Polarization-Dependent Optoelectronic Performances in Hybrid Halide

Dec 19, 2017 - As the most popular HOIP member, single crystals of MAPbX3 (X = Br, Cl) are deemed as important candidates for ultraviolet–visible ph...
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Polarization-Dependent Optoelectronic Performances in Hybrid Halide Perovskite MAPbX3 (X=Br, Cl) Single Crystal Photo-detectors Jianxu Ding, Xiaohua Cheng, Lin Jing, Tianliang Zhou, Ying Zhao, and Songjie Du ACS Appl. Mater. Interfaces, Just Accepted Manuscript • DOI: 10.1021/acsami.7b13111 • Publication Date (Web): 19 Dec 2017 Downloaded from http://pubs.acs.org on December 19, 2017

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Polarization-Dependent Optoelectronic Performances in Hybrid Halide Perovskite MAPbX3 (X=Br, Cl) Single Crystal Photo-detectors Jianxu Ding 1, 3, *, Xiaohua Cheng 1, Lin Jing 1, Tianliang Zhou 2, *, Ying Zhao 1, Songjie Du 1 (1. College of Materials Science and Engineering, Shandong University of Science and Technology, Qingdao 266590, China; (2. College of Materials, Xiamen University, Xiamen 361005, China; (3. State Key Laboratory of Mining Disaster Prevention and Control Co-founded by Shandong Province and the Ministry of Science and Technology, Shandong University of Science and Technology, Qingdao 266590, China.

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ABSTRACT: Hybrid organic-inorganic lead halide perovskites (HOIPs) have received significant attentions due to their impressive performances in the fields of solar cells and photoelectric detection. In the past 5 years, great efforts have been made to improve the crystallinity, reduce grain boundaries, and enhance stabilities of perovskites films. Compared with films, HOIPs single crystals possess fewer grain boundaries and stronger optoelectronic properties and can be applied in optoelectronic devices. As the most popular HOIPs members, single crystals of MAPbX3 (X=Br, Cl) are deemed as important candidates for ultraviolet-visible photo-detectors, in which the crystal structure anisotropy largely affects the detection performance. In the study, high-quality cubic single crystals of MAPbBr3 and MAPbCl3 were successfully grown from solutions. Taking advantages of their smooth (100) facets, planar metal-semiconductor-metal (MSM) photo-detector devices were fabricated using Au interdigitated electrodes. The optoelectronic performances under non-polarized and linearly polarized lights were explored. The optoelectronic performances were dependent on linearly polarized lights. Interestingly, both responsivity and EQE were greatly enhanced under the excitation with linearly polarized lights. Moreover, the polarized related optical absorptions and the electron densities within (100) plane could be used to interpret the different optoelectronic performances of single crystals of MAPbX3 (X=Br, Cl) under various linearly polarized lights. KEYWORDS: perovskite; single crystal, photo-detector, optoelectronic performance, polarized light

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1. INTRODUCTION Organic-inorganic hybrid methylammonium lead halide (MAPbX3, X=Cl, Br, I) perovskite structure materials have attracted wide attention for their potential applications in photo-voltaic devices, especially in solar cells.1−4 A record of more than 22% in the power conversion efficiency of perovskite solar cells has already been achieved.

5

Due to the outstanding optoelectronic properties, direct and

tunable band gap,6 large absorption coefficient,3 long-range carrier transport lengths and mobility,7 as well as the tolerance of optical and electronic characteristics to crystal structure, MAPbX3 may be used as narrowband or broadband photo-detectors operating in the ultraviolet-visible and near infrared regions.8 To improve the corresponding optoelectronic properties, previous works have been focusing on reducing grain boundaries and defects of MAPbX3 films.9-10 Despite these achievements in MAPbX3 processing technologies and optoelectronic devices, such as solar cell, photo-detectors, lasers and LEDs, the significant differences in optoelectronic properties between single crystal and polycrystalline counterpart could not be neglected. As there are more grain boundaries and higher defect densities in MAPbX3 films, the optoelectronic properties of film, 1D and 2D nano structured crystalline are inferior to those of single crystals.11 Therefore, it is necessary to deeply understand the intrinsic optoelectronic properties of MAPbX3 single crystal. Great progresses have been made in MAPbX3 single crystal growth technology recently. By virtue of the high solubility in solvents, MAPbX3 single crystals can be grown via inverse temperature crystallization method from organic

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solvents or cooling temperature method from hydrogen halides.12-13 In addition, it has been pointed out that crystal structure anisotropy plays a crucial role in optoelectronic properties of MAPbX3. Leblebici and coworkers reported that trap states densities and photovoltaic properties in thin MAPbI3 films were facet-dependent.14 Cho et al also found crystal orientation and charge transport anisotropy in hybrid perovskite films.15 Similarly, investigation results of MAPbBr3 single crystal with various facets revealed that the optoelectronic properties were dependent on facet.16 However, there still lacks systematic research about crystal anisotropy related optoelectronic properties for MAPbX3. The optical absorption, and carrier’s generation and transport in MAPbX3 are related to crystal anisotropy, which is in connection with atom packing and electron density. It is well known that single crystals can provide various exposed facets, thus facilitating the studies on facet-dependent optoelectronic properties in MAPbX3. As for the crystal anisotropy in a crystal, the crystal orientation within a plane should be taken into consideration because planar MAPbX3-based optoelectronic devices, such as planar photodetectors, are important. However, the crystal orientation within a plane for MAPbX3 based optoelectronic devices is still uncharted. Therefore, it is necessary to explore the influence of the crystal orientation within a plane on the optoelectronic application of MAPbX3. To fill the gap, a convenient method utilizing linearly polarized light as incident illumination can be adopted to inspect the optoelectronic properties. Such optoelectronic properties based on linearly polarized light have been studied in other materials, such as black

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phosphorus17 and Bi2Ti318. It should retrospect that the stabilized phase of MAPbI3 single crystal is tetrahedral at room temperature, whereas the stabilized phases of MAPbBr3 and MAPbCl3 single crystals are cubic. In order to analyze the influences of crystal orientation within a plane on optoelectronic properties, cubic MAPbBr3 and MAPbCl3 single crystals were chosen to fabricate planar photo-detectors. Here, we first report the observation of polarization-dependent photocurrents of cubic MAPbBr3 and MAPbCl3 single crystals under linearly polarized lights based on planar type photo-detector. The photocurrents, responsivity and EQE revealed that linearly polarized light greatly affected the optoelectronic performance. The influence could be interpreted based on crystal orientation-related optical absorption and the calculated electron density.

2. EXPERIMENTAL AND FIRST-PRINCIPLE CALCULATIONS 2.1 Single crystal growth Both MAPbBr3 and MAPbCl3 single crystals were grown from solutions via inverse temperature crystallization method.12, 19-21 The MAPbBr3 single crystal was grown from a transparent N-dimethylformamide (DMF, ≥99.5%) solution by dissolving PbBr2 (98%, Sigma Aldrich) and MABr with a molar ratio of 1:1. A seed crystal with the size of 1 mm was added into the solution, which was maintained at 80 °C for 2 days. Finally, a large size MAPbBr3 single crystal was obtained. MAPbCl3 single crystal was grown from a mixed solution of DMF and DMSO (1:1 in volume) with dissolved PbCl2 (98%, Sigma Aldrich) and MACl with a molar ratio of 1:1. At the

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initial stage, the transparent solution was sealed and maintained at 90 °C for 7 days. When the solution became cream color, a small cubic crystal was added into the solution. Large MAPbCl3 single crystal could grow within 3 days.

2.2 Photo-detector device fabrications Planar photo-detectors were fabricated on (100) facets of cubic MAPbBr3 and MAPbCl3 single crystals. As previously reported,22-24 the surface of perovskite single crystal is sensitive to moisture and other dried gases, thus leading to surface hydration and transformation to disordered polycrystalline. Such a surface hydration will further mask carrier transport and increase surface traps, which lead to resistive losses and high leakage current in optoelectronic devices. Therefore, to minimize surface decomposition, polycrystalline, and surface traps related defects, the crystal facets were well polished by using dried silk without any dispersing agent or polishing powder before photo-detector fabrication. After polishing, the devices were fabricated as soon as possible. The alloy hollow contact pattern masks were laid on the polished facets of single crystals, and Au interdigitated electrodes were formed on the blank area of the hollow mask during the sputtering process. The width of Au interdigitated electrode was designed as 150 µm and the depth was controlled as about 100 nm. The light absorption area was calculated according to the overlapping area between the mask area and the illumination area.

2.3 Characterizations and measurements XRD patterns of MAPbBr3 and MAPbCl3 powders were previously reported. Here,

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in order to evaluate the quality of single crystals, both powder and (100) facet XRD were characterized under D/Max2500PC X-ray diffractometer with Cu KαI irradiation. The absorption spectra of MAPbBr3 and MAPbCl3 powders were obtained on a UV-2550 spectrometer with an integrating sphere. The linearly polarized light dependent optoelectronic properties of the planar photo-detectors were investigated in air at room temperature using Keithly 2450 to collect photocurrents. In order to compare the influence of crystal species on optoelectronic properties, the measurements were performed with the same excitation light sources, semiconductor laser diodes (LD, 405 nm, 100 mW). The linearly polarized lights at various polarization angles were obtained by adjusting the angles of calibrated polarizer.

2.4 Computation details The calculation was performed using Cambridge Serial Total Energy Package (CASTEP) code based on the first-principles density-functional theory (DFT). Perdew-Wang GGA exchange correlation functional was adopted. For all calculations, the electronic wave functions at each k-point were expanded in terms of plane-wave basis set, and an energy cutoff of 600 eV was used. The Monkhorst-Pack grid parameter for k-point sampling was 5×5×5. After structural optimization, the imaginary parts of the dielectric functions, for MAPbBr3 and MAPbCl3 were obtained by calculating the optical properties under various polarization directions. The band

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structures and charge density maps were analyzed according to electronic properties within (100) slices for MAPbBr3 and MAPbCl3 crystals.

3. RESULTS AND DISCUSSION The XRD patterns of MAPbBr3 and MAPbCl3 powders (Figure S1) have been indexed as cubic symmetry (Pm3m). The lattice parameters of MAPbBr3 and MAPbCl3 are respectively calculated to be 5.92 Å and 5.68 Å. Figs. 1(a-b) show the XRD patterns of the (100) planes of MAPbBr3 and MAPbCl3 single crystals. Insets show the optical images of large-size single crystals. The sharp {100} crystal plane peaks suggest that the qualities of MAPbX3 (X=Br, Cl) single crystals are high. From the UV-visible spectra in Figs. 1(c-d), the absorption edges of MAPbBr3 and MAPbCl3 are assigned to 576 nm and 436 nm, respectively. The optical band gaps are calculated to be 2.14 eV and 2.84 eV. Such band gaps are narrower than the previously reported data of thin films and facilitate optoelectronic applications.25

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Fig. 1 (a-b) Planar XRD patterns of cubic MAPbBr3 and MAPbCl3 single crystals (inset were the grown single crystals); (c-d) Absorptions and optical band gaps of MAPbBr3 and MAPbCl3 single crystals, respectively.

Fig. 2a illustrates schematic diagram of measuring photocurrents under linearly polarized light for MAPbBr3 and MAPbCl3 single crystal based photo-detectors. In order to investigate the influence of linearly polarized light on optoelectronic response of planar devices, the interdigital electrodes were designed to be parallel to crystal edges. As a result, the interaction between polarized light and crystal surface was defined. The optoelectronic performances of MAPbBr3 and MAPbCl3 single crystal photo-detectors under linearly polarized light by using 405 nm LD with light power of 100 mW are displayed in Figs. 2(b-c). Higher dark current acquired for MAPbBr3 is 1.14×10-7 A, in contrast to 3.55×10-8 A for MAPbCl3 at an applied voltage of 10 V because of the narrower band gap of MAPbBr3. The photocurrents increase dramatically with increasing of applied voltages for MAPbBr3 and MAPbCl3 single crystal photo-detectors under linearly polarized light. Besides, the photocurrents show diversified features with various polarization angles, suggesting that linearly

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polarized light caused dramatic anisotropic effect on optoelectronic performances. In particular, the photocurrent under 0° is almost equal to that under 180°, giving apparent proof that the optoelectronic performances exhibit a periodicity of 180°. The periodicity is consistent with the incident light’s polarization angle and cubic crystal surface. In addition, in the inserted figures, both dark current and photocurrents increase dramatically when the bias is lower than 2.0 V, which is attributed to the formation of Au-MAPbX3 (X=Br, Cl) Schottky junction.26 When the bias is over 2.0 V, the photocurrents linearly increase, implying that Ohmic regime occurs.

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Fig. 2 (a) Schematic diagram for measuring photocurrents of the devices under linearly polarized light of MAPbBr3 and MAPbCl3 single crystals; (b) and (c) reveal the photocurrents under various polarization angles of MAPbBr3 and MAPbCl3 single crystals respectively.

The above results show that linearly polarized light largely affected optoelectronic performances (Figs. 2(b-c)). To further study the interaction between linearly polarized light and crystal surface, the photocurrents under non-polarized light and linearly polarized light at the same power of illuminations for MAPbBr3 and MAPbCl3 single crystals were measured (Figure S2 a-b). Apparently, under the same illumination powers, linearly polarized light generates higher photocurrents than non-polarized light. Under non-polarized light, photocurrents increase linearly with the increase of voltage for MAPbBr3, whereas, for MAPbCl3, the slopes are reduced when the applied voltages are over 2.0 V. In addition to photocurrents, responsivity (R) and external quantum efficiency (EQE) are also key parameters to evaluate

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photo-detectors, and can be calculated as: I −I dark R = PC P ⋅S irra

EQE =

R ⋅ hc



(1)

(2)

where IPC and Idark are illumination and dark photocurrents, respectively. Pirra is irradiation power density, S is effective area, c is the light speed of and λ is the wavelength of illumination.27

Fig. 3 (a-b) Responsivities and EQEs under linearly polarized light for MAPbBr3 and MAPbCl3 single crystals respectively.

The R and EQE values for non-polarized lights are displayed in Figure S3. Under the same illumination power densities, both R and EQE values under linearly polarized light are much higher than those under non-polarized light. For MAPbBr3 single crystal, under the non-polarized irradiation power density of 3.3 mW/cm2, the highest R and EQE values are 5.23 mA/W and 16.2%, respectively. However, under the same irradiation power density of linearly polarized light, the highest R and EQE are respectively 9.03 mA/W and 28.5%. These phenomena remarkably demonstrate

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that linearly polarized light is beneficial to optoelectronic performances and light harvesting capability. For MAPbCl3 single crystal, the similar increasing trend also proves that linearly polarized light causes more photons as photo-detectors.

Fig. 4 (a-b) Imaginary parts of the dielectric function with various polarized lights

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for MAPbBr3 and MAPbCl3 single crystals; (c-d) Band structures and decomposed charge density maps corresponding to VBM and CBM of MAPbBr3 and MAPbCl3 single crystals.

The crystal surface anisotropy induced optoelectronic anisotropy could be the reason for the interaction between linearly polarized light and crystal surface. It is believed that two important factors co-determine the optoelectronic anisotropy under linearly polarized light. The first is the linearly polarized light absorption, which is related to the imaginary part of the dielectric functions.28 Figs. 4(a-b) display the imaginary parts of the dielectric functions with various polarized directions of MAPbBr3 and MAPbCl3 single crystals. It is obvious that the optical absorptions show different features. For MAPbCl3 single crystal, the optical absorptions for both 30° and 90° are lower than the unpolarized results below 389 nm. However, we can gain more information from the absorption around 405 nm and the absorption threshold. The inset in Fig. 4 gives evidence that the optical absorptions for both 30° and 90° are higher than those of 0° and 150°, suggesting that both (100) faces of MAPbBr3 and MAPbCl3 single crystals are prone to absorb 30° and 90° polarized light. The result is consistent with the experimental result mentioned above. However, the optical absorption over 400 nm for 90° polarized light is higher than that for 30° polarized light, indicating that 90° polarized light is more suitable for photo-detector. Secondly, the electronic property, is also believed to largely determine the optoelectronic property.29 In order to further clarify the influence of crystal structure

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of (100) face on optoelectronic anisotropy, the band structure and charge density maps corresponding to VBM and CBM were calculated (Figs. 4(c-d)). The smaller calculated band gap (2.095 eV for MAPbBr3 and 2.803 eV for MAPbCl3) is attributed to the exchange and correlation potential of GGA. Although the crystal structure of MAPbBr3 and MAPbCl3 are cubic, the charge densities for (100) planes present anisotropic features. The electron densities along the defined 0° and 90° are not as the same, which is attributed to the random distributions of CH3NH3+ groups in the crystal lattices.30 The optical absorption anisotropy and diversified charge densities in (100) planes bring diversities of light absorption, electron-hole pairs generation, charge transfer and recombination after photoexcitation.31 The anisotropic optoelectronic performances of MAPbBr3 and MAPbCl3 single crystals under linearly polarized lights, might help evoke further investigations on anisotropic properties of perovskite materials.

4. CONCLUSIONS In summary, the optoelectronic anisotropy related to crystal orientation within a plane was investigated with single crystals of MAPbBr3 and MAPbCl3 based on planar MSM photo-detectors. Under different linearly polarized lights, photocurrents, responsivity and EQE displayed optoelectronic anisotropy. Our experimental results revealed that linearly polarized lights triggered higher photocurrents, responsivity and EQE than non-polarized lights. The calculated band structure and charge density maps corresponding to VBM and CBM of single crystals of MAPbBr3 and MAPbCl3

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under polarized lights were used to interpret the optoelectronic anisotropy. Such strong anisotropic photoelectric properties related to crystal orientations within a plane should be taken into consideration for further research on planar perovskite photo-detectors.

ASSOCIATED CONTENT Supporting Information The supporting information is available free of charge via http://pubs.acs.org. The Powder X-ray diffraction patterns of MAPbBr3 and MAPbCl3, photoelectric performances of MAPbBr3 and MAPbCl3 single crystal based devices under unpolarized light, responsivities and EQE under unpolarized lights for MAPbBr3 and MAPbCl3 single crystals.

AUTHOR INFORMATION Corresponding Authors *

E-mail: [email protected] (J. X. Ding), Tel +86(532) 80691739

E-mail: [email protected] (T. L. Zhou), Tel +86 (532) 80691739 Notes The authors declare no competing financial interest.

ACKNOWLEDGEMENTS This work was financially supported by Natural Science Foundation of Shandong

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Province (ZR2016EMQ10), National Natural Science Foundation of China (No. 51202131), SDUST Research Fund and Joint Innovative Center for Safe and Effective Mining Technology and Equipment of Coal Resources, Shandong Province (No. 2014JQJH102), Major Fundamental Research of Shandong Province, China (ZR2017ZB0318) and Distinguished Taishan Scholars in Climbing Plan (No. tspd20161006).

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Photocurrent in the Bi2Te3 Topological Insulator Film for Multifunctional Photodetection. Sci. Rep. 2015, 5, 14184. (19) Maculan, G.; Sheikh, A. D.; Abdelhady, A. L.; Saidaminov, M. I.; Haque, M. A.; Murali, B.; Alarousu, E.; Mohammed, O. F.; Wu, T.; Bakr, O. M. CH3NH3PbCl3 Single

Crystals:

Inverse

Temperature

Crystallization

and

Visible-Blind

UV-Photodetector. J. Phys. Chem. Lett. 2015, 6, 3781-3786. (20) Ding, J. X.; Zhao, Y.; Du, S. J.; Sun, Y. S.; Cui, H. Z.; Zhan, X. Y.; Cheng, X. H.; Jing, L. Controlled Growth of MAPbBr3 Single Crystal: Understanding the Growth Morphologies of Vicinal Hillocks on (100) Facet to Form Perfect Cubes. J. Mater. Sci. 2017, 52, 7907-7916. (21) Liu, Y.; Yang, Z.; Cui, D.; Ren, X.; Sun, J.; Liu, X.; Zhang, J.; Wei, Q.; Fan, H.; Yu, F.; Zhang, X.; Zhao, C.; Liu, S. Two-Inch-Sized Perovskite CH3NH3PbX3 (X=Cl, Br, I) Crystals: Growth and Characterization. Adv. Mater. 2015, 27, 5176-5183. (22) Murali, B.; Yengel, E.; Yang, C.; Peng, W.; Alarousu, E.; Bakr, O. M.; Mohammed, O. F. The Surface of Hybrid Perovskite Crystals: A Boon or Bane. ACS Energy Lett. 2017, 2, 846-856. (23) Murali, B.; Dey, S.; Abdelhady, A. L.; Peng, W.; Alarousu, E.; Kirmani, A. R.; Cho, N.; Sarmah, S. P.; Parida, M. R.; Saidaminov, M. I.; Zhumekenov, A. A.; Sun, J.; Alias, M. S.; Yengel, E.; Ooi, B. S.; Amassian, A.; Bakr, O. M.; Mohammed, O. F. Surface Restructuring of Hybrid Perovskite Crystals. ACS Energy Lett. 2016, 1, 1119-1126. (24) Fang, H. H.; Adjokatse, S.; Wei, H.; Yang, J.; Blake, G. R.; Huang, J.; Even, J.; Loi, M.

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A. Ultrahigh Sensitivity of Methylammonium Lead Tribromide Perovskite Single Crystals to Environmental Gases. Sci. Adv. 2016, 2, e1600534. (25) Grancini, G.; Kandada, A. R. S.; Frost, J. M.; Barker, A. J.; Bastiani, M. D.; Gandini, M.; Marras, S.; Lanzani, G.; Walsh, A.; Petrozza, A. Role of Microstructure in the Electron-Hole Interaction of Hybrid Lead Halide Perovskites. Nat. Photon. 2015, 9, 695-701. (26) Werner, J. H. Schottky Barrier and pn-Junction I/V Plots- Small Signal Evaluation. Appl. Phys. A, 1988, 47, 291-300. (27) Lian, Z.; Yan, Q.; Lv, Q.; Wang, Y.; Liu, L.; Zhang, L.; Pan, S.; Li, Q.; Wang, L.; Sun, J. High-Performance Planar-Type Photodetector on (100) Facet of MAPbI3 Single Crystal. Sci. Rep. 2015, 5, 16563. (28) Luo, K.; Yuan, X.; Zhao, Z.; Yu, D.; Xu, B.; Liu, Z.; Tian, Y.; Gao, G.; He, J. New Hexagonal Boron Nitride Polytypes with Triple-Layer Periodicity. J. Appl. Phys. 2017, 121, 165102. (29) Wei, L.; Fan, W.; Li, Y.; Zhao, X.; Yang, L. Effect of Cation Ordering on the Electronic and Lattice Dynamic Properties of Ag2CdGeS4 Polytypes: First-Principle Calculation. J. Solid State Chem. 2013, 201, 48-55. (30) Selig, O.; Sadhanala, A.; Müller, C.; Lovrincic, R.; Chen, Z.; Rezus, Y. L. A.; Frost, J. M.; Jansen, T. L. C.; Bakulin, A. A. Organic Cation Rotation and Immobilization in Pure and Mixed Methylammonium Lead-Halide Perovskites. J. Am. Chem. Soc. 2017, 139, 4068-4074. (31) Huang, J.; Yuan, Y.; Shao, Y.; Yan, Y. Understanding the Physical Properties of

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Hybrid Perovskites for Photovoltaic Applications. Nat. Rev. Mater. 2017, 2, 17042.

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Figure Captions Fig. 1 (a-b) Planar XRD patterns of cubic MAPbBr3 and MAPbCl3 single crystals (inset were the grown single crystals); (c-d) Absorptions and optical band gaps of MAPbBr3 and MAPbCl3 single crystals, respectively. Fig. 2 (a) Schematic diagram for measuring photocurrents of the devices under linearly polarized light of MAPbBr3 and MAPbCl3 single crystals; (b) and (c) reveal the photocurrents under various polarization angles of MAPbBr3 and MAPbCl3 single crystals respectively. Fig. 3 (a-b) Responsivities and EQEs under linearly polarized light for MAPbBr3 and MAPbCl3 single crystals respectively. Fig. 4 (a-b) Imaginary parts of the dielectric function with various polarized lights for MAPbBr3 and MAPbCl3 single crystals; (c-d) Band structures and decomposed charge density maps corresponding to VBM and CBM of MAPbBr3 and MAPbCl3 single crystals.

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Fig. 1 (a-b) Planar XRD patterns of cubic MAPbBr3 and MAPbCl3 single crystals (inset were the grown single crystals); (c-d) Absorptions and optical band gaps of MAPbBr3 and MAPbCl3 single crystals, respectively.

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Fig. 2 (a) Schematic diagram for measuring photocurrents of the devices under linearly polarized light of MAPbBr3 and MAPbCl3 single crystals; (b) and (c) reveal the photocurrents under various polarization angles of MAPbBr3 and MAPbCl3 single crystals respectively.

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Fig. 3 (a-b) Responsivities and EQEs under linearly polarized light for MAPbBr3 and MAPbCl3 single crystals respectively.

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Fig. 4 (a-b) Imaginary parts of the dielectric function with various polarized lights for MAPbBr3 and MAPbCl3 single crystals; (c-d) Band structures and decomposed charge density maps corresponding to VBM and CBM of MAPbBr3 and MAPbCl3 single crystals.

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