Band-Gap Tuning of Organic–Inorganic Hybrid Palladium Perovskite

Oct 24, 2018 - The band gaps of (CH3NH3)2PdCl4, (CH3NH3)2PdCl4–xBrx, and CH3NH3PdI3 are determined to be approximately 2.15, 1.87, and 1.25 eV, ...
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Article Cite This: ACS Omega 2018, 3, 13960−13966

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Band-Gap Tuning of Organic−Inorganic Hybrid Palladium Perovskite Materials for a Near-Infrared Optoelectronics Response Huawei Zhou,* Xiaolei Cui, Cang Yuan, Jiawen Cui, Shaozhen Shi, Guohang He, Yunying Wang, Jiazhen Wei, Xipeng Pu, Wenzhi Li, Dafeng Zhang, Jie Wang, Xiaozhen Ren, Huiyan Ma, Xin Shao, Xinting Wei, Jinsheng Zhao, Xianxi Zhang, and Jie Yin* School of Chemistry and Chemical Engineering, College of Materials Science and Engineering, Shandong Provincial Key Laboratory of Chemical Energy Storage and Novel Cell Technology, Liaocheng University, Liaocheng 252059, China

ACS Omega 2018.3:13960-13966. Downloaded from pubs.acs.org by 185.223.164.92 on 10/24/18. For personal use only.

S Supporting Information *

ABSTRACT: Organic−inorganic hybrid material is a recent hot topic in the scientific community. The best band gap for the entire solar absorption spectrum is about 1.1 eV. However, the lead perovskite band gap is about 1.5 eV. Therefore, developing organic−inorganic hybrid material toward the broader light harvesting of the solar spectrum is extremely urgent. In this study, we prepare three kinds of organic−inorganic hybrid palladium perovskite materials, including (CH3NH3)2PdCl4, (CH3NH3)2PdCl4−xBrx, and CH3NH3PdI3, for an optoelectronic response. The absorption cut offs of (CH3NH3)2PdCl4, (CH3NH3)2PdCl4−xBrx, and CH3NH3PdI3 are approximately 600, 700, and 1000 nm, respectively. The band gaps of (CH3NH3)2PdCl4, (CH3NH3)2PdCl4−xBrx, and CH3NH3PdI3 are determined to be approximately 2.15, 1.87, and 1.25 eV, respectively. To the best of our knowledge, this is the first study that discusses adsorption properties and photoelectric behavior of organic−inorganic hybrid palladium perovskite materials. Interestingly, the photoelectric response of the devices based on CH3NH3PdI3 reaches 950 nm. The results will attract attention in the fields of optical recorders, optical memory, security, light capture, and light treatment.



INTRODUCTION Organic−inorganic hybrid material is a recent hot topic in the scientific community. Especially, organic−inorganic lead perovskite materials show good physical and chemical properties. They are widely used in many fields such as solar cells,1,2 photoconductivity and electroluminescence,3 light-emitting diode,4−6 field-effect transistor,7,8 and so on. The most successful study is the application of organic−inorganic lead perovskite for solar cells. Power conversion efficiency (PCE) of lead-perovskite-based solar cells is boosted to 22%.9 Their performance has still room for improvement. One important direction to improve their performance is to broaden the spectral absorption. The best band gap of a semiconductor for the entire solar absorption spectrum is about 1.1 eV. However, the lead perovskite band gap is about 1.5 eV.10 One of the strategies to broaden the spectral absorption is to make a tandem solar cell. Buonassisi group,11 Buecheler group,12 and Shen group13 carried out research on a tandem solar cell by stacking MAPbI3 perovskite and silicon solar cells. In addition, Snaith14 and Baikie15 expanded the absorption spectrum to 840 nm by replacing a methylammonium cation with a formamidinium cation. Ma16 extended absorption spectrum by replacing lead metal ions with bismuth metal ions. Multiabsorption was observed in the composite film because of the band gap difference between BiI3 and (CH3NH3)3Bi2I9 perovskite. The crystal structures of CsPdCl317 and CsPd2Cl518 © 2018 American Chemical Society

have been investigated by X-ray diffraction (XRD) methods. However, photoelectric response of the palladium perovskite materials has not been reported. In this article, we synthesize three kinds of organic− inorganic hybrid palladium perovskite materials, including (CH3NH3)2PdCl4, (CH3NH3)2PdCl4−xBrx, and CH3NH3PdI3. Among them, (CH3NH3)2PdCl4 and (CH3NH3)2PdCl4−xBrx are two-dimensional layered structures. CH3NH3PdI3 is a three-dimensional structure. The structure of CH3NH3PdI3 is very similar to that of MAPbI3. In addition, we study the spectral properties, crystal structures, nanomicrostructures, and photoelectric responses of (CH3NH3)2PdCl4, (CH3NH3)2PdCl4−xBrx, and CH3NH3PdI3.



RESULTS AND DISCUSSION (CH3NH3)2PdCl4, (CH3NH3)2PdCl4−xBrx, and CH3NH3PdI3 thin films are shown in Figure 1a. The colors of (CH3NH3)2PdCl4, (CH3NH3)2PdCl4−xBrx, and CH3NH3PdI3 thin films are pale-yellow, red-brown, and dark-brown, respectively. To determine the structures of these films, we measured the X-ray diffraction (XRD) profiles of (CH3NH3)2PdCl4, (CH3NH3)2PdCl4−xBrx, and CH3NH3PdI3 Received: August 13, 2018 Accepted: October 10, 2018 Published: October 24, 2018 13960

DOI: 10.1021/acsomega.8b02012 ACS Omega 2018, 3, 13960−13966

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Figure 1. (a) Picture of (CH3NH3)2PdCl4, (CH3NH3)2PdCl4−xBrx, and CH3NH3PdI3 thin films on the TiO2 layer. (b) XRD profiles of (CH3NH3)2PdCl4, (CH3NH3)2PdCl4−xBrx, and CH3NH3PdI3 thin films on the TiO2 layer. (c) UV−vis absorption spectra of (CH3NH3)2PdCl4, (CH3NH3)2PdCl4−xBrx, and CH3NH3PdI3 thin films. (d) Diffuse reflection spectra of (CH3NH3)2PdCl4, (CH3NH3)2PdCl4−xBrx, and CH3NH3PdI3 thin films. (e) Kubelka−Munk spectra of (CH3NH3)2PdCl4, (CH3NH3)2PdCl4−xBrx, and CH3NH3PdI3 thin films.

thin films. XRD results of (CH3NH3)2PdCl4, (CH3NH3)2PdCl4−xBrx, and CH3NH3PdI3 thin films on TiO2 are shown in Figure 1b. To determine the structural phase of the (CH3NH3)2PdCl4 thin film, a (CH3NH3)2PdCl4 single crystal was synthesized by slowly evaporating a mixed precursor of PdCl2 and CH3NH3Cl in dimethylformamide (DMF) solution. Single-crystal diffraction data were collected on a Bruker Smart CCD diffractometer with the use of Mo Kα radiation (λ = 0.71073 Å). The structures were solved by a direct method and expanded using difference Fourier techniques with the SHELXL-97 program. The single-crystal diffraction data, which revealed the two-dimensional layered structure of (CH3NH3)2PdCl4, were assigned to the orthorhombic crystal system (space group = P212121, unit cell parameters of a = 7.4417(7) Å, b = 7.7401(8) Å, c = 18.2596(18) Å, α = 90.000, β = 90.000, and γ = 90.000). A unit cell contains one molecule with the chemical formula of (CH3NH3)2PdCl4. Detailed crystal data and structural refinement for the (CH3NH3)2PdCl4 single crystals can be observed in the Supporting Information. The experimental patterns are consistent with calculated curves from single-crystal diffraction data, as shown in Figure 1b. Two diffraction peaks of (CH3NH3)2PdCl4 are observed at 8.85 and 16.39°, which are assigned to the (002) and (111) planes, respectively. Two diffraction peaks of (CH3NH3)2PdCl4−xBrx are also observed at 8.48 and 27.61°. By comparing with the XRD pattern of (CH3NH3)2PdCl4, the diffraction peak assigned to the crystal plane (002) in (CH3NH3)2PdCl4−xBrx is found to have shifted from 8.85 to 8.48°. The result indicates that the (002) lattice spacing of (CH3NH3)2PdCl4−xBrx becomes larger. This is mainly because that the Cl atoms in the unit cell are replaced by Br atoms with a larger atomic radius. The XRD pattern of CH3NH3PdI3 is shown in Figure 1b. Two obvious diffraction peaks can be clearly seen at 14.64 and 29.60°. XRD patterns of CH3NH3PdI3 are very close to those of CH3NH3PdI3. Typically, XRD patterns of CH3NH3PbI3 thin film appear at 14.12° (110) and 28.44° (220). Thus, the main diffraction

peaks of (CH3NH3)2PdCl4 at 14.64 and 29.60° can be assigned to the (110) and (220), respectively. To characterize the optical properties of (CH3NH3)2PdCl4, (CH3NH3)2PdCl4−xBrx, and CH3NH3PdI3 thin films, UV−vis absorption spectroscopy was carried out. The UV−vis absorption spectra of these thin films are shown in Figure 1c. Two absorption peaks of (CH3NH3)2PdCl4 thin film are observed at 420 and 491 nm. The absorbance of (CH3NH3)2PdCl4 thin film is decreased quickly from 420 nm. The absorption peak of (CH3NH3)2PdCl4−xBrx thin film is observed at 494 nm. The absorption intensity of (CH3NH3)2PdCl4−xBrx thin film begins to decrease at 494 nm. The hump Q peak for all three materials appearing at 490 nm may be originated from charge-transfer transition from d orbitals.19 The absorption intensity of (CH3NH3)2PdCl4−xBrx thin film (600 nm) is higher than that of (CH3NH3)2PdCl4 thin film (600 nm). The absorption peak of CH3NH3PdI3 thin film is observed at 491 nm. Absorption intensity begins to decrease at 678 nm. Amazingly, the absorption of CH3NH3PdI3 thin film is cut off at the near-infrared region (about 950 nm). To characterize the reflection properties of (CH3NH3)2PdCl4, (CH3NH3)2PdCl4−xBrx, and CH3NH3PdI3 thin films, diffuse reflection spectroscopy was carried out. Diffuse reflection spectra of these thin films are shown in Figure 1d. The reflection intensity of (CH3NH3)2PdCl4 thin film begins to increase obviously at 420 nm. The reflection intensity of (CH3NH3)2PdCl4−xBrx thin film also is increased significantly at 420 nm. The reflectivity of CH3NH3PdI3 thin film is increased from 678 nm. However, the reflectivity of CH 3 NH 3 PdI 3 thin film is weaker than those of (CH3NH3)2PdCl4 and (CH3NH3)2PdCl4−xBrx thin films in the range of 548−1000 nm. To obtain the band gaps of (CH3NH3)2PdCl4, (CH3NH3)2PdCl4−xBrx, and CH3NH3PdI3, the diffuse reflectance spectrum was converted into the Kubelka−Munk spectrum. According to the Kubelka−Munk formula, F(R) = (1 − R)2/2R, where R represents the percentage of reflection. The relationship of the incident 13961

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Figure 2. (a, b) SEM images of the surface of FTO/TiO2/(CH3NH3)2PdCl4 device. (c, d) SEM images of the surface of (CH3NH3)2PdCl4−xBrx device. (e, f) SEM images of the surface of FTO/TiO2/CH3NH3PdI3 device.

Figure 3. (a) SEM image of the surface of FTO/TiO2/CH3NH3PdI3 device. (b) Distribution of carbon. (c) Distribution of nitrogen. (d) Distribution of chlorine. (e) Distribution of iodine. (f) Distribution of palladium. (g, h) Elemental content of CH3NH3PdI3 by spot mode in SEMEDX.

photon energy (hν) and Eg can be expressed as the transformed Kubelka−Munk, [F(R)·hν]p = A (hv − Eg), where Eg is the band-gap energy, A is the absorption constant, h is Planck’s constant, ν is the frequency of the light (S−1), and P is the power index that is related to the optical absorption process. Theoretically, P equals to 1/2 or 2 for an indirect or a direct allowed transition, respectively. (CH3NH3)2PdCl4, (CH3NH3)2PdCl4−xBrx, and CH3NH3PdI3 can be regarded as a direct allowed transition. The band gaps of (CH3NH3)2PdCl4, (CH3NH3)2PdCl4−xBrx, and CH3NH3PdI3 are shown in Figure 1e. The band gap of (CH3NH3)2PdCl4 is 2.15 eV, which is consistent with the results in the literature.20 The band gap of (CH3NH3)2PdCl4−xBrx is 1.87 eV, which is smaller than that of (CH3NH3)2PdCl4. The band gap of CH3NH3PdI3 is 1.25 eV, which is smaller than those of (CH3NH3)2PdCl4 and (CH3NH3)2PdCl4−xBrx.

To study the morphologies of (CH 3 NH 3 ) 2 PdCl 4 , (CH3NH3)2PdCl4−xBrx, and CH3NH3PdI3 thin films, we carried out scanning electron microscopy (SEM) analysis. The results are shown in Figure 2. The SEM images of the surface of FTO/TiO2/(CH3NH3)2PdCl4 device are shown in Figure 2a,b. We can see that (CH3NH3)2PdCl4 is a twodimensional layered structure. The horizontal size of twodimensional (CH3NH3)2PdCl4 is about 2 μm. The SEM images of the surface of FTO/TiO2/(CH3NH3)2PdCl4−xBrx device are shown in Figure 2c,d. It can be clearly observed that the coverage of (CH3NH3)2PdCl4−xBrx thin film on the TiO2 thin film is not good and the distribution is not uniform. The inferior quality of (CH3NH3)2PdCl4−xBrx thin film will result in a relatively poor photoelectrical response. The highmagnification SEM image of the surface of (CH3NH3)2PdCl4−xBrx is shown in Figure 2d. The SEM 13962

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Figure 4. (a, b) SEM images of the cross section of the FTO/TiO2/CH3NH3PdI3 device. (c) Photocurrent density on/off curves of (CH3NH3)2PdCl4, (CH3NH3)2PdCl4−xBrx, and CH3NH3PdI3 under a standard solar simulator (100 mW cm−2) with an AM 1.5G filter.

Figure 5. (a−c) Photocurrent-density on/off curves of the devices based on (CH3NH3)2PdCl4, (CH3NH3)2PdCl4−xBrx, and CH3NH3PdI3 at different wavelengths. (d) Magnified graph of the dashed part of (c). 13963

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devices based on (CH3NH3)2PdCl4, (CH3NH3)2PdCl4−xBrx, and CH3NH3PdI3 thin films at different wavelengths. The chopper frequency of monochromatic light is 1.33 Hz. The photocurrent-density on/off curves of (CH3NH3)2PdCl4 device at different wavelengths are shown in Figure 5a. The on/off curve of the photocurrent density does not show periodic changes under 300, 400, and 500 nm monochromatic light. Also, the contrast between Jon (current density under irradiation) and Joff (current density under the dark) is not obvious. Some periodic changes are observed in the photocurrent-density on/off curves when irradiated with monochromatic light of 330 nm. However, the periodic change is not very strong. The photocurrent-density on/off curves of the devices based on(CH3NH3)2PdCl4−xBrx at different wavelengths are shown in Figure 5b. The on/off curve of the photocurrent density does not exhibit a periodic change when irradiated with monochromatic light at 300, 400, 500, and 800 nm. Compared with that of (CH3NH3)2PdCl4 devices, a strong periodic change in the photocurrent-density on/off curve is observed when irradiated with 330 nm monochromatic light. The photocurrent-density on/off curves of the devices based on CH3NH3PdI3 at different wavelengths are shown in Figure 5c. Figure 5d is a magnified graph of the dashed part of Figure 5c. Compared with that of (CH 3 NH 3 ) 2 PdCl 4 and (CH3NH3)2PdCl4−xBrx, the photocurrent-density on/off curve of the devices based on CH3NH3PdI3 has a strong periodic change when irradiated with 330 nm monochromatic light. Also, the contrast between Jon and Joff is most obvious. Figure 5c shows that the photocurrent-density on/off curve has a strong periodic change when irradiated with 300, 600, 800, and 900 nm monochromatic light. Compared with the on/off signal at 300 nm, on/off signals at 600, 800, and 900 nm are relatively large. The on/off curve at 950 nm photocurrent still has a periodic change, but the periodic variation is weak. This periodic change disappears beyond 1000 nm. Generally, the photoelectric response is up to about 800 nm for MAPbI3 perovskite. Interestingly, the photoelectric response of the devices based on CH3NH3PdI3 reaches 950 nm. Light harvesting of the solar spectrum based on CH3NH3PdI3 is wider than those of (CH3NH3)2PdCl4 and (CH3NH3)2PdCl4−xBrx. Therefore, CH3NH3PdI3 can be used as a near-infrared absorption material in the fields of optical recorders, optical memory, security, light capture, and light treatment.

images of the surface of FTO/TiO2/CH3NH3PdI3 device are shown in Figure 2e,f. The morphology of CH3NH3PdI3 is similar to a semicircular sphere assembled by a large number of small particles. Its diameter is between 1 and 2 μm. To determine the elemental distribution of CH3NH3PdI3 thin film, we conducted elemental mapping analysis by SEMenergy-dispersive X-ray (EDX). The SEM image of the surface of FTO/TiO2/CH3NH3PdI3 device is shown in Figure 3a. The blue-green area in Figure 3b is the surface distribution of carbon. Compared with that in Figure 3a, carbon is mainly distributed in the area where CH3NH3PdI3 is present. However, other areas also have some carbon. This may be because that the CH3NH3PdI3 thin film adsorbs carbon dioxide in the air. The dark-red area in Figure 3c is the surface distribution of nitrogen. The bright-green area in Figure 3d is the distribution of chlorine. A very small amount of chlorine is present on the surface of CH3NH3PdI3 because of the presence of chlorine in the raw materials we used. The bright-yellow area in Figure 3e is the distribution of iodine. Iodine is distributed in the area where CH3NH3PdI3 is present. The bright-purple area in Figure 3f is the distribution of palladium. The distribution of palladium is almost the same as the distribution of iodine. To determine the elemental composition of CH3NH3PdI3, we performed SEM-EDX in spot mode. The results are shown in Figure 3g,h. CH3NH3PdI3 obviously contains C, N, Pd, and I elements. The atomic ratio of C, N, Pd, and I is 2:5:1:3. The number of Pd and I atoms matches the formula of CH3NH3PdI3. However, the number of C and N atoms is higher than that in the formula of CH3NH3PdI3. It may be because the N2 and CO2 in the air were adsorbed on the surface of the CH3NH3PdI3 thin film during the measurement. To analyze the thickness of each layer of the FTO/TiO2/CH3NH3PdI3 device and the uniformity of the film, we recorded the SEM image of the cross section of the FTO/TiO2/CH3NH3PdI3 device. The SEM images are shown in Figure 4a,b. CH3NH3PdI3 thin film is uniformly covered on the TiO2 film. The thickness of the CH3NH3PdI3 thin film is from 667 to 906 nm. In addition, CH3NH3PdI3 diffused into the porous TiO2 films, which is favorable for an interface electron transfer. The thickness of dense TiO2 film is 68 nm. The thickness of the porous TiO2 film is 218 nm. To compare the photoelectric responses of the devices based on (CH 3 NH 3 ) 2 PdCl 4 , (CH 3 NH 3 ) 2 PdCl 4 − x Br x , and CH3NH3PdI3 , the on/off curves of (CH3 NH3)2 PdCl4, (CH3NH3)2PdCl4−xBrx, and CH3NH3PdI3 under AM 1.5, 100 mW cm−2 simulated illumination were compared, as shown in Figure 4c. The photocurrent density of the device based on (CH3NH3)2PdCl4 thin film is slowly increased with the increase in light time exposure, and without the light, it is slowly reduced with the increasing time. This phenomenon indicates that the device based on (CH3NH3)2PdCl4 thin film is sensitive to light. The photocurrent density of (CH3NH3)2PdCl4−xBrx thin film is weak. The reason may be that the coverage of (CH3NH3)2PdCl4−xBrx thin film on the TiO2 thin film is not good, as shown in Figure 2c. The photocurrent density of the device based on CH3NH3PdI3 thin film is increased rapidly under the light irradiation. Without the light, the photocurrent density is decreased rapidly with the increasing time. This phenomenon indicates that the CH 3 NH 3 PdI 3 thin film is more photosensitive than (CH3NH3)2PdCl4 and (CH3NH3)2PdCl4−xBrx. To investigate the monochromatic photoresponses of the devices, we examined the photocurrent responses of the



CONCLUSIONS We synthesize organic-−inorganic palladium perovskite materials (CH3NH3)2PdCl4, (CH3NH3)2PdCl4−xBrx, and CH3 NH3 PdI 3 , whose spectral absorption cut offs are approximately 600, 700, and 1000 nm, respectively. The photoelectric response of the devices based on CH3NH3PdI3 reaches the near-infrared region. Although palladium perovskite materials have a good band gap, and near-infrared and strong photoelectric response, they are expensive. Therefore, we are studying perovskite materials with reduced content of palladium by mixing with other metals.



EXPERIMENTAL SECTION

Growth of (CH3NH3)2PdCl4 Single Crystals. 202.5 mg of CH3NH3Cl and 177 mg of PdCl2 were dissolved in 1 mL of DMF solution. The mixed solution was heated to 80 °C and maintained at a constant temperature for 2 h using an oil bath. 13964

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Then, the above solution was transferred to an 80 °C oven. The single crystal was observed by slow solvent evaporation (from 80 to 40 °C over 4 d). Fabrication of FTO/TiO2/Organic−Inorganic Hybrid Palladium Perovskite/Carbon Electrode Devices. Glass/FTO/CTiO2/M-TiO2 were prepared following our previous procedures.21 202 mg of CH3NH3Cl, 177 mg of PdCl2; 335 mg of CH3NH3Br, 177 mg of PdCl2; and 477 mg of CH3NH3I, 177 mg of PdCl2 were added into three glass vial, respectively. DMF (1 mL) was added to each vial. The vials were placed on a hot plate to heat the solutions (the temperature of the hot plate was set to 80 °C). After heating for 10 min, a clean and dry magnet was added to each vial for magnetic stirring. Finally, the solution in the vial was filtered with a filter head. The mixed solution was spin-coated on Glass/FTO/C-TiO2/ M-TiO2. Then, FTO/TiO2/organic−inorganic hybrid palladium perovskite materials were placed on a hot plate (80 °C) and heated for 30 min. Carbon electrodes were prepared following our previous procedures.17 Nanostructures of the film were analyzed by scanning electron microscopy (SEM, Hitachi SEM S-4800). UV−vis absorption spectra and diffuse reflectance spectra were recorded using a UV−vis−NIR spectrometer (PerkinElmer, λ, 750S). The photocurrent−time performance was measured using an electrochemical workstation system (CHI760, Chenhua, and Shanghai) and a solar simulator (IV5, PV Measurements, Inc.). The photocurrent−time performance with monochromatic light was measured by an electrochemical workstation system (CHI760, Chenhua, and Shanghai) and measurement system of the incident photon to current conversion efficiency (IPCE) (QEX10, PV Measurements, Inc.). Powder XRD profiles were measured using PANalyticalX́ Pert diffractometer (Cu Kα radiation at λ = 1.54 Å) sampling at 2°/min, 40 ekV, and 100 mA. Single-crystal X-ray diffraction profiles were measured on a Bruker SMART CCD diffractometer with the use of Mo Kα radiation (λ = 0.71073 Å).



Notes

The authors declare no competing financial interest.



ACKNOWLEDGMENTS This work was financially supported by Shandong Province Natural Science Foundation (Grant nos. ZR2016BQ20, BS2015NJ013, ZR2014BQ010, and ZR2016BQ21), Colleges and Universities in Shandong Province Science and Technology Projects (Grant nos. J16LC05 and J17KA097), Science and Technology Innovation Foundation for the University or College Students (Grant no. 26312160502), National Science and Technology Innovation Foundation for the University or College Students (Grant no. 201510447021), Research Fund for the Doctoral Program of Liaocheng University (Grant no. 31805), National Natural Science Foundation of China (Grant nos. 21503104, 21601078, and 21401095), and National Basic Research Program of China (Grant no. 2011CBA00701).



ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acsomega.8b02012.



REFERENCES

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Unit cell of (CH3NH3)2PdCl4; crystal data and structure refinement of (CH3NH3)2PdCl4; atomic coordinates (×104) and equivalent isotropic displacement parameters (A2 × 103) of (CH3NH3)2PdCl4. U(eq) is defined as one-third of the trace of the orthogonalized Uij tensor; bond lengths (A) and angles (deg) for (CH3NH3)2PdCl4; anisotropic displacement parameters (A2 × 103) of (CH3NH3)2PdCl4. The anisotropic displacement factor exponent takes the form: −2pi2 [h2a*2U11 + ... + 2hka*b*U12] (PDF)

AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected] (H.Z.). *E-mail: [email protected] (J.Y.). ORCID

Huawei Zhou: 0000-0002-9428-5400 Xipeng Pu: 0000-0002-8225-5706 13965

DOI: 10.1021/acsomega.8b02012 ACS Omega 2018, 3, 13960−13966

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DOI: 10.1021/acsomega.8b02012 ACS Omega 2018, 3, 13960−13966