Pressure-Induced Band Structure Evolution of Halide Perovskites: A

Article Cite This: J. Phys. Chem. C XXXX, XXX, XXX−XXX

pubs.acs.org/JPCC

Pressure-Induced Band Structure Evolution of Halide Perovskites: A First-Principles Atomic and Electronic Structure Study Yang Huang,†,§ Lingrui Wang,‡ Zhuang Ma,† and Fei Wang*,† International Laboratory for Quantum Functional Materials of Henan, School of Physics and Engineering and ‡Key Laboratory of Materials Physics of Ministry of Education, School of Physics and Engineering, Zhengzhou University, Zhengzhou 450001, China § Materials Science and Engineering Program, University of California San Diego, La Jolla, California 92093, United States

Downloaded via UNIV OF WINNIPEG on December 27, 2018 at 18:40:34 (UTC). See https://pubs.acs.org/sharingguidelines for options on how to legitimately share published articles.

†

ABSTRACT: Density functional theory-based calculations have been carried out to draw a broad picture of pressureinduced band structure evolution in various phases of organic and inorganic halide perovskite materials. Under a wide range of applied pressures, distinct band structure behaviors, including the magnitude change of band gaps, direct− indirect/indirect−direct band-gap transitions, and conduction band minimum/valence band maximum (CBM/VBM) shifts, have been observed between organic and inorganic perovskites among different phases. Through atomic and electronic structure calculations, band-gap narrowing/widening has been rationalized through crystal orbital coupling transformations; direct−indirect mutual transitions were explained on the basis of structural symmetry evolution; different VBM/ CBM shift behaviors between organic and inorganic perovskites were analyzed focusing on orientation and polarity of molecules/atoms outside the octahedrals. These results provide comprehensive guidance for further experimental investigations on pressure engineering of perovskite materials.

■

INTRODUCTION Halide perovskites have emerged as promising materials for optoelectronic devices and solar cells. The power conversion efficiency of solar cells based on this family of materials has significantly increased in the last several years, from 3.81 to 23.3%.2 Halide perovskites can be typically divided into four classes: organic lead perovskites, inorganic lead perovskites, organic lead-free perovskites, and inorganic lead-free perovskites, each of which have outstanding advantages. For example, MAPbX3 (MA = methylammonium; X = Cl, Br, and I) stands out in low manufacturing cost;3 CsPbX3 (X = Cl, Br, and I) has a higher thermal stability than its organic counterparts; 4 and lead-free ones get rid of toxicity, which promotes the commercialization of perovskites. The band gap of perovskites, the proxy for evaluating the ability to absorb light in solar spectrum, can be tuned in three ways: temperature-induced phase transition (typically, Eg,cubic < Eg,tetragonal < Eg,orthorhombic5,6), chemical modification,7 and hydrostatic pressure application. Compared to others, pressure application is a green and facile method that can successively alter band gaps. Kong et al. provided experimental evidence that by applying hydrostatic pressure to MAPbI3 and MAPbBr3, band gaps narrow down and then widen up with increasing pressure.8 Xiao et al. experimentally investigated that increasing the pressure applied on the orthorhombic nanocrystal CsPbBr3 can sequentially induce band-gap narrowing, widening, and direct-to-indirect transformation.9 Ying et al. theoretically investigated pressure effects on various © XXXX American Chemical Society

cubic inorganic halide perovskites through different computational methods and observed that band gaps narrow down to zero and then inverse as the pressure increases.10 According to these reported results, it seems that band gaps under pressure behave differently in various perovskite crystal structures (organic vs inorganic and different phases), so it is necessary to perform a comparative study among different phases and between organic and inorganic crystals. For different phases, the intrinsic difference is the structural symmetry. In a threedimensional perspective, for inorganic halide perovskites, cubic phases have the highest structural symmetry, tetragonal phases have the intermediate, and orthorhombic phases have the lowest symmetry. Because of the orientation and polarity of MA molecules, organic halide perovskites often show lower symmetry compared with their inorganic counterparts. In this work, for representation, highly symmetric cubic CsPbBr3 and cubic CsSnBr3 and less symmetric cubic MAPbBr3, cubic MASnBr3, orthorhombic CsPbBr3, and orthorhombic CsSnBr3 are selected, and by applying the first-principles calculations, evolutions of band-gap properties under a wide range of pressures are systematically investigated. Received: November 28, 2018 Revised: December 13, 2018

A

DOI: 10.1021/acs.jpcc.8b11500 J. Phys. Chem. C XXXX, XXX, XXX−XXX

Article

The Journal of Physical Chemistry C

Table 1. DFT-PBE-Calculated and Reported Lattice Constants and Band-Gap Values of Six Crystal Structures Studied in This Work results calculated in this work a (Å) cubic MAPbBr3 cubic MASnBr3 cubic CsPbBr3 cubic CsSnBr3 orthorhombic CsPbBr3 orthorhombic CsSnBr3

6.0926 6.1296 5.9924 5.8880 8.5241 8.3634

b (Å)

11.9125 11.7609

reported results

c (Å)

Eg (eV)

a (Å)

8.2162 8.1782

1.9761 1.4628 1.7716 0.6334 2.1163 0.9442

5.92918 5.9722 5.8423 5.88724 8.20725 8.196527

b (Å)

8.25525 11.583027

c (Å)

Eg (eV)

11.75925 8.024327

1.971,19 1.96,20 2.1821 2.02,21 1.1222 1.623 0.62724 2.14,9 2.3026 1.0128

Figure 1. Band gap vs pressure for the six crystals: cubic MAPbBr3, cubic MASnBr3, cubic CsPbBr3, cubic CsSnBr3, orthorhombic CsPbBr3, and orthorhombic CsSnBr3. Both band gaps between CBM and VBM and band gaps at R−R (Γ−Γ) are presented.

■

center of 7 × 7 × 7 and a Γ center of 5 × 3 × 5 Monkhorst− Pack mesh15 of the Brillouin zone was used in the cubic and orthorhombic structural optimizations. All of the structures were fully relaxed until the forces on each atom were smaller than 0.01 eV/Å using a tetrahedron method with Blöchl corrections with a broadening of 0.05 eV. According to our test, MA molecules in cubic MAPbBr3 and cubic MASnBr3 tend to orient along ⟨111⟩ direction because of the lower energy compared to that of ⟨110⟩ and ⟨100⟩ directions. This is consistent with the results on MAPbI3 by Giorgi et al.16

COMPUTATIONAL METHODS The first-principles calculations were performed using the plane-wave pseudopotential as implemented in the VASP code.11,12 The electron−core interactions were described with the frozen-core projector-augmented wave pseudopotentials.13 The generalized gradient approximation formulated by Perdew, Burke, and Ernzerhof (PBE) as the exchange− correlation functional14 with cutoff energies of 500 eV for organic and 300 eV for inorganic halide perovskites was chosen in all of our calculations. A reciprocal space sampling with an R B


Article


Figure 2. Band structures close to the Fermi level of cubic MAPbBr3 and orthorhombic CsPbBr3 under four critical pressure values.

Figure 3. Top: evolution of MAPbBr3 structures under four critical pressure values. Bottom: evolution of CsPbBr3 structures under pressure. Corresponding pressure and space group symbols are shown below each structure.

Therefore, MA orientation was set to be ⟨111⟩ direction in all of the calculations. Pressure was modeled with a fixing volume while allowing all lattice constants and atomic positions to relax. Pressure values were calculated through the relation ∂E p = − ∂V , where E is the energy of the crystal and V is the cell volume. As has been documented, density functional theory (DFT)PBE shows an obvious underestimation of band-gap calculation relative to experimental measurements. An advanced and computationally expensive method, spin−orbital coupling GW quasiparticle correlation (soc-GW), has been proved to be accurate in band-gap calculations.17 However, DFT-PBE is still effective for the discussions in this work. This is because that it has been shown that compared with the band structure calculated by DFT-PBE, soc-GW changes neither the band edge orbital characters nor the band-gap position in kspace;17,18 thus, DFT-PBE is able to qualitatively provide the picture of the evolution of band-gap properties under pressure.

■

demonstrated experimentally and theoretically, these unpressed perovskites are direct band-gap semiconductors. The variations of band-gap values of all six crystals under pressure are computed and plotted in Figure 1. The band edge gap represents the energy difference between the conduction band edge (i.e., conduction band minimum (CBM)) and the valence band edge (i.e., valence band maximum (VBM)) in the total density of states, whereas the R−R (Γ−Γ) band gap equals the energy difference between the conduction band and the valence band at R (Γ) point, the Brillouin zone position under ambient pressure. According to Figure 1, for the two crystal structures with the highest structural symmetry, cubic CsPbBr3 and CsSnBr3 (Figure 1a,b), band gaps remain direct and monochromatically decrease to zero as the pressure increases, which is consistent with previous computational results.10 For the other four less symmetric structures, cubic MAPbBr3, cubic MASnBr3, orthorhombic CsPbBr3, and orthorhombic CsSnBr3, interesting variations in band gaps occur. According to Figure 1c−f, four critical pressures (CP_I−IV) exist: (1) under CP_I (0−4 GPa), all crystals have direct band gaps and show band-gap contraction with increasing pressure. (2) When the pressure reaches beyond CP_I, band-gap widening happens. Band gaps of organic perovskites become indirect, whereas band gaps of inorganic perovskites remain direct. (3) With pressure being continu-

RESULTS AND DISCUSSION

The six perovskite structures studied in this work with both calculated and reported lattice constants and band gaps under ambient pressure are listed in Table 1. As has been C


Article


Figure 4. (a, b) Averaged Pb−Br−Pb angle vs averaged Pb−Br bond length. Linear fittings are shown in red. (c, d) Amplified band gap vs volume and pressure before CP_III. Data points are vertically matched between (a) and (c), and (b) and (d).

are shown in Figure 3. Space groups of these eight crystal structures are determined using the software Accelrys Materials Studio and shown below the figures in Figure 3. For cubic MAPbBr3, the crystal is in the cubic phase (Pm3̅m) under ambient pressure, in the trigonal phase with a symmetric mirror (R3m) at direct band-gap state (1.6 GPa) before CP_I, and in a low-symmetry trigonal phase (R3) at indirect bandgap state (5.1, 8.2 GPa) after CP_I. For orthorhombic CsPbBr3, the crystal remains in the orthorhombic phase (Pnma) under ambient pressure, at direct band-gap state (1.8 GPa) before CP_II, and at indirect band-gap state (7.4 GPa) between CP_II and CP_IV, with more and more severe octahedral rotation/distortion and lower and lower structural symmetry sequentially. The crystal structure transforms to the high-symmetry hexagonal phase at direct band-gap state (13 GPa) after CP_IV. Therefore, direct-to-indirect and indirectto-direct transitions might be closely related to the reduction and enhancement of crystal symmetry, respectively. Actually, it had been demonstrated that structural deviation of perovskite crystals away from high symmetry would lead to space group change30 and the structural alternations happen in three forms, octahedral tilt (rotation), cation displacement, and octahedral distortion.31 As can be observed in Figure 3, all of these three structural alternation components participate in the pressureinduced structural distortion. In a relatively low-pressure domain, the main components are cation displacement and octahedral tilt, which is shown in MAPbBr3 under 1 atm to 5.1 GPa transition and in CsPbBr3 under 1 atm to 1.8 GPa transition. In a higher-pressure domain, octahedral distortion starts to play an important role, which is shown in MAPbBr3 under 5.1−8.2 GPa transition and in CsPbBr3 under 1.8−7.4− 13.0 GPa transitions. As for the magnitude evolution of band gaps, before CP_III, lattice contraction, which reduces band gaps, and octahedral

ously increased beyond CP_II (around 5 GPa), band gaps of inorganic perovskites become indirect. (4) As the pressure keeps going up to CP_III (8−15 GPa), band gaps of all crystals begin to decrease. (5) When the pressure goes beyond CP_IV (10−25 GPa), band gaps of inorganic perovskites become direct again, whereas organic perovskites still maintain indirect band gaps. (6) Band gaps of all crystals will decrease to zero without any direct−indirect/indirect−direct band-gap transitions under further increasing pressure. The results (1), (2), and (3) are consistent with previous experimental results on cubic MAPbBr38 and orthorhombic CsPbBr3;9 the results (4) and (6) are consistent with previous experimental results on cubic MAPbI3; 29 the result (5) has no reported correspondings. Band structures close to the Fermi level of cubic MAPbBr3 and orthorhombic CsPbBr3 (similar for MASnBr3 and CsSnBr3 and thus not presented) under four critical pressure values are plotted in Figure 2. According to Figure 2, when direct-to-indirect and indirect-to-direct bandgap alternations happen, in organic perovskites, both conduction band minimum (CBM) and valence band maximum (VBM) move away from the original R point in the Brillouin zone, whereas in inorganic perovskites, only VBM moves away from the original Γ point and CBM remains unmoved. These two revealed trends have no reported correspondings either. These variations of electronic band-gap properties of perovskites in this study can be explained by pressure-induced atomic structural changes. To rationalize the direct-to-indirect band-gap transition in cubic organic crystals at CP_I, direct-toindirect and inverse transitions in orthorhombic inorganic crystals at CP_II and CP_IV, respectively, and crystal structures of cubic MAPbBr3 (similar to MASnBr3) and orthorhombic CsPbBr3 (similar to CsSnBr3) under pressures in the four critical stages (the same pressure values in Figure 2) D


Article


Figure 5. (a, b) CBM and VBM electron density characters of cubic MAPbBr3 under ambient pressure and after CP_I, respectively. (c, d) CBM and VBM electron density characters of orthorhombic CsPbBr3 under ambient pressure and after CP_I, respectively. (e, f) Bond angles and cloud distances for Pb−Br−Pb of cubic MAPbBr3 and orthorhombic CsPbBr3. Electron cloud distances decrease and then increase with increasing pressure, corresponding to narrowing and widening of band gaps, respectively.

rotation, which tends to enlarge band gaps, compete with each other.32 The relation between averaged angle Pb−Br−Pb, which can describe octahedral rotation, and averaged Pb−Br bond length, which can evaluate the lattice contraction magnitude of cubic MAPbBr3 (similar to MASnBr3) and orthorhombic CsPbBr3 (similar to CsSnBr3), is plotted in Figure 4. Corresponding band gap−pressure relationships before CP_III are also plotted in Figure 4. As can be noticed, for both organic and inorganic perovskites, abstract values of slopes increase suddenly with increasing pressure exactly at CP_I (fourth data point for cubic MAPbBr3 and fifth data point for orthorhombic CsPbBr3). After CP_I, the effect of octahedral rotation exceeds lattice contraction and band gaps begin to increase. In an electronic landscape, the phenomenon of band-gap narrowing followed with band-gap widening can be comprehended as follows: for both organic perovskites and inorganic perovskites, only Pb (Sn) and Br orbitals contribute to CBM and VBM. VBM is the antibonding hybridization between Pb 6s and Br 4p orbitals. CBM state is governed by orbital interaction between Pb 6p and Br 4s orbitals. As can be identified in Figure 5a,c, CBM is mostly a nonbonding localized state of Pb 6p orbital and is thus not sensitive to pressure. Therefore, band gaps are determined by the coupling

between Pb 6s orbitals and Br 4p orbitals in VBM. Aforementioned Pb−Br bond-length shortening facilitates the coupling effect, pushes up VBM, and narrows the band gap. This explanation can also be applied to the two highly symmetric structures, cubic CsPbBr3 and cubic CsSnBr3. At CP_I, as shown in Figure 5e,f, the electron cloud distance between Pb 6s and Br 4p orbitals reaches minimum and is ready to increase because of octahedral rotation evaluated by the aforementioned Pb−Br−Pb angle, so the coupling effect starts to become weaker, which leads to VBM drop and bandgap widening. When the pressure goes beyond CP_III, pressure-induced metallization happens and band gaps begin to narrow down all the way to zero when band crossing occurs,33 which may be the result of strong coupling effect between Pb 6s and Br 4p orbitals in the small pressed crystal cells. Another way to explain this pressure-induced metallization phenomenon is Goldhammer−Herzfeld criterion,34 which suggests that electrons can be ripped off the atoms or molecules with an infinitesimal perturbation originated from a high crystal packing factor under high pressure. For the difference in CBM/VBM participation in a direct−indirect mutual band-gap transition between organic and inorganic perovskites, a possible explanation has been provided as follows: as shown in Figure 5a,b, in organic perovskites, MA E


Article

The Journal of Physical Chemistry C has polarity and orients along ⟨111⟩, the same direction as that of Pb 6p orbital in CBM. This orientational match may induce a strong Coulomb interaction between MA and Pb, which can be identified from the morphology change of Pb 6p orbital under high pressure (Figure 5b) and may facilitate the CBM movement away from the R point. The strong MA−Pb interaction may derive from the experimentally demonstrated organic molecule-to-octahedral interactions enhanced by pressure in organic halide perovskites.35 On the other hand, in inorganic perovskites (Figure 5c,d), no crystal orbital morphology change has been observed under high pressure (Figure 5d), which may be subject to the nonpolarity of Cs atom and the resulting small magnitude of Coulomb interaction between Cs and Pb, which is too small to trigger CBM deviation. Compared to direct semiconductors, indirect semiconductors tend to have a longer carrier lifetime, which is beneficial for photovoltage enhancement. It is worth pointing out that it has been demonstrated that spin−orbital-coupling (SOC) effect can lead to k-dependent band splitting in noncentrosymmetric space groups.36 Because SOC has not been taken into consideration in this study, other effects besides SOC that displace the CBM/VBM away from the symmetric point of the Brillouin zone, i.e., structural evolution, have been discussed in this study.

(2) NERL. NREL Efficiency Chart, 2018-2020. https://www.nrel. gov/Pv/Assets/Pdfs/Pv-Efficiencies-07-17-2018.Pdf (accessed Dec 20, 2018). (3) Wang, K.-H.; Li, L. C.; Shellaiah, M.; Sun, K. W. Structural and Photophysical Properties of Methylammonium Lead Tribromide (MAPbBr3) Single Crystals. Sci. Rep. 2017, 7, No. 13643. (4) Zhang, M.; Zheng, Z.; Fu, Q.; Chen, Z.; He, J.; Zhang, S.; Yan, L.; Hu, Y.; Luo, W. Growth and Characterization of All-Inorganic Lead Halide Perovskite Semiconductor CsPbBr 3 Single Crystals. CrystEngComm 2017, 19, 6797−6803. (5) Grote, C.; Berger, R. F. Strain Tuning of Tin-Halide and LeadHalide Perovskites: A First-Principles Atomic and Electronic Structure Study. J. Phys. Chem. C 2015, 119, 22832−22837. (6) Knutson, J. L.; Martin, J. D.; Mitzi, D. B. Tuning the Band Gap in Hybrid Tin Iodide Perovskite Semiconductors Using Structural Templating. Inorg. Chem. 2005, 44, 4699−4705. (7) Akkerman, Q. A.; D’Innocenzo, V.; Accornero, S.; Scarpellini, A.; Petrozza, A.; Prato, M.; Manna, L. Tuning the Optical Properties of Cesium Lead Halide Perovskite Nanocrystals by Anion Exchange Reactions. J. Am. Chem. Soc. 2015, 137, 10276−10281. (8) Kong, L.; Liu, G.; Gong, J.; Hu, Q.; Schaller, R. D.; Dera, P.; Zhang, D.; Liu, Z.; Yang, W.; Zhu, K.; et al. Simultaneous Band-Gap Narrowing and Carrier-Lifetime Prolongation of Organic−inorganic Trihalide Perovskites. Proc. Natl. Acad. Sci. U.S.A. 2016, 113, 8910− 8915. (9) Xiao, G.; Cao, Y.; Qi, G.; Wang, L.; Liu, C.; Ma, Z.; Yang, X.; Sui, Y.; Zheng, W.; Zou, B. Pressure Effects on Structure and Optical Properties in Cesium Lead Bromide Perovskite Nanocrystals. J. Am. Chem. Soc. 2017, 139, 10087−10094. (10) Ying, Y.; Luo, X.; Huang, H. Pressure-Induced Topological Nontrivial Phase and Tunable Optical Properties in All-Inorganic Halide Perovskites. J. Phys. Chem. C 2018, 122, 17718−17725. (11) Kresse, G.; Furthmüller, J. Efficient Iterative Schemes for Ab Initio Total-Energy Calculations Using a Plane-Wave Basis Set. Phys. Rev. B 1996, 54, 11169−11186. (12) 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. (13) Blöchl, P. E. Projector Augmented-Wave Method. Phys. Rev. B 1994, 50, 17953−17979. (14) Perdew, J. P.; Burke, K.; Ernzerhof, M. Generalized Gradient Approximation Made Simple. Phys. Rev. Lett. 1996, 77, 3865−3868. (15) Monkhorst, H. J.; Pack, J. D. Special Points for Brillouin-Zone Integrations. Phys. Rev. B 1976, 13, 5188−5192. (16) Giorgi, G.; Fujisawa, J. I.; Segawa, H.; Yamashita, K. Small Photocarrier Effective Masses Featuring Ambipolar Transport in Methylammonium Lead Iodide Perovskite: A Density Functional Analysis. J. Phys. Chem. Lett. 2013, 4, 4213−4216. (17) Even, J.; Pedesseau, L.; Jancu, J. M.; Katan, C. Importance of Spin-Orbit Coupling in Hybrid Organic/Inorganic Perovskites for Photovoltaic Applications. J. Phys. Chem. Lett. 2013, 4, 2999−3005. (18) Brivio, F.; Butler, K. T.; Walsh, A.; van Schilfgaarde, M. Relativistic Quasiparticle Self-Consistent Electronic Structure of Hybrid Halide Perovskite Photovoltaic Absorbers. Phys. Rev. B 2014, 89, No. 155204. (19) Tan, M.; Wang, S.; Rao, F.; Yang, S.; Wang, F. Pressures Tuning the Band Gap of Organic−Inorganic Trihalide Perovskites (MAPbBr3): A First-Principles Study. J. Electron. Mater. 2018, 47, 7204−7211. (20) Castelli, I. E.; García-Lastra, J. M.; Thygesen, K. S.; Jacobsen, K. W. Bandgap Calculations and Trends of Organometal Halide Perovskites. APL Mater. 2014, 2, No. 081514. (21) Ju, D.; Dang, Y.; Zhu, Z.; Liu, H.; Chueh, C. C.; Li, X.; Wang, L.; Hu, X.; Jen, A. K. Y.; Tao, X. Tunable Band Gap and Long Carrier Recombination Lifetime of Stable Mixed CH3NH3PbxSn1- XBr3Single Crystals. Chem. Mater. 2018, 30, 1556−1565. (22) Ma, Z. Q.; Pan, H.; Wong, P. K. A First-Principles Study on the Structural and Electronic Properties of Sn-Based Organic−Inorganic Halide Perovskites. J. Electron. Mater. 2016, 45, 5956−5966.

■

CONCLUSIONS In summary, with a wide range of pressures being applied, band structure evolution of organic and inorganic perovskites with different structural symmetries has been investigated and rationalized. Both the magnitude and direct−indirect nature of band gaps can be tuned with the help of pressure, which implies a green and facile way for engineering optoelectronic materials. In addition, from a scientific point of view, pressureenhanced structural symmetry alternation is highly possible for triggering direct−indirect mutual transitions of band gaps and unidentical CBM/VBM behaviors in organic and inorganic perovskites may be subject to different molecular polarities outside octahedrals. We believe that the whole picture drawn in this work on perovskites under pressure effects provides useful implications for further design and property enhancement of perovskite materials.

■

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Fei Wang: 0000-0002-3442-9396 Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS This work was jointly supported by the National Natural Science Foundation of China (Grant No. 11504332) and the Outstanding Young Talent Research Fund of Zhengzhou University (Grant No. 1521317008). The calculations were performed in the high-performance computational center of Zhengzhou University.

■

REFERENCES

(1) Kojima, A.; Teshima, K.; Shirai, Y.; Miyasaka, T. Organometal Halide Perovskites as Visible-Light Sensitizers for Photovoltaic Cells. J. Am. Chem. Soc. 2009, 131, 6050−6051. F


Article

The Journal of Physical Chemistry C (23) Murtaza, G.; Ahmad, I. First Principle Study of the Structural and Optoelectronic Properties of Cubic Perovskites CsPbM3(M = Cl, Br, I). Phys. B 2011, 406, 3222−3229. (24) Ma, C. G.; Krasnenko, V.; Brik, M. G. First-Principles Calculations of Different (001) Surface Terminations of Three Cubic Perovskites CsCaBr3, CsGeBr3and CsSnBr3. J. Phys. Chem. Solids 2018, 115, 289−299. (25) Li, G.; Wang, H.; Zhu, Z.; Chang, Y.; Zhang, T.; Song, Z.; Jiang, Y. Shape and Phase Evolution from CsPbBr3perovskite Nanocubes to Tetragonal CsPb2Br5nanosheets with an Indirect Bandgap. Chem. Commun. 2016, 52, 11296−11299. (26) Heidrich, K.; Schäfer, W.; Schreiber, M.; Söchtig, J.; Trendel, G.; Treusch, J.; Grandke, T.; Stolz, H. J. Electronic Structure, Photoemission Spectra, and Vacuum-Ultraviolet Optical Spectra of CsPbCl3 and CsPbBr3. Phys. Rev. B 1981, 24, 5642−5649. (27) Fabini, D. H.; Laurita, G.; Bechtel, J. S.; Stoumpos, C. C.; Evans, H. A.; Kontos, A. G.; Raptis, Y. S.; Falaras, P.; Van Der Ven, A.; Kanatzidis, M. G.; et al. Dynamic Stereochemical Activity of the Sn2+Lone Pair in Perovskite CsSnBr3. J. Am. Chem. Soc. 2016, 138, 11820−11832. (28) Jaroenjittichai, A. P.; Laosiritaworn, Y. Band Alignment of Cesium-Based Halide Perovskites. Ceram. Int. 2018, 44, S161−S163. (29) Jaffe, A.; Lin, Y.; Mao, W. L.; Karunadasa, H. I. PressureInduced Metallization of the Halide Perovskite (CH3NH3)PbI3. J. Am. Chem. Soc. 2017, 139, 4330−4333. (30) Li, W.; Wang, Z.; Deschler, F.; Gao, S.; Friend, R. H.; Cheetham, A. K. Chemically Diverse and Multifunctional Hybrid Organic−inorganic Perovskites. Nat. Rev. Mater. 2017, 2, No. 16099. (31) Glazer, A. M. Simple Ways of Determining Perovskite Structures. Acta Crystallogr., Sect. A: Found. Adv. 1975, 31, 756−762. (32) Prasanna, R.; Gold-Parker, A.; Leijtens, T.; Conings, B.; Babayigit, A.; Boyen, H.-G.; Toney, M. F.; McGehee, M. D. Band Gap Tuning via Lattice Contraction and Octahedral Tilting in Perovskite Materials for Photovoltaics. J. Am. Chem. Soc. 2017, 139, 11117− 11124. (33) Grochala, W.; Hoffmann, R.; Feng, J.; Ashcroft, N. W. The Chemical Imagination at Work in Very Tight Places. Angew. Chem., Int. Ed. 2007, 46, 3620−3642. (34) Herzfeld, K. F. On Atomic Properties Which Make an Element a Metal. Phys. Rev. 1927, 29, 701−705. (35) Wang, L.; Wang, K.; Zou, B. Pressure-Induced Structural and Optical Properties of Organometal Halide Perovskite-Based Formamidinium Lead Bromide. J. Phys. Chem. Lett. 2016, 7, 2556−2562. (36) Amat, A.; Mosconi, E.; Ronca, E.; Quarti, C.; Umari, P.; Nazeeruddin, M. K.; Grätzel, M.; De Angelis, F. Cation-Induced Band-Gap Tuning in Organohalide Perovskites: Interplay of SpinOrbit Coupling and Octahedra Tilting. Nano Lett. 2014, 14, 3608− 3616.

G


Pressure-Induced Band Structure Evolution of Halide Perovskites: A

Recommend Documents