Electronic, Structural, Optical, and Electrical Properties of CsPbX 3 Powders (X = Cl, Br, and I) Prepared Using a Surfactant-Free Hydrothermal Approach

: Recently, several strategies have been adopted for the cesium lead halide, CsPbX 3 (X = Cl, Br, and/or I), crystal growth with a perovskite-type structure, paving the way for the further development of innovative optoelectronic and photovoltaic applications. The optoelectronic properties of advanced materials are controlled, in principle, by effects of morphology, particle size, structure, and composition, as well as imperfections in these parameters. Herein, we report a detailed investigation, using theoretical and experimental approaches to evaluate the structural, electronic, optical, and electrical properties of CsPbX 3 microcrystals. The microcrystals are synthesized successfully using the hydrothermal method without surfactants. This synthetic approach also offers an easy upscaling for perovskite-related material synthesis from low-cost precursors. Lastly, in this direction, we believe that deeper mechanistic studies, based on the synergy between theory and practice, can guide the discovery and development of new advanced materials with highly tailored properties for applications in optoelectronic devices, as well as other emergent technologies.


Introduction
Due to their extraordinary physical properties, lead halide perovskites have attracted noteworthy interest in emerging technologies (photovoltaic, sensor, optoelectronic, etc.) [1][2][3][4]. Notably, lead halide perovskite structures are found in related compounds with the general formula APbX 3 , usually consisting of a ternary combination of corner-sharing [PbX 6 ] polyhedral clusters in the lattice with an organic or inorganic monovalent cation A, such as methylammonium (MA), formamidinium (FA), or cesium (Cs), with the X site being primarily a monovalent halide (i.e., Cl, Br, I, or a combination thereof) anion [3]. It is well known that APbX 3 -related compounds can adopt four phases (a-cubic, b-tetragonal, and gand d-orthorhombic) depending on the tilt and rotation of the [PbX 6 ] polyhedral clusters in the lattice [4][5][6][7]. For this reason, the formation mechanisms of the most likely crystal structure of lead halide perovskites have been widely studied in the literature from the perspective of the Goldschmidt tolerance factor, t, defined as t = (rA + rX)/[sqrt(2)(rB + rX)], where rA, rB, and rX are the ionic radii of the individual A, B, and X species, respectively [7]. Hence, according to this empirical relation, when t ranges from 0.7 to 1, stable lead halide perovskites can generally be formed [3,8,9].
Such materials have a high power conversion efficiency (PCE) with a record of 25.8% (certified 25.5%), which has been achieved over the last decade [10]. Despite this significant PCE result, however, the stability of APbX 3 -based devices is still weak with regard to well-established photovoltaic technologies [9][10][11][12]. It has also been reported that the metallization method of perovskite solar cells significantly impacts device efficiency (i.e., mainly due to the well-known plasmonic effect) [13,14]. Overall, the addition of nanoscale additives in the form of metallic nanoparticles is an important strategy for enhancing the optoelectronic properties and performance/durability of perovskite-based solar cells, as they can act as nucleation sites for the growth of larger perovskite crystals [13][14][15][16]. On the other hand, recent studies have reported that, among these materials, cesium lead halide (e.g., CsPbCl 3 , CsPbBr 3 , and CsPbI 3 ) crystals with a perovskite-type structure have higher chemical stability and are far less soluble (in the significant solvents) compared with organic/inorganic (hybrid) compounds [2,[17][18][19]. Indeed, diverse synthetic strategies have widely been adopted to obtain ternary Cs-Pb-X compounds, including solid-state reaction [20], coprecipitation [21], hot injection [2], Bridgman growth [22], sol-gel [23], and hydrothermal [24][25][26][27][28][29]. Among them, hydrothermal methods (Scheme 1) are a promising approach to the large-scale production of these materials with a low-cost and low-temperature process [24][25][26][27][28]. Although this synthetic approach can be considered highly innovative, mainly thanks to the leading role in obtaining a considerable variety of metastable phases with attractive and entirely new properties, interesting in the technological field [24][25][26][27][28][29], it should be noted that the use of hydrothermal methods for the preparation of lead halide perovskites has been neglected in the literature, when compared to the other methods mentioned. However, because of the current need to obtain perovskite powders from low-cost precursors for large-scale device manufacturing, applied in numerous industrial and scientific research possibilities in the field of energy, we believe that using this synthetic approach can be quite enjoyable for this purpose in the future [30,31].
noscale additives in the form of metallic nanoparticles is an important strategy ing the optoelectronic properties and performance/durability of perovskite-b cells, as they can act as nucleation sites for the growth of larger perovskite c 16]. On the other hand, recent studies have reported that, among these materi lead halide (e.g., CsPbCl3, CsPbBr3, and CsPbI3) crystals with a perovskite-typ have higher chemical stability and are far less soluble (in the significant solv pared with organic/inorganic (hybrid) compounds [2,[17][18][19]. Indeed, divers strategies have widely been adopted to obtain ternary Cs-Pb-X compounds solid-state reaction [20], coprecipitation [21], hot injection [2], Bridgman growt gel [23], and hydrothermal [24][25][26][27][28][29]. Among them, hydrothermal methods (Sch a promising approach to the large-scale production of these materials with a lo low-temperature process [24][25][26][27][28]. Although this synthetic approach can be highly innovative, mainly thanks to the leading role in obtaining a considerabl metastable phases with attractive and entirely new properties, interesting in logical field [24][25][26][27][28][29], it should be noted that the use of hydrothermal methods fo aration of lead halide perovskites has been neglected in the literature, when co the other methods mentioned. However, because of the current need to obtain powders from low-cost precursors for large-scale device manufacturing, app merous industrial and scientific research possibilities in the field of energy, we using this synthetic approach can be quite enjoyable for this purpose in the fut Scheme 1. Hydrothermal synthesis of CsPbX3 crystals from precursor dispersion.
For instance, Kayalvizhi et al. [27] reported the stoichiometric control of t Pb-Br crystals based on the Cs/Pb ratios used in hydrothermal synthesis. It is to emphasize that the solvent usually used in and after perovskite synthesis For instance, Kayalvizhi et al. [27] reported the stoichiometric control of ternary Cs-Pb-Br crystals based on the Cs/Pb ratios used in hydrothermal synthesis. It is important to emphasize that the solvent usually used in and after perovskite synthesis can change the stoichiometry, as previously discussed in [29]. For this reason, many recent studies have used mechanochemical methods for the production of large amounts of perovskite crystals, which is a well-known synthetic strategy for the preparation of solvent-free materials [32][33][34]. Despite this, it is important to highlight here that the hydrothermal method makes it possible to easy obtain of huge variety of materials with a high level of purity and unique properties, which most of the time cannot be achieved via other synthetic methods [35,36]. Hence, the hydrothermal method is an interesting choice to meet the development of a surfactant-free lead halide perovskites crystals synthesis with practical applications, with the advantage of easy tailoring desired parameters based on the tuning of the synthesis conditions and, in turn, the final material properties, thus enlarging the window of applications [24][25][26][27][28][29]31].
In this paper, we report a combined experimental/computational investigation on the electronic, structural, optical, and electrical features of CsPbX 3 microcrystals (X = Cl, Br, and I) synthesized successfully using the surfactant-free hydrothermal method. To complement the experiments, we performed periodic density functional theory (DFT) calculations for a better understanding of the experimental data. Of course, computational design methods are at the forefront of knowledge and have a pivotal role in elucidating the electronic structure of several advanced materials, i.e., contributing to accelerating the development of better materials. Our work highlights the importance of controlling and understanding the physical properties, and our approach is relevant to address the issue of the structural and electronic disorder degree in crystalline materials [37].

Materials and Hydrothermal Synthesis of CsPbX 3 Powders
All reagents were purchased from Sigma-Aldrich, including lead carbonate (PbCO 3 , 98%), cesium carbonate (Cs 2 CO 3 , 99%), hydrogen chloride (HCl, 36 wt.%), hydrogen bromide (HBr, 48 wt.%), and hydrogen iodide (HI, 47 wt.%), and they were used without further purification. CsPbX 3 powders were synthesized according to the hydrothermal method using stoichiometric amounts of PbCO 3 and Cs 2 CO 3 in a 1:1 molar ratio that were dissolved in 15 mL of 6 M haloid acid solution (HCl, HBr, or HI, respectively) under constant stirring for approximately 10 min. In sequence, the mixture reaction was transferred into a Teflon autoclave that was properly sealed and placed inside a muffle furnace. For all cases, the hydrothermal process was performed free of any template and/or surfactants using a heating rate of 10 • C·min −1 at 140 • C for 2 h.

Characterization
The as-prepared powders were characterized using a Raman spectrometer model NRS-3100 (JASCO) with He-Ne and Argon ion lasers used for excitation at 633 nm. X-ray powder diffraction measurements in a 2θ range from 10 • to 70 • at 0.01 • ·min −1 using an X-ray diffractometer (D8 Advance, Bruker-AXS) with Cu K α radiation (λ = 1.5406 Å) are shown in the Figure S1 (in Supplementary Materials). The morphology of the prepared CsPbX3 powders was analyzed using field-emission scanning electron microscopy (SEM, JEOL 7001F). In this case, the optical properties were then analyzed using UV/Vis absorption spectroscopy with a Cary 300 Bio spectrophotometer operating in diffuse reflection mode. For measurement of the electrical response, polycrystalline pellets (with a diameter of 13.0 cm and a thickness of 4.0 mm) were prepared from the powders by cold-pressing at approximately 5 tons for 15 min, and then dried at 80 • C for 180 min. Subsequently, both sides of the pelletized samples were coated with a gold (Au) layer (approximately 100 nm thick), which was thermally evaporated at a rate of 0.8 A·s −1 in an ultrahigh vacuum chamber. The capacitance and impedance spectroscopy measurements of the CsPbX 3 pellet coated with Au were acquired using a Solartron 1260A Impedance/Gain-Phase Analyzer.
We also investigated CsPbX 3 crystals with halide vacancy defects. The computed defective supercells were composed of 134 atoms in the case of CsPbCl 3 (3 × 3 × 3 unit cells), 159 atoms in the case of CsPbBr 3 (2 × 2 × 2 unit cells), and 159 atoms in the case of CsPbI 3 (2 × 4 × 1 unit cells). Since one anion was missing from the studied crystal (either Cl, Br, or I), the considered vacancy concentration was approximately 1%. This anion yielded a color center at the vacancy site and one Bohr magneton per unit cell. All these spin-polarized DFT calculations were run on the Γ point without including spin-orbit interactions.
We also calculated the activation energy for halide migration inside CsPbCl 3 , CsPbBr 3 , and CsPbI 3 materials. To simulate the diffusion process, the referred ion was displaced in a series of small regular steps within the crystal. In the case of CsPbCl 3 , the supercell contained 39 atoms in eight unit cells, and its dimensions were 11.46/11.46/11.46 Å; in the case of CsPbBr3, 19 atoms were in a single unit cell with size 8.54/11.93/8.23 Å; in the case of CsPbI 3 , 39 atoms were in two unit cells with size 10.75/9.77/18.18 Å. The total energies were calculated for every position of the migrating ion along the diffusion path using the Quantum ESPRESSO code [38], Optimized Norm-Conserving Vanderbilt pseudopotentials, a 2 × 2 × 2 k-point grid, and a kinetic energy cutoff of 70 Ry. For initial and final steps, we relaxed the positions of all the atoms in the cells; however, for the intermediate steps, we relaxed all but the position of the migrating ion, which was kept fixed.

Results and Discussion
Figure 1A-C show the micro-Raman spectra obtained at room temperature for the CsPbX 3 crystals synthesized using the hydrothermal method at 140 • C. We experimentally observed four Raman-active modes for both CsPbCl 3 (at approximately 78, 160, 300, and 490 cm −1 ) and CsPbBr 3 (at approximately 76, 128, 152, and 308 cm −1 ) crystals, as shown in Figure 1A,B, while the pure CsPbI 3 crystals exhibited Raman-active modes at 85 and 375 cm −1 . These Raman data are in good agreement with those reported in the literature [41,42]. The insets of Figure 1A-C show a schematic representation of the unit cells, cubic phase for CsPbCl 3 , and orthorhombic phase in both CsPbBr 3 and δ-CsPbI 3 . The structural parameters of CsPbX 3 crystals were obtained from DFT calculations (for CsPbCl 3 , a = 5.73 Å; for CsPbBr 3 a = 8.54 Å, b = 11.93 Å, and c = 8.23 Å; for δ-CsPbI 3 , a = 10.75 Å, b = 4.89 Å, and c = 18.18 Å), which are in accordance with the literature values related to the same compounds but synthesized using different methods [22,[43][44][45]. The calculated Pb-anion bond lengths and bond angles (Pb-X-Pb) in CsPbX 3 are also in accordance with the literature [22,[43][44][45]. The SEM images in Figure 1D-F show the synthesis route produces for both CsPbCl3 and CsPbBr3, with two different morphologies (ranging from cube to octahedral-like), while CsPbI3 exhibited a uniform morphology, only microrod-like. Energy-dispersive Xray spectroscopy (EDXS) mapping revealed a similar profile for all samples, indicating that the products contained only Cs, Pb, and X (X = Cl, Br, and I) and were uniformly distributed in the desired compositional atomic percentage as synthesized ( Figure 1D-F). However, a comparison between the micro-Raman spectra obtained for these as-prepared samples yielded a distinct characteristic for the CsPbI3 crystals. The peculiar CsPbI3 morphology and the different Raman spectrum compared to CsPbCl3 and CsPbBr3 highlights a higher density of structural defects.
To investigate the optical properties of the crystalline perovskite, a comparison between the projected density of states (DOS) and Tauc plot of the CsPbX3 powders are presented (Figure 2A-C). From the combination of experimental and theoretical approaches, we elucidated the bandgap nature of these materials. Our electronic structure calculations showed that the cubic CsPbCl3 and orthorhombic CsPbBr3 phases have a direct bandgap, while the orthorhombic CsPbI3 structure has an indirect transition. Thus, the experimental bandgap values for the as-synthesized CsPbX3 crystals were calculated from the Tauc plot as 2.60 eV, 2.14 eV, and 2.56 eV for CsPbCl3, CsPbBr3 and CsPbI3, respectively. Hence, this trend is in good agreement with the literature and confirms the formation of δ-CsPbI3 [18,[45][46][47][48][49]. These bandgap energy values are strongly dependent on the crystalline perovskite structure. It is well known that, among all-inorganic perovskite materials, the cubic CsPbI3 structure (black phase) as an n-type semiconductor has a suitable bandgap of about 1.70 eV for photovoltaic applications [12,[50][51][52][53]. However, due to small Cs + cation, the cubic CsPbI3 structure is metastable at temperatures below 320 °C [12,[51][52][53]. As a general strategy, researchers have partially replaced Cs + with some larger cations, such as methylammonium (abbreviated as MA + ) [54,55] and formamidinium (abbreviated as FA + ) [53,54,56,57]. Hence, stabilizing the cubic CsPbI3 structure in hydrothermal treatment conditions is still challenging and represents an open field of investigation. The SEM images in Figure 1D-F show the synthesis route produces for both CsPbCl 3 and CsPbBr 3 , with two different morphologies (ranging from cube to octahedral-like), while CsPbI 3 exhibited a uniform morphology, only microrod-like. Energy-dispersive X-ray spectroscopy (EDXS) mapping revealed a similar profile for all samples, indicating that the products contained only Cs, Pb, and X (X = Cl, Br, and I) and were uniformly distributed in the desired compositional atomic percentage as synthesized ( Figure 1D-F). However, a comparison between the micro-Raman spectra obtained for these as-prepared samples yielded a distinct characteristic for the CsPbI 3 crystals. The peculiar CsPbI 3 morphology and the different Raman spectrum compared to CsPbCl 3 and CsPbBr 3 highlights a higher density of structural defects.
To investigate the optical properties of the crystalline perovskite, a comparison between the projected density of states (DOS) and Tauc plot of the CsPbX 3 powders are presented (Figure 2A-C). From the combination of experimental and theoretical approaches, we elucidated the bandgap nature of these materials. Our electronic structure calculations showed that the cubic CsPbCl 3 and orthorhombic CsPbBr 3 phases have a direct bandgap, while the orthorhombic CsPbI 3 structure has an indirect transition. Thus, the experimental bandgap values for the as-synthesized CsPbX 3 crystals were calculated from the Tauc plot as 2.60 eV, 2.14 eV, and 2.56 eV for CsPbCl 3 , CsPbBr 3 and CsPbI 3 , respectively. Hence, this trend is in good agreement with the literature and confirms the formation of δ-CsPbI 3 [18,[45][46][47][48][49]. These bandgap energy values are strongly dependent on the crystalline perovskite structure. It is well known that, among all-inorganic perovskite materials, the cubic CsPbI 3 structure (black phase) as an n-type semiconductor has a suitable bandgap of about 1.70 eV for photovoltaic applications [12,[50][51][52][53]. However, due to small Cs + cation, the cubic CsPbI 3 structure is metastable at temperatures below 320 • C [12,[51][52][53]. As a general strategy, researchers have partially replaced Cs + with some larger cations, such as methylammonium (abbreviated as MA + ) [54,55] and formamidinium (abbreviated as FA + ) [53,54,56,57]. Hence, stabilizing the cubic CsPbI 3 structure in hydrothermal treatment conditions is still challenging and represents an open field of investigation.
In addition, in order to investigate the influence of defects on the fundamental properties of these crystals, DFT calculations were performed. For this purpose, we removed one anion from the DFT supercell, either Cl, Br, or I, leading to a vacancy concentration of approximately 1%. As expected, the projected DOS ( Figure 2D-I) exhibited a vacancy state within the bandgap. This localized state has a p-like character provided that the released electron is occupying one of the partially filled Pb 6p orbitals around the vacancy. The effective masses of the bulk compounds were obtained as the following mean values: me = Σime,i/3 and mh = Σimh,i/3, where I = x, y, and z are correspond to the cartesian directions in the reciprocal space [58]. To estimate me,i and mh,i, we calculated the electronic energies at 13 k points in the vicinity of the bandgap, and fit them to the parabola E(k) = Eg + ħ 2 k 2 (m0/m)/(2m0), where Eg is the bandgap, m0 is the electron mass, and m is the effective mass. From the dispersion band structure, we also estimated the effective masses of carriers and the resulting reduced masses µ = me × mh/(me + mh) (see Table 1), which can be accessed experimentally [1], thereby serving as a reference to positively evaluate the theoretical level employed here [59,60]. In addition, me and mh for mixed-halide CsPb(I1−xBrx)3 and CsPb(Br1−xClx)3 perovskites in the orthorhombic phase are also reported in the literature [61].  In addition, in order to investigate the influence of defects on the fundamental properties of these crystals, DFT calculations were performed. For this purpose, we removed one anion from the DFT supercell, either Cl, Br, or I, leading to a vacancy concentration of approximately 1%. As expected, the projected DOS ( Figure 2D-I) exhibited a vacancy state within the bandgap. This localized state has a p-like character provided that the released electron is occupying one of the partially filled Pb 6p orbitals around the vacancy.
The effective masses of the bulk compounds were obtained as the following mean values: m e = Σ i m e,i /3 and m h = Σ i m h,i /3, where I = x, y, and z are correspond to the cartesian directions in the reciprocal space [58]. To estimate m e,i and m h,i , we calculated the electronic energies at 13 k points in the vicinity of the bandgap, and fit them to the parabola E(k) = E g +h 2 k 2 (m 0 /m)/(2m 0 ), where E g is the bandgap, m 0 is the electron mass, and m is the effective mass. From the dispersion band structure, we also estimated the effective masses of carriers and the resulting reduced masses µ = m e × m h /(m e + m h ) (see Table 1), which can be accessed experimentally [1], thereby serving as a reference to positively evaluate the theoretical level employed here [59,60]. In addition, m e and m h for mixed-halide CsPb(I 1−x Br x ) 3 and CsPb(Br 1−x Cl x ) 3 perovskites in the orthorhombic phase are also reported in the literature [61]. Lastly, the electrical response of the prepared CsPbX 3 pellets as n-type semiconductors was investigated in different humidity conditions at room temperature, as summarized in Figure 3. For this analysis, an impedance spectroscopy (IS) analysis was carried out directly on the CsPbX 3 pellets, fitted with an equivalent circuit ( Figure 3B,C). The proposed equivalent circuit consists of a contact resistance (denoted as R S ), connected in series with the elements representing the processes in the polycrystalline perovskite: the parallel combination of the charge transport resistance (denoted as R tr ) and dielectric capacitance (denoted as C d ). An interesting feature is that, at room temperature, a decrease in the transport resistance could be observed when the samples were exposed to humidity (see Figure 3B). These results are consistent with the literature [62]. However, a more significant variation could be observed for the CsPbI3 pellet. We believe that this is associated with its different morphology observed in SEM analysis. In other words, it suggests that the prepared CsPbI 3 pellets had a higher porosity, when compared to CsPbCl 3 and CsPbBr 3 samples, which could in principle allow a better mobility for water ions or ease the formation of hydrated phases. Therefore, this contributed to higher resistance in the CsPbI 3 pellet. Our analysis also demonstrated that the dielectric capacities of these pellets remained practically constant between the different humidity conditions (dry and wet, see Figure 3C), which may support intrinsic electronic polarization effects for these samples [62,63]. Lastly, the electrical response of the prepared CsPbX3 pellets as n-type semiconductors was investigated in different humidity conditions at room temperature, as summarized in Figure 3. For this analysis, an impedance spectroscopy (IS) analysis was carried out directly on the CsPbX3 pellets, fitted with an equivalent circuit ( Figure 3B,C). The proposed equivalent circuit consists of a contact resistance (denoted as RS), connected in series with the elements representing the processes in the polycrystalline perovskite: the parallel combination of the charge transport resistance (denoted as Rtr) and dielectric capacitance (denoted as Cd). An interesting feature is that, at room temperature, a decrease in the transport resistance could be observed when the samples were exposed to humidity (see Figure 3B). These results are consistent with the literature [62]. However, a more significant variation could be observed for the CsPbI3 pellet. We believe that this is associated with its different morphology observed in SEM analysis. In other words, it suggests that the prepared CsPbI3 pellets had a higher porosity, when compared to CsPbCl3 and CsP-bBr3 samples, which could in principle allow a better mobility for water ions or ease the formation of hydrated phases. Therefore, this contributed to higher resistance in the CsPbI3 pellet. Our analysis also demonstrated that the dielectric capacities of these pellets remained practically constant between the different humidity conditions (dry and wet, see Figure 3C), which may support intrinsic electronic polarization effects for these samples [62,63].  From the cyclic voltammetry (see Figure 3D-F), we found an increase in hysteresis with the decrease in monovalent halide radius (i.e., X = Cl, Br and I). For a full description of this behavior, we performed DFT calculations upon diffusion barriers as present in CsPbX 3 bulk structures. We considered the vacancy-mediated migration of halide ions along a direction relevant to the overall diffusion flow, and generated the potential barriers as shown in Figure 3G,H.
On the basis of our DFT calculations, the diffusion barriers for CsPbCl 3 , CsPbBr 3 , and CsPbI 3 were 0.45, 0.44, and 0.39 eV, respectively [64][65][66]. The decrease in barrier height for ion migration was likely due to a progressive reduction in the orbital overlap, strongly dependent on the crystal structure. Due to the complex nature of inhomogeneity in CsPbX 3 structures, the observed experimental trend can be explained, in principle, by the mechanism of vacancy-mediated anion diffusion, which has been studied for lead halide perovskite materials [64].

Conclusions
In summary, the hydrothermal method was developed to prepare CsPbX 3 powders at 140 • C for 120 min, highlighting its potential to obtain single-phase perovskite materials at low temperatures with a high reaction yield; this can be considered a very attractive strategy for their obtention on a large scale. Thus, given the wide versatility of these halide perovskite-based materials, the understanding of the structural/electronic differences observed for these materials was analyzed from periodic models based on DFT calculations. The analysis of theoretical results indicated that a breaking symmetry process in these structures is, in principle, strongly associated by order-disorder effects; furthermore, this disordered structure leads to the formation of new electronic states in the bandgap. Our findings also suggest that defect states, in turn, play a pivotal role in the optical and electronic responses of CsPbX 3 perovskite structures. Therefore, the combined use of such strategies based on the synergy between theory and practice might provide clues to obtain novel advanced materials that will give rise to new technological applications in the future.