Band Gap Insensitivity to Large Chemical Pressures in Ternary

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Band Gap Insensitivity to Large Chemical Pressures in Ternary Bismuth Iodides for Photovoltaic Applications Xing Huang, Su Huang, Pratim Biswas, and Rohan Mishra J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.6b09567 • Publication Date (Web): 30 Nov 2016 Downloaded from http://pubs.acs.org on December 5, 2016

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The Journal of Physical Chemistry

Band Gap Insensitivity to Large Chemical Pressures in Ternary Bismuth Iodides for Photovoltaic Applications Xing Huang,†,* Su Huang,‡ Pratim Biswas,‡ and Rohan Mishra†,* †Department

of Mechanical Engineering & Materials Science, and Institute of Materials Science

& Engineering, Washington University in St. Louis, St. Louis, Missouri 63130, USA ‡Department

of Energy, Environmental and Chemical Engineering, Washington University in St.

Louis, St. Louis, Missouri 63130, USA Email: [email protected]; [email protected] ABSTRACT Ternary bismuth iodides (A3Bi2I9, where A is a monovalent cation) have been recently suggested as less-toxic alternatives to lead halide perovskites for photovoltaic applications. Using density functional theory based calculations, we predict that the band gap in these compounds is insensitive to chemical pressure applied by changing the size of A-site cations, which is confirmed experimentally. We further show that the band gap in A3Bi2I9 compounds increases (or decreases) by stretching (or compressing) Bi2I9 bioctahedra, and the observed band gap insensitivity is a direct result of the counteractive interplay of three factors: the size of the A-site cations, the presence of H-bonds with organic A-site cations and spin-orbit coupling (SOC) effects. Our study demonstrates that the layered structure of A3Bi2I9 compounds intrinsically limits any significant modification of their band gap and highlights the need for three1 ACS Paragon Plus Environment


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dimensional connectivity of BiI6 octahedra in order to achieve high efficiency Bi-based photovoltaics. INTRODUCTION Lead iodide perovskites have shown a remarkable increase in photovoltaic efficiency and have emerged as a promising semiconductor material for photovoltaic and optoelectronic applications.1-7 They have a stoichiometry of APbI3, where A is a monovalent organic or inorganic cation and their structure can be described as a network of corner-connected PbI6 octahedra with the A-site cation filling cuboctahedron (12-coordinate) cavities. The PbI6 octahedra can undergo cooperative tilts to accommodate A-site cations with widely varying sizes, which is used to change the chemical pressure.8 The application of chemical pressure, in turn, leads to a systematic modulation of the band gap and allows optimization for different applications.2,9 Typically, larger A-site cations reduce octahedral tilts, which increases the overlap between Pb and I states, and results in a reduction of the band gap.2,9,10 For instance, the band gap of APbI3 can be reduced from 2.19 eV in KPbI311 to 1.48 eV in formamidinium lead iodide ([HC(NH2)2]PbI3, or FAPbI3).12 Despite the unprecedented increase in their photovoltaic efficiency, APbI3 perovskites, especially the ones having methylammonium (CH3NH3+ or MA) cation, are found to be unstable under ambient operating conditions13. Their chemical instability combined with the highly toxic nature of lead has made it necessary to search for less-toxic alternatives having comparable photovoltaic properties and ease in fabrication.14 The family of ternary bismuth iodides with a stoichiometry of A3Bi2I9 display similar compositional flexibility as the perovskites and have recently been proposed as less-toxic alternatives to lead-based photovoltaic materials.15-26 Instead of forming corner-connected octahedral network like in the perovskites, in A3Bi2I9 compounds, Bi and I atoms form face-

2 ACS Paragon Plus Environment

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sharing Bi2I9 bioctahedra with A-site cations present in a cuboctahedral coordination of I− ions, as shown in Fig. 1a. In view of such structural similarity to the perovskites, chemical pressure can also be applied to A3Bi2I9 compounds by using A-site cations of different sizes. Since the first report on Cs3Bi2I9 and MA3Bi2I9 for photovoltaic applications appeared in 2015, several A3Bi2I9 compounds with varying size of A-site cations, from the smaller K+ ions22,24 to NH4+ ions,26 Rb+ ions,19,21,22,24 Cs+ ions,15-24 and larger MA+ ions23,25,26 have been reported. However, unlike APbI3 perovskites, whose band gap shows a systematic decrease from 2.19 eV in KPbI311 to 1.48 eV in FAPbI3,12 there is no clear band gap variation with chemical pressure in the reported A3Bi2I9 compounds. The band gap of synthesized A3Bi2I9 compounds is found to be within 1.89 – 2.2 eV, which is sub-optimal for photovoltaic applications. In a recent study of inorganic A3Bi2I9 compounds (A = K, Rb, Cs), Lehner et al. also came to the same conclusion about the band gap insensitivity to the A-site cation size.24 However, the reason for such counterintuitive behavior is currently unknown. Therefore, to realize the full potential of A3Bi2X9 compounds, a systematic understanding of the evolution of band gap with chemical pressure is needed, which would allow their rational design and optimization as lead-free semiconductors for photovoltaic and optoelectronic applications. In this Article, we have systematically investigated the band gap evolution in the family of A3BiI9 compounds (A = K, Rb, Cs, NH4+, MA, FA) with chemical pressure by changing the size of A-site cations from the smaller K+ ions to the larger FA+ ions.27,28 Based on first principles density functional theory (DFT) calculations, we predict that increasing the size of the A-site cations in A3Bi2I9 leads to only a small variation of ~0.1 eV in band gap, which is found to be within 1.77 – 1.84 eV. We show that the band gap in A3Bi2I9 compounds, which arises due to the hybridization of Bi 6s, 6p and I 5p states, is controlled by the interplay of three factors: the



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chemical pressure due to the size of the A-site cations; the strength of H-bonds between H+ ions in organic A-site cations and I− ions; and spin-orbit coupling (SOC) effects. In the absence of SOC effects, increasing the size of the inorganic A-site cations enhances the overlap between Bi 6s/6p and I 5p states that favors a reduction of the band gap. In contrast, for compounds with organic cations, the formation of H-bonds leads to a weakening of the bonding between Bi and I atoms, thereby increasing the band gap. Finally, on including SOC effects, the band gap of A3Bi2I9 compounds decreases substantially due to the heavy Bi and I atoms. The magnitude of band gap reduction due to SOC cancels out the changes due to chemical pressure and results in the observed band gap insensitivity. Our theoretical predictions are further confirmed by experiments where we obtain a band gap of 1.98 eV for K3Bi2I9 in agreement with previous reports22,24 and 2.00 eV for FA3Bi2I9, which is reported here for the first time. Our observations constitute the basis to develop strategies for band gap engineering of ternary bismuth halides for photovoltaic and optoelectronic applications.

METHODS Computational Details For A3BiI9 compounds (A = K, Rb, Cs, NH4+, MA), previous studies have shown that the DFT-calculated crystal structures are in good agreement with experiments.23-26 In particular, lattice constants and band structures can be accurately reproduced using the Perdew-BurkeErnzerhof (PBE) functional and the Heyd-Scuseria-Ernzerhof (HSE06) hybrid exchangecorrelation functional, respectively.23-26 DFT calculations were performed using the Vienna Abinitio Simulation Package (VASP).29 Geometry-optimization calculations were carried out using the PBE exchange-correlation functional30 until the maximal residual atomic forces were less


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than 0.01 eV/Å. The band-structure calculations were carried out using PBE and the HSE06 hybrid exchange-correlation functional31,32 with the fraction of Hartree-Fock exchange fixed at 0.25. Core-electrons were modeled using the projector-augmented wave method.33 We used a plane-wave cutoff energy of 500 eV for the PBE calculations and 400 eV for the HSE06 calculations. The Brillouin zone was sampled using a 3×3×1 Γ-point included Monkhorst-Pack k-points mesh34 for the relaxations, and a 6×6×2 mesh for the electronic structure calculations with PBE, and 2×2×1 mesh for the HSE06 calculations. Experimental Synthesis and Characterization The following chemicals were purchased from Sigma-Aldrich and used as supplied: bismuth iodide (99%), potassium iodide (>99.5%), rubidium iodide (99.9%), cesium iodide (99.9%), methylamine (33% solution in absolute ethanol), formamidinium iodide (FAI, 99%), hydriodic acid (57 wt. % in H2O, 99.95%), ethanol (anhydrous, 99.5%), diethyl ether (anhydrous,

99.0%),

dimethyl

sulfoxide

(DMSO,

anhydrous,

99.9%)

and

N,N-

dimethylformamide (DMF, anhydrous, 99.8%). Methylammonium iodide (MAI) was synthesized following a previous report.35 Briefly, 10 mL of HI was slowly added to 24 mL of CH3NH2 solution in a round-bottom flask under stirring and reacted in a nitrogen atmosphere at 0 °C for 2 hours. A rotary evaporator was used to remove the solvents to precipitate MAI. The as-obtained product was re-dissolved in absolute ethanol and precipitated by the addition of diethyl ether. This procedure was repeated twice. The final product was collected and dried at 60 °C in a vacuum oven overnight. Thin films of A3Bi2I9 were fabricated on FTO-coated glass and common glass slides for optical and structural studies. The substrates were cleaned with detergent and water followed by sonication in acetone and isopropanol for 10 min each. After that the substrates were treated with



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a UV-ozone cleaner for 10 min. Common glass slides were then directly used, while for FTO slides, a diluted TiO2 paste (Sigma-Aldrich, 22nm titania paste 1:3 by weight in ethanol) was spin-coated on the substrates at 7000 rpm and sequentially annealed at 500 °C for 30 minutes, resulting in a 150 nm thick mesoporous TiO2 layer. The A3Bi2I9 precursor solutions were made using a mixed-solvent system containing DMF and DMSO (7:3 by volume).23 To make the FA3Bi2I9 thin film, 1.5M FAI and 1M BiI3 were dissolved in the solvent mixture and spin-coated on the substrate at 1000 rpm for 20s. Then the film was annealed at 110 °C for 30 minutes. All other A3Bi2I9 thin films were made following similar processes. X-ray diffraction (XRD) patterns were used to analyze the crystal structure of the synthesized A3Bi2I9 thin films (see Supporting Figure S1). The patterns were recorded by a Bruker D8 Advance Diffractometer operated at 40 kV voltage and 40 mA current using Cu Kα1 radiation (λ = 1.5406 Å) under 2θ-θ configuration. The scan was performed in the range of 5-60° with 0.019° step size and 0.5 second per step count time under 15 turn/minute sample rotation. The acquired patterns were processed with Diffrac.EVA to strip off the influence from the TiO2/FTO substrate and the Cu Kα2 radiation. The resulted patterns were compared peak by peak with standard XRD PDF cards from International Centre for Diffraction Data (ICDD PDF-4+ database) and published results to determine the indices.23-25,36 The lattice constants were then calculated from the indexed XRD patterns using an intensity-weighted regression algorithm. With the XRD results, we confirm that the desired compounds were successfully synthesized. UV-vis absorption spectra of the A3Bi2I9 thin films were measured with a Shimadzu UV2600 spectrophotometer in the range of 300 nm to 900 nm. Standard Tauc plots for indirect allowed transition were generated by plotting (h)1/2 against photon energy (h


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RESULTS AND DISCUSSIONS A3Bi2I9 compounds have been reported to exist in two different crystal structures. In K3Bi2I9,22,24 Rb3Bi2I924 and (NH4)3Bi2I9,26 Bi and I atoms form a layered structure along c-axis. Each individual layer consists of a bilayer network of corner-connected BiI6 octahedra. However, in Cs3Bi2I923,24 and MA3Bi2I9,23,26 two neighboring octahedra along the c-axis form a facesharing Bi2I9 bioctahedron, and these Bi2I9 bioctahedra are separated by A-site cations. We find crystal structures having face-shared Bi2I9 bioctahedra to be the ground state for all the examined A3Bi2I9 compounds based on the DFT results, which are performed at 0 K (see Supporting Figure S2). We have further obtained the structural information of A3Bi2I9 compounds through XRD characterization of experimentally synthesized compounds. The experimental lattice parameters were obtained by comparing the XRD results to previously reported values from the literature.2325

The comparison of the lattice parameters of synthesized and relaxed ground state structures of all A3Bi2I9 compounds are summarized in Table 1. We observe good agreement between the computationally predicted and the experimentally measured lattice parameters for Cs3Bi2I9 and FA3Bi2I9, which are within 3%. For K3Bi2I9, Rb3Bi2I9 and MA3Bi2I9, we observe a larger deviation in lattice parameters of up to 5.5%. K3Bi2I9 and Rb3Bi2I9 were previously reported to exist in a structure having bilayer network of corner-connected BiI6 octahedra with P21/n space group symmetry.24, while XRD of our synthesized K3Bi2I9 and Rb3Bi2I9 both show C2/c space group symmetry (see discussion in the Supporting Information). In contrast, the relaxed ground-state structure of K3Bi2I9 and Rb3Bi2I9 has a layered network of face-sharing Bi2I9 bioctahedra with Cc space group symmetry, which could be a possible reason for the large



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difference in the theoretical and experimental lattice parameters. Indeed, we observe a better agreement on using the experimental P21/c space group symmetry for K3Bi2I9 and Rb3Bi2I9 (see Supporting Table S1). However, as the band gap change between the two phases is less than 0.1 eV, we use the ground state with Cc space group symmetry for K3Bi2I9 and Rb3Bi2I9 for comparing the change in electronic properties with chemical pressure. Similarly, previous study on MA3Bi2I9 has shown the hexagonal crystal phase with P63/mm space group symmetry,23 whereas our calculated ground state structure has triclinic crystal phase with P1 space group symmetry and experimental characterization suggests monoclinic phase with C2/c space group symmetry. The difference in the theoretical and experimental lattice structure of MA3Bi2I9 could be due to the rotational motion of the MA cations that occurs at finite-temperatures experimentally,37 which are static in the theoretical calculations. We observe only minor changes in band gap (< 0.1 eV) for MA cations with different orientation and therefore use the theoretical ground state for comparing the electronic structure changes with chemical pressure. Figure 1a shows the crystal structure of Cs3Bi2I9 with layers of Bi2I9 bioctahedra with the Cs+ ions present in a symmetrical cuboctahedral coordination of I− ions. We find that different Asite cations lead to the distortion of AI polyhedra and Bi2I9 bioctahedra to different degrees, which is discussed below. However, the theoretical band gap remains within 1.77 – 1.84 eV for all the A3Bi2I9 compounds studied here. These results are also confirmed experimentally, where the band gap of different A3Bi2I9 compounds stays within 1.81 – 2.00 eV (see Figure 1b). A Tauc plot of Cs3Bi2I9 and FA3Bi2I9 shows only ~0.2 eV band gap difference, the two compounds that show the largest band gap variation in the A3BiI9 family, both theoretically and experimentally (see Figure 2a). The similar band gap of these two compounds is also evident from the indistinguishable color of their thin films deposited on glass substrates (see Figure 2a). We have


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further characterized A3Bi2I9 thin films using scanning electron microscopy (SEM). The surface morphology of two representative compounds, Cs3Bi2I9 and FA3Bi2I9, is shown in Figure 2b. SEM images show that both thin films have highly crystalline, layered structure, which is more apparent in the Cs3Bi2I9 thin film. On the whole, individual crystals are larger in Cs3Bi2I9 thin films having an average size of ~5 μm and thickness of ~600 nm, whereas they are smaller in FA3Bi2I9 thin films, with average size of ~1.5 μm and thickness of ~100 nm. Despite the intrinsic structural differences between the compounds, both theoretical and experimental results demonstrate that their band gap is insensitive to the size of A-site cations. To gain a better understanding of the factors that lead to the observed insensitivity of band gap with chemical pressure, we have investigated the electronic structure of A3BiI9 compounds using Cs3Bi2I9 as a representative compound. An atom-projected electronic density of states (DOS) of Cs3Bi2I9 obtained using the PBE functional without including SOC indicates that the valence band is predominantly comprised of I 5p states with a small contribution of Bi 6s states while the conduction band is dominated by Bi 6p states hybridized with I 5p states (see Figure 3a). The contribution of Bi 6s states to the conduction band is negligible as shown in the inset of Figure 3a. There is only a small contribution from Cs+ ions to the valence band from – 3.7 to 0 eV and to the conduction band from 2.3 to 3.5 eV. The empty Cs 5d states are present above 4.6 eV (see Supporting Figure S3). Therefore, the band gap of Cs3Bi2I9 is unambiguously determined by the overlap between Bi 6s/6p and I 5p states. Without including SOC effects, we obtain a band gap of 2.2 eV for Cs3Bi2I9. However, due to the presence of heavy Bi and I atoms, SOC effects are expected to be nontrivial. We observe a reduction in the band gap from 2.2 eV to 1.77 eV with a splitting of the conduction band between 2.2 and 3.5 eV on including SOC effects to the PBE functional (PBE+SOC) as shown in Figure 3b. Generally, the PBE functional is



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known to underestimate the experimental band gap, however, in the case of A3Bi2I9 compounds, we find that the PBE functional gives a good estimation of the band gap with a maximum discrepancy of only 0.12 eV with respect to the experimental values (see Supporting Table S2). We have also employed the HSE06 hybrid exchange-correlation functional31,32 without and with SOC effects to calculate the band gap (see supporting Table S2). We find that while the predicted band gap for A3Bi2I9 compounds using HSE shows a similar trend to that obtained using PBE, the HSE functional overestimates the band gap on an average by ~0.5 eV. Therefore, we use the PBE functional to describe the electronic structure of other A3Bi2I9 compounds. To understand the nature of Bi–I interactions in Cs3Bi2I9, we performed a crystal orbital Hamilton population (COHP) analysis.38-40 As shown in Figure 3c, we find that the highest occupied bands near the valence band maximum (VBM) and lowest unoccupied bands near the conduction band minimum (CBM) are dominated by Bi 6s – I 5p and Bi 6p – I 5p antibonding interactions, respectively. This is similar to the lead halide perovskites, for instance in MAPbI3, where the band gap is defined by Pb–I antibonding states.26 In addition, it is worth noting that significant contribution of I 5p states within ~2 eV below the VBM in DOS plot (see Figure 3a) is substantially reduced in the corresponding COHP plot (see Figure 3c), indicating that a good portion of I 5p states are of non-bonding nature. We have calculated the band structure of Cs3Bi2I9 along high-symmetry points in the reciprocal space using PBE+SOC as shown in Figure 3d. We find that Cs3Bi2I9 exhibits an indirect band gap of 1.77 eV, with VBM positioned at L and CBM situated along the Γ → A direction. The direct band gap is 1.89 eV and occurs at the C point in the reciprocal space. We find that all the examined A3Bi2I9 compounds show an indirect band gap based on their band structure (see Supporting Figure S5), which is also confirmed from the experimental Tauc plots (see Supporting Figure S6).


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Given that the band gap is determined by the overlap between Bi 6s/6p and I 5p states, we now probe the structural changes to the Bi2I9 bioctahedra introduced by changing the size of A-site cations. In the closely related AMX3 perovskites (M is the cation that is under an octahedral coordination of anions X), the A–X interactions drive the tilting of MX6 octahedral network (for instance, M–X–M angle) and change the overlap between M and X states.9,41 In the inorganic A3Bi2I9 compounds, we observe that larger A-site cations result in longer A–I bonds, which in turn leads to a smaller Bi–I–Bi angle. To illustrate this effect, a comparison of the bonding network in the AI12 cuboctahedra and Bi2I9 bioctahedra in Cs3Bi2I9 and K3Bi2I9 is shown in Figure 4a. In the case of Cs3Bi2I9, the Cs+ ion is sufficiently large to coordinate with twelve neighboring I− ions in a largely symmetric manner with Cs–I bond lengths between 3.89 – 4.16 Å. In contrast, in K3Bi2I9, where the ionic radius of the K+ ion is 30 Å smaller than that of the Cs+ ion,27 we find that the K+ ion shifts closer towards six of the twelve I− ions. This shift leads to six shorter K-I bonds of 3.50 – 4.13 Å and six longer bonds of 4.81 – 5.71 Å. In this study, Asite cations and I− ions are considered bonded when their distance is no greater than 4.2 Å. Under this assumption, K+ ions are only bonded to six I− ions. The distortions from cuboctahedral A–I coordination to a lower symmetry A–I coordination is also observed in perovskites with smaller A-site cations, as they minimize the electrostatic energy of the system.39 Within the Bi2I9 bioctahedron, Bi forms three shorter Bi–I bonds involving I atoms directed away from the shared face, and three longer Bi–I bonds that are oriented towards the shared face. Iodine atoms shared between two Bi atoms are highlighted in dark green color in Figure 4a along with the Bi–I–Bi bond angle. We find that the Bi–I–Bi angle decreases from 79.9° to 78° in response to the shortening of average A–I bonds from 4.06 Å in Cs3Bi2I9 to 3.63 Å in K3Bi2I9 (see Figure 4b). In addition, on moving from the K+ ion to the Cs+ ion, we find that the Bi–Bi distance within the



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Bi2I9 bioctahedra is reduced from 4.11 to 4.03 Å. There is only a small change of 0.02 Å in Bi–I bonds (see Supporting Table S3). Overall, the asymmetric shift of A-site cations drives the Bi2I9 bioctahedra to compress along c-axis as it reduces Bi–I–Bi angle and the Bi–Bi distance. Such structural changes are expected to affect the overlap between Bi 6s/6p and I 5p states and accordingly the band gap of A3Bi2I9 compounds, which will be discussed in detail below. The A3Bi2I9 compounds containing organic cations, however, do not show a compression of the Bi2I9 bioctahedra on increasing the organic A-site cation size. This is shown by the increase of Bi–I–Bi angle with NH4+, MA and FA substitution as shown in Figure 4b. This reversal from the trend observed for inorganic A-site cations can be attributed to the presence of H-bonds between H+ ions of the organic cation and the I− ions. As an example, NH4+ has an ionic radius of 146 Å,28 which is between that of K+ (138 Å) and Rb+ (152 Å) ions. From (NH4)3Bi2I9 to K3Bi2I9, we find an increment of both Bi–I-Bi angle and Bi-Bi distance from 79.29° to 79.85° and 4.09 to 4.11 Å, respectively. Each NH4+ forms four H-bonds of average 2.6 Å between its H+ ions and the nearest I− ions with a distorted tetrahedral coordination. These short-range H-bonds (defined below 3.0 Å) together with the chemical pressure induced by small NH4+ ions lead to less stretched Bi2I9 bioctahedra compared to that in K3Bi2I9. In contrast to the smaller NH4+ ions, the larger MA and FA cations become increasingly non-spherical, which results in different H–I bonding network. Figure 4c shows the distribution of H bonds ranging from 2.5 to 3.5 Å for (NH4)3Bi2I9, MA3Bi2I9 and FA3Bi2I9 with short-range and long-range H-bonds highlighted in cyan and pink, respectively. Compared to (NH4)3Bi2I9, the number of long-range H bonds is greater than that of short-range H-bonds in both MA3Bi2I9 and FA3Bi2I9 and that long-range Hbonds play a more prominent role. For organic cations, we use the center-of-mass of organic cations to calculate the A–I bond length. As a result of the H-bonds, we find that despite their


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larger ionic size than Cs, MA3Bi2I9 and FA3Bi2I9 show similar average A–I bond length to that in Cs3Bi2I9. The H-bonds also lead to an elongation of the Bi2I9 bioctahedra along the c-axis on moving from NH4+ ion to FA+ ion as shown by the increased Bi–I–Bi angle and Bi–Bi distance in Figure 4b. We now discuss the change in electronic structure due to the changes in the Bi2I9 bioctahedra for the different A3Bi2I9 compounds without including SOC effects. We find that the width of the valence and conduction bands is sensitive to the distortion of Bi2I9 bioctahedra, and in particular to the Bi–I–Bi bond angle. Figure 5a shows the Bi 6p contribution to the conduction band DOS (without SOC) for K3Bi2I9, Cs3Bi2I9, and FA3Bi2I9. Qualitatively, the width of the conduction band is reduced on moving from Cs3Bi2I9 that has an average Bi–I–Bi angle of 78.01° to either K3Bi2I9 or FA3Bi2I9, both having a larger Bi–I–Bi angle of 79.85° and 80.1°, respectively. A similar trend is also observed for the width of the valence band. The change in width of both the valence band and conduction band for the different A3Bi2I9 compounds is shown in Figure 5b. On moving from K3Bi2I9 to Cs3Bi2I9, we find that both the valence band and conduction band are broadened by 0.16 eV and 0.3 eV, respectively, which is followed by a decrease in width by 0.4 and 0.24 eV, respectively, with further increase in cation size to FA. This variation in width of the valence and conduction bands with change in A-site cation size is exactly opposite to the change in Bi–I–Bi angle shown in Figure 4b. The broadening (or narrowing) of both the valence band and the conduction band in turn leads to a reduction (increase) of the band gap, as illustrated schematically in Figure 5c. In other words, decreasing Bi–I–Bi angle and Bi–Bi distance enhances the overlap of Bi 6p/6s and I 5p states and widens both the valence band and the conduction band, which in turn leads to a reduced band gap. For A3Bi2I9 compounds containing organic cations, H-bonds increase the Bi–I–Bi angle and Bi–Bi



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distance that weakens the overlap between Bi 6s/6p and I 5p states, yielding a larger band gap compared to Cs3Bi2I9. Based on this analysis, we can conclude that compressing Bi2I9 bioctahedra leads to enhanced overlap of Bi 6p/6s and I 5p states and consequently reduces the band gap. As discussed earlier, the experimental band gap of the A3Bi2I9 compounds, however, is found to be insensitive to chemical pressure. This insensitivity actually arises due to the large SOC effects as a result of heavy Bi and I atoms. On including SOC in the calculations, the variation in the theoretical band gap of the A3Bi2I9 compounds due to changes in the size of the A-site cations is eliminated (see Figure 6a), making them consistent with the experimentally observed band gap insensitivity. Figure 6b shows the difference in band gap obtained with and without including SOC for both PBE and HSE06 functionals. For both the functionals, we observe a similar trend of band gap reduction due to SOC effects as a function of different A-site cations. On comparing the atom-projected DOS of Cs3Bi2I9 near the conduction band edge with and without including SOC (see Figure 6c), we find that SOC leads to a splitting of the conduction band, shifting the CBM to lower energy (from 2.2 to 1.77 eV), thus reducing the band gap. The split-off band at lower energy is primarily due to Bi 6p states hybridized with the 5p states of those I atoms that are bonded to two Bi atoms forming the shared face of the Bi2I9 bioctahedron (dark green atoms in Figure 4a), whereas the band at higher energy has a greater contribution from I atoms that are directed away from the shared face and are bonded to only one Bi atom (see Supporting Figure S4a, b). In a word, this suggests that SOC-induced band splitting is due to the face-sharing Bi2I9 bioctahedral network having two different anion coordination. Previously, Amat et al. have shown that for MAPbI3, band gap reduction due to SOC effects increases when the number of Pb 5p and I 5p states near the CBM increases.9 In view of


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similar chemical bonding in the MAPbI3 and A3Bi2I9 compounds, we also study the variation of Bi 6p and I 5p states near the CBM. To quantify the change in Bi 6p and I 5p states, we first integrate the DOS within 0 – 0.5 eV above CBM in all the studied A3Bi2I9 compounds, which is plotted as a function of A-site cation size in Figure 6d. Then, we compare the integrated electronic states for Bi 6p and I 5p states to the values of band gap reduction due to SOC effects shown in Figure 6b. Qualitatively, we find that an increase of Bi 6p and I 5p states around the CBM indeed enhances the band gap reduction due to SOC in the studied A3Bi2I9 compounds. On moving from Cs+ ions to either K+ or FA+ ions, the Bi2I9 bioctahedron is stretched as both the Bi–Bi distance and Bi–I–Bi angle increase (see Figure 4b). This stretching of the Bi2I9 octahedron gives rise to weaker Bi 6p – I 5p interactions and narrows the width of the conduction band, leading to an increase in the Bi 6p and I 5p states around the CBM. This increase in the number of Bi and I states at the CBM increases the band gap reduction due to SOC effects, cancelling out the increase in band gap caused by the stretching of the Bi2I9 octahedron, which results in the overall insensitivity to chemical pressure.

CONCLUSIONS In summary, we find that the band gap of A3Bi2I9 compounds is governed by the overlap of the Bi 6s/6p and I 5p states, whose variation is subject to the structural distortion of the facesharing Bi2I9 bioctahedra. Both the size and nature of A-site cations can cause the stretching or compressing of Bi2I9 bioctahedra, thus modulating the band gap of A3Bi2I9 compounds. In general, larger-sized A-site cations can induce chemical pressure to compress Bi2I9 bioctahedra. As a result, the overlap between Bi 6s/6p and I 5p states is enhanced and the band gap of A3Bi2I9 compounds is reduced. For A3Bi2I9 compounds containing organic cations, H-bonds formed



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between H+ ions of the organic cations and the I− ions lead to a stretching of Bi2I9 bioctahedra, increasing the Bi-Bi distance and the band gap. Finally, SOC reduces the band gap with the reduction being enhanced for A3Bi2I9 compounds with stretched Bi2I9 bioctahedra. The degree of band gap reduction is correlated with the number of Bi 6p and I 5p states around the CBM. The band gap reduction induced by SOC cancels out the band gap enlargement from the chemical pressure imposed by A-site cations, resulting in the band gap insensitivity of A3Bi2I9 compounds to different A-site cations. Based on our systematic study where we find that the band gap variations are controlled by the stretching or compressing of the Bi2I9 bioctahedra along the caxis, one possible strategy to induce a large band gap variation could be to apply uniaxial strain along the c-axis or an epitaxial strain along the ab-plane, which are likely to have a stronger coupling with the bioctahedral stretching or compression. It is also instructive to compare the structural changes in A3Bi2I9 with chemical pressure to that observed in ASnO3 perovskites. Due to the three-dimensional corner connectivity of the SnO6 octahedra in ASnO3 perovskites, chemical pressure results in a large change of the Sn–O– Sn bond angle. For example, the Sn–O–Sn bond angle increases from 147° to 180° on moving from CaSnO3 to BaSnO3, an overall change of 33°.42 This large change in bond angle in turn has a large effect on the overlap between Sn and O states and their bandwidth. As a result, the band gap of these compounds can be tuned from 4.4 to 3.1 eV.42 However, in layered-structured A3Bi2I9 compounds, the compression or stretching of Bi2I9 bioctahedra is limited and the Bi–I–Bi angle variation in is comparatively much smaller (~2 degrees) and as a result the band gap is found to be insensitive to chemical pressure. Based on this comparison with the perovskites, a more likely approach to tune the band gap of Bi-compounds, would be to use a 3D polyhedral network, either by including Bi in the double perovskite network,43-45 or by using A-site cations


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that are more covalent and can contribute to the valence and conduction bands.42,46 In addition, previous studies have highlighted the role of aromatic amines as alternative A-site cations to inorganic ions or aliphatic amines in tuning the band gap of Sn- and Cu-based perovskites.47 We have tested this hypothesis for ternary A3Bi2I9 compounds using pyridine, as a representative aromatic amine as the A-site cation. In contrast to the Sn- and Cu-based perovskites, we do not observe any significant band gap alteration, which we find to be 1.71 eV using the PBE+SOC functional. While a more detailed study on the effect of other aromatic amines as A-site cations in A3Bi2I9 remains to be done, our preliminary results using the pyridine cation suggests that such a strategy may have limited success in tuning the band gap. Nevertheless, strategies based on the idea of manipulating the connection and/or distortion of BiX polyhedra could serve as a more viable avenue to optimize the band gap and rationally design new and more efficient Bi-based compounds for photovoltaic and optoelectronic applications.

Acknowledgements: XH and RM were supported by a start-up funding from Washington University. PB and SH were supported by the Solar Energy Research Institute for India and the U.S. (SERIIUS) funded jointly by the U.S. Department of Energy under subcontract DE AC3608G028308 and the Government of India subcontract IUSSTF/JCERDC-SERIIUS/2012, dated 22nd Nov. 2012. SH also thanks the International Center for Advanced Renewable Energy and Sustainability (I-CARES) for partial support. This work used computational resources of the Extreme Science and Engineering Discovery Environment (XSEDE), which is supported by National Science Foundation grant number ACI-1053575, and the Washington University Center for High Performance Computing, which were partially funded by NIH grants 1S10RR02298401A1 and 1S10OD018091-01. 17 ACS Paragon Plus Environment


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Table 1: Structural parameters of A3Bi2I9 compounds (A = K, Rb, Cs, NH4+, MA, FA) obtained after relaxation using PBE functional and experimental estimation obtained from XRD patterns. The deviation (or error) of computation from experiment is defined as (PBE-Expt.)/Expt.×100%. formula crystal PBE system Expt. space PBE group Expt. PBE a (Å) Expt. Error (%) PBE b (Å) Expt. Error (%) PBE c (Å) Expt. Error (%) PBE α Expt. (deg.) Error (%) PBE β Expt. (deg.) Error (%) PBE γ Expt. (deg.) Error (%) PBE V Expt. (Å3) Err (%)

K3Bi2I9 monoclinic monoclinic Cc C2/c 14.49 14.47 0.14 8.15 8.05 1.2 21.03 20.78 1.2 90.00 90.00 0 96.09 91.09 5.5 90.00 90.00 0 2468.49 2396.86 3.0

Rb3Bi2I9 monoclinic monoclinic Cc C2/c 14.46 14.63 -1.2 8.12 8.08 0.5 21.23 20.89 1.6 90.00 90.00 0 95.33 91.25 4.5 90.00 90.00 0 2480.54 2446.13 1.4

Cs3Bi2I9 monoclinic monoclinic C2/c C2/c 8.31 8.35 -0.48 14.43 14.52 -0.62 21.42 21.15 1.3 90.00 90.00 0 93.80 91.16 2.9 90.00 90.00 0 2561.72 2539.59 -0.9

(NH4)3Bi2I9 monoclinic monoclinic Cc ─ 8.46 ─ ─ 14.75 ─ ─ 23.12 ─ ─ 90.00 ─ ─ 91.59 ─ ─ 90.00 ─ ─ 2883.52 ─ ─

MA3Bi2I9 triclinic monoclinic P1 C2/c 8.74 8.57 2.0 14.59 14.85 -1.8 21.79 21.72 0.32 87.58 90.00 -2.7 91.30 91.19 0.12 86.32 90.00 -4.1 2769.30 2737.76 1.2

FA3Bi2I9 monoclinic monoclinic C2/c C2/c 8.48 8.69 -2.4 14.95 15.11 -1.1 22.54 22.05 2.2 90.00 90.00 0 92.97 91.05 2.1 90.00 90.00 0 2852.24 2866.73 -0.51


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Figure 1.

(a) Crystal structure of Cs3Bi2I9 with a monoclinic space group C2/c. (b)

Computationally predicted (using PBE functional with SOC effects) and experimentally measured band gap of A3Bi2I9 compounds as a function of ionic radius of the A-site cations with A = K, Rb, Cs, NH4, MA (CH3NH3), and FA (CH(NH2)2.

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Figure 2. (a) Tauc plots for indirect allowed transition for two representative A3Bi2I9 compounds, Cs3Bi2I9 and FA3Bi2I9 together with pictures (on right) of their thin films deposited on glass substrates, showing no apparent change in band gap or color when substituting Cs cation with the larger FA cation. (b) SEM images of Cs3Bi2I9 and FA3Bi2I9 thin films formed on FTO/TiO2 substrates with higher magnification shown in the insets highlighting the layered structure.


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Figure 3. (a) Atom-projected electronic density of states (DOS) of Cs3Bi2I9 obtained with PBE functional without SOC. The inset shows Bi 6s states near the valence band maximum. (b) Total DOS of Cs3Bi2I9 obtained using PBE functional without and with SOC. (c) Crystal orbital Hamilton population (COHP) bonding analysis shows that the band gap of Cs3Bi2I9 is defined by the antibonding interactions between Bi 6s and I 5p states (red color) as well as the antibonding interactions between Bi 6p and I 5p states at the conduction band edge (blue color). Positive (negative) values indicate bonding (antibonding) character. (d) Electronic band structure of Cs3Bi2I9 (based on PBE+SOC) along high symmetry points in reciprocal space showing an indirect band gap of 1.77 eV between L-point in the valence band and along Γ → A direction in the conduction band. The direct band gap is 1.89 eV and occurs at C-point. (Γ: (0, 0, 0), A: (0, 0, 1/2), H: (-1/3, 2/3, 1/2), K: (-1/3, 2/3, 0), M: (0, 1/2, 0), L: (0, 1/2, 1/2), Z: (1/2, 0, 0), L: (1/2, 1/2, 0)).



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Figure 4. (a) Comparison of the coordination environment around A and Bi cations in Cs3Bi2I9 and K3Bi2I9. On moving from Cs3Bi2I9 and K3Bi2I9, the d cation shifts from a centrosymmetric coordination to ambient I- ions to a lower symmetric coordination to ambient I- ions, leading to the stretching of the Bi2I9 bioctahedra. The longer Bi-I bonds within the Bi2I9 bioctahedra are highlighted in dark green color. (b) Variation of A–I bond length (upper panel), Bi–I–Bi bond angle (middle panel) and Bi-Bi distance (lower panel) within the Bi2I9 bioctahedra as a function of A-site cation size. (c) Distribution of hydrogen bonds in three hyrbrid organic-inorganic A3Bi2I9 compounds, (NH4)3Bi2I9 (yellow), MA3Bi2I9 (green) and FA3Bi2I9 (purple). Short-range H-bonds are highlighted in the cyan color regime while long-range H bonds in the pink color regime.


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Figure 5. (a) Bi 6p DOS contributing to the conduction band in K3Bi2I9, Cs3Bi2I9 and FA3Bi2I9. (b) Variation in the width of valence and conduction band around the band gap for A3Bi2I9 compounds as a function of ionic radius of the A-site cations. (c) Schematic illustrating band gap reduction as a result of increase in the width of the valence and conduction bands.



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Figure 6.

(a) Band gap evolution as a function of the A-site cation size based on DFT

calculations with and without including SOC effects. (b) Difference of the calculated band gap by DFT and DFT+SOC methods as a function of A-site cations sizes. (c) Integrated electronic DOS for Bi 6p and I 5p orbitals from the conduction band minimum up to 0.5 eV above for A3Bi2I9 compounds as a function of the varying A-site cation sizes. (d) Splitting of Bi 6p and I 5p orbitals near the conduction band minimum for Cs3Bi2I9 as a result of including SOC effects.


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