Effects of the PbBr2:PbI2 Molar Ratio on the Formation of Lead Halide Thin Films, and the Ratio’s Application for High Performance and Wide Bandgap Solar Cells

We investigate the effects of the molar ratio (x) of PbBr2 on the phases, microstructure, surface morphology, optical properties, and structural defects of mixed lead halides PbI2(1−x)Br2x for use in solar cell devices. Results indicate that as x increased to 0.3, the surface morphology continued to improve, accompanied by the growth of PbI2 grains. This resulted in lead halide films with a very smooth and continuous morphology, including large grains when the film was formed at x = 0.3. In addition, the microstructure changed from (001)-oriented pure PbI2 to a highly (001)-oriented β (PbI2-rich) phase. The plausible mechanism for the enhanced morphology of the lead halide films by the addition of PbBr2 is proposed based on the growth of a Br-saturated lead iodide solid solution. Furthermore, iodine vacancies, identified by X-ray photoelectron spectroscopy, decreased as the ratio of PbBr2 increased. Finally, an electrical analysis of the solar cells was performed by using a PN heterojunction model, revealing that structural defects, such as iodine vacancies and grain boundaries, are the main contributors to the degradation of the performance of pure PbI2-based solar cells (including high leakage, low stability, and high hysteresis), which was significantly improved by the addition of PbBr2. The solar cell fabricated at x = 0.3 in air showed excellent stability and performance. The device lost merely 20% of the initial efficiency of 4.11% after 1500 h without encapsulation. This may be due to the dense microstructure and the reduced structural defects of lead halides formed at x = 0.3.


Introduction
PbI 2 is a highly photoconductive semiconductor with a direct bandgap, high absorption coefficient, and good flexibility [1][2][3][4][5][6]. PbI 2 is frequently used to fabricate organicinorganic halide perovskite solar cells [7], and as γ-ray or X-ray detectors, photovoltaics, photodetectors, and lasing devices [5,[8][9][10][11][12][13]. In addition, PbI 2 is a layered material with a repeating unit of a hexagonal close-packed layer of lead ions sandwiched between two layers of iodide ions. Each of these PbI 2 layers interacts weakly with adjacent layers, giving rise to different stacking patterns, and thus leading to various polytypes in single crystals. PbI 2 single crystals have commonly been fabricated by the Bridgeman-based technique, vapor growth, and the hot wall technique [1,9,11,[13][14][15][16][17][18], while polycrystalline thin films are formed by vacuum evaporation or the spin/spray coating of PbI 2 solutions [19][20][21][22][23][24]. Among these techniques, the deposition of PbI 2 polycrystalline layers from a solution is very simple, reliable, and economical. However, it is difficult to grow high quality PbI 2 films, partly due to the decomposition of PbI 2 during the crystal growth at high temperatures, and partly due to the weak Van Der Waals (VDW) bonding between the layers that

Experimental Setup and Methods
Device fabrication: Fluorine-doped tin oxide (FTO) coated glass substrates (7 Ω/sq, Sigma-Aldrich, Darmstadt, Germany) were partially etched using a chemical treatment with Zn powder and hydrochloric acid (2 M). Each substrate was cleaned ultrasonically in deionized (DI) water, acetone, and ethanol for 10 min, and then dried with N 2 gas. Finally, the substrates were treated in an ultraviolet (UV)-ozone treatment for 30 min. A compact titanium dioxide (c-TiO 2 ) layer was deposited on the FTO glass by spin-coating with a titanium diisopropoxide bis(acetylacetonate) solution (0.15 M in 1-butanol, Sigma-Aldrich, Darmstadt, Germany) at 500 rpm for 5 s and 3000 rpm for 30 s, and then dried at 100 • C for 10 min, followed by baking at 500 • C for 1 h in air. The mesoporous TiO 2 film was deposited by spin-coating a 20 nm sized TiO 2 paste (diluted in ethanol with a weight ratio of 1:3.5, Sigma-Aldrich, Darmstadt, Germany) at 500 rpm for 5 s and 3000 rpm for 30 s, dried at 100 • C for 10 min, and then baked at 500 • C for 1 h in air. Different contents of mixed lead halide precursor solutions were prepared to make the 1.0 M lead halide precursor solution: (A) 0.461 g (1.0 mmol) PbI 2 powder, (B) 0.4159 g (0.9 mmol) PbI 2 and 0.0367 g (0.1 mmol) PbBr 2 , (C) 0.3227 g (0.7 mmol) PbI 2 and 0.1101 g (0.3 mmol) PbBr 2 , (D) 0.2305 g (0.5 mmol) PbI 2 and 0.1835 g (0.5 mmol) PbBr 2 , and (E) 0.1383 g (0.3 mmol) PbI 2 and 0.2569 g (0.7 mmol) PbBr 2 were dissolved in 1 mL of N, N-dimethylformamide (DMF, 99.8%). All lead halide precursors and DMF were purchased from Sigma-Aldrich in Darmstadt, Germany. These solutions were stirred at 80 • C for 30 min in water bath. The lead halide solution was spin-coated at 3000 rpm for 30 s on the substrates in air at room temperature. The samples were annealed at 100 • C for 10 min on a hot plate in air. After that, the hole transport layer (HTL) was deposited by spin-coating a chlorobenzene solution (1 mL) containing 72.3 mg (2,2 ,7,7 -tetrakis(N,N -di-p methoxyphenylamine)-9,9-spirobifluorene) (spiro-OMeTAD), 28.8 µL of 4-tertbutyl pyridine, and 17.5 µL of a stock solution of 520 mg/mL lithium bis(trifluoromethyl sulphonyl) imide in acetonitrile (520 mg/mL) at 3000 rpm for 30 s. All the processes were performed in a clean room maintained at the temperature of 28-30 • C and relative humidity of 25-30%. Finally, 80-nm thick Au was thermally evaporated with a shadow mask under vacuum at 2 × 10 −6 torr to act as the cathode.
Measurements and characterization: Devices with an active area of 0.3 cm × 0.3 cm were characterized in air under an Air Mass 1.5 Global (AM 1.5 G) solar simulator with an irradiation intensity of 100 mW/cm 2 . The simulator was calibrated using a standard crystalline silicon solar cell (Oriel, CA, USA). I-V curves were obtained by sweeping between −0.1 V and 1.4 V with a scan rate of 10 mV/s, whereas dark I-V curves by sweeping between −1 V and 1.4 V with a scan rate of 20 mV/s. All the measurements of the solar cells were performed under ambient conditions (relative humidity of 25-30%, temperature between 28-30 • C) without encapsulation.
The optical absorbance of the lead halide films was measured by UV-visible spectrometry (UV-3150, Shimadzu, Kyoto, Japan). The XRD patterns of the lead halide films were measured using Cu Kα radiation (λ = 0.154056 nm, 40 kV, and 200 mA, Rigaku, Tokyo, Japan). A scanning rate of 5 • /min was applied to record the pattern in the range of 3-60 • . The morphological features were examined by field emission scanning electron microscopy (FE-SEM, JEOL-7401F) and atomic force microscopy (AFM, Seiko, Tokyo, Japan).
The X-ray photoelectron spectroscopy of the lead halide films was performed using a K-alpha XPS system (Thermo VG, British Virgin Islands, UK). The XPS spectrum of the lead halide films was measured using mono Al X-ray sources (Al Kα line: 1486.6 eV) with a sampling area of 400 µm in diameter. A survey scan was performed using a pass energy of 200 eV and a step size of 1 eV. The vacuum level was maintained at 3.6 × 10 −9 torr with a base pressure of 2.2 × 10 −9 torr. We investigated the effects of the molar ratio (x) of PbBr 2 on the crystal structure, the preferred orientation, absorption spectra, and the morphology of a lead halide layer formed on the meso-TiO 2 substrate. Figure 1a shows the XRD patterns of the lead halide films deposited on a meso-TiO 2 layer using the mixed lead halide precursor with different molar ratios (x). For comparison, a pure PbI 2 film was formed, and it exhibited a hexagonal structure that was oriented along the <001> direction, as shown in Figure 1. In the case of the lead halides, as the x value increases from 0.0 to 0.1 to 0.3, the intensity of the PbI 2 (001) peak continues to increase, and the grain sizes also increases. It is also noted that the peak corresponding to the (001) plane shifts to the right with the addition of PbBr 2 , as shown in Figure 1b, implying that shrinkage of the lattice occurs in the <001> direction. This may be the result of the inclusion of Br ion, whose size is smaller than that of I ion, into I sites within a solubility limit, approximately 5% of PbBr 2 in PbI 2 [32]. Additionally, by increasing the PbBr 2 concentration above 5%, which is the solid solubility, the peak continues to shift toward the right, representing a continual decrease in the c-value of the PbI 2 unit cell along the c-axis. According to the quasi-binary phase diagram [32], two phases consisting of the β phase and intermetallic compound PbBr 1.2 I 0.8 are formed at the molar ratio of 0.05~0.5. However, only β (PbI 2 -rich) single phase and no intermetallic compound was detected by XRD at the ratio of both 0.1 and 0.3. This implies that the Br-supersaturated PbI 2 solid solutions are formed at x = 0.1 and 0.3 by the spin-coating of the lead halide solutions.

Results and Discussion
Furthermore, the grains of β phase continue to grow when x increases from x = 0 to 0.1 to 0.3, and then it decreases at the ratio x = 0.5, where the two phases, the β phase and PbBr 1.2 I 0.8 , are formed, as shown in Figure 1a. The dashed lines indicate the weak intensity peaks attributed to PbBr 1.2 I 0.8 . The peaks at 20.48 • and 22.38 • can be assigned to the (120) and (210) planes of PbBr 1.2 I 0.8 , respectively. In addition, a further increase in the ratio to x = 0.7 produced a mixture of PbBr 1.2 I 0.8 and PbBr 2 , as shown in Figure 1b, which is consistent with the phases predicted by the phase diagram [32]. Very low intensities of the peaks of the two phases are observed, indicating that the phases are made of very fine particles. with the phases predicted by the phase diagram [32]. Very low intensities of the peaks of the two phases are observed, indicating that the phases are made of very fine particles.  Figure 2 shows the surface morphologies of the lead halide films deposited on meso-TiO2 substrates using a pure PbI2 solution and mixed lead halide solution, respectively. The pure PbI2 films show elongated-nanoslab features with relatively large voids in Figure  2a. The addition of the mole ratio x = 0.1 of PbBr2 decreases the size of the voids, leading to improved surface morphology. As x increases to 0.3, the surface voids are significantly decreased, leading to a smooth surface morphology. However, at the mole fraction x =0.5, a rough surface morphology was obtained with the increase in voids, possibly due to the different characteristics of the two phases, such as nanoslab PbI2 and fine-grained PbBr1.2I0.8. According to the phase diagram of the PbI2-PbBr2, a eutectic product consisting Figure 1. XRD patterns of (a) lead halide films deposited on a mesoporous TiO 2 at various mole fractions of PbBr 2 to PbI 2 ; (b) the peak shift of the (001) plane of PbI 2 to a higher 2θ with the increase in the ratio x and the schematic indicating the decreased distance between PbI 2 layers due to the replacement of I ions by Br ions. Figure 2 shows the surface morphologies of the lead halide films deposited on meso-TiO 2 substrates using a pure PbI 2 solution and mixed lead halide solution, respectively. The pure PbI 2 films show elongated-nanoslab features with relatively large voids in Figure 2a. The addition of the mole ratio x = 0.1 of PbBr 2 decreases the size of the voids, leading to improved surface morphology. As x increases to 0.3, the surface voids are significantly decreased, leading to a smooth surface morphology. However, at the mole fraction x = 0.5, a rough surface morphology was obtained with the increase in voids, possibly due to the different characteristics of the two phases, such as nanoslab PbI 2 and fine-grained PbBr 1.2 I 0.8 . According to the phase diagram of the PbI 2 -PbBr 2 , a eutectic product consisting of an intimate mixture of β phase and PbBr 1.2 I 0.8 can be produced at the eutectic composition x = 0.5. The two phases in eutectics characteristically form as an alternative structure, where the fine particles of intermetallic compound may form adjacent to the elongated β phase. As a result, the morphology may be characterized mainly by the elongated-nanoslab PbI 2 rather than the fine-grained PbBr 1.2 I 0.8 . Moreover, the growth of β phase of the eutectic structure can be decreased by fine-grained PbBr 1.2 I 0.8 for the molar ratio x = 0.5, which is in contrast with the enhanced grain growth of single β phase by the addition of PbBr 2 for both x = 0.1 and x = 0.3. In addition to the morphological change with x, the thickness of lead halide layers coated on meso-TiO 2 (265 nm) measured by the cross-sectional SEM decreases from 280 nm to 210 nm to 200 nm to 190 nm as x increases from 0 to 0.1 to 0.3 to 0.5.
phase. As a result, the morphology may be characterized mainly by the elongatednanoslab PbI2 rather than the fine-grained PbBr1.2I0.8. Moreover, the growth of β phase of the eutectic structure can be decreased by fine-grained PbBr1.2I0.8 for the molar ratio x= 0.5, which is in contrast with the enhanced grain growth of single β phase by the addition of PbBr2 for both x = 0.1 and x = 0.3. In addition to the morphological change with x, the thickness of lead halide layers coated on meso-TiO2 (265 nm) measured by the cross-sectional SEM decreases from 280 nm to 210 nm to 200 nm to 190 nm as x increases from 0 to 0.1 to 0.3 to 0.5.  X-ray photoelectron spectroscopy was used to analyze the variation in the concentration ratio of pure PbI2 to Br-included lead halide, as a function of the molar ratio.   Figure 4a shows the XPS Pb 4f spectra associated with the Pb atoms, whereas Figure  4b present the spectra associated with Br atoms [32][33][34]. The Pb core-level spectra measured at different molar ratios were de-convoluted into three peaks in Figure 4a at (138.8, 138.7, and 137) eV, which can be assigned to the Pb 4f7/2 core-levels in the PbI2, PbBr2, and Pb atom chemical states, respectively. As the molar ratio increases, the PbBr2: PbI2 ratio increases accordingly. In addition, Pb atoms are detected, indicating the presence of va- X-ray photoelectron spectroscopy was used to analyze the variation in the concentration ratio of pure PbI 2 to Br-included lead halide, as a function of the molar ratio. Figure 4a shows the XPS Pb 4f spectra associated with the Pb atoms, whereas Figure 4b present the spectra associated with Br atoms [32][33][34]. The Pb core-level spectra measured at different molar ratios were de-convoluted into three peaks in Figure 4a at (138.8, 138.7, and 137) eV, which can be assigned to the Pb 4f 7/2 core-levels in the PbI 2 , PbBr 2 , and Pb atom chemical states, respectively. As the molar ratio increases, the PbBr 2 :PbI 2 ratio increases accordingly. In addition, Pb atoms are detected, indicating the presence of vacancies in the films because lead atoms in the charge state Pb 0 are produced by the formation of halide vacancies around the Pb-centered polyhedra [34]. It is also noted that increasing the ratio of PbBr 2 to PbI 2 significantly reduces the contents of Pb 0 , implying that the addition of PbBr 2 effectively decreases defects such as iodide vacancies. The peaks in Figure 4b at 68.8 eV are associated with Br 3d in PbBr 2 , showing that as the PbBr 2 ratio increases from x = 0 to 0.1 to 0.3, the content of Br dissolved in PbI 2 increases. This is consistent with Figure 4a.   Figure 5 shows the absorption spectra of the lead halide films deposited at various molar ratios of PbBr2. The absorption spectrum of PbI2 shows an absorption onset at approximately 2.41 eV. For the sample with x = 0.1, a similar sharp peak is observed around 520 nm, which is slightly lower than that of pure PbI2. For the sample fabricated at the  Figure 5 shows the absorption spectra of the lead halide films deposited at various molar ratios of PbBr 2 . The absorption spectrum of PbI 2 shows an absorption onset at approximately 2.41 eV. For the sample with x = 0.1, a similar sharp peak is observed around 520 nm, which is slightly lower than that of pure PbI 2 . For the sample fabricated at the ratios of x = 0.5, the spectra are rather different. The absorption onsets for the samples at the ratios of x = 0.5 are seen at both 520 nm and 450 nm, representing the existence of the mixture of two phases, PbI 2 and PbBr 1.2 I 0.8 . Because the absorbance is an additive function [35], the total absorbance, A, of the mixture of 1 and 2, where phase 1 and phase 2 have a bandgap of Eg1 and Eg2, respectively, can be expressed in terms of molar fractions as the following equation [35,36]: where A is the absorbance, B1 and B2 are constants, f is the fraction of the phase, and d is the thickness of the sample. The inset shows the Tauc plot of the sample at the ratio x = 0.5, indicating the estimated bandgaps for PbI2 and PbBr1.2I0.8 at 2.45 and 2.79 eV, respectively, which are in agreement with the reported values for the two phases [32].
We propose a mechanism that explains the formation of the smooth morphology of lead halide films due to the addition of PbBr2 during the crystallization based on the investigation of the compositional effects on the microstructure and morphology of lead halide films. For PbBr2 ratios up to x = 0.3, the morphology of the lead halides continues to improve, accompanied by the grain growth of PbI2, achieving a highly smooth surface with well-connected grains at the ratio of x = 0.3. It has been reported that in the mixed crystal Pb-I-Br, the substitution of Br for I in the solid solution generates faulted structures during the crystallization process [37,38], leading to various polytypic structures [37]. That is to say, local compositional and structural disturbance may lead to local stresses, which are relieved by creating edge (or screw) dislocations along the (001) basal planes, acting as nucleation centers for the formation of new polytypic structure [37]. This may result in many polytypes, with the dominant crystal growth taking place in the vertical direction. In addition, the spin-coated solutions consisting of PbI2-PbBr2-DMF complexes [39][40][41][42][43] undergo nucleation and growth by a post-heat treatment to complete the transformation [44]. Although such a system would be in a non-equilibrium or metastable state, the use of the quasi-binary phase diagram of PbI2-PbBr2 provides insight for the development of the microstructure through the phase transformation. For the ratio x up to x = ~0.3, only the single phase (β phase solid solution) is observed, as shown in Figure 1a, implying that approximately 30% of PbBr2 is dissolved in the β phase, which is much higher than the solubility limit (~5%). The rapid cooling of molten solid solution has been known to form supersaturated sold solutions with the maximum solid solubility much higher than the equilibrium value [39,[45][46][47]. This can apply to the spinning process. The Because the absorbance is an additive function [35], the total absorbance, A, of the mixture of 1 and 2, where phase 1 and phase 2 have a bandgap of Eg 1 and Eg 2 , respectively, can be expressed in terms of molar fractions as the following equation [35,36]: where A is the absorbance, B 1 and B 2 are constants, f is the fraction of the phase, and d is the thickness of the sample. The inset shows the Tauc plot of the sample at the ratio x = 0.5, indicating the estimated bandgaps for PbI 2 and PbBr 1.2 I 0.8 at 2.45 and 2.79 eV, respectively, which are in agreement with the reported values for the two phases [32]. We propose a mechanism that explains the formation of the smooth morphology of lead halide films due to the addition of PbBr 2 during the crystallization based on the investigation of the compositional effects on the microstructure and morphology of lead halide films. For PbBr 2 ratios up to x = 0.3, the morphology of the lead halides continues to improve, accompanied by the grain growth of PbI 2 , achieving a highly smooth surface with well-connected grains at the ratio of x = 0.3. It has been reported that in the mixed crystal Pb-I-Br, the substitution of Br for I in the solid solution generates faulted structures during the crystallization process [37,38], leading to various polytypic structures [37]. That is to say, local compositional and structural disturbance may lead to local stresses, which are relieved by creating edge (or screw) dislocations along the (001) basal planes, acting as nucleation centers for the formation of new polytypic structure [37]. This may result in many polytypes, with the dominant crystal growth taking place in the vertical direction. In addition, the spin-coated solutions consisting of PbI 2 -PbBr 2 -DMF complexes [39][40][41][42][43] undergo nucleation and growth by a post-heat treatment to complete the transformation [44]. Although such a system would be in a non-equilibrium or metastable state, the use of the quasi-binary phase diagram of PbI 2 -PbBr 2 provides insight for the development of the microstructure through the phase transformation. For the ratio x up to x =~0.3, only the single phase (β phase solid solution) is observed, as shown in Figure 1a, implying that approximately 30% of PbBr 2 is dissolved in the β phase, which is much higher than the solubility limit (~5%). The rapid cooling of molten solid solution has been known to form supersaturated sold solutions with the maximum solid solubility much higher than the equilibrium value [39,[45][46][47]. This can apply to the spinning process. The spin-coating of PbI 2 -PbBr 2 -DMF liquid solution may have a rapid cooling impact on the samples owing to the evaporation of solvent to produce supersaturated solid solutions with highly increased solubility. Subsequent annealing of the metastable solid solution provides a high nucleation rate and grain growth, thus resulting in the enhanced connectivity between the PbI 2 grains.

Photovoltaic Performance and Long-Term Stability of Lead Halide Solar Cell
Lead halide solar cells were fabricated to investigate the effects of PbBr 2 added to the PbI 2 solution on device performance and stability. Figure 6a shows a schematic of the layered structures of the fabricated lead halide solar cell. In addition, Figure 6b shows the energy level of each layer [48]. The J-V characteristics of the devices are measured to reveal the initial performance, and the degradation with storage time. Figure 6c shows the device performances obtained with the first scan, demonstrating the excellent performance of all devices, except for the device with pure PbI 2 . More specifically, the results indicate a power conversion efficiency (PCE) of 3.97-4.15% with an open circuit voltage V oc of 0.86-0.94 V, a short circuit current J sc of 6.31-7.09 mA/cm 2 , and a fill factor (FF) of 67-68%, as shown in Table 1. To investigate the shelf-life stability and durability of the devices, we performed an aging test of the devices fabricated at different ratios (x). Figure 6d presents the PCE of the fabricated devices at different ratios as a function of storage time. All fabrications of the lead halide solar cells were conducted in ambient air at 28-30 • C and 25-30% humidity, and then age-tested in the same environments. The pure PbI 2 device degraded down to almost zero within 72 h, whereas the lead halide devices demonstrated excellent stability, i.e., t 80 = 1500 h for the device fabricated at x = 0.3, t 80 = 500 h at x = 0.5, and t 80 = 250 h at x = 0.1. (t 80 implies the storage time when the PCE of the device decreases to 80% of the initial value). Such exceptional ambient stability obtained in the device fabricated at x = 0.3 can be attributed to the improved connectivity between the grains and interfaces of the β phase. The performance insensitivity of the lead halide solar cell against the environment is a major advantage for practical applications. spin-coating of PbI2-PbBr2-DMF liquid solution may have a rapid cooling impact on the samples owing to the evaporation of solvent to produce supersaturated solid solutions with highly increased solubility. Subsequent annealing of the metastable solid solution provides a high nucleation rate and grain growth, thus resulting in the enhanced connectivity between the PbI2 grains.

Photovoltaic Performance and Long-Term Stability of Lead Halide Solar Cell
Lead halide solar cells were fabricated to investigate the effects of PbBr2 added to the PbI2 solution on device performance and stability. Figure 6a shows a schematic of the layered structures of the fabricated lead halide solar cell. In addition, Figure 6b shows the energy level of each layer [48]. The J-V characteristics of the devices are measured to reveal the initial performance, and the degradation with storage time. Figure 6c shows the device performances obtained with the first scan, demonstrating the excellent performance of all devices, except for the device with pure PbI2. More specifically, the results indicate a power conversion efficiency (PCE) of 3.97-4.15% with an open circuit voltage Voc of 0.86-0.94 V, a short circuit current Jsc of 6.31-7.09 mA/cm 2 , and a fill factor (FF) of 67-68%, as shown in Table 1. To investigate the shelf-life stability and durability of the devices, we performed an aging test of the devices fabricated at different ratios (x). Figure 6d presents the PCE of the fabricated devices at different ratios as a function of storage time. All fabrications of the lead halide solar cells were conducted in ambient air at 28-30 °C and 25-30% humidity, and then age-tested in the same environments. The pure PbI2 device degraded down to almost zero within 72 h, whereas the lead halide devices demonstrated excellent stability, i.e., t80 = 1500 h for the device fabricated at x = 0.3, t80 = 500 h at x = 0.5, and t80 = 250 h at x = 0.1. (t80 implies the storage time when the PCE of the device decreases to 80% of the initial value). Such exceptional ambient stability obtained in the device fabricated at x = 0.3 can be attributed to the improved connectivity between the grains and interfaces of the β phase. The performance insensitivity of the lead halide solar cell against the environment is a major advantage for practical applications.   The P-N junction model under illumination, described as Equation (2) [49], was used to determine the origin of the performance enhancement as a result of the addition of PbBr 2 .
where J sc is the light induced current density, J 0 is the reverse saturated current density of a PN heterojunction, R s is the series resistance, R sh is the shunt resistance, J is the current density flowing through the external load, m is the ideality factor of a heterojunction, K B is the Boltzmann constant, T is the absolute temperature, e is the elementary charge, and V is the bias applied to the cell. By differentiating, Equation (2) can be expressed as [49] −dV dJ Figure 7a,b show the plots of −dV/dJ vs. (1 + R sh −1 (dV/dJ))/(J sc − J − V/R sh ) and ln (J sc − J − V/R sh ) vs. (V + JR s ) and the linear fitting curves for the PbI 2(1−x) Br x solar cells according to Equations (3) and (4). From the results of the linear fitting, m, R s , and J 0 can be calculated by the slope and intercept, respectively. The R sh is calculated from the inverse of the slope of the J-V curves near the zero bias. The measured parameters J 0 , m, R sh , and R s under illumination are shown in Table 2. Relatively low R s was obtained for all the devices. However, low shunt resistance of approximately 675 Ω cm 2 and high ideality factor of 3.1 were obtained by the pure PbI 2 device. Such large ideality factors (>2) imply that the carrier transport is more complex for lead iodide solar cells, compared with that for the well-behaved single heterojunction solar cell, where the ideality factor is in the range of 1 < m < 2. The addition of PbBr 2 significantly increased the shunt resistance, accompanied by a slight increase in the ideality factor. Since the shunt resistance reflects the leakage current associated with bulk defects, we investigated the dark J-V curves.
The dark J-V curves shown in Figure 8 were used for analysis. The leakage current significantly decreased as x increased. In addition, the dark current at low voltage is likely to consist of capacitive current and shunt current, as seen in Figure 9. Capacitive current is a result of a formed ionic capacitor from the metallic positive ions and iodide vacancies near the TiO 2 /PbI 2 interface. Relatively low Rs was obtained for all the devices. However, low shunt resistance of approximately 675 Ω cm 2 and high ideality factor of 3.1 were obtained by the pure PbI2 device. Such large ideality factors (>2) imply that the carrier transport is more complex for lead iodide solar cells, compared with that for the well-behaved single heterojunction solar cell, where the ideality factor is in the range of 1 < m < 2. The addition of PbBr2 significantly increased the shunt resistance, accompanied by a slight increase in the ideality factor. Since the shunt resistance reflects the leakage current associated with bulk defects, we investigated the dark J-V curves.
The dark J-V curves shown in Figure 8 were used for analysis. The leakage current significantly decreased as x increased. In addition, the dark current at low voltage is likely to consist of capacitive current and shunt current, as seen in Figure 9. Capacitive current is a result of a formed ionic capacitor from the metallic positive ions and iodide vacancies near the TiO2/PbI2 interface.
The dark current can be written as Equation (5) to include both the shunt and capacitive contributions: where Jcap is the capacitive current (=CdV/dt, C is the capacitance per unit area, and dV/dt is the bias scan rate). The fitting of Equation (5) to the J-V curve was performed on the lead halide solar cell to calculate parameters such as Jcap and Rsh. The well fitted solid line to the J-V curve at low bias for the pure lead iodide device can be observed in Figure 9, indicating that the obtained parameters are physically meaningful.     Table 3 shows parameters, including J0, Jcap, Jsh, and C, for lead halide solar cells fabricated at various x ratios. J0 (dark) and Jsh are the reverse saturated current and shunt current in the dark, respectively. The dark current can be written as Equation (5) to include both the shunt and capacitive contributions: where J cap is the capacitive current (=CdV/dt, C is the capacitance per unit area, and dV/dt is the bias scan rate). The fitting of Equation (5) to the J-V curve was performed on the lead halide solar cell to calculate parameters such as J cap and R sh . The well fitted solid line to the J-V curve at low bias for the pure lead iodide device can be observed in Figure 9, indicating that the obtained parameters are physically meaningful. Table 3 shows parameters, including J 0 , J cap , J sh , and C, for lead halide solar cells fabricated at various x ratios. J 0 (dark) and Jsh are the reverse saturated current and shunt current in the dark, respectively. At low voltages, the dark current is the sum of J 0 , J cap , and the shunt current. In pure PbI 2 solar cells, the capacitive current dominates, indicating that the formed ion capacitor is the main contributor. The equation J cap = CdV/dt with dV/dt = 20 mV/s can be used to obtain the capacitance of the ionic capacitors, which results in 100 uF/cm 2 for the PbI 2 device [50]. Such a high capacitance can be created by the accumulation of ionic charges [51][52][53] at the contact interface which leads to a large dielectric constant of the resulting thin space charge regions near the contacts, an effect known as electrode polarization for ionic conductors [54][55][56]. For pure PbI 2 , which is known as an ionic conductor, we propose the interpretation of the capacitance as originated by the mobile ions accumulated at the mesoporous TiO 2 -PbI 2 interface. The mobile ionic charge can be formed by the iodine anions, whose mobility can increase proportionally with the concentration of defects, such as iodine vacancies, grain boundaries, and interlayer voids. As the PbBr 2 ratio increases, the content of iodine vacancies decreases, as shown in Figure 4, and the capacitive current decreases accordingly. As a result, the addition of PbBr 2 significantly decreases the defects, such as vacancies, grain boundaries, and voids, and thus leads to enhanced electrical performance and stability.
In addition to a long shelf-life, the hysteresis-free electrical characteristics are desirable for photovoltaic devices. Figure 10 presents the J-V curves for solar cells fabricated with pure PbI 2 and the mixture of PbI 2 and PbBr 2 solutions, measured in forward (that is, from J sc to V oc ) and reverse (from V oc to J sc ) modes under standard air mass 1.5 global (AM 1.5 G) illumination. It can be observed that there is a large hysteresis in the J-V curve of the pure PbI 2 based solar cell, showing a pronounced discrepancy of approximately 10% in overall efficiency. In contrast, the J-V curves of the forward and reverse scans of the mixture-based cells were relatively coincident with a decreased discrepancy of approximately 2% in the overall efficiency. The improvement in hysteresis can be due to the reduction in mobile ions such as iodine ions, probably resulting from the reduction in the structural defects, including iodine vacancies, grain boundaries, and dislocations.

Conclusions
In this paper, we investigate the compositional effects of the molar ratio (x) of PbBr2 on the crystal structure, preferred orientation, optical property, microstructure, surface morphology, and defects of the mixed lead halides PbI2(1−x)Br2x formed on meso-TiO2 substrates. For the ratio x ≤ 0.3, the addition of PbBr2 has a remarkable effect on the morphology and microstructure of lead halide films. As PbBr2 increases, the size of the (001)-ori-

Conclusions
In this paper, we investigate the compositional effects of the molar ratio (x) of PbBr2 on the crystal structure, preferred orientation, optical property, microstructure, surface morphology, and defects of the mixed lead halides PbI 2(1−x) Br 2x formed on meso-TiO 2 substrates. For the ratio x ≤ 0.3, the addition of PbBr 2 has a remarkable effect on the morphology and microstructure of lead halide films. As PbBr 2 increases, the size of the (001)-oriented PbI 2 grains increases, and the surface morphology significantly improves, indicating that the growth of the PbI 2 grains dominates and is responsible for the continuous and uniform surface of the lead halides films coated with a molar ratio x = 0.3. The mechanism for the growth of the Br-supersaturated β phase from the spin-coated PbI 2 -PbBr 2 -DMF complexes is proposed by considering the quasi-binary phase diagram of PbI 2 -PbBr 2 . The use of the phase diagram provided an insight regarding the control of the microstructure of thin films, which can be applicable to the development of metal-halide perovskite films. In addition, XPS analysis confirmed the anion vacancies associated with metal Pb in the lead halide films, which decreased by the addition of PbBr 2 . At x = 0.5, discontinuous lead halides consisting of the two phases, of β phase plus PbBr 1.2 I 0.8 , were formed, producing a rough surface. Measurement of the optical absorbance of the lead halide films fabricated at x = 0.5 shows the two absorption edges for saturated PbI 2 and PbBr 1.2 I 0.8 , indicating that the energy bandgap of PbI 2 and PbBr 1.2 I 0.8 is 2.48 and 2.79 eV, respectively.
Finally, we fabricated lead halide-based solar cells at various ratios of PbBr 2 to PbI 2 . The solar cell produced at x = 0.3 exhibited excellent device performance with long-term stability and without any encapsulation. The enhanced performance with long-term stability is due to the reduction in structural defects by the addition of PbBr 2 . These results demonstrate the device quality of lead halide films produced from mixed lead halides, offering their potential feasibility for wide bandgap device applications, including semitransparent/transparent and tandem solar cells.