Ferroelectricity in RuddlesdenâPopper Chalcogenide Perovskites for

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Ferroelectricity in Ruddlesden-Popper Chalcogenide Perovskites for Photovoltaic Application: A Role of Tolerance Factor Yajun Zhang, Takahiro Shimada, Takayuki Kitamura, and Jie Wang J. Phys. Chem. Lett., Just Accepted Manuscript • DOI: 10.1021/acs.jpclett.7b02591 • Publication Date (Web): 07 Nov 2017 Downloaded from http://pubs.acs.org on November 7, 2017

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The Journal of Physical Chemistry Letters

Ferroelectricity in Ruddlesden-Popper Chalcogenide Perovskites for Photovoltaic Application: A Role of Tolerance Factor Yajun Zhang†, Takahiro Shimada‡, Takayuki Kitamura‡, and Jie Wang†* †

Department of Engineering Mechanics & Key Laboratory of Soft Machines and Smart Devices of

Zhejiang Province, Zhejiang University, 38 Zheda Road, Hangzhou 310027, China ‡

Department of Mechanical Engineering and Science, Kyoto University, Nishikyo-ku, Kyoto 615-8540,

Japan *

Corresponding author, Email: [email protected]

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ABSTRACT Chalcogenide perovskites with optimal bandgap and desirable light absorption are promising for photovoltaic devices, whereas the absence of ferroelectricity limits their potential in application. Based on first-principles calculations, we reveal the underlying mechanism of the paraelectric nature of Ba3Zr2S7 observed in experiments and demonstrate a general rule for the appearance of ferroelectricity in chalcogenide perovskites with Ruddlesden–Popper (RP) A3B2X7 structures. Group theoretical analysis shows that tolerance factor is the primary factor that dominates the ferroelectricity. Both Ba3Zr2S7 and Ba3Hf2S7 with large tolerance factors are paraelectric due to the suppression of in-phase rotation that is indispensable to hybrid improper ferroelectricity. In contrast, Ca3Zr2S7, Ca3Hf2S7, Ca3Zr2Se7 and Ca3Hf2S7 with small tolerance factors exhibit in-phase rotation and can be stable in the ferroelectric Cmc21 ground state with non-trivial polarization. These findings not only provide useful guidance to engineering ferroelectricity in RP chalcogenide perovskites but also suggest potential ferroelectric semiconductors for photovoltaic applications.

TOC Graphic

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The ferroelectric photovoltaic (PV) materials have recently attracted continuous attention due to their promising energy conversion efficiency.1-8 In general, ferroelectrics lack an inversion symmetry center. As a result, the bulk photovoltaic effect (BPVE) provides an alternative avenue to separate the carriers and promotes steady photocurrent in the absence of p-n junctions.9-11 In addition, domain walls1, 12-13 and depolarization field2, 14 in ferroelectrics have also been demonstrated to enhance the separation of carriers and improve the efficiency. On the other hand, ferroelectrics fabricated by sol-gel and sputtering method are inexpensive and can be stable under a wide range of chemical, thermal and mechanical conditions.8, 15 In contrast, the fabrication of traditional PV materials with p-n junctions is costly and quite complicated because of heavy doping, lattice mismatch and band alignment at the interface. Therefore, developing suitable ferroelectric PV materials with extraordinarily high energy conversion efficiency is the main aim of intensive research explorations. Up to now, a large amount of investigations have been done on the development of semiconducting ferroelectric oxides for PV application. In particular, great progress have been achieved in the PV properties of BiFeO31-5 and PZT.16-17 However, the large band gap of these materials can only allow the absorption of 8%–20% solar spectrum. In order to lower the band gap of oxides and improve the efficiency, chemical doping method is widely adopted. During the doping process, a large concentration of oxygen vacancies or non-stoichiometric defects are inevitably produced, which may result in low carrier mobility and poor transport properties, and also affect the switching of polarization. Recently, a number of transition metal perovskite chalcogenides ABX3 (X = S, Se; A, B =metals) with low band gap have been experimentally synthesized and theoretically predicted by DFT calculations.18-20 Perera et al. synthesized the distorted perovskites of BaZrS3 and CaZrS3 with the band gaps of 1.73 eV and 1.90 eV, respectively, by high temperature sulfurization of their oxide counterparts.18 Niu et al. reported the synthesis of BaZrS3 with band gap of 1.81 eV by a novel catalytic synthesis procedure.19 Theoretically, Sun et al. predicted six stable distorted perovskite structure (BaZrS3, CaZrS3, BaHfS3, CaHfS3, CaZrSe3 and CaHfSe3) with a space group of Pbnm through first-principles calculations.20 In addition to the suitable band gap, perovskite chalcogenides are demonstrated to contain good carrier mobility,19 and are more environmentally friendly and more stable than the widely investigated lead perovskite halide. All these properties suggest that perovskite 3



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chalcogenides are promising candidates for PV applications. However, the distorted perovskite chalcogenides belong to the paraelectric Pbnm phase without spontaneous polarization.20 Thus, engineering ferroelectricity by material design technology is necessary to develop new ferroelectric PV materials. Cammarata et al. recently found that ferroelectric phase can be realized through mode coupling between the cooperation of octahedral rotations and Jahn-Teller distortion in RP LaSrMnO4, which provides a novel pathway to engineering ferroelectricity.21 Benedek et al. proposed that hybrid improper ferroelectricity (HIF) may be realized when the parent materials form the Ruddlesden– Popper (RP) A3B2O7 structure,22 which was confirmed by experiments in (Ca,Sr)3Ti2O7 single crystal.23 As candidates for solar cell applications, RP perovskites have been demonstrated to exhibit better performance than parent materials.24-25 This structure could overcome the insufficient long-term stability problem in parent materials and be more stable over long-term operation compared with parent materials based devices. For the perovskite chalcogenides, which are promising for PV applications, the mechanism of ferroelectricity in their RP A3B2X7 system has yet to be explored. Wang et al. propose that ferroelectricity could be induced in the RP perovskites of Ca3Zr2S7 and Ba3Zr2S7.26 In contrast, the experimentally synthesized RP Ba3Zr2S7 exhibits a paraelectric state.27 To understand this discrepancy, systematical investigation on the mechanism of ferroelectricity in RP A3B2X7 chalcogenide perovskites is necessary. In particular, finding a general rule for the design of ferroelectricity in such A3B2X7 structure is crucial for experimentalists to prepare the chalcogenide perovskite based ferroelectric semiconductor for photovoltaic applications. In this letter, we investigate the relationship between the tolerance factor, distortion mode and ferroelectricity, and try to find a general rule for designing chalcogenide based ferroelectric semiconductor. Here, we focus on six compounds including CaZrS3, CaHfS3, BaZrS3, BaHfS3, CaHfSe3 and CaZrSe3 as the parent materials for RP A3B2X7 because other compounds in the (Ca, Sr, Ba)3 (Zr, Hf)2 (S, Se)7 family are unstable in the perovskite structure based on the previous first-principles calculations in Ref. 20. It is predicted that tolerance factor plays a dominant role in the distortion mode and ground state (GS) of RP chalcogenide perovskites. Systems with small tolerance factor (CaZrS3, CaHfS3, CaHfSe3 and CaZrSe3) stabilize in the Cmc21 ferroelectric phase. In contrast, the in-phase rotation in those with relative large tolerance factor (BaZrS3 and BaHfS3) is 4


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completely suppressed, and the structures form the paraelectric P42/mnm phase. These ﬁndings are important not only for explaining the driving force behind the paraelectric/ferroelectric GSs in RP A3B2X7, but also for predicting the lower band gap ferroelectric semiconductor for promising applications in solar cells. Density functional theory (DFT) calculations are performed with the projector augmented-wave (PAW)28-29 method which are implemented in the Vienna ab initio simulation package (VASP) .30 The Perdew-Burke-Ernzerhof exchange-correlation functional revised for solids (PBEsol)31 is used for exchange−correlation. More reliable hybrid Hartree−Fock density functional theory (HSE06)32 is used for the calculation of electronic structure. In our calculations, the following valence electron configurations: 3s23p64s2 for Ca, 4s24p65s2 for Sr, 5s25p66s2 for Ba, 4s24p64d25s2 for Zr, 5p65d26s2 for Hf, 3s23p4 for S and 4s24p4 for Se are considered. The Brillouin zone is sampled33 using 8 × 8 × 4 and 9 × 9 × 7 k-point mesh for 48 atoms A3B2X7 and 20 atoms ABX3 compounds, with √2 × √2 in-plane lattice vectors in both cases. Kinetic-energy cutoff of 500 eV is selected for structural optimization. The geometry structure and all ionic coordinates are considered to be converged until the Hellmann-Feynman forces on the atoms become smaller than 0.01 eV/Å. Berry-phase approach34 is used to evaluate the spontaneous polarization P. The group-subgroup relationships and group theoretical analysis is analyzed by the ISOTROPY program.35 Before the study on the RP perovskites, the structural and electronic properties of parent materials are investigated to verify the accuracy of present methods. Firstly, full relaxation of the structures is performed to obtain the GS properties. The GS of six chalcogenide perovskites namely CaZrS3, CaHfS3, BaZrS3, BaHfS3, CaHfSe3 and CaZrSe3 exhibits the orthorhombic Pbnm structure described by 𝑎− 𝑏 − 𝑐 + in Glazer’s notation.36 The schematic description of Pbnm structure in (001) and (110) plane is plotted in Figure S1 (a), and the lattice vectors and atomic coordinates of all calculated structures are listed Table S1 in the Supplementary Information. The corresponding lattice constants and experimental values are listed in Table 1. It is found that PBEsol provides good description of structural parameters, in which the relaxed lattice constants are in excellent agreement with the experimental values.37 These results guarantee the reliability of PBEsol method in the description of the structural properties of RP perovskites. Table 1 also illustrates their band gap from the hybrid functionals. It is found that BaZrS3 possesses a band gap of 1.94 eV, which agrees well 5



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with the experimental value of 1.81 eV. The calculated band gaps for other perovskites range from 1.65 to 2.5 eV, in which CaZrSe3 is more suitable for PV applications due to their band gaps are more close to the ideal value of 1.3 eV.

Table 1. The lattice constants and band gaps of ABX3 obtained from first-principles calculations. The corresponding experimental values are also listed for comparison.

Tolerance Materials

a

b

c

Gap (eV)

Cal.

6.94

7.01

9.88

2.15

Exp.36

7.00

7.00

9.92

-

Cal.

6.97

7.07

9.94

1.94

Exp.36

7.03

7.06

9.98

1.81

Cal.

6.45

6.96

9.48

2.50

Exp.36

6.52

6.98

9.54

-

Cal.

7.02

6.47

9.53

2.22

Exp.36

7.03

6.54

9.59

1.90

factor

BaHfS3

BaZrS3

CaHfS3

CaZrS3

0.96

0.95

0.88

0.88

CaHfSe3

0.87

Cal.

7.28

6.72

9.91

1.94

CaZrSe3

0.87

Cal.

7.34

6.72

9.96

1.65

Now, we focus on the GS of RP structures that can be described as general formula of A 3B2X7, in which an extra A-X sheet inserts every unit along [001] direction. To determine theoretically the structure with minimum energy, we investigate several types of low-symmetry structures that have 6


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been considered in Ref. 38, including P42/mnm, Ccca, Cmc21 (i.e., the A21am phase in Ref. 26) and Pbcn phases by imposing individual and/or coupled distortions. Here, in-phase rotation around the [001] direction (irreps X1− ), out-of-phase rotation around [110] or [100] direction (irreps X3− ), in-plane polar mode along the [110] axis (irreps Γ5− ) and anti-polar mode along the [110] axis (irreps M5+ ) are considered. After full structural optimization, the energy difference between four low-symmetry phases and the high-symmetry I4/mmm phase is plotted in Figure 1. For Ba3Zr2S7, the energy difference between different phases is very small, the inset shows the magnified energy differences related to Ba3Zr2S7 and Ba3Hf2S7. The most stable phase found in present simulations is the P42/mnm phase which contains lower energy than Cmc21 phase proposed by Wang et al. This is consistent with the experiments, in which Ba3Zr2S7 is paraelectric and P42/mnm phase.27 The corresponding atomic structure of P42/mnm phase is shown in Figure S1(b) in the in the Supplementary Information. The same phase and distortion mode is found in Ba3Hf2S7. It is found that the GS is characterized by only tilting mode without in-phase or out-of-phase rotations around the [001] axis. Analysis of the ionic displacements reveals that there is no polarization in the present system.

Figure 1. The energy differences of four low-symmetry phases from the high-symmetry I4/mmm phase for different compounds. The inset shows the magnified energy differences for Ba3Zr2S7 and Ba3Hf2S7. 7



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However, for the other four materials, the lowest-energy structures stabilize in the polar Cmc21 phase as shown in Figure S1(c) in the Supplementary Information. The energy difference between the ferroelectric and paraelectric phase is significant. The energy loss of Ca3Zr2Se7, Ca3Hf2Se7, Ca3Zr2Se7 and Ca3Hf2Se7 between paraelectric I4/mmm phase and ferroelectric Cmc21 phase changes from 2.38 to 2.67 eV/ f.u. (0.49 eV/ f.u. in Ref. 39), which corresponds to an ultrahigh Curie temperature above 5000 K (1100 K in Ref. 39). From the above analysis, we can conclude that not all the A3B2X7 systems can be used to design ferroelectric semiconductor in chalcogenide perovskites. Even though the same Pbnm space group and 𝑎 − 𝑏 − 𝑐 +oxygen octahedral tilting pattern exhibits in their parent materials, Ba3B2X7 shows a totally different behavior from the Ca3B2X7. To guide future experimental works to design chalcogenide based ferroelectric semiconductor, it is therefore crucial to clearly identify the competition between different distortion modes and the origin of the ferroelectric/paraelectric GS. We next explore in detail the physical mechanism responsible for the ferroelectric/paraelectric GS by crystallographic mode analysis. To understand the role of displacive modes in stabilizing the structure, we examine the contribution of different modes to the total energy of the system. Here, we take paraelectric Ba3Zr2S7 and ferroelectric Ca3Zr2S7 for example. Figure 2 shows the change in total energy with respect to the mode amplitude frozen into the paraelectric I4/mmm structure. For paraelectric Ba3Zr2S7, the energy associated with the 𝑋3− mode shows a double-well character, indicating that tilting mode is favorable. In contrast, the energy of in-phase rotation exhibits a single-well potential-energy indicating this mode is dynamically stable and will be inhibited in the GS. For the ferroelectric Ca3Zr2S7, it is interesting to find that the energy changes related to in-phase rotation and out-of-phase tilting exhibit deep double-well character, which means that they can coexist in the GS. Benedek et al. theoretically demonstrated that ferroelectricity could be induced in RP perovskite oxides Ca3Mn2O7 due to trilinear coupling between rotation, tilting and polarization in the form of 𝑃𝑄1 𝑄2, where 𝑄1 and 𝑄2 denote the in-phase rotation and tilting modes.22 In Ba3Zr2S7 and Ba3Hf2S7, the in-phase rotation is absent and the trilinear coupling is unlikely to occur. In terms of Ca3B2X7, notable in-phase rotation and tilting modes are found, thus macroscopic electric polarization appears along the [110] direction due to the trilinear coupling mechanism. It should be 8


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noted that ferroelectricity can also be realized in cation ordered AA’BX4 Ruddlesden-Popper structure through mode coupling between Jahn-Teller, rotation and polar modes like LaSrMnO4.21 In the chalcogenide perovskites, the d0 electronic configuration makes B-site atom free from electronic instability and Jahn-Teller distortion. Thus, it seems difficult to induced ferroelectricity in AA’BX4 chalcogenide perovskites.

Figure 2. Energy variations as functions of (a) in-phase rotation and (b) tilting mode with respect to the I4/mmm structure of paraelectric Ba3Zr2S7.The corresponding energy variations for ferroelectric Ca3Zr2S7 are plotted in (c) and (d).

To fully understand the appearance of ferroelectricity in Ca3B2X7, we freeze the in-plane polar mode into the high-symmetry I4/mmm phase and low-symmetry structure, in which the initial rotation and tilting have the same amplitude as the GS. Figure 3 shows the energy variation as a function of in-plane polar mode for Ca3Zr2S7, Ca3Hf2S7, Ca3Zr2Se7 and Ca3Hf2Se7, respectively. It can be found that the energy curves exhibit very shallow double-well and the energy change is quite small compared with the rotation and tilting modes as shown in Figure 2, indicating this mode is weakly unstable. However, when initial rotation and tilting are imposed, the energy curves become a 9



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significant deep single well and the minimum shifts to a nonzero value, which demonstrates the validity of hybrid improper ferroelectricity.

Figure 3. Energy variation as a function of in-plane polar mode for (a) Ca3Zr2S7, (b) Ca3Hf2S7, (c) Ca3Zr2Se7 and (d) Ca3Hf2Se7 in high-symmetry I4/mmm phase (green curve) and low-symmetry structure with initial rotation and tilting with the same amplitude as the GS (red curve).

The intriguing ferroelectricity in RP chalcogenide perovskites presents an exciting opportunity for the improvements of power conversion efficiency in photovoltaic applications. Since ferroelectric polarization and band gap are key properties in the photovoltaic devices, we next quantify the amplitude of polarization and band gap using Berry phase method and HSE06 method. Figure 4 displays the in-plane polarization of A3B2X7, it can be observed that the polarization of Ba3Zr2S7 and Ba3Hf2S7 is zero. On the contrary, the polarization of Ca3B2X7 is significant ranging from 13.85 to 16.15 𝜇𝐶/𝑐𝑚2 . We also give the band gap of six A3B2X7 compounds in Figure 4. Even though Ca3Zr2S7 and Ca3Hf2S7 contain notable polarization, the band gaps are much larger, which may result 10


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in relative poor optical absorption and make them unsuitable for solar cells. Interestingly, we find that Ca3Zr2Se7 and Ca3Hf2Se7 have the lowest band gap. Moreover, they also possess sizable ferroelectric polarization as show in Figure 4, which make them the suitable candidates for the solar cell applications.

Figure 4.

Amplitude of polarization and band gap of ferroelectric phases by Berry phase and

HSE06 method.

Since ferroelectric semiconductor plays an important role in the solar cell application, one may ask how to design such ferroelectric semiconductor and why some structures are paraelectric, while others are ferroelectric. A general rule is necessary to guide the experimentalists to engineering ferroelectricity in RP chalcogenide perovskites. To address this question and give a deeper understanding on the origin of ferroelectric phase, we focus on the structural property from view of tolerance factor , which can be defined as ≡

𝑅𝐴 +𝑅𝑋

. Here, (𝑅𝐴 + 𝑅𝑋 ) corresponds to the bond

√2(𝑅𝐵 +𝑅𝑋 )

length of A-X, and (𝑅𝐵 + 𝑅𝑋 ) describes the bond length of B-X. It is well known that the structural distortion of perovskites is strongly determined by the size of the ions. We firstly analyze the effect of tolerance factor on the rotation and tilting modes of ABX3. The tolerance factor of ABX3 is calculated by the ionic radii from Shannon ionic radii.40-41 It is found that the tolerance factor of six 11



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materials is less than 1, which means the space between the corner-sharing BX3 octahedral is large enough for the A atom to move and lead to the rotation of the octahedron.

Figure 5.

In-phase rotation and tilting modes of (a) ABX3 and (b) A3B2X7 as a function of

tolerance factor of ABX3 compounds.

Figure 5(a) shows the in-phase rotation and tilting modes of ABX3 as a function of tolerance factor. It can be seen that both modes are nearly linearly decreased when  gradually increases. The rotation and tilting modes for CaZrSe3 are almost twice of those for BaZrS3. This means that the rotation and tilting modes related with hybrid improper ferroelectricity is strongly depended on the tolerance factor. Figure 5(b) displays the rotation and tilting modes of A3B2X7 with respect to the 12


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amplitude of tolerance factor. Note that the denotation of the same distortion is different in the ABX3 and A3B2X7 systems, the rotation and tilting mode can be describes as 𝑀2+ and 𝑅5− , respectively in ABX3 system, while they are denoted as 𝑋2+ and 𝑋3− in the A3B2X7 system. From Figure 5(b), it can be seen that the distortion modes show similar decreasing trend with the parent materials as tolerance factor increases, and the rotation mode finally vanishes when the tolerance factor is above 0.95 as for Ba3Zr2S7 and Ba3Hf2S7. This is because when the parent materials form the RP structure, the collective motion of octahedral rotation along the z direction is broken, which suppresses the rotation of the octahedron and leads to the complete disappearance of rotation along z direction in Ba3Zr2S7 and Ba3Hf2S7 because of the large tolerance factor. From the above analysis, we can conclude that tolerance factor is crucial for the design of RP chalcogenide ferroelectrics.

Figure 6. Mechanism of the PE or FE ground state determined by tolerance factor. The compounds with small tolerance factor favor both rotation and tilting mode, while the compounds with large tolerance factor contain only tilting mode. Ferroelectric polarization is induced due to the trilinear 13



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coupling between rotation, tilting and polarization in the form of 𝑃𝑄1 𝑄2.

The general avenue to design chalcogenide perovskites based ferroelectric semiconductor is described in Figure 6, one should select parent materials with small tolerance factor or materials with small ionic radius at the A-site. In these materials, rotation and tilting distortions could be remained to generate the hybrid improper ferroelectricity. For materials with large tolerance factor, cation substitution with small ionic radius may be effective ways to tune in-phase rotation and realize ferroelectricity in RP layered perovskites. Recently, it was suggested that cation substitution and tailoring electrostatic chemical strain in RP phases could effectively tune the electronic and structural properties.42 Hence, it is interesting to explore the existence of ferroelectricity for paraelectric Ba3Zr2S7 substituted by Ca atom, which will be the future work. In summary, we successfully reveal the underlying mechanism on the paraelectric phase of Ba3Zr2S7 observed in experiments and provide a theoretical guidance for the design of Ruddlesden-Popper chalcogenide ferroelectric semiconductor for solar energy conversion devices. The results highlight that the ferroelectricity depends crucially on the tolerance factor of the parent materials for Ruddlesden-Popper chalcogenide perovskites. The ferroelectric GS is more favorable for materials with small tolerance factor. From the Berry phase method and the art of the state hybrid functional, it is found that Ca3Hf2Se7 and Ca3Zr2Se7 can be the best candidates for solar cell applications due to their notable polarization and lowest band gap. We hope the present work could stimulate experimental investigations on the Ruddlesden-Popper chalcogenide perovskites to design high efficiency ferroelectric photovoltaic devices.

ACKNOWLEDGMENTS We would like to thank Dr. Hongjian Zhao for the valuable discussions. This work was financially supported by the National Natural Science Foundation of China (Grant No. 11672264, 11472242, 11621062), Zhejiang Provincial Natural Science Foundation (Grant No. LZ17A020001) and the Fundamental Research Funds for the Central Universities (2017FZA4030). The calculations in this work were conducted at the National Supercomputing Center of Tianjin, China.

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SUPPORTING INFORMATION Figure S1. The structure of Pbnm phase ABX3, P42/mnm phase A3B2X7 and Cmc21 phase A3B2X7. Table S1. The lattice vectors and atomic coordinates of all the structures used in the calculations.

REFERENCES (1) Yang, S. Y.; Seidel, J.; Byrnes, S. J.; Shafer, P.; Yang, C. H.; Rossell, M. D.; Yu, P.; Chu, Y. H.; Scott, J. F.; Ager, J. W.; et al. Above-Bandgap Voltages From Ferroelectric Photovoltaic Devices. Nat. Nanotechnol. 2010, 5, 143−147. (2) Ji, W.; Yao, K.; Liang, Y. C. Bulk Photovoltaic Effect at Visible Wavelength in Epitaxial Ferroelectric BiFeO3 Thin Films. Adv. Mater. 2010, 22, 1763-1766. (3) Seidel, J.; Fu, D.; Yang, S.-Y.; Alarcón-Lladó, E.; Wu, J.; Ramesh, R.; Ager, J. W. Efficient Photovoltaic Current Generation at Ferroelectric Domain Walls. Phys. Rev. Lett. 2011, 107, 126805. (4) Choi, T.; Lee, S.; Choi, Y. J.; Kiryukhin, V.; Cheong, S.-W. Switchable Ferroelectric Diode and Photovoltaic Effect in BiFeO3. Science 2009, 324, 63−66. (5) Yang, S. Y.; Martin, L. W.; Byrnes, S. J.; Conry, T. E.; Basu, S. R.; Paran, D.; Reichertz, L.; Ihlefeld, J.; Adamo, C.; Melville, A.; et al. Photovoltaic Effects in BiFeO3. Appl. Phys. Lett. 2009, 95, 062909. (6) Young, S. M.; Rappe, A. M. First Principles Calculation of the Shift Current Photovoltaic Effect in Ferroelectrics. Phys. Rev. Lett. 2012, 109, 116601−116605. (7) Zhang, Y.; Sahoo, M.P.K.; Wang, J. Tuning the Band Gap and Polarization of BaSnO3/SrSnO3 Superlattices for Photovoltaic Applications. Phys. Chem. Chem. Phys. 2017, 19, 7032-7039. (8) Grinberg, I.; West, D. V.; Torres, M.; Gou, G.; Stein, D. M.; Wu, L.; Chen, G.; Gallo, E. M.; Akbashev, A. R.; Davies, P. K.; et al. Perovskites Oxides for Visible-Light-Adsorbing Ferroelectric and Photovoltaic Materials. Nature 2013, 503, 509−512. (9) Zheng, F.; Takenaka, H.; Wang, F.; Koocher, N. Z.; Rappe, A. M.

First-Principles Calculation

of Bulk Photovoltaic Effect in CH3NH3PbI3 and CH3NH3PbI3−xClx. J. Phys. Chem. Lett. 2015, 6, 31−37. (10) Sturman, B. I.; Fridkin, V. M. The Photovoltaic and Photorefractive Effects in Noncentrosymmetric Materials; Gordon and Breach: Philadelphia, 1992. (11) Glass, A. M.; von der Linde, D.; Negran, T. J. High-voltage Bulk Photovoltaic Effect and 15



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 16 of 18

Photorefractive Process in LiNbO3. Appl. Phys. Lett. 1974, 25, 233−235. (12) Seidel, J.; Fu, D.; Yang, S.-Y.; Alarcon-Llado ́ , E.; Wu, J.; Ramesh, ́R.; Ager, J. W. Efficient Photovoltaic Current Generation at Ferroelectric Domain Walls. Phys. Rev. Lett. 2011, 107, 126805. (13) Seidel, J.; Martin, L. W.; He, Q.; Zhan, Q.; Chu, Y. H.; Rother, A.; Hawkridge, M. E.; Maksymovych, P.; Yu, P.; et al. Conduction at Domain Walls in Oxide Multiferroics. Nat. Mater. 2009, 8, 229–234 (14) Pintilie, L.; Vrejoiu, I.; Rhun, G. L.; Alexe, M. J. Short-Circuit Photocurrent in Epitaxial Lead Zirconate-Titanate Thin Films. J. Appl. Phys. 2007, 101, 064109. (15) Lin, Z.; Cai, W.; Jiang, W.; Fu, C.; Li, C.; Song, Y. Effects of Annealing Temperature on the Microstructure, Optical, Ferroelectric and Photovoltaic Properties of Bifeo3 Thin Films Prepared by Sol–gel method. Ceram. Int. 2013, 39, 8729−8736. (16) Chen, B.; Zuo, Z.; Liu, Y.; Zhan, Q.-F.; Xie, Y.; Yang, H.; Dai, G.; Li, Z.; Xu, G.; Li, R.-W. Tunable Photovoltaic Effects in Transparent Pb(Zr0. 53, Ti0. 47)O3 Capacitors. Appl. Phys. Lett. 2012, 100, 173903. (17) Anoop, G.; Seo, J.; Han, C. J.; Lee, H. J.; Kim, G. W.; Lee, S. S.; Park, E. Y.; Jo, J. Y. Ultra-thin Platinum Interfacial Layer Assisted-Photovoltaic Response of Transparent Pb(Zr, Ti)O3 Thin Film Capacitors. Sol. Energy 2015, 111, 118−124. (18) Perera, S.; Hui, H.; Zhao, C.; Xue, H.; Sun, F.; Deng, C.; Gross, N.; Milleville, C.; Xu, X.; Watson, D.F.; Weinstein, B. Chalcogenide Perovskites–An Emerging Class of Ionic Semiconductors. Nano Energy, 2016, 22, 129-135. (19) Niu, S.; Huyan, H.; Liu, Y.; Yeung, M.; Ye, K.; Blankemeier, L.; Orvis, T.; Sarkar, D.; Singh, D.J., Kapadia, R.; Ravichandran, J. Bandgap Control via Structural and Chemical Tuning of Transition Metal Perovskite Chalcogenides. Adv. Mater. 2017, 29, 1604733. (20) Sun, Y. Y.; Agiorgousis, M. L.; Zhang, P.; Zhang, S. Chalcogenide Perovskites for Photovoltaics Nano Lett. 2015, 15, 581−585. (21) Cammarata, A.; Rondinelli, J. M. Ferroelectricity From Coupled Cooperative Jahn-Teller Distortions and Octahedral Rotations in Ordered Ruddlesden-Popper Manganates. Phys. Rev. B: Condens. Matter Mater. Phys. 2015, 92, 14102. (22) Benedek, N. A.; Fennie, C. J. Hybrid Improper Ferroelectricity: A Mechanism for Controllable Polarization-Magnetization Coupling. Phys. Rev. Lett. 2011, 106, 107204. 16


Page 17 of 18

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(23) Oh, Y. S.; Luo, X.; Huang, F.-T.; Wang, Y.; Cheong, S.-W. Experimental Demonstration Of Hybrid Improper Ferroelectricity and the Presence of Abundant Charged Walls in (Ca,Sr)3Ti2O7 Crystals. Nat. Mater. 2015, 14, 407−413. (24) Stoumpos, C. C.; Cao, D. H.; Clark, D. J.; Young, J.; Rondinelli, J. M.; Jang, J. I.; Hupp, J. T.; Kanatzidis, M. G. Ruddlesden–Popper Hybrid Lead Iodide Perovskite 2D Homologous Semiconductors. Chem. Mater. 2016, 28, 2852−2867 (25) Tsai, H.; Nie, W.; Blancon, J.-C.; Stoumpos, C. C.; Asadpour, R.; Harutyunyan, B.; Neukirch, A. J.; Verduzco, R.; et al. High-Efficiency Two-Dimensional Ruddlesden–Popper Perovskite Solar Cells. Nature 2016, 536, 312−316. (26) H. Wang, G. Gou, J. Li, Ruddlesden–Popper perovskite Sulfides A3B2S7: A New Family of Ferroelectric Photovoltaic Materials for the Visible Spectrum. Nano Energy 2016, 22, 507. (27) Hung, Y.-C.; Fettinger, J. C.; Eichhorn, B. W. Acta Crystallogr., Sect. C: Cryst. Struct. Commun. 1997, 53, 827. (28) Blöchl, P. E. Projector Augmented-Wave Method. Phys. Rev. B: Condens. Matter Mater. Phys. 1994, 50, 17953. (29) Kresse, G.; Joubert, D. From Ultrasoft Pseudopotentials to The Projector Augmented-Wave Method. Phys. Rev. B: Condens. Matter Mater. Phys. 1999, 59, 1758−1775. (30) Kresse, G.; Furthmüller, J. Efficiency of Ab-initio Total Energy Calculations for Metals and Semiconductors Using a Plane-Wave Basis Set. Comput. Mater. Sci. 1996, 6, 15−50 (31) Perdew, J. P.; Ruzsinszky, A.; Csonka, G. I.; Vydrov, O. A.; Scuseria, G. E.; Constantin, L. A.; Zhou, X.; Burke, K. Restoring the Density-Gradient Expansion for Exchange in Solids and Surfaces. Phys. Rev. Lett. 2008, 100, 136406. (32) Heyd, J.; Scuseria, G. E.; Ernzerhof, M. Hybrid Functionals Based on a Screened Coulomb Potential. J. Chem. Phys. 2003, 118, 8207−8215. (33) Monkhorst, H. J.; Pack, J. D. Special Points for Brillouin-Zone Integrations. Phys. Rev. B. 1976, 13, 5188−5192 (34) King-Smith, R. D.; Vanderbilt, D. Theory of Polarization of Crystalline Solids. Phys. Rev. B. 1993, 47, 1651−1654. (35) Stokes, H. T.; Hatch, D. M. Isotropy. http://stokes.byu.edu/isotropy.html, June 2006. (36) Glazer, A. M. The Classification of Tilted Octahedra in Perovskites. Acta Cryst. B 1972, 28, 17



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 18 of 18

3384−3392. (37) R. Lelieveld, D. J. W. Ijdo, Sulphides with the GdFeO3 Structure. Acta Crystallogr., Sect. B: Struct. Crystallogr. Cryst. Chem. 1980, 36, 2223. (38) Lu, X.-Z.; Rondinelli, J. M. Epitaxial-Strain-Induced Polar-To-Nonpolar Transitions in Layered Oxides. Nat. Mater. 2016, 15, 951. (39) Liu, X. Q.; Wu, J. W.; Shi, X. X.; Zhao, H. J.; Zhou, H. Y.; Qiu, R. H.; Zhang, W. Q. and Chen, X. M. Hybrid Improper Ferroelectricity in Ruddlesden-Popper Ca3(Ti, Mn)2O7 Ceramics. Appl. Phys. Lett. 2015, 106, 202903. (40) Shannon, R. D.; Prewitt, C. T. Effective Ionic Radii in Oxides and Fluorides. Acta Crystallogr., Sect. B: Struct. Crystallogr. Cryst. Chem. 1969, 25, 925−946. (41) Shannon, R. D. Revised Effective Ionic Radii and Systematic Studies of Interatomic Distances in Halides and Chalcogenides. Acta Crystallogr., Sect. A: Cryst. Phys., Diffr., Theor. Gen. 1976, 32, 751−767. (42) Balachandran, P. V.; Cammarata, A.; Nelson-Cheeseman, B. B.; Bhattacharya, A.; Rondinelli, J. M. Inductive Crystal Field Control in Layered Metal Oxides with Correlated Electrons. APL Mater. 2014, 2, 076110.

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