Lead-Free Mixed Tin and Germanium Perovskites ... - ACS Publications

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Lead-Free Mixed Tin and Germanium Perovskites for Photovoltaic Application Ming-Gang Ju, Jun Dai, Liang Ma, and Xiao Cheng Zeng* Department of Chemistry, University of Nebraska-Lincoln, Lincoln, Nebraska 68588, United States S Supporting Information *

ABSTRACT: The power-conversion efficiency (PCE) of lead halide perovskite photovoltaics has reached 22.1% with significantly improved structural stability, thanks to a mixed cation and anion strategy. However, the mixing element strategy has not been widely seen in the design of lead-free perovskites for photovoltaic application. Herein, we report a comprehensive study of a series of lead-free and mixed tin and germanium halide perovskite materials. Most importantly, we predict that RbSn0.5Ge0.5I3 possesses not only a direct bandgap within the optimal range of 0.9−1.6 eV but also a desirable optical absorption spectrum that is comparable to those of the state-of-the-art methylammonium lead iodide perovskites, favorable effective masses for high carrier mobility, as well as a greater resistance to water penetration than the prototypical inorganic−organic lead-containing halide perovskite. If confirmed in the laboratory, this new lead-free inorganic perovskite may offer great promise as an alternative, highly efficient solar absorber material for photovoltaic application.

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ratio,12 such as the FA/Cs or Cl/I ratios. This bandgap tunability is particularly suitable for making tandem solar-cell devices. Indeed, Eperon et al.13 and McMeekin et al.14 have recently reported exciting results of tandem PVs by employing mixed perovskites with optimally tuned bandgaps. Meanwhile, an intensive research effort has also been devoted to finding efficient lead-free perovskites for PVs.15−18 A straightforward chemical modification of lead iodide perovskites is through homovalent substitution of lead with another divalent element (e.g. Sn or Ge). However, the same stability issue can arise for the lead-free perovskites. For example, because of the susceptibility of tin toward oxidation from +2 to +4 oxidation states upon exposure to air, the PVs using the tin halide perovskite as an absorber, such as MASnI3, achieve a PCE of only 6%,16,17 much lower than PCEs of typical lead halide perovskites reported in the literature. Recently, Wang et al.19 and Marshall et al.20 have reported that PVs based on CsSnI3 can achieve PCE of 3.31% and 3.56%, respectively. Thus, lead-free perovskites that can result in a PCE greater than 6% are badly needed. Recently, composition ratios of mixed lead halide perovskites have been systematically investigated to enhance the PCE and the stability of mixed lead halide perovskite PVs.12 A mixed lead halide perovskite material, FA0.75Cs0.25Sn0.5Pb0.5I3, was found to possess outstanding thermal and atmospheric stability with respect to Sn-based perovskites.13 However, to our knowledge, no analogous study for the lead-free perovskites has been

INTRODUCTION Inorganic−organic halide perovskites represent a major breakthrough in the development of highly efficient photovoltaic materials.1,2 Within only several years, polycrystalline thin-film perovskite photovoltaic (PV) devices have achieved a PCE of 22.1%.3 The rapid rise in PCE, coupled with the prospect of low-cost precursors and facile synthesis, render the perovskite photovoltaic devices highly competitive for commercial applications. However, there are well-known obstacles that are yet to be overcome for outdoor applications. To date, most perovskites that give rise to a high PCE still contain a toxic element: lead. This includes the popular methylammonium (MA) lead iodide4,5 (MAPbI3) and formamidinium (FA) lead iodide6 (FAPbI3). Moreover, most lead-containing perovskites tend to degrade in the presence of moisture, which is a challenging issue for long-term outdoor usage. For example, the photovoltaic devices based on FAPbI3 have shown a PCE up to 20%,6 but the FAPbI3 tends to transform from the black phase to yellow phase,7 resulting in a dramatically reduced device efficiency. Several recent studies suggest that the fractional substitution of the organic cations (MA) with cesium (Cs) and FA can markedly enhance the thermal stability of the hybrid perovskites.5,8,9 The iodide can be also simultaneously replaced by other halides, (e.g. chloride and bromide).10,11 Indeed, the mixed perovskites have led to several highly certified records in the NREL-chart. As a result of their high efficiencies and higher stability with respect to stand-alone perovskites, the search for improved mixed perovskites has become a hot area of research. Moreover, the mixing element strategy allows the realization of tunable bandgaps for perovskites by changing the component © 2017 American Chemical Society

Received: April 29, 2017 Published: May 24, 2017 8038

DOI: 10.1021/jacs.7b04219 J. Am. Chem. Soc. 2017, 139, 8038−8043

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Journal of the American Chemical Society

alternative structure formation, such as a hexagonal structure or an NH4CdCl3 structure. In this work, the sites B and A are both occupied by two different cations. To establish the t, we adopt the mean ionic radius for both the B site and the A site, namely, r +r r +r rB = B′ 2 B″ and rA = A′ 2 A″ , following previous work.34 The calculated Goldschmidt tolerance factors are summarized in Figure 2a. It can be seen that the stable perovskites with distorted structures are predicted. Their Goldschmidt tolerance factors are highlighted with a light-brown horizontal bar; whereas the predicted perovskites with perfect cubic structures are those with their Goldschmidt tolerance factor values being within the light-yellow horizontal bar. Other perovskites with tfactors outside the two horizontal bars are no longer considered in this work. Here we identify 17 perovskites likely being stable because of their favorable Goldschmidt tolerance factors. Among the 17, nine perovskite structures have a formula of AB′0.5B″0.5X3, and the other structures have a formula of A′0.5A″0.5B′0.5B″0.5X3. Considering t factors of most perovskites are within the range of 0.9 to 1, we adopt a 2 × 2 × 2 supercell with respect to the cubic unit cell, in which 4 B′ and 4 B″ occupy 8 B sites, respectively; whereas 4 A′ and 4 A″ occupy the 8 A sites, respectively. Following a previous theoretical study,35 both A and B sites are alternatively occupied by A′ and A″, and B′ and B″, forming the rock-salt structure (see Figure 1).

reported in the literature. Can the composition change result in marked improvement in the stability and the PCE? In this article, we report a series of mixed lead-free perovskites, AB′0.5B″0.5X3 and A′0.5A″0.5B′0.5B″0.5X3, where A is an organic or inorganic cation and X is a halogen ion. Mixed B′ and B″ are Sn and Ge, respectively, and they hold the role of replacing Pb in lead halide perovskite APbX3. In addition, A can be substituted with combinations of various inorganic and organic cations, such as Cs, Rb, MA, and FA to form A′0.5A″0.5B′0.5B″0.5X3. On the basis of first-principles computation, many mixed tin and germanium halide perovskites are predicted to have a direct bandgap, one of the key prerequisites for being a good absorber material in solar cells.

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COMPUTATIONAL METHODS

All first-principles computations are performed on the basis of densityfunctional theory (DFT) methods as implemented in the Vienna ab initio simulation package (VASP 5.4).21 An energy cutoff of 520 eV is employed, and the atomic positions are optimized using the conjugate gradient scheme without any symmetric restrictions until the maximum force on each atom is less than 0.02 eV Å−1. The electronic structures and the optical properties are computed using PBE0 functional with a cutoff energy of 400 eV.22 Here, the computed PBE0 bandgap (about 1.3 eV) of CsSnI3 is in good agreement with the experimental value23 (see Supporting Information Figure S1). The ion cores are described by using the projector-augmented wave (PAW) method.24 Grimme’s DFT-D3 correction is adopted to describe the long-range van der Waals interaction.25 A 3 × 3 × 3 k-point grid is used for the mixed tin and germanium halide perovskites.

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RESULTS AND DISCUSSION Because some tin or germanium halide perovskites have already been synthesized experimentally,16,26,27 we use these perovskites to identify possible phases for mixed tin and germanium halide perovskites. CsSnI3 is known to have four phases, but the black phase with the space group Pnma (i.e. B-γ-CsSnI3)19,20,28 is the most studied for solar-cell application. If Cs is substituted with MA, MASnI3 would exhibit a tetragonal perovskite structure with the space group P4mm. On the other hand, all germanium perovskites, CsGeI3, MAGeI3, and FAGeI3 exhibit the trigonal perovskite structure with the space group R3m.27,29 Note that for tin and germanium halide perovskites, if the Asite cation entails too large of an ionic radius to fill the cavity between the octahedrons BX6, the perovskite structures may be destabilized and degraded into two-dimensional or onedimensional compounds.27,30 Once structures for mixed tin and germanium halide perovskites are constructed, Goldschmidt’s tolerance factor can be used as an empirical indicator to assess the structural stability of the putative perovskites.31−33 For perovskites with the general formula ABX3, Goldschmidt’s tolerance factor t is defined as rA + rX t= 2 (rB + rX)

Figure 1. Crystal structures of ABX 3 , AB′ 0.5 B″ 0.5 X 3 , and A′ 0. 5 A″ 0.5 B′ 0 .5 B″ 0 .5 X 3 perovskites. Both AB′ 0. 5 B″ 0. 5 X 3 and A′0.5A″0.5B′0.5B″0.5X3 are rock-salt-ordered double perovskites.

To assess the potential performance of absorber materials, the electronic bandgap of the materials is a key quantity. It should be within the optimal range of 0.9−1.6 eV (to achieve a Shockley−Queisser efficiency of ∼25%). Figure 2b shows the computed PBE0 bandgaps for the 17 perovskites. Here, nine materials exhibit bandgaps within the optimal region (as highlighted by the light-gray horizontal bar). For these nine perovskites with the formula AB′0.5B″0.5X3, the bandgaps increase in the order of iodide < bromide < chloride; they increase with the decrease of the ionicity of the halogen elements. The lead halide perovskites show the same trend. The lead-free chloride perovskites exhibit notably wider bandgaps than their iodide and bromide counterparts. The computed bandgaps of the former are mostly outside of optimal range. Another observed trend is that with the increasing ionic radius for occupation of the A site, the bandgap of the corresponding compound increases. For the eight perovskites with the formula A′0.5A″0.5B′0.5B″0.5X3, a similar trend can be seen for iodide and bromide. However, there is no clear trend with respect to the change of the A-site elements. The complex local structure of the materials resulting from the tilting of octahedron BX6, which is induced by different A-site elements (inorganic and organic), results in different electronic structures. To gain

where rA and rB are the ionic radii of the A- and B-site cations, respectively, and the rX is the ionic radius of anion X. The tolerance factor empirically evaluates whether the A-site cation can fit within the cavities between the BX6 octahedrons. The range of 0.9 ≤ t ≤ 1 is generally viewed as a very good fit for perovskites, implying the likelihood of cubic structures. The range of 0.71 ≤ t ≤ 0.9 is implied as the likely formation of the orthorhombic or rhombohedral structure because of the tilting of the BX6 octahedrons. For t ≤ 0.71 or t ≥ 1, there can be an 8039

DOI: 10.1021/jacs.7b04219 J. Am. Chem. Soc. 2017, 139, 8038−8043

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Journal of the American Chemical Society

Figure 2. (a) Calculated Goldschmidt’s tolerance factors (data denoted by circles) for mixed tin and germanium perovskites. The predicted stable distorted perovskites are highlighted by a light-brown horizontal bar, whereas the predicted perfect perovskites are highlighted by a light-yellow horizontal bar. (b) The calculated electronic bandgaps of perovskites with favorable Goldschmidt’s tolerance factors. The range of optimal bandgaps for solar-cell materials is highlighted by the light-gray horizontal bar.

Figure 3. Computed band structures (based on PBE0 functional) of (a) CsSn0.5Ge0.5I3, (b) RbSn0.5Ge0.5I3, (c) MASn0.5Ge0.5I3, and (d) Rb0.5FA0.5Sn0.5Ge0.5I3. Γ (0.0, 0.0, 0.0), X (0.5, 0.0, 0.0), Z (0.0, 0.0, 0.5), M (0.5, 0.5, 0.0), and R (0.5, 0.5, 0.5) refer to the high-symmetry special points in the first Brillouin zone.

contrast, the two bands are split at the Γ pint because of the loss of the symmetries of the local structures under the influence of organic cations. Another key factor that can affect the performance of solar cells is the carrier mobility, a property closely related to the effective mass of the carriers. We calculated the effective masses of the four perovskites by fitting their energy dispersion curves at VBM and CBM to parabolic functions along different k directions in the vicinity of the Γ point. Table S1 presents the effective mass tensors corresponding to the [001], [010], [001], [110], and [111] directions, respectively. For holes, the calculation of effective mass tensors is straightforward because all the bands are nondegenerate and parabolic at the Γ point. Low hole mass was found and the mass increased with the increasing radius of A-site cations for AB′0.5B″0.5X3. If only inorganic cations occupy the A sites, the band dispersions are nearly isotropic because of the symmetries of the cubic structures. If organic cations occupy A-sites, their irregular radii can significantly distort the cubic structures, resulting in anisotropic band dispersions. These features are clearly seen from the values of effective masses corresponding to the [001], [010], and [001] directions, respectively. For CsSn0.5Ge0.5I3 and RbSn0.5Ge0.5I3, each has two bands converging at CBM. We denote the obtained electronic effective masses as the heavy (he) and light electron (le) masses, following the terminology used for the holes in tetrahedral semiconductors. As shown in Table S1, he masses are an order of magnitude higher than hole effective masses, whereas the le ones are comparable to the hole effective masses. For MASn0.5Ge0.5I3 and Rb0.5FA0.5Sn0.5Ge0.5I3,

insight into the electronic properties of the perovskites, we computed the electronic structures of four perovskites with bandgaps within the optimal range, namely, CsSn0.5Ge0.5I3 (1.31 eV), RbSn0.5Ge0.5I3 (1.21 eV), MASn0.5Ge0.5I3 (1.58 eV), and Rb0.5FA0.5Sn0.5Ge0.5I3 (1.50 eV). We also estimated the possible variation in the bandgaps of CsSn0.5Ge0.5I3 resulting from some other arrangements of Sn and Ge. The variation is typically less than 0.2 eV. Figure 3 shows the computed band structures (based on PBE0 functional) of the identified four perovskites. All of the four perovskites exhibit direct bandgaps with the valence band maximum (VBM) and conduction band minimum (CBM) being located at the Γ point. The dispersion of the top valence band is larger than that of the bottom conduction band, indicating that the hole has a smaller effective mass. From the projected density of states (PDOS) onto the Sn 5s, Sn 5p, Ge 4s, Ge 4p, and I 5p orbitals, it can be seen that the top valence bands are predominantly contributed by the Sn 5s, Ge 4s, and I 5p orbitals, whereas the bottom conduction bands are predominantly contributed by the Sn 5p and Ge 4p orbitals (Figure S2 and S3). Similar to the lead halide perovskite MAPbI3, the A-site elements cannot directly contribute to the band edges, but can indirectly affect the electronic structure by inducing the tilting of octahedrons BX6, because of the different ionic radii of A-site elements. Interestingly, when A-sites are occupied by Cs and Rb, two conduction bands converge at the CBM because of the preserved cubic structure, as in the case of α-CsSnI3.28 The flatter band and steeper band are generally referred to as the heavy band and the light band, respectively. In 8040

DOI: 10.1021/jacs.7b04219 J. Am. Chem. Soc. 2017, 139, 8038−8043

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materials. For other predicted materials, although their absorption intensities are slightly lower, some of them still possess suitable bandgaps and show reasonably good opticalabsorption behavior. At room temperature or greater, the tilting of octahedrons can be induced. Thus, the materials with a distorted perovskite structure should be considered as well. RbSn0.5Ge0.5I3, with the distorted perovskite structure, was considered as a benchmark in our study (see Figure S4a). As shown in Figure S4b, the computed bandgap of this RbSn0.5Ge0.5I3 increases to about 1.50 eV. Similarly to the mixed Sn and Pb perovskites, the effective masses of this RbSn0.5Ge0.5I3 also increase slightly and become anisotropic because of the symmetry increase (see Table S1). It is known that for the lead halide perovskites, spin−orbit coupling (SOC) can significantly lower the bandgap.39−42 Here, the inclusion of SOC can also reduce the bandgap (see Figure S5). For the cubic structure of RbSn0.5Ge0.5I3, the bandgap decreases to about 0.9 eV, whereas the effective masses slightly decrease and the lowest two conduction bands split at the CBM because of the effect of SOC. For RbSn0.5Ge0.5I3, with the distorted perovskite structure, the bandgap also is reduced to about 1.2 eV (see Figure S6) by including the SOC effect. Interestingly, the effects of SOC and the tilting of octahedrons on the bandgap tend to offset with one another. Additionally, we calculated decomposition energies with respect to the possible decomposition pathways. For example, if a compound [A]Sn0.5Ge0.5I3 decomposes into its corresponding binary materials, the decomposition enthalpy is defined as ΔH = E [AI] + 0.5E [SnI2] + 0.5E [GeI2] − E [ASn0.5Ge0.5I3] Here, a positive value of ΔH means an energy release occurs during the formation of ASn0.5Ge0.5I3, demonstrating that the compound is energetically favorable. Figure S7 shows the decomposition enthalpy ΔH of different decomposition pathways for RbSn 0 . 5 Ge 0 . 5 I 3 , MASn 0 . 5 Ge 0 . 5 I 3 , and Rb0.5FA0.5Sn0.5Ge0.5I3. Note that RbSn0.5Ge0.5I3 gives a fairly large positive value of ΔH, whereas MASn0.5Ge0.5I3 and Rb0.5FA0.5Sn0.5Ge0.5I3 yield smaller positive values of ΔH, because organic cations interact relatively weakly with the inorganic framework. Although CsSn0.5Ge0.5I3 has a suitable Goldschmidt tolerance factor, it gives rise to a negative value of ΔH for the corresponding decomposition pathways, suggesting that the Goldschmidt tolerance factors are not always reliable in evaluating the structure stabilities of [A]Sn0.5Ge0.5I3 compounds with mixed ionic and covalent bonding, because of the difficulty in assigning an accurate ionic radius.43 We also examine the thermal stabilities of the predicted materials using ab initio molecular dynamics (AIMD) simulations (see Figure S8). We find that the predicted materials are still intact after 5 ps simulations with the temperature of the system being controlled at 300 and 500 K, respectively. Lastly, we use a computational method to assess the stability of the perovskite under a humid environment, for which we also use MAPbI3 as a benchmark model system. It has been reported that the water molecule can easily penetrate MAPbI3, turning the compound into the monohydrate state and then disrupting the perovskite structure.44 To assess the stability of the materials considered here under a humid environment, we compute the activation barrier for water penetrating RbSn0.5Ge0.5I3 through the surface by using the nudged elastic band (NEB) method45 (see Figure S9). As a comparison, the activation barrier for water penetrating MAPbI3 is computed as well (Figure S10). It is seen that the activation barrier (0.23 eV)

most electronic effective masses are greater than the corresponding hole effective masses. As for CsSnI3, the relatively low hole effective masses affect carrier mobility, implying that the materials may be p-type semiconductors. To evaluate exciton effects, we calculated the exciton-binding energies using a simple Wannier exciton model.36 The excitonbinding energy is given by E b = mass, 1/ 37

(

1 me

+

1 mh

μe 4 2ℏε∞2

(μ: the reduced effective

); ε : the high-frequency dielectric con∞

stant). Table S2 shows that all of the four perovskites exhibit a low exciton-binding energy. MASn0.5Ge0.5I3 has the highest binding energy (21.07 meV), comparable to that of MAPbI3 (reported in the range of 19−50 meV38), implying there is fast exciton dissociation for these four materials. The calculated exciton-binding energies exhibit the same trend as the effective masses, being that they decrease with decreasing radius of Asite cations. In addition to the bandgap and carrier mobility, the optical absorption is another critical property for assessing the performance of absorber materials. Figure 4 shows the

Figure 4. Computed optical-absorption spectra (based on PBE0 functional) of several predicted materials, compared with the computed spectra of the prototype Si and MAPbI3. The absorption coefficient of Si is calculated using the HSE06 functional. The absorption coefficient of MAPbI3 is computed using the PBE functional without considering the spin−orbit coupling (SOC) effect. Note that the computed absorption spectrum of MAPbI3 is coincidentally in good agreement with the experiment because of the cancellation of errors of using the PBE functional without SOC.

computed absorption spectra of the predicted materials. Computed absorption spectra for prototypical high-efficiency solar materials, Si and MAPbI3, are also included for comparison. The absorption coefficient is given by 2e

α(ϖ) = ℏc [(ε12 + ε2 2)1/2 − ε1]1/2 , where ε1 and ε2 are the real and the imaginary parts of dielectric function, respectively. According to the AM 1.5 solar spectrum, 98% of the solar power reaching the earth’s surface is composed of photons below 3.4 eV. Clearly, CsSn0.5Ge0.5I3 and RbSn0.5Ge0.5I3 exhibit a stronger absorption than the other predicted materials, and their absorption spectra are very close to that of MAPbI3. Moreover, both materials display moderate absorption in the infrared region. These favorable absorption properties render both materials as promising candidates for being solar absorber 8041

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Journal of the American Chemical Society for water penetrating RbSn0.5Ge0.5I3 is markedly higher than that for MAPbI3 (0.09 eV; this value is consistent with the previous computational result. 46 ) This suggests that RbSn0.5Ge0.5I3 is much less prone to water attack than MAPbI3 under a humid environment. We also performed two independent AIMD simulations for the MAPbI3−H2O and the RbSn0.5Ge0.5I3−H2O systems. (They are constructed with a 2 × 2 × 1 supercell, which is based on optimized configurations with the water molecule adsorbed on the surface of MAPbI3 and RbSn0.5Ge0.5I3.) For MAPbI3−H2O, one water molecule can penetrate into the MAPbI3 and replace an I-site of octahedron [PbI6] within a few ps, thereby disrupting the perovskite structure of MAPbI3 (consistent with result of Mosconi et al.; 47 Figure S11). In stark contrast, for RbSn0.5Ge0.5I3−H2O, four water molecules initially adsorbed on the surface of RbSn0.5Ge0.5I3 still exhibit their initial state after a 5 ps AIMD simulation (Figure S12), without showing any sign of penetration by water. On the basis of the computed decomposition energies, thermal stabilities, and stability under humid conditions, RbSn0.5Ge0.5I3 appears to be the most easily synthesized in the laboratory among the mixed tin and germanium halide perovskites considered in this study. A possible synthesis route for inorganic perovskites (e.g. RbSn0.5Ge0.5I3) may utilize a previously reported method for synthesis of CsSnI3.19 As an example, the synthesis of RbSn0.5Ge0.5I3 may be proceeded by placing an appropriate amount of SnI2, GeI2, and RbI in pyrex tubes. The tubes are evacuated and sealed. The evacuated tubes are then heated to a high temperature to produce RbSn0.5Ge0.5I3. For mixed tin and germanium halide perovskites containing organic molecules, like MASn 0.5 Ge 0.5 I3 and Rb0.5FA0.5Sn0.5Ge0.5I3, the synthesis of these compounds may be proceeded using solution synthesis as previously reported for mixed lead and tin halide perovskites, such as MAPb0.5Sn0.5I3.48

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AUTHOR INFORMATION

Corresponding Author

*[email protected] ORCID

Liang Ma: 0000-0003-4747-613X Xiao Cheng Zeng: 0000-0003-4672-8585 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS X.C.Z. was supported by the National Science Foundation (NSF) through the Nebraska Materials Research Science and Engineering Center (MRSEC) (grant No. DMR-1420645), an NSF EPSCoR Track 2 grant (OIA-1538893), and by the University of Nebraska Holland Computing Center.

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REFERENCES

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CONCLUSION In conclusion, we have predicted a series of lead-free mixed tin and germanium halide perovskite materials for photovoltaic applications. Nine materials are identified to possess suitable bandgaps. Among them, most importantly, RbSn0.5Ge0.5I3 exhibits a comparable absorption spectrum of sunlight, similar to the well-known prototype MAPbI3. Meanwhile, small effective masses and low exciton-binding energies are predicted for the new material, indicating that the material is extremely promising as a solar absorber. Moreover, the bandgap can be tuned over a wide range (about 0.90−3.15 eV) with respect to the composition change involved in the mixing element strategy. If confirmed by experiments, the mixed tin and germanium halide perovskites may serve as a highly efficient absorption material, while also addressing some known challenging issues inherent in lead halide perovskite solar cells.

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the periodic slab model of CsSn0.5Ge0.5I3; effective masses and binding energy; snapshots of CsSn0.5Ge0.5I3, RbSn0.5Ge0.5I3, MASn0.5Ge0.5I3, and Rb0.5FA0.5Sn0.5Ge0.5I3 from AIMD simulation; decomposition energies of RbSn0.5Ge0.5I3, MASn0.5Ge0.5I3, and Rb0.5FA0.5Sn0.5Ge0.5I3 with respect to possible pathways; calculated mechanism of water penetrating into the MAPbI3 and RbSn0.5Ge0.5I3 by nudged elastic band (NEB) calculation; snapshots of MAPbI3−H2O and RbSn0.5Ge0.5I3−H2O from AIMD simulation(PDF)

ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/jacs.7b04219. Computed DOSs of CsSnI3, CsSn0.5Ge0.5I3, RbSn0.5Ge0.5I3, MASn0.5Ge0.5I3, and Rb0.5FA0.5Sn0.5Ge0.5I3.; computed band structure and DOS of RbSn0.5Ge0.5I3 with SOC; computed chargedensity distributions of the highest VB and lowest CB of 8042

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DOI: 10.1021/jacs.7b04219 J. Am. Chem. Soc. 2017, 139, 8038−8043