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A Computational Study of Structural and Electronic Properties of Lead-Free CsMI3 Perovskites (M = Ge, Sn, Pb, Mg, Ca, Sr, Ba) Debmalya Ray, Catherine Clark, Hung Q. Pham, Joshua Borycz, Russell J. Holmes, Eray S. Aydil, and Laura Gagliardi J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.8b00226 • Publication Date (Web): 15 Mar 2018 Downloaded from http://pubs.acs.org on March 15, 2018

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The Journal of Physical Chemistry

Prepared for J Phys Chem C.

A Computational Study of Structural and Electronic Properties of Lead-Free CsMI3 Perovskites (M = Ge, Sn, Pb, Mg, Ca, Sr, Ba). Debmalya Raya, Catherine Clarkb, Hung Q. Phama, Joshua Borycza, Russell J. Holmesb, Eray S. Aydilb, Laura Gagliardia* a

Department of Chemistry, Chemical Theory Center, and Supercomputing Institute, University

of Minnesota, 207 Pleasant Street SE, Minneapolis, MN 55455 b

Department of Chemical Engineering and Materials Science, 421 Washington Ave. SE,

Minneapolis, MN 55455 KEYWORDS: perovskites, local density functionals, bandgap, band structures, phase stability

ABSTRACT Electronic structure calculations of five crystallography-imitated structures of CsMI3 perovskites with M = Ge, Sn, Pb, Mg, Ca, Sr, Ba, were performed. The formation energy of different perovskite phases, their relative stability and structural and electronic properties were explored. The sensitivity of the calculations to the choice of the density functional was investigated and the predictions were compared with experimental results. The outcome of this study is that Mg and Ba perovskites are unlikely to form in the cubic, tetragonal or orthorhombic phases because they have positive formation energies. While Ca and Sr perovskites have negative formation energies with respect to the metal iodide precursors, they exhibit wide bandgaps and high hygroscopicity,

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making these unlikely candidates for applications in photovoltaic devices. Our results suggest that the performance of a local density functional with a non-separable gradient approximation is similar to hybrid functionals in terms of bandgap predictions when M in CsMI3 is a p-block element (Pb, Sn, Ge). However, local density functionals with non-separable gradient approximation predictions for the bandgap are similar to other local functionals with a generalized gradient approximation (PBE, PBEsol, PBE-D3) and are worse than those of HSE06 when M is an s-block element (Mg, Ca, Sr, Ba). 1. INTRODUCTION Inorganic and hybrid organic-inorganic halide perovskites have emerged in the last decade as promising materials for efficient, low-cost, thin film solar cells that can be deployed on a largescale.1–16 Devices based on lead halide perovskites have reached power conversion efficiencies of >22%,12 rivaling established solar cell materials including cadmium telluride (CdTe), copper indium gallium selenide (CIGS), and single-crystal Si.17 The archetypal hybrid organic-inorganic halide perovskite, CH3NH3PbI3, has a bandgap near the Shockley-Quessier optimum,18,19 strong absorption in the visible spectrum,2,20–22 long carrier lifetimes,23,24 and high charge carrier mobilities.9,25,26 Consequently, CH3NH3PbI3 can act both as a light absorber and as an efficient charge transporting layer in a solar cell. One of the major concerns, however, is the toxicity of lead. The use of lead is particularly problematic because lead perovskites tend to decompose in ambient conditions, releasing harmful compounds such as PbI2.27–29 In an effort to find novel non-toxic perovskites for photovoltaics, significant experimental and computational work has sought to identify metal cation replacements for lead.26,30–39 Experimentally, the most well-studied alternative to lead is tin (e.g. CH3NH3SnI3). While tin is


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electronically similar to lead and can exist in the +2 oxidation state, tin favors the +4 oxidation state. So far, tin halide solar cells have only achieved a reported maximum efficiency of 9.0%,40 considerably lower than devices based on lead. These low efficiencies are thought to be due to oxidation of Sn(II) to Sn(IV).41,42 No other lead-free perovskites have approached the high efficiencies realized in lead-based solar cells. Computationally, a broad array of potential lead cation replacements have been explored.34,43,44 However, most studies typically examine only one crystal structure (e.g., tetragonal or cubic), without comparing the formation energies between different structures. Since many of these compounds have not been experimentally synthesized, comparison between multiple crystal structures is necessary to help identify the structural properties of those that may be stable and synthesized in the laboratory. Furthermore, computational studies use different types of functionals, but often only one in a single study, making it difficult to compare results from different investigations. Herein, we report the results of a systematic computational study that elucidates the electronic structures of inorganic CsMI3 (M = Pb, Sn, Ge, Mg, Ca, Sr, Ba) perovskites across five crystallography-imitated structures. We compute these results using several Kohn-Sham density functionals, namely generalized gradient approximation (GGA), non-separable gradient approximation (NGA), and hybrid functionals. We also investigated the effect of spin-orbit coupling (SOC) on the bandgaps of all the CsMI3 structures and show the importance of including SOC on the bandgap for different s-block and p-block metals. While it is well known that the predicted values of the bandgap can depend on the functional used, few studies report the formation energy for different crystal structures and their relative stabilities45 and even fewer consider the dependence of formation energy on the choice of the functional. To the best of our


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knowledge, this is the first comprehensive DFT study that compares formation energy and relative stability across several functionals for halide perovskites. We consider the alkaline earth metals Mg, Ca, Sr, Ba as potential replacements for lead in an ABX3 perovskite, and compare the results with those from calculations for Ge, Sn, and Pb. We focus on the structural and electronic properties, the formation energies, and the relative stabilities of the different perovskite phases. We explore how predictions of these properties depend on the choice of the density functional. Finally, we reconcile these predictions with experimental data. 2. COMPUTATIONAL DETAILS The perovskites (see Figure 1a) modeled in this work are CsMI3 (M = Pb, Sn, Ge, Mg, Ca, Sr, Ba).

Cesium was chosen for the A-site due to significant recent interest in all-inorganic

perovskites.46,47 Additionally, modeling perovskites with the spherically symmetric cesium cation is much more computationally affordable than with its similarly-sized organic counterpart CH3NH3+, allowing extensive comparisons between different combinations of functionals and structures.43 We considered five different initial structures as the starting atomic configuration in the geometry optimization. These were constructed using the perovskite platonic model43,48 (the high symmetry point of platonic model are shown Figure 1b) where the CsMI3 crystal structure consists of corner-sharing MI6 octahedra. Following Filip et al.,43 the metal-iodide bond lengths were initially set at 3.1 Å and different values of apical (αa) and equatorial (αe) metal-halidemetal bond angles were used in order to create different orientations of the MI6 octahedra, resulting in five crystallographically-imitated structures: cubic, tetragonal 1, tetragonal 2 (out-ofplane tetragonal), orthorhombic 1, and orthorhombic 2 (see Figure 1c).43,48 The “conventional


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unit cells” in the platonic perovskite model are tetragonal, and are composed of four CsMI3 units. To facilitate the comparison of calculated and experimentally determined lattice parameters, the computationally determined structures were transformed into standard conventional unit cells. With the exception of CsGeI3, the space groups of the computationally determined structures matched the experimental data when such data were available. For CsGeI3, the computationally determined structure was cubic with space group Pm3m, whereas the reported experimental structure is trigonal with space group R3m.49 The Pm3m CsGeI3 structure was further transformed into the R3m space group by using the transformation matrix [(1, 0, -1); (-1, 1, 0); (1, 1, 1)]. All transformations were done using the Material Studio 6.1 software. Periodic density functional theory (DFT) calculations of the CsMI3 (M = Pb, Sn, Ge, Mg, Ca, Sr, Ba) structures were performed using the Vienna Ab Initio Simulation Package (VASP).50–53 Starting with initial guesses of the atomic coordinates in each of the five structures shown in Figure 1c, the crystal structures were determined by minimizing the energy while retaining the symmetry of the initial guess. These structural relaxation calculations were repeated using different functionals, including PBE,54 PBE-D3,55 PBEsol,56 GAM,57 and HSE06.58–61 Among these functionals PBE, PBE-D3, PBEsol are GGA functionals, while GAM is a NGA functional and HSE06 is a hybrid functional. In the GGA approximation, the total energy of the system is expressed in terms of the electron density and its gradient. In NGA functionals, the total exchange and the correlation part are not separated, and instead are treated together. Hybrid functionals like HSE06 account for the non-local exchange interactions by including a percent of Hartree-Fock exchange (25% Hartree-Fock exchange for HSE06). The projected augmented wave (PAW)62,63 potentials were used to describe the interactions between the core and the valence electrons. A plane-wave kinetic energy cutoff of 670 eV was used for all the functionals


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except for HSE06, for which the cutoff was set to 400 eV to reduce the computational time (as HSE06 calculations are computationally intense). The structural relaxation was done by sampling the Brillouin zone over a 6×6×6 k-point grid centered at the Г point. An energy convergence criterion of 10-5 eV was used in the geometry optimization. The atomic positions were relaxed until the forces were less than 0.02 eV/Å. The effect of spin-orbit coupling64 on the CsMI3 bandgaps was investigated using the HSE06 functional with a 4×4×4 k-point mesh. Since we use a tetragonal unit cell with four CsMI3 units for all perovskite phases studied here, we are able to explore their Brillouin zones using the same paths, i.e. Y-Γ and Γ-Z, as defined in Figure 1b. The band structures computed by HSE06 and GAM were plotted along these paths to benchmark the capability of the GAM functional in computing the band dispersions of halide perovskites against HSE06.


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Figure 1. Cesium metal iodide perovskites (CsMI3, M = Ge, Sn, Pb, Mg, Ca, Sr, Ba): (a) Generic CsMI3 crystal structure viewed along the [100] direction; (b) First Brillouin zone (FBZ) of a tetragonal cell and its high symmetry points (Г, X, Y, Z); (c) Five starting structures of perovskite viewed along the [001] direction: cubic, tetragonal 1, tetragonal 2, orthorhombic 1, orthorhombic 2. As discussed in literature,43,48 αa and αe are the initial apical and equatorial metal-halide-metal bond angles used to construct five different phases of perovskite. 3. RESULTS AND DISCUSSION 3.1. Structural Characterization


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It is well known that hybrid DFT functionals such as HSE06 can accurately predict certain experimentally measured structural properties such as lattice parameters.65 In our calculations, we used HSE06 as a benchmark, and found that all other functionals perform similarly in predicting the lattice parameters, with PBEsol and PBE-D3 underestimating them by 1-2%. We compared the HSE06 predictions to experimentally determined lattice parameters, when available, and found that they are within the experimentally reported range for the cubic phase of CsPbI3 and within 1% or less of the experimental values for the cubic and tetragonal phases of CsSnI3 (Table 1). The calculated orthorhombic 1 and orthorhombic 2 lattice parameters are different, due to different tilting of the MI6 octahedra (see Supporting Information Section 1). The experimentally synthesized orthorhombic phase is expected to exhibit dynamic disorder of the MI6 units,66 making head-to-head comparison with calculations difficult. Perhaps for this reason the deviation between some of the experimentally measured and predicted parameters is slightly worse for the orthorhombic phases (1-2% as opposed to 6.2 eV. To support our experimental observation, an HSE06 calculation was performed for the orthorhombic 2 phase of CsSrBr3 yielding a formation energy of -21.8 kcal/mol, similar to that of CsSrI3. The calculated XRD pattern using the orthorhombic 2 phase is similar to the pattern of the XRD peaks obtained by experimental synthesized peaks, however, all the predicted XRD peaks obtained using HSE06 optimized orthorhombic 2 structure are shifted towards left. This is due to the fact that HSE06 optimized orthorhombic 2 structure overestimates the lattice parameter by 0.1 Å when compared to experimental values. Similar disagreements in lattice parameters between theory and experiment are not uncommon and, in fact, are observed in the literature for different perovskites and perovskite like compounds.35,39,109,110 The orthorhombic 2 structure showed a bandgap of 5.7 eV using the HSE06 functional. Comparison of lattice parameters, formation energy and bandgap using different functionals are reported in Supporting Information Section 8.


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+ + CsBr * SrBr2

2:1 CsBr:SrBr2 +

Normalized Intensity (a.u.)

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+

+

1:1 CsBr:SrBr2

1:2 CsBr:SrBr2

*

*

*

*** *

35

40

*

CsSrBr3 orthorhombic 2

CsSrBr3

15

20

25

30

45

50

2θ (°)

Figure 6: X-ray diffraction patterns for different stoichiometries of CsBr and SrBr2 precursors used to synthesize CsSrBr3. All three ratios (blue traces) show the formation of the CsSrBr3 perovskite (black sticks). As expected, the 1:2 ratio also contains excess SrBr2 (red asterisks), and the 2:1 ratio contains excess CsBr (orange crosses). The stability of CsSrBr3 in ambient conditions (Supporting Information Section 6, Figure S2) was evaluated as a function of air exposure time via in situ XRD. A significant change in the diffraction pattern was observed after only 15 minutes of air exposure. Within 60 minutes, the


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XRD pattern was almost completely that of SrBr2·6H2O. This rapid degradation in the presence of moisture, along with its large optical bandgap, indicates this material is unlikely to be useful in PV applications. CONCLUSION We computed formation energies, structural and electronic properties of CsMI3 perovskites, where M = Ge, Sn, Pb, Mg, Ca, Sr, Ba, using several density functionals. We found that Mg and Ba perovskites are unlikely to form in cubic, tetragonal or orthorhombic perovskite phases, which is corroborated by experimental evidence presented here and in the literature. We also found that the formation energy of Sr perovskites is more negative than that of Pb perovskites. While their predicted wide bandgap makes them unlikely candidates as solar absorbers, they may find other applications where wider gaps are desired. However, extreme hygroscopicity of Sr perovskites is a significant challenge. Finally, we showed that the local functional GAM performed similar to the hybrid functional HSE06 for p-block element perovskites, but had less satisfactory performance for s-block perovskites. ASSOCIATED CONTENT Supporting Information. Details of the lattice constants, formation energies, bandgaps, projected band states at Г by different XC functional. AUTHOR INFORMATION Corresponding Author * E-mail: [email protected] (Laura Gagliardi). Author Contribution


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The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript. Notes The authors declare no competing financial interest. ACKNOWLEDGMENT This work was supported primarily by the National Science Foundation through the University of Minnesota MRSEC under Award Number DMR-1420013 and the iSuperseed program. Parts of this work were carried out in the College of Science and Engineering Characterization Facility, University of Minnesota, which has received capital equipment funding from the NSF through the UMN MRSEC program under Award Number DMR-1420013. We would also like to thank Minnesota Supercomputing Institute for computing resources.

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CsMI3 Perovskites (M = Ge, Sn, Pb, Mg, Ca, Sr, Ba) studied with different density functionals 341x254mm (96 x 96 DPI)


M = Ge, Sn, Pb, Mg, Ca, Sr, Ba - ACS Publications

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