 was considered as the metallic system. This step reduced the number of possible compounds from 11,025 to 2,143. The structures of the remaining compounds were reoptimized by the SR-PBE functional with no smearing scheme. 2. After all the optimized structures were obtained, we examined whether the structures were perovskite or not. The following criteria were set to confirm the perovskite structure: (i) the X B X bond angle is greater than 160, and (ii) the ratio of the minimum B X length to the maximum B X length in one BX6 octahedron is more than 2/3. 3. The compounds with band s larger than 3.5 ev at the SR-PBE level were excluded from the subsequent procedure. This criterion reduced the number of possible compounds from 2,143 to 1, For all of the remaining 1,923 compounds, more accurate band s were evaluated with the hybrid HSE functional 5 since the pure PBE functional generally underestimates the band. In addition, since the SO effect is known to be important for the present system, 6 the SO-HSE calculation was performed to obtain accurate band s. In this work, since the full SO-HSE calculation required demanding computational resources, approximate SO-HSE calculation was performed for total energy and band by an extension of the ONIOM extrapolation scheme 7,8 to the band calculation. In this scheme, the SO-HSE energy, ESO-HSE k, obtained with a k-point grid, k, can be written as E k E k E k E k, (S1) SO-HSE SO-PBE SR-HSE S SR-PBE S S4

5 where ESO-PBE k is the SO-PBE energy with the k-point grid, k, and ESR-HSE k S E k are the SR-HSE and SR-PBE energies with the smaller k-point grid, and SR-PBE S ks, respectively. By extrapolating the energy differences between the highest-level valence band and lowest-level conduction band, the band, E, can be similarly evaluated with E k E k E k E k, (S2) SO-HSE SO-PBE SR-HSE S SR-PBE S where [ ] indicates the band at the point. Alternatively, the SO-HSE energy, E k, and E and SO-HSE SO-HSE k can be written as E k E k E k E k, (S3) SO-HSE SR-PBE SO-HSE S SR-PBE S E k E k E k E k. (S4) SO-HSE SR-PBE SO-HSE S SR-PBE S In this study, the former approximation was adopted for most of the systems, whereas the latter approximation was used when the system was metallic at the SO-PBE level. The centered grid was adopted as the small k-point grid. For SO-PBE and SR-PBE calculations with the k-point grid, k, and centered grids were adopted, respectively. An extended version of the HSE functional (HSE12) proposed by Moussa, Schultz, and Chelikowsky 9 was adopted in this study. The preliminary band- calculations for the compounds showed that HSE12 is, on average, superior to HSE06 of Heyd, Scuseria, and Ernzerhof 10 for the present systems: for MAPbI3 (Exptl. E = ev 11,12,13,14,15,16,17,18 ), MASnI3 (Exptl. E = ev 13,19,20,21,22 ), MAGeI3 (Exptl. E = ev 23,24,25 ), MAPbBr3 (Exptl. E = ev 14,17,26 ), MASnBr3 (Exptl. E = 2.25 ev 14 ), MAPbCl3 (Exptl. E = S5

6 ev 14,26 ), FAPbI3 (Exptl. E = ev 12,13,15 ), FASnI3 (Exptl. E = ev 13,27,28,29 ), FAPbBr3 (Exptl. E = 2.23 ev 15 ), CsPbI3 (Exptl. E = 1.73 ev 15 ), and CsSnI3 (Exptl. E = ev 30,31,32,33,34 ), HSE12 yields the band s of 1.87, 1.43, 1.83, 2.45, 1.91, 3.01, 1.54, 0.98, 1.98, 1.22, and 0.81 ev, respectively, while HSE06 yields 1.57, 1.15, 1.54, 2.13, 1.63, 2.62, 1.22, 0.70, 1.59, 0.87, and 0.74 ev, respectively, when the approximations of Eqs. (S3) and (S4) were adopted. 5. The hole and electron effective masses were further calculated for all the 1,923 candidate compounds at the SR-PBE level. The effective masses were computed based on the semi-classical Boltzmann transport theory by the BoltzTraP program. 35,36 The BoltzTraP calculation was performed at a temperature of 300 K with the centered grid. 6. The positions of the band edges were further calculated for each candidate compound. An empirical scheme 37,38 was employed to evaluate the band edges. In this scheme, the middle of the band on the absolute vacuum scale is positioned at A B B' X for AB0.5Bʹ0.5X3, where M is the electronegativity of a neutral atom M in the Mulliken scale. The conduction band minimum (CBM) and the valence band maximum (VBM) were then calculated by adding and subtracting half of the band, respectively. In this study, the positions of the band edges were shifted by 1.95, 1.70, and 0.30 ev for MA, FA, and Cs systems, respectively, so that the experimental band edges of CBM and VBM for MAPbI3, 39 FAPbI3, 39 and CsPbI3 40 could be well reproduced. 7. The computational results were compiled as a materials database, which includes the total energies from SR-PBE, SO-PBE, and SO-HSE12, lowest direct and indirect band s, positions of the band edges of VBM and CBM, hole and electron effective masses, S6

7 toxicity, and information on whether the material forms the perovskite structure or not. DETAILS OF SCREENING PROCEDURE The details of the screening procedure adopted in this study are as follows: A. The compounds with perovskite structure were retained. In order to comprehensively discuss the stability of perovskites, demanding calculations of the phonon dispersion relations and quaternary convex hulls would be required. 41 In our study, instead, the stability of the perovskite structure was determined by relaxing the structure from several distorted initial structures in Step 1. When the optimization yields a perovskite structure, the possibility that a compound has a stable perovskite structure increases. B. The compounds with band s between 0.8 and 2.2 ev at the SO-HSE12 level were selected since the band of a typical good light absorber lies between 1.3 and 1.7 ev. 42,43 C. Perovskites with direct band s were selected because a direct- material is capable of efficiently using strong photo-absorption in the thin film form and is beneficial as an efficient photovoltaic absorber. In addition, indirect- materials with small deviations (less than 0.25 ev in this work) from the lowest direct band- value were also retained. D. It is known that the charges in perovskite solar cells act as free holes and electrons rather than as excitons, 44 and have high mobility. Thus, perovskites with absolute values of hole and electron effective masses (mh and me, respectively) smaller than 1.5 m0 were selected. E. The compounds whose CBM CBM and VBM VBM satisfactorily match the CBM of the electron transport layer (ETL), ETL CBM, and the VBM of the hole transport layer S7

8 (HTL), HTL VBM, respectively, were retained. In this study, TiO2 and spiro-ometad were adopted as typical electron and hole transport layers, respectively. The experimental values of 4.1 and 5.22 ev were used for the CBM of TiO2 and the VBM of spiro-ometad, respectively. Since an empirical scheme was employed to evaluate the band edges, the candidate materials were identified by the design criteria with an error correction, : ETL CBM ETL CBM CBM and ETL ETL CBM CBM HTL VBM HTL VBM VBM. Here, the energies of band alignments between the different HTL HTL VBM VBM layers of materials ETL CBM and HTL VBM were considered. ETL CBM = 0.07 ev, HTL VBM = 0.21 ev, 45 and = 0.5 ev were used in this work. F. Since perovskites with low toxicity are desirable, compounds containing Pb, Hg, Cd, As, and Tl were rejected. S8

9 CANDIDATE PEROVSKITES Table S1. Direct, indirect, and lowest band s (in ev), positions of the band edges of VBM and CBM (in ev), and hole and electron effective masses (in m0) for group-14 group-14 double perovskites (including group-14 single perovskites). Direct Indirect Lowest VBM CBM mh me CsSnI direct FASnI direct Cs2GeSnI direct CsSnBr direct MA2SiSnI direct FA2GeSnI direct CsGeI direct Cs2GeSnBr direct MASnI direct MASiI direct CsGeBr direct MA2GeSnI direct FA2SiGeI direct MA2SiGeI direct MAGeI direct MASnBr direct S9

10 Table S2. Direct, indirect, and lowest band s (in ev), positions of the band edges of VBM and CBM (in ev), and hole and electron effective masses (in m0) for group-13 group-15 double perovskites. Direct Indirect Lowest VBM CBM mh me MA2InBiI direct MA2InSbI direct FA2GaBiI direct MA2GaBiI direct MA2InBiBr direct FA2InBiI direct MA2GaSbI direct Cs2GaBiI direct Cs2GaBiBr direct MA2InSbBr direct Cs2GaBiCl direct Cs2GaSbCl direct Cs2InBiBr direct MA2GaPBr direct MA2GaBiBr direct MA2GaSbBr direct S10

11 Table S3. Direct, indirect, and lowest band s (in ev), positions of the band edges of VBM and CBM (in ev), and hole and electron effective masses (in m0) for group-11 group-11 double perovskites (including group-11 single perovskites). Direct Indirect Lowest VBM CBM mh me MA2AgAuBr indirect MA2CuAuBr indirect MA2CuAuI indirect MAAuI indirect FA2AgAuI indirect FAAuI direct MAAuBr direct Table S4. Direct, indirect, and lowest band s (in ev), positions of the band edges of VBM and CBM (in ev), and hole and electron effective masses (in m0) for group-9 group-13 double perovskites. Direct Indirect Lowest VBM CBM mh me Cs2RhInI direct FA2RhInI direct MA2RhGaI direct Cs2RhGaI direct Cs2RhInBr indirect MA2RhInBr direct S11

12 Table S5. Direct, indirect, and lowest band s (in ev), positions of the band edges of VBM and CBM (in ev), and hole and electron effective masses (in m0) for group-11 group-13 double perovskites. Direct Indirect Lowest VBM CBM mh me MA2CuInI indirect FA2AuGaI indirect MA2AuInI indirect MA2AuGaI indirect Table S6. Direct, indirect, and lowest band s (in ev), positions of the band edges of VBM and CBM (in ev), and hole and electron effective masses (in m0) for group-11 group-15 double perovskites. Direct Indirect Lowest VBM CBM mh me MA2AgBiI indirect MA2CuBiI indirect S12

13 Table S7. Direct, indirect, and lowest band s (in ev), positions of the band edges of VBM and CBM (in ev), and hole and electron effective masses (in m0) for the perovskites containing toxic elements retained additionally when the screening criterion for toxicity is ignored. Direct Indirect Lowest VBM CBM mh me group-14 group-14 Cs2SnPbI direct Cs2SiPbBr direct Cs2SiPbI direct Cs2GePbI direct CsPbI direct Cs2SnPbBr direct FA2SnPbI direct MA2SiPbI direct FA2SiPbBr direct FA2GePbI direct Cs2GePbBr direct FAPbI direct MA2SnPbI direct CsPbBr direct MA2GePbI direct MAPbI direct MA2SnPbBr direct S13

14 group-13 group-15 FA2GaAsI direct Cs2TlSbI direct Cs2TlBiI direct Cs2TlPI direct Cs2TlAsI direct MA2GaAsI direct FA2TlPI direct FA2TlSbI direct FA2TlBiI direct FA2TlAsI direct Cs2TlSbBr direct Cs2TlBiBr direct FA2GaAsBr direct Cs2TlPBr direct Cs2TlAsBr direct MA2InAsBr direct MA2TlPI direct MA2TlBiI direct MA2TlSbI direct MA2TlAsI direct MA2TlSbBr direct group-2 group-12 FA2MgCdI direct S14

15 group-10 group-12 MA2PtHgI indirect MA2NiHgI indirect group-13 group-13 MA2GaTlI indirect MA2InTlI indirect REPRESENTATIVE BAND STRUCTURES AND PROJECTED DENSITIES OF STATES Figure S1. Electronic band structure and projected density of states of MAPbI3. S15

16 Figure S2. Electronic band structure and projected density of states of MA2GeSnI6. Figure S3. Electronic band structure and projected density of states of FA2SiGeI6. S16

17 Figure S4. Electronic band structure and projected density of states of FA2InBiI6. Figure S5. Electronic band structure and projected density of states of MA2GaPBr6. S17

18 Figure S6. Electronic band structure and projected density of states of MA2CuAuBr6. Figure S7. Electronic band structure and projected density of states of FA2RhInI6. S18

19 Figure S8. Electronic band structure and projected density of states of MA2CuInI6. Figure S9. Electronic band structure and projected density of states of MA2CuBiI6. COMPARISON WITH PREVIOUS THEORETICAL STUDIES The group-13 group-15 double perovskites were theoretically proposed by Zhao et al. 46 and Giorgi and Yamashita. 47 Zhao et al. proposed two candidate materials, Cs2InSbCl6 and Cs2InBiCl6, with direct band s of 1.02 and 0.91 ev, respectively, as high-performance solar absorbers. In our SO-HSE12 calculation, these perovskites exhibit direct band s of 1.15 and 1.03 ev, respectively, which satisfy our band- S19

20 criterion. However, our band-alignment criterion rejected these chloride perovskites from candidate materials because the inclusion of chlorine anions yields the lower VBM. Giorgi and Yamashita predicted that a thallium bismuth iodide perovskite, MA2TlBiI6, can be a potential alternative photovoltaic material although the material includes the toxic thallium element. They reported that MA2TlBiI6 has a direct band of 1.62 ev at the SR-PBE level. Our result shown in Table S7 of the Supporting Information also confirms that MA2TlBiI6 is a potential alternative candidate for solar cells when the criterion for toxicity is ignored. Our computation predicted a direct band of 1.67 ev at the SO-HSE12 level for this compound. This value is similar to that obtained by Giorgi and Yamashita although the computational levels are different, which indicates that a pure GGA functional without SO interactions reproduces the band of MA2TlBiI6 obtained by the hybrid GGA with the SO contribution well due to an error cancellation between strong-correlation and SO effects, as in the MAPbI3 system. 48 Volonakis et al. 49 and Jain et al. 50 proposed Cs2AgInCl6 as a group-11 group-13 halide perovskite solar cell. The band s of Cs2AgInCl6, as computed by Volonakis et al. and Jain et al., are and 2.42 ev, respectively. In our calculation, the band is 2.84 ev. Thus, Cs2AgInCl6 was excluded from the candidate list because it has a large band and is not a typical good light absorber. Volonakis et al. 51 proposed all the combinations of the compound Cs2BBʹX6 with B (group-15) = Bi or Sb; Bʹ (group-11) = Cu, Ag, or Au; and X = Cl, Br, or I, as promising photovoltaic materials. In the calculations of Volonakis et al., these materials exhibited indirect band s. Since our calculation also shows that the group-11 group-15 double perovskites have indirect and large band s, these cesium compounds were removed from the candidate list. S20

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