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Inorganic and lead-free AgBiI4 rudorffite for stable solar cell applications Chaojie Lu, Jing Zhang, Hongrui Sun, Dagang Hou, Xinlei Gan, MingHui Shang, Yuanyuan Li, Ziyang Hu, Yuejin Zhu, and Liyuan Han ACS Appl. Energy Mater., Just Accepted Manuscript • DOI: 10.1021/acsaem.8b01202 • Publication Date (Web): 24 Aug 2018 Downloaded from http://pubs.acs.org on August 26, 2018
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Inorganic and Lead-Free AgBiI4 Rudorffite for Stable Solar Cell Applications Chaojie Lu1, Jing Zhang1,*, Hongrui Sun1, Dagang Hou1, Xinlei Gan1, Ming-hui Shang2, Yuanyuan Li3, Ziyang Hu1, Yuejin Zhu1,* and Liyuan Han4,* 1
Department of Microelectronic Science and Engineering, Ningbo University, Zhejiang, 315211,
China. 2
School of Materials Science and Engineering, Ningbo University of Technology, Zhejiang,
315016, China. 3
Department of Applied Physics, School of Physics and Electronics, Hunan University, Hunan,
410082, China. 4
Photovoltaics Materials Unit, National Institute for Materials Science, Tsukuba, Ibaraki, 305-
0047, Japan.
Corresponding author *Jing Zhang, E-mail:
[email protected]. *Yuejin Zhu, E-mail:
[email protected]. *Liyuan Han, E-mail:
[email protected]. 1
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ABSTRACT
Organic-inorganic hybrid lead halide perovskites have recently realized significant development. However, the toxicity of lead (Pb) and the poor stability might eventually hamper the commercialization of perovskite solar cells (PSCs). Here, we present an environment friendly and stable all inorganic rudorffite AgBiI4 as solar absorber by solution-based synthesis of thinfilms. AgBiI4 films fabricated by 0.6 M solution and annealed at 150℃ show dense grains and high surface coverage. Furthermore, the AgBiI4 films exhibit greater thermal stability and photostability than CH3NH3PbI3. Ultimately, by judiciously choosing the hole transport material with appropriate energy level, the solar cell device demonstrates high carrier extraction efficiency and achieve a power conversion efficiency (PCE) of 2.1% under standard 1sun (AM 1.5). The devices also show excellent long-term air stability and still maintain 96% of its initial PCE even after 1000h at relative humidity of 26%. This work highlights new directions for further exploration of Pb-free and stable solar cells.
KEYWORDS
AgBiI4, Pb-free material, photostability, long-term air stability, solar cells
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Organic-inorganic hybrid perovskites have aroused widespread attention as promising absorbers in photovoltaic devices due to their excellent photoelectrical properties1-3. The PCE of perovskite solar cells have rapidly increased up to 22.7% within only a few years4,5. Unfortunately, the toxic Pb in lead hybrid perovskites and the low stability of perovskites against moisture, light and temperature hinder the commercial applications of this new technology6,7. Consequently, it is absolutely necessary to further explore non or low-toxicity and stable light absorbing material to promote the commercial applications of the photovoltaic technology8. Recently, many studies have been devoted to research on lead-free material to solve the toxicity issue9. As a member of IVA group elements as Pb, tin (Sn) and germanium (Ge) have been explored to replace Pb and the PSCs based on Sn show a PCE of 7%10. However, the perovskites based on Sn or Ge still have an extremely inferior stability due to the easy oxidation of Sn2+ to Sn4+, Ge2+ to Ge4+ when exposed to ambient air, limiting their popularization11. Meanwhile, Bismuth (Bi), a VA group element adjacent to Pb, has also been studied as a replaceable element of Pb to form Pb-free and much more stable perovskites such as A3Bi2I9 (A = CH3NH3, Rb, Cs, NH4 X = Br, Cl) and (CH3NH3)3Bi2I9-based solar cells with an efficiency of 1.64% have been reported12. However, layer structured A3Bi2I9 shows large band gaps (Eg > 2.1 eV) and poor surface morphology of the films which might lead to the low PCE12. Furthermore, all inorganic double perovskites Cs2AgBiBr6 (2.19 eV) and Cs2AgBiCl6 (2.77 eV) with larger band gaps have been reported, which are also not suitable for light absorbing material in solar cells13. Recently, layer-structured (two-dimensional) BiI3 with smaller band gap of 1.8 eV has also been considered as light absorbing material14. However, BiI3-based solar cells exhibit the PCE of less than 0.5%15. Researches show that the three-dimensional (3D) materials have greater 3
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semiconducting properties than the two-dimensional (2D) materials16. Therefore, the transition metal monovalent element silver (Ag) cation is introduced into close-packed iodide sublattice to increase the dimension of iodobismuthates, improving the PCE of the device17. For instance, AgBi-I ternary family exhibits edge-shared [AgI6] and [BiI6] octahedra 3D structure which named rudorffites18. Ag3BiI618, Ag2BiI519, AgBi2I720 with the PCE of 4.3%, 2.1% and 1.22% respectively have been reported in solar cells and show an excellent stability, which have attracted significant attention in the search for stable and Pb-free light absorbing material. Here, we explore AgBiI4, a member of Ag-Bi-I family, as a Pb-free light absorbing material by solution-based synthesis of thin-films and assembling in mesoporous solar cell devices for the first time. A dense and smooth AgBiI4 thin-film is obtained by using anti-solvent treatment during spin-coating and subsequent annealing. The material exhibits a low Eg of 1.86 eV and relatively wide absorption spectrum compared with Bi based double perovskite Cs2AgBiX6 and layer structure A3Bi2I9, suggesting that it is more suitable for light absorption. Importantly, AgBiI4 shows strong thermal stability and photostability. We also study AgBiI4 solar cells with appropriate hole transport material which achieve 2.1% performance (AM1.5, 1sun) and longterm air stability. To check the crystalline property of AgBiI4, we show the X-ray diffraction (XRD) pattern of AgBiI4 film on glass (Figure 1a), and the main dominant diffraction peaks at 2θ = 12.85°, 29.28°, and 41.65° are assigned to the crystallographic planes (111), (400), and (440) of AgBiI4 cubic-phase, respectively. It is obvious that the experimental XRD result is consistent with XRD simulation results using the AgBiI4 structure reported by Oldag et al21, indicating that AgBiI4 films are cubic defect spinel structure and have the space group of with the lattice parameters of 4
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a =12.222 Å, similar to the cubic structure of the AgBi2I7 films20. The crystal structure of AgBiI4 is showed in Figure 1b. The structure is cubic close packed iodide lattice, but edge-sharing octahedra are occupied by Ag+ and Bi3+ cations, giving rise to an extended 3D network where tetrahedral sites are entirely vacant22.
Figure 1. (a) The experimental and simulated XRD pattern of AgBiI4 film. (b) AgBiI4 crystal structure. (c) The XRD of AgBiI4 films made by different solution concentrations and annealed at 150℃. (d) The XRD of 0.6 M AgBiI4 films at 130℃, 150℃ and 180℃ annealing on glass.
The large grain size and high surface coverage of solution prepared absorber thin films are beneficial for solar cells. The large grains could facilitate charge transport by reducing the 5
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number of defects and trap states23; while the full coverage of the films can eliminate the detrimental cracks and pinholes which might lead to low shunt resistance or even worse, shorted cells24. The crystalline growth mechanism determines the film quality of AgBiI4. Nucleation and further growth obeying the Oswald-ripening mechanism are important for film growth25. The solution concentration and annealing temperature are two important factors governing the nucleation and Oswald-ripening process. Thus, it is valuable to explore the solution concentration and annealing temperature for high quality film growth. Firstly, concentration of precursor solution is varied and we use the XRD to check the phase purity and the grain size of the absorber thin film. The XRD patterns of AgBiI4 films made by different solution concentrations at 150℃ annealing are shown in Figure 1c. We find that the AgBiI4 films all form the cubic-phase. Furthermore, a distinct change can be observed in Figure 1c with increasing the concentration of the AgBiI4 precursor solution. The intensity of main diffraction peaks achieves the strongest at 0.6 M compared with other concentration, indicating the 0.6 M solution fabricated AgBiI4 films have the highest crystallinity property. Then, the grain size is calculated by the full-width-at-half-maximum (FWHM) of diffraction peaks (Table S1). The grain size of 0.6 M AgBiI4 is 66 nm which is the biggest than the grain size of 0.4 M AgBiI4 (61 nm) and 0.8 M AgBiI4 (47 nm), which facilitates the full coverage of the films and high crystallization. In addition, it is noteworthy that small shoulder peaks appear near the (440) peaks at 0.4 M and 0.8 M AgBiI4 films, which are attributed to (110) and (108) facets of the Ag2BiI5 crystal, respectively26. We assume the Ag2BiI5 hexagonal impurity crystals are formed aside from the AgBiI4 when the nucleation is from undersaturate (0.4 M) and supersaturate (0.8 M) solution. Similar cases have been studied in the previous report of the AgBi2I720. Secondly, the annealing temperature of the absorber thin films also plays an important role during the 6
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crystallizing process. Figure 1d shows the XRD patterns of the 0.6 M AgBiI4 films at 130℃, 150℃, 180℃ annealing, respectively. It is clear that AgBiI4 films all form the cubic-phase. Furthermore, the strongest diffraction peaks are observed when AgBiI4 film is annealed at 150℃ , indicating the best crystallization. When the annealing temperature increases to 180℃, the intensity of main diffraction peaks weaken, which is likely due to the crystallization is destroyed at higher temperature. Furthermore, the calculated grain sizes are showed in Table S1. The grain size of AgBiI4 annealed at 150℃ (66 nm) is the biggest compared to the grain size of AgBiI4 at 130℃ (53 nm) and the grain size of AgBiI4 at 180℃ (47 nm). The insets in Figure 1c and d show the color images of the six films, revealing the different light-absorbing properties which will be discussed below. In order to further explore the crystalline properties of AgBiI4 films, the surface morphologies of AgBiI4 films are visually showed by the scanning electron microscopy (SEM) in Figure 2. The Figure 2 (a-c) shows different solution concentration fabricated AgBiI4 films. It is evident that higher surface coverage is obtained at 0.6 M AgBiI4. However, there are some pinholes and vacancies in 0.4 M and 0.8 M AgBiI4 films, resulting in the poor crystallization morphologies. The crystalline size is also the biggest in 0.6 M solution fabricated film, which is consistent with the XRD results. The images of 0.6 M AgBiI4 films at 130℃, 150℃ and 180℃ annealing temperature are shown in Figure 2 (d-f). We find that some vacancies are formed at 130℃ annealing. The AgBiI4 film annealed at 150℃ exhibits a pinhole-free surface with fully grown big grains. At a higher temperature of 180℃, much more vacancies are observed, indicating the higher temperature might give rise to the damaged surface and the poor crystallization 7
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morphologies. The same conclusion is verified with the XRD. Therefore, the 0.6 M AgBiI4 films annealed at 150℃ exhibit the highest crystallinity and surface coverage. Furthermore, the energy dispersive spectroscopy (EDS) mappings of 0.6 M AgBiI4 film annealed at 150℃ are showed in Figure 2 (g-i), it is observed that Ag, Bi and I elements are evenly distributed throughout the films.
Figure 2. Top-view SEM images of the 0.4 M (a), 0.6 M (b), 0.8 M (c) AgBiI4 films on mesoporous TiO2 annealed at 150℃ and the SEM images of 0.6 M AgBiI4 at 130℃ (d), 150℃ (e) and 180℃ (f) annealing, respectively. EDS elemental maps of Ag (g), Bi (h) and I (i) in 0.6 M AgBiI4 annealed at 150℃. 8
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Time(ns)
Figure 3. (a) The absorption spectra of 0.6 M AgBiI4 at 130℃, 150℃ and 180℃ annealing on glass. (b) absorption spectra of the 0.4 M, 0.6 M and 0.8 M AgBiI4 films annealed at 150℃. (c) Time-resolved PL decay curves on glass and (d) the absorption spectra of the 0.8 M AgBiI4 film annealed at 150℃ and 0.8 M CH3NH3PbI3 film annealed at 100℃.
Figure 3a shows the UV-visible absorption spectra of AgBiI4 films annealed at 130℃, 150℃ and 180℃. The AgBiI4 films annealed at 150℃ have the highest absorption, which are attributed to the increased crystallinity and improved surface coverage. The UV-visible 9
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absorption spectra of the AgBiI4 films made by different concentration are displayed in Figure 3b. The intensity of UV-visible shows a progressive enhancement with increasing the concentration of AgBiI4 solution. We ascribe the enhanced absorption to the increased shade of film color (insets of Figure 1a). Furthermore, the film thickness of absorbent layer is a crucial factor in the intensity of UV-visible spectra. 144 nm, 177 nm and 239 nm is obtained by measuring the thickness of 0.4 M, 0.6 M and 0.8 M AgBiI4 films, respectively. The 0.8 M AgBiI4 films are the thickest than other concentration, indicating the 0.8 M AgBiI4 films have the highest absorption intensity. Although the intensity of UV-visible is the highest at 0.8 M, the thick multicrystalline film might increase charge recombination. It is further verified by the timeresolved PL (TRPL) decay spectra of AgBiI4 films on glass in Figure 3c. The extracted charge lifetime τave is the average decay time. The maximum τave = 5.8 ns is obtained at 0.6 M AgBiI4 films compared to 0.4 M (τave = 3.8 ns) and 0.8 M (τave = 3.6 ns) AgBiI4 films. The long decay time means that 0.6 M AgBiI4 films have the fewest defects and nonradiative recombination. Furthermore, the UV-visible absorption spectra of the 0.8 M AgBiI4 annealed at 150℃ and CH3NH3PbI3 are showed in Figure 3d. The absorption spectrum of AgBiI4 over the range 400720 nm shows substantial absorption, suggesting the AgBiI4 is suitable for the absorption layer of solar cell. However, the overall absorption properties of AgBiI4 (the absorption range and intensity) still are inferior to the CH3NH3PbI3, which might lead to the lower performance in solar cell devices.
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Figure 4. (a) The TGA heating curve of AgBiI4, CH3NH3PbI3 and (b) BiI3. (c) CH3NH3PbI3 illuminated 1h, 2h and 3h and (d) The XRD patterns of AgBiI4, respectively. The long-term stability toward light and heat are major factors to restrict the commercial applications of solar cells and popularization at present. Firstly, the most important concern for thermal stability is the thermal decomposition of materials. The thermal behaviors of the AgBiI4 and CH3NH3PbI3 are examined by thermogravimetric analysis (TGA) in Figure 4a. For CH3NH3PbI3, the first sign of mass loss at 200℃ is due to decomposition of CH3NH3PbI3 and sublimation of CH3NH3I. When the temperature approaches to 310 ℃ , the CH3NH3PbI3 11
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undergoes 37% mass loss, which is attributed to that the CH3NH3I is totally thermal degraded into NH3 and CH3I gases27. However, when the temperature is between 310℃ and 380℃, the material mass remains constant. Keeping increasing the temperature to 680℃, we find the material mass loss is ongoing due to sublimation of PbI2. The mass loss stops when the temperature reaches 680℃. Therefore, the decomposition formula is: ∆ CH 3 NH 3 PbI 3
PbI 2 + NH 3 ↑ + CH 3 I ↑
(1)
By contrast, the TGA studies on AgBiI4 powders show the first sign of mass loss is 260℃ higher than the CH3NH3PbI3, indicating high thermal stability of AgBiI4. When the temperature approaches to 382℃, the material mass loss increases sharply. Then it increases very slowly with the temperature exceeding 382℃. Whereas up to 700℃ the mass loss is increased sharply until the material mass loss is nearly 100%. The Figure 4b shows the thermal behavior of BiI3. The first sign of mass loss is 260℃, then the mass loss increases sharply under higher temperature until the BiI3 mass loss is 100%, which is consistent with the thermal behavior of AgBiI4 before 382℃. Therefore, the result suggests the first mass loss is due to the decomposition of AgBiI4 and the sublimation of BiI3, followed by sublimation of AgI. The decomposition formula of AgBiI4 is:
∆ AgBiI 4
BiI 3 ↑ + AgI ↑
(2)
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As stated in the previous section, the CH3NH3PbI3 with unstable organic components might not overcome such thermal decomposition. The all inorganic AgBiI4 with better thermal stability might be considered as a promising compound for long term operation at elevated temperatures. Furthermore, the photostability of AgBiI4 and CH3NH3PbI3 are investigated under controlled gastight conditions (in a sample sack sealed under inert gas) to avoid the influence of oxygen and humidity, the sealed samples are illuminated 1h, 2h, 3h, respectively, using a solar simulator at 1000 Wm-2. It is well known that the PSCs based CH3NH3PbI3 demonstrate worse stability under illumination28. Two distinct changes can be observed in Figure 4c. Firstly, the XRD results indicate there is a PbI2 impurity peak appears when the illumination time is 1h, suggesting the CH3NH3PbI3 has decomposed. It confirms that the CH3NH3PbI3 has a worse photostability. As the illumination time increases to 2 and 3h, the diffraction peak intensity of PbI2 increases obviously, indicating the CH3NH3PbI3 is decomposing continuously. In addition, as the illumination time increases to 2 h, although the diffraction peak intensity of CH3NH3PbI3 constantly increases, representing a high crystallinity, the phase structure has been destroyed. The diffraction peak intensity of CH3NH3PbI3 begin to decrease when the illumination time increases to 3 h, indicating the crystallization has been damaged under long time irradiation. The XRD data of AgBiI4 under different irradiation time are shown in Figure 4d. Compared to the initial state, there is no new diffraction peak to appear with increasing illumination time, suggesting there is no structural degradation in AgBiI4, It demonstrates that the AgBiI4 have stronger photostability.
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Figure 5. (a) (αhѵ)2 VS hѵ and (b) the UPS spectrum of AgBiI4 and CH3NH3PbI3. By plotting (αhѵ)2 versus photon energy hѵ curve as shown in Figure 5a, the band gap of the AgBiI4 (1.86 eV) is determined by the transformed Kubelka-Munk function, which is suitable for a bismuth halide solar absorber in single junction solar cells. However, the band gap is still wider than the CH3NH3PbI3 (1.59 eV) and out of the ideal 1.1-1.5 eV range suggested by the ShockleyQueisser limit29. In order to investigate the Fermi energy (Ef) and the valence band energy (Ev) level of the AgBiI4 films, the ultraviolet photoelectron spectroscopy (UPS) spectra is shown in
Figure 5b. The Ef is -4.59 eV (under vacuum energy level) determined by the equation Ef = 21.22 eV (He I)-Ecutoff. Wherein, the cutoff energy (Ecutoff) is 16.63 eV. The value of (Ev-Ef) obtained by the linear extrapolation in low binding-energy region, leading Ev to be -5.87 eV. The conduction band energy (Ec) is estimated to be -4.01 eV by the equation Ec = Ev + Eg. Furthermore, we also calculate the Ef of CH3NH3PbI3 (-3.97 eV), the Ev and Ec of the CH3NH3PbI3 are -5.47 eV and -3.88 eV, respectively.
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Based on the obtained energy structure of AgBiI4, it is observed that valence band maximum (VBM) of -5.87 eV is much deeper compared to CH3NH3PbI3 with VBM of
-5.47 eV.
Therefore, it is necessary to utilize appropriate hole transport materials with deeper VBM in order to favor high prospective optoelectronic device performance. We further investigate solar cell performance based on well crystallized AgBiI4 (0.6 M solution and annealed at 150℃). The effect of different electron hole transporting layer (HTL) on the device performance is researched. At the beginning of the experiment, we used spiro-MeOTAD with additives such as lithium salts, 4-tertbutyl pyridine (TBP) as HTL. However, we observe obviously that the AgBiI4 thin films are corroded when the spiro-MeOTAD solution is spin-coated on. We find the additive TBP corrodes the AgBiI4 thin films after a series of comparative experiments in Figure S1. Furthermore, the similar phenomenon has been found in PSCs based on CH3NH3PbI3. There are reports confirm that TBP corrodes the CH3NH3PbI3 thin films and causes the appearance of large pits on the surface of the HTL30. Therefore, we fabricate photovoltaic device with the structure of FTO/compact (c)-TiO2/mesoporous (m)-TiO2+AgBiI4/HTL/Ag (HTL is PTAA, P3HT without TBP addition) (Figure 6a). Figure 6b shows the cross-sectional SEM image of solar cell device with the structure of FTO/c-TiO2/m-TiO2+AgBiI4/PTAA/Ag, which shows that all of the thin films are well layered.
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Glass
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Figure 6. (a) Schematic view and (b) the cross-sectional SEM image of solar cell device with the structure of FTO/ c-TiO2/m-TiO2+AgBiI4/PTAA/Ag. (c) The current density-voltage (J-V) curves of PTAA-based and P3HT-based solar cell device, and the insets show the performance parameters. (d) The TRPL spectra of the AgBiI4 on P3HT and PTAA. (e) Energy level diagrams of solar cell based on AgBiI4. (f) The device PCE without any encapsulation at relative humidity of 26%.
Figure 6c shows the current density-voltage (J-V) curves of PTAA and P3HT-based solar cell devices tested under standard 1sun (AM 1.5), and the performance parameters are presented in inset of Figure 6c. The PTAA-based device obtained a higher PCE of 2.1% with open-circuit voltage (Voc) of 0.53 V, short-current density (Jsc) of 7.63 mA/cm2 and fill factor (FF) of 0.52, compared with the P3HT-based device with PCE of 0.53%, Voc of 0.53 V, Jsc of 2.68 mA/cm2, and FF of 0.44. The EQE spectra of PTAA-based and P3HT-based solar cell device are shown in
Figure S2, where integral current density as a function of wavelength is also presented. The EQE values of PTAA are exceeding 40% in the absorbance range from 300 to 700 nm, which exceed that of P3HT, and the Jsc of PTAA obtained from integrating the EQE is higher than the Jsc of P3HT, agrees with directly measured Jsc. Therefore, the PTAA-based cell displays relatively excellent photovoltaic performance. Furthermore, the TRPL spectra of the AgBiI4 thin films based on different HTLs are shown in Figure 6d. The τave of the AgBiI4 on glass (5.8 ns) is longer than that of AgBiI4/HTL samples. In addition, the minimum τave (3.8 ns) is obtained at AgBiI4/PTAA, compared with the AgBiI4/P3HT (4.7 ns), indicating the PTAA exhibits even higher electron extraction efficiency than that of P3HT. The Schematic energy level diagram is shown in Figure 6e. The VBM energy gap between AgBiI4 and PTAA is smaller than that 17
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between AgBiI4 and P3HT, thus guarantees efficient charge transport and smaller energy loss from AgBiI4 to PTAA. The TRPL results verify that the well matching of gradient energy band between the AgBiI4 layer and PTAA layer, results in the photo-generated electron effectively extracted from AgBiI4 layer to PTAA. The J-V curves for the PTAA-based solar cell device measured with reverse and forward scans are shown in Figure S3. Unfortunately, the hysteresis still exists. In addition, the insets present the histogram of PCE for 25 solar cells, which shows a high average PCE of 1.90% and half numbers of the tested 25 cells exhibit efficiencies over 1.93%. To further investigate the long-term stability of the solar cell based on the AgBiI4, the PCE of device without any encapsulation along with time is examined at relative humidity of 26% in
Figure 6f. The device retains around 96% of their initial PCE after 1000 h of storage, showing excellent air stability. In summary, we fabricate Pb-free AgBiI4 films through a one-step spin-coating process followed by a mild thermal annealing. By optimizing the concentration of the AgBiI4 precursor and the annealing temperature, we obtained films with excellent crystallinity and high surface coverage. Furthermore, the AgBiI4 exhibits a low Eg of 1.86 eV and the absorption spectrum of the range 400 to 720 nm, which approaches suitable light-harvesting in thin film solar cells. More importantly, the AgBiI4 films exhibits a greater thermal stability and photostability than CH3NH3PbI3. By using different HTL (PTAA and P3HT) in devices, better energy alignment between PTAA and AgBiI4 results in more efficient hole extraction efficiency in active materials and much higher PCE of 2.1%. The device also showed excellent long-term air stability and still maintained 96% of its initial PCE even after 1000h at relative humidity of 26%. Although the 18
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PCE of solar cell is still lower than that organic-inorganic perovskites solar cell, the Pb-free, simple processes, better stability make solar cell based on AgBiI4 promising in developing advanced photovoltaic materials. ASSOCIATED CONTENT
Supporting Information. Experimental methods and the AgBiI4 film's color, the EQE spectrum , the J-V curves for the PTAA-based solar cell device measured with reverse and forward scans and the insets present the histogram of PCE for 25 solar cells, etc. AUTHOR INFORMATION Corresponding author
*E-mail:
[email protected]. *E-mail:
[email protected]. *E-mail:
[email protected].
Notes The authors declare no competing financial interest. ACKNOWLEDGMENTS This work was supported by the National Natural Science Foundation of China (grant number: 11374168), Zhejiang Provincial Natural Science Foundation of China (LY18F040004), and the K.C. Wong Magna Fund in Ningbo University, China.
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