Disparity of the Nature of the Band Gap between Halide and

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Disparity of Bandgap Nature Between Halide and Chalcogenide Single Perovskites for Solar Cell Absorbers Yujie Peng, Qingde Sun, Hangyan Chen, and Wan-Jian Yin J. Phys. Chem. Lett., Just Accepted Manuscript • DOI: 10.1021/acs.jpclett.9b01657 • Publication Date (Web): 25 Jul 2019 Downloaded from pubs.acs.org on July 25, 2019

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The Journal of Physical Chemistry Letters

Disparity

of

Bandgap

Nature

Between

Halide

and

Chalcogenide Single Perovskites for Solar Cell Absorbers Yujie Peng1,2,3, Qingde Sun1,2, Hangyan Chen4, Wan-Jian Yin1,2,3* 1Colledge

of Energy, Soochow Institute for Energy and Materials InnovationS (SIEMIS), Soochow University, Suzhou 215006, China 2Jiangsu Provincial Key Laboratory for Advanced Carbon Materials and Wearable Energy Technologies, Soochow University, Suzhou 215006, China 3Key Lab of Advanced Optical Manufacturing Technologies of Jiangsu Province & Key Lab of Modern Optical Technologies of Education Ministry of China, Soochow University, Suzhou 215006, China 4School of Physical Science and Technology, Soochow University, Suzhou 215006, China

Abstract： Chalcogenide perovskites ABX3 (A = Ca, Sr, Ba; B = Ti, Zr, Hf; X = O, S, Se) have been considered as promising candidates to overcome the stability and toxic issues of halide perovskites. In this work, we unveiled the disparity of bandgap nature between halide and chalcogenide perovskites. First-principles calculations show that the prototype cubic phase of chalcogenide perovskites exhibit indirect bandgaps with valence band maximum and conduction band minimum located at R and Γ points respectively in Brillion zone. Therefore, the optical transitions near band edges of chalcogenide perovskites differ from its halide counterparts, although its stable orthorhombic phase embodies a direct bandgap. We have further found that the direct-indirect bandgap difference of chalcogenide perovskites in cubic phase demonstrates a linear correlation with t+µ, where t and μ are the tolerance and octahedral factor, respectively, therefore, providing a viable way to search chalcogenide perovskites with a quasi-direct bandgap.

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Perovskite with a six-coordinated crystal structure has been a class of revolutionary materials in solar cell field during the last decade. The certified power conversion efficiency of solar cells, made of organic-inorganic hybrid perovskites, typically as CH3NH3PbX3 (X = Cl, Br, I), is constantly being updated and has been surged to an unprecedented level from 3.8% in 20091 to 24.2%2, surpassing the mature commercial thin-film solar cells materials such as CdTe and Cu(In,Ga)Se2.3 However, the main problems of halide perovskites remain the long-term stability and toxicity of Pb.4-7 To address the intrinsic stability issue of halides and accomplish the sacred mission of green chemistry, chalcogenide perovskites have been proposed as potential thin-film solar-cell materials.8-11 Notably, a class of ABX3 perovskites (A = Ca, Sr, Ba; B = Ti, Zr, Hf; and X = O, S, Se) have been theoretically investigated by Sun et al.12 and synthesized experimentally13-19,20. One of main reasons that chalcogenide perovskites could be considered as potential solar cell absorbers is because first-principles calculations exhibit their similar electronic and optical properties with halide perovskites, such as direct bandgaps and strong optical absorptions. Although many chalcogenide perovskites such as BaZrS3, CaZrS3, SrTiS3 and SrZrS3, have been

experimentally

synthesized21,

so

far,

this

class

of

chalcogenide

perovskites-based solar cell devices have been rarely reported. Apart from its difficulty in materials synthesis and device processing, the fundamental electronic and optical properties of chalcogenide perovskites and its difference with halide perovskites have been rarely explored. In this paper, first-principles calculations on band structure and optical absorption analysis have shown the disparity of bandgap nature of halide and chalcogenide perovskites. Using the first-principle calculation based on the density functional theory (DFT) as implemented in the VASP program.22 We have found that, in contrast to halide perovskite, in which high optical absorption can be attributed to its direct bandgap nature in cubic phases, with both valence band maximum (VBM) and conduction band minimum (CBM) located at R points in Brillion zone (BZ), chalcogenide perovskite with cubic phases bears indirect bandgap with VBM and


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CBM located at R and Γ points respectively. Although k-points folding in conjunction with octahedral distortion and symmetry reduction may lead to direct bandgap in room-temperature orthorhombic phase, the transition dipole moments near band edge of chalcogenide perovskites are limited and directly correlated with amount of octahedral rotation.23-24 During structural transition from cubic phase to orthorhombic phase, valence bands originated from Γ points at cubic phase (called Γ-derived states hereafter) increase in energy level relative to the energy of R-derived valence bands. Due to the band crossing, the VBM to CBM transition may become forbidden, leading to dipole-forbidden transition from VBM to CBM for chalcogenide perovskites. We have further found that the indirect-direct bandgap difference for cubic chalcogenide perovskites (defined as ΔEg) has a linear correlation with simple descriptor t+µ, which may be used to guided search for (pseudo)-direct bandgap chalcogenide perovskites with strong optical absorption.

Figure 1. (a) The band structures of cubic-phase BaZrS3 at cubic and orthorhombic BZ (corresponding to a BZ of a

2  2  2 cubic supercell structure). The purple

dots indicate the CBM and VBM at Γ points, the yellow dot is the R-derived VBM, and the green dot is the M-derived VBM. (b) The band structures of cubic-phase CsPbI3, (c) the BZ of cubic and orthorhombic structures and the corresponding k-points folding. The blue color corresponds to Zr 4d states, the green color to Zr 4p



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states, and the olive color to S 3d states in the band structure of cubic-phase BaZrS3 while the green color corresponds to Pb 6p, the red color to Pb 6s, the wine color to I 5s, and the olive color to I 5p in the band structure of cubic-phase CsPbI3. The band structures of a class of chalcogenide perovskite ABX3 (A= Ca, Sr, and Ba; B = Ti, Zr, and Hf; X= O, S, and Se) and a class of halide perovskites A'B'X'3 (A'= K, Rb, and Cs; B'= Sn, Pb; X'= Cl, Br, and I) in cubic phase are systematically investigated. All the chalcogenides as shown in Figure S1 exhibit indirect bandgap, while all the halides as shown in Figure S2 exhibit direct bandgap. BaZrS3 (as a prototype chalcogenide perovskite) and CsPbI3 (as a prototype halide perovskite) have been shown in Figure 1a and Figure 1b, respectively, it can be seen that CsPbI3 has direct band gap with both VBM and CBM at R points and BaZrS3 has indirect bandgap with VBM and CBM at R and Γ points respectively. The direct-indirect bandgap difference for BaZrS3 is about 0.34 eV in Figure 1a, which cannot be negligible. The disparity of bandgap between BaZrS3 and CsPbI3 can be explained by their electronic structures. The valence band maximum (VBM) state of BaZrS3 is contributed predominantly by S 3p-orbitals, while the conduction band minimum (CBM) state is mostly composed of transition mental Zr 4d-orbitals,which is consistent with Sun’s result12 as shown in Figure 1a. Whereas, for CsPbI3, the VBM is contributed mainly by I 5p-orbitals and Pb 6s-orbitals, while the CBM is mainly composed of Pb 6p-orbitals, which is consistent with Huang’s result25 as shown in Figure 1b. Band structure calculations by Sun et al.26 show that BaZrS3 has direct bandgap in orthorhombic phase, which is more stable than its prototype cubic phase. Since orthorhombic phase can be considered as a kind of octahedral rotation from cubic phase27, it would be interesting to see the evolution of electronic structure and optical transition from cubic phase to orthorhombic phase. In this sense, a

2 22

super-cell structure which possesses the same BZ28 as orthorhombic phase has been constructed based on cubic phase and its super-cell structure seems to possess a direct bandgap as shown in Figure 1a. Since its VBM and CBM are derived from different high-symmetry k-points in cubic phase, therefore, the optical transition dipole


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moment (P)

ih VBM p CBM  is zero. The high-symmetry k-points Γ, M and R m Eg

of cubic phase would be folded into the Γ point in new BZ of cubic super-cell phase in Figure 1a and Figure 1c, thereby rendering BaZrS3 with cubic super-cell structure as a (pseudo)-direct band gap material.

Figure 2. Four intermediate crystal structures of BaZrS3 perovskite from cubic phase to orthorhombic phase, together with their diagrams of the square of transition dipole moment (P2) at Γ points,PBE calculated band structure and corresponding P2 at various k points along high symmetry line. The crystal structures are characterized by the angle of octahedral rotations: (a) 0° (cubic phase), (b) 3°, (c) 6° and (d) 9° (orthorhombic phase). The orange arrows in optical transition diagrams show the P2between upper valence bands to lower conduction bands. In band structures, VBM and Γ-derived VBM are marked with red horizontal lines and their corresponding energy differences are given, the states colored in blue, green, and olive are for Zr 4d, Zr 4p, and S 3p states, respectively. Black letters and red symbols are Koster notations and the point groups with inversion symmetry of Γ points.



To see the band structure evolution of BaZrS3 from cubic phase to orthorhombic phase, [ZrS6] octahedra23-24,

29

are distorted manually to produce nine intermediate

crystal structures with equal structural displacements between those two phases, with four of them shown in Figure 2. Accordingly, we have calculated their band structures and the square of transition dipole moments (P2)30 via first-principle calculations, and analyzed the evolutions of band structures. Figure 2a shows the band structure of cubic BaZrS3 in the BZ of an orthorhombic crystal structure. The state degeneracy of cubic symmetry has been kept since the crystal structures do not have any rotations. The triply-degenerated CBM (T2g state) is derived from original Γ point in cubic phase. The T2u, B1g and T1u states at upper valence bands are derived from R, M and Γ points respectively. Therefore, optical transition from T2u (VBM) and B1g to T1u (CBM) is forbidden. When crystal symmetry is reduced by [ZrS6] octahedral rotation as shown in Figure 2b, T2g, T2u, B1g and T1u states are split to (B1g, Ag, B2g), (B3g, Ag, B1g), Ag, (B1u, B3u, B2u) states respectively. Although the reduced crystal symmetry (from Oh to D2h) may make optical transitions from T2u- and B1g-derived states to T1u-derived states possible, their optical transitions are limited due to the origin of their state characters. Therefore, as shown in Figure 2b, the optical transitions near band edge are similar to that of cubic phases. When the amount of rotation increases, the Γ (T1u)-derived states consisting of the mixture of Zr 4p and S 3p orbitals move up relatively to M-derived (B1g) and R-derived (T2u) states consisting of S 3p orbitals, as shown in Figure 2(a-d). As a result, the P2 from highest valence band to the third counduction band is become more and more positive.

In Figure 2c with rotational

angle of 6°, Γ (T1u)-derived states move above M-derived (B1g) states. Therefore, along with the octahedral rotation, the original Γ to Γ transition gap is more and more close to the fundamental gap. In Figure 2d with rotational angle of 9°, Γ (T1u)-derived states move above R-derived (T2u) states and become VBM, leading to dipole-allowed transition at Γ point from highest three valence band to lowest three conduction bands. The VBM exhibits odd parity (  2 ), whereas Γ point of third conduction band -

has even parity ( 1 ). As a result, it exhibits no parity-forbidden transitions and have +


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large P2 of 205.89 Debye2. However, due to band crossing, the VBM to CBM transition is forbidden. As a contrast, this phenomenon has not happen in CsPbI3 perovskite since the strong Pb lone-pair 6 s orbital and I 5p orbital antibonding coupling pushes up the VBM, while the rotation haves no effect on the upper valence band as shown in Figure S3. Based on the analysis above, the disparity of bandgap nature between halide and chalcogenide perovskites originate from the energy difference of upper valence band at R and Γ points. Therefore, it would be interesting to find a general trend of such difference to provide guidance for searching chalcogenide perovskite with band structure close to halide perovskites. Interestingly, we have found that for all the 27 chalcogenide compounds, the ΔEg is connected to Goldschmidt tolerance factor (t) and octahedral factor (µ).31-34 As shown in Figure 3, it can be seen that ΔEg is almost linearly correlated with (t+µ), and t and µ alone as shown in Figure S4 as a contrast. It indicates that the sum of the Goldschmidt tolerance factor (t) and octahedral factor (µ) can be a good descriptor for assessing the potential of ABX3 chalcogenides to be direct band gap materials based on the research into changing electronic structures of perovskites with octahedral distortion or ion exchange.35



Figure 3. The indirect-direct band gap difference (ΔEg) as a function of sum of tolerance factor (t) and octahedral factor (µ) for 27 chalcogenide perovskites ABX3 (A = Ca, Sr, Ba; B = Ti, Zr, Hf; X = O, S, Se). The oxides, sulfides and selenides are marked with orange, Prussian blue and light coral dots respectively. Here, the fitted curve is marked by red dot line. The coefficient of determination (R-Square), root-mean-square error (RMSE) and normalized root-mean-square error (NRMSE) for the best fit line are also shown in the left corner. R-Square and NRMSE are dimensionless, while RMSE is in eV unit. In conclusion, we have discovered and analyzed band structure disparity between halide and chalcogenide perovskites. Although both of their room-temperature phases (tetragonal and orthorhombic phases for halide and chalcogenide perovskites respectively) exhibit direct bandgap, the band structures of their prototype cubic phases are different. The distortion of [BX6] octahedra is capable to reduce crystal symmetry from cubic phase to more stable orthorhombic phases hence becoming crucial factor impacting the optical absorption of chalcogenide perovskite. We have further found that the direct-indirect gap difference for chalcogenide perovskite linearly correlate with t+µ, which may provide a single descriptor to screen chalcogenide perovskites with direct or quasi-direct bandgap.

EXPERIMENTAL METHODS The first-principles calculations were carried out using DFT as implemented in VASP code22,36. The electron and core interactions are included using the frozen-core projected augmented wave (PAW)37. The generalized gradient approximation of PBE38 was used for the exchange correlation functional. The kinetic energy cutoff for plane-wave basis functions set to 400 eV. The k-point meshes with grid spacing of 2π × 0.02 Å−1 or less is used for Brillouin zone integration. All atoms were relaxed until the force on each atom is less than 0.01 eV Å-1. The band symmetry and parity analyses were carried out with the QUANTUM ESPRESSO package39 based on GBRV PBE scalar relativistic potentials40. ASSOCIATED CONTENT Supporting Information. The Supporting Information is available free of charge on the ACS Publications website at DOI:  Band structure of 27 chalcogenide perovskites (Figure S1), 18 halide perovskites (Figure S2), Band structure of CsPbI3 in cubic-phase at orthorhombic BZ and in orthorhombic-phase, Band gap difference (ΔEg) as a function of tolerance factor (t)


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and octahedral factor (µ). AUTHOR INFORMATION Corresponding author: Wan-Jian +86-0512-67167457

Yin,

Email:

[email protected]

,

Tel:

Notes The authors declare no competing final interest.

ACKNOWLEDGMENT The authors acknowledge the funding support from National Natural Science Foundation of China (under Grant No. 11674237, No. 51602211,) National Key Research and Development Program of China under grant No. 2016YFB0700700, Natural Science Foundation of Jiangsu Province of China (under Grant No. BK20160299), the Priority Academic Program Development of Jiangsu Higher Education Institutions (PAPD), and Suzhou Key Laboratory for Advanced Carbon Materials and Wearable Energy Technologies, China. The work was carried out at National Supercomputer Center in Tianjin and the calculations were performed on TianHe-1(A).

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Disparity of the Nature of the Band Gap between Halide and

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