Electronic Structures and Photoelectric Properties in Cs3Sb2X9 (X = Cl, Br, or I) under High Pressure: A First Principles Study

Lead-free perovskites of Cs3Sb2X9 (X = Cl, Br, or I) have attracted wide attention owing to their low toxicity. High pressure is an effective and reversible method to tune bandgap without changing the chemical composition. Here, the structural and photoelectric properties of Cs3Sb2X9 under high pressure were theoretically studied by using the density functional theory. The results showed that the ideal bandgap for Cs3Sb2X9 can be achieved by applying high pressure. Moreover, it was found that the change of the bandgap is caused by the shrinkage of the Sb-X long bond in the [Sb2X9]3− polyhedra. Partial density of states indicated that Sb-5s and X-p orbitals contribute to the top of the valence band, while Sb-5p and X-p orbitals dominate the bottom of the conduction band. Moreover, the band structure and density of states showed significant metallicity at 38.75, 24.05 GPa for Cs3Sb2Br9 and Cs3Sb2I9, respectively. Moreover, the absorption spectra showed the absorption edge redshifted, and the absorption coefficient of the Cs3Sb2X9 increased under high pressure. According to our calculated results, the narrow bandgap and enhanced absorption ability under high pressure provide a new idea for the design of the photovoltaic and photoelectric devices.


Introduction
In recent years, halide perovskites have received a great amount of attention because of their excellent performances in photoelectric and photovoltaic applications [1][2][3], such as, lasers, light emitting diodes (LED), solar cell, and photocatalysis [4][5][6]. Lead halide perovskites are typical representatives due to their excellent performances. However, it is well known that lead halide perovskites suffer from low stability and high toxicity of lead in the development and applications [2,7]. Therefore, to solve the problem of toxicity, lead-free perovskites have attracted more and more attention. Since Sb 3+ has a similar electronic structure and ionic radius as Pb 2+ , it exhibits lower toxicity and better chemical stability than the neighboring heavy metals Pb 2+ . Thus, Cs 3 Sb 2 X 9 (X = Cl, Br, or I) becomes a superior candidate for low-toxicity polymer solar cells (PSCs) [8]. Cs 3 Sb 2 I 9 microplates were already synthesized by the two-step chemical vapor deposition process and demonstrated superior thermal stability within a wide temperature range from 80 K to 380 K [9]. Arto Hiltunen et al. found that the average power conversion efficiency (PCE) doubled by using P3HT (poly(3-hexylthiophene-2,5-diyl)) as a hole transport material for a Cs 3 Sb 2 I 9 solar cell with a PCE of 2.5%. The signal did not diminish during the storage for 1 month [10]. Cs 3 Sb 2 Br 9 was first proposed as an absorber layer in PSCs to absorb solar energy by Sachchidanand et al. A maximum PCE of 15.69% for PSCs with this absorber layer was already reported [11]. The first LED with Cs 3 Sb 2 I 9 fabricated by the vapor-anion exchange method as an emitter were reported by Anupriya Singh et al. The Cs 3 Sb 2 I 9 film obtained by this method had exhibited wide photoluminescence spectrum with a essential reasons of the phenomena. On the other hand, it can also predict the properties of new materials and thus provide theoretical guidance for the design of new experiments and the selection of materials for specific properties.
The layered form of Cs 3 Sb 2 X 9 is more suitable for photovoltaic applications than the dimeric form [24]. Therefore, all calculations were chosen in layered form. The initial structure was downloaded from the Crystallography Open Database and further optimized in VASP [25][26][27]. In order to determine optical properties for Cs 3 Sb 2 X 9 , both the HSE06 hybrid exchange-correlation functional and PBE algorithms were used. We adjusted the PSTRESS in the INCAR file to change the pressure value in optimizations of the structure. The kinetic cut-off energy for the plane wave expansion was taken to be 500 eV. The structural optimizations were stopped when all the total forces on each atom were below 0.01 eV/A. The convergence criterion for the energy was set to be 10 −6 eV [28]. The 5 × 5 × 5 k-point grid was applied to structure optimization and HSE calculated optical properties, while the dense 18 × 18 × 18 grid was applied to the PBE algorithm for calculated optical properties. To make the density of states seem smooth, 16 × 16 × 16 k-point was used for the calculations. The high-symmetry points for the band structure were taken as Γ (0 0 0), M (0.5 0 0), K (0.33 0.33 0), Γ (0 0 0), A (0 0 0.5), L (0.5 0 0.5), H (0.33 0.33 0.5) and A (0 0 0.5), respectively [24]. The crystal structures were visualized using VESTA [29].

Results and Discussion
Cs 3 Sb 2 X 9 belongs to the trigonal crystal structure with the space group P3(-)m1 (no.164). Figure 1a, b showed the optimized crystal structure of the Cs 3 Sb 2 X 9 . Cs 3 Sb 2 X 9 is composed of two [Sb 2 X 9 ] 3− polyhedra in a single unit, with the two Sb 3+ ions located on the body diagonal of the unit cell and eight top corners occupied by Cs + . These connected [Sb 2 X 9 ] 3− polyhedra of the bilayer are stacked together. Cs 3 Sb 2 X 9 is considered as layered material ( Figure 1c) and exhibits triangular symmetry [28]. The optimized atomic coordinates without high pressure are listed in Supplementary Materials Table S1. In order to indicate that the structures are still stable under pressure, we calculated the pressure-dependent Gibbs free energy and show it in Supplementary Materials Figure S1. Ab-initio Simulation Package [21,22]. A single point at the generalized gradient approximation (GGA) of Perdew-Burke-Ernzerh (PBE) was used for obtaining the optimized lattice parameter, atomic position, density of state and electronic band structure [23]. On the one hand, DFT can provide microscopic explanations for experimental phenomena and identify the essential reasons of the phenomena. On the other hand, it can also predict the properties of new materials and thus provide theoretical guidance for the design of new experiments and the selection of materials for specific properties. The layered form of Cs3Sb2X9 is more suitable for photovoltaic applications than the dimeric form [24]. Therefore, all calculations were chosen in layered form. The initial structure was downloaded from the Crystallography Open Database and further optimized in VASP [25][26][27]. In order to determine optical properties for Cs3Sb2X9, both the HSE06 hybrid exchange-correlation functional and PBE algorithms were used. We adjusted the PSTRESS in the INCAR file to change the pressure value in optimizations of the structure. The kinetic cut-off energy for the plane wave expansion was taken to be 500 eV. The structural optimizations were stopped when all the total forces on each atom were below 0.01 eV/A. The convergence criterion for the energy was set to be 10 −6 eV [28]. The 5 × 5 × 5 k-point grid was applied to structure optimization and HSE calculated optical properties, while the dense 18 × 18 × 18 grid was applied to the PBE algorithm for calculated optical properties. To make the density of states seem smooth, 16 × 16 × 16 k-point was used for the calculations. The high-symmetry points for the band structure were taken as Γ (0 0 0), M (0.5 0 0), K (0.33 0.33 0), Γ (0 0 0), A (0 0 0.5), L (0.5 0 0.5), H (0.33 0.33 0.5) and A (0 0 0.5), respectively [24]. The crystal structures were visualized using VESTA [29].

Results and Discussion
Cs3Sb2X9 belongs to the trigonal crystal structure with the space group P3 -m1 (no.164). Figure 1a, b showed the optimized crystal structure of the Cs3Sb2X9. Cs3Sb2X9 is composed of two [Sb2X9] 3− polyhedra in a single unit, with the two Sb 3+ ions located on the body diagonal of the unit cell and eight top corners occupied by Cs + . These connected [Sb2X9] 3− polyhedra of the bilayer are stacked together. Cs3Sb2X9 is considered as layered material ( Figure 1c) and exhibits triangular symmetry [28]. The optimized atomic coordinates without high pressure are listed in Supplementary Materials Table S1. In order to indicate that the structures are still stable under pressure, we calculated the pressure-dependent Gibbs free energy and show it in Supplementary Materials Figure S1.  The previous and present theoretical values of lattice parameters a, b and c bandgap energy E g for Cs 3 Sb 2 X 9 are presented in Table 1. According to Table 1, the PBE optimized lattice parameters are in good agreement with the previously reported and experimental values. For example, the lattice parameters of Cs 3 Sb 2 Cl 9 are 7.817, 7.817 and 9.494 Å obtained in this work, which are very close to the reported theoretical values of 7.827, 7.827 and 9.472 Å and slightly larger than those of the experimental values. As the atomic number increases from Cl to I, the lattice parameter increases in turn. In addition, the ionic radii of Cl − , Br − , and I − are 1.81, 1.96 and 2.20 Å, respectively, which showed similar behavior as the lattice parameters [28]. Moreover, the bandgap energies calculated by PBE are 2.40, 2.01 and 1.55 eV without pressure for Cs 3 Sb 2 Cl 9 , Cs 3 Sb 2 Br 9 and Cs 3 Sb 2 I 9 , respectively. Compared to the reported theoretical and experimental values, the bandgap energies calculated by PBE are small [30]. Exp. 8.420 [33] 8.420 [33] 10.386 [33] 2.05 [27,33] The photoelectric properties of the materials are closely related with their band structures. Therefore, we calculated the band structures of Cs 3 Sb 2 X 9 under the pressure from 0 to 40 GPa.  Figure 2a, Cs 3 Sb 2 I 9 is a direct bandgap structure without pressure, with both the conduction band minimum (CBM) and the valence band maximum (VBM) at point Γ [28]. In addition, the CBM still remains at point Γ, while the VBM moves towards point K under the high pressure. The shift of the high symmetry points from Γ to the K point also appeared in the calculation of the energy band of CsYbCl 3 at high pressure (160 GPa) [34]. As shown in Figure 2e, the valence band consists of Sb-5s and I-5p, and the conduction band mainly consists of Sb-5p and I-5p when no pressure is applied. Figure 2f shows that at a pressure of 40 GPa, the valence band still consists of Sb-5s and I-5p, while the conduction band is dominated by Sb-5p, I-5p and I-4d. The interaction between the I and Sb orbitals leads to a change in the high symmetry point of the energy band. The inter-conversion of direct and indirect bandgap owing to the change in composition has also been reported previously [35]. The band structures of Cs 3 Sb 2 Cl 9 and Cs 3 Sb 2 Br 9 under pressure are shown in Supplement Figures S2 and S3. Cs 3 Sb 2 Br 9 is also a direct bandgap semiconductor without pressure with both CBM and VBM at point Γ, which is similar as that of Cs 3 Sb 2 I 9 . However, Cs 3 Sb 2 Cl 9 exhibits an indirect bandgap with CBM at point A and VBM at point Γ when the pressure is not applied [24]. The CBM shifts towards point Γ,  [19,20]. According to Supplementary Materials Figures S2 and S3, Cs 3 Sb 2 I 9 and Cs 3 Sb 2 Cl 9 also exhibit significant metallicity at 24.05 and 38.75 GPa. Therefore, it is possible to obtain the desired bandgap energy by tuning the pressure. Nanomaterials 2022, 12, x FOR PEER REVIEW 5 of 12 eV, while the position of the CBM is 1.48, 0.58, 0.15 and −0.23 eV for Cs3Sb2I9. The conduction band and valence band gradually move to the Fermi energy level and then overlap with each other, indicating that the material presents metallic properties [19,20]. According to Supplementary Materials Figures S2 and S3, Cs3Sb2I9 and Cs3Sb2Cl9 also exhibit significant metallicity at 24.05 and 38.75 GPa. Therefore, it is possible to obtain the desired bandgap energy by tuning the pressure. It is noted that the bandgap calculated by PBE is smaller than that measured by the experiment. According to a previous study, the ideal bandgap of Cs3Sb2I9, namely 1.36 eV, was achieved under a pressure of 20 GPa [19]. Because the PBE calculation underestimates It is noted that the bandgap calculated by PBE is smaller than that measured by the experiment. According to a previous study, the ideal bandgap of Cs 3 Sb 2 I 9 , namely 1.36 eV, was achieved under a pressure of 20 GPa [19]. Because the PBE calculation underestimates the bandgap value, the bandgap calculated in this work is only 0.17 eV at 20 GPa. According to our calculated results, Cs 3 Sb 2 X 9 (X = Cl, Br, or I) reaches ideal bandgap values (1.34 eV) at 19.02, 6.82 and 1.14 GPa, respectively. The more theoretical values of the bandgap energies under pressure for Cs 3 Sb 2 Cl 9 , Cs 3 Sb 2 Br 9 and Cs 3 Sb 2 I 9 are listed in Supplementary Materials Tables S2-S4. Figure 3a-c showed the calculated lattice parameters of Cs 3 Sb 2 X 9 under pressure. All lattice parameters displayed a decreasing trend when the pressure increased. Since Cs 3 Sb 2 X 9 is a trigonal crystal structure, the lattice constants of the a and b are equal. Lattice constants for a and b varied in the range 7.82-6.31, 8.14-7.73 and 8.68-6.99 Å for Cs 3 Sb 2 Cl 9 , Cs 3 Sb 2 Br 9 and Cs 3 Sb 2 I 9 , respectively. In contrast, the lattice constant in the c-direction decreases from 9.49 to 7.77 Å, 9.97 to 8.05 Å and 10.61 to 8.43 Å for Cs 3 Sb 2 Cl 9 , Cs 3 Sb 2 Br 3 and Cs 3 Sb 2 I 3 , respectively. The decrease in lattice constant indicated that the continuous pressure induced a contraction of the unit cell. S. Idrissi et al. reported that the changes in the lattice constant cause a shrinkage in the bandgap energies [36]. Both lattice constants and bandgaps calculated in this paper for Cs 3 Sb 2 X 9 had the same variation trend. Figure 3d showed the change in unit cell volume, which indicated that the volume of Cs 3 Sb 2 X 9 gradually decrease. As the pressure increases, the interatomic distance decreases, leading to gradual shrinkage in both lattice constant and unit cell volume [36]. This trend follows the similar behavior as the change in lattice constants, decreasing rapidly at first and then gradually slowing down. The reason is that as the space between atoms decreases, the repulsive forces between atoms become stronger, resulting in more difficult to compress [37].  Figure 3a-c showed the calculated lattice parameters of Cs3Sb2X9 under pressure. All lattice parameters displayed a decreasing trend when the pressure increased. Since Cs3Sb2X9 is a trigonal crystal structure, the lattice constants of the a and b are equal. Lattice constants for a and b varied in the range 7.82-6.31, 8.14-7.73 and 8.68-6.99 Å for Cs3Sb2Cl9, Cs3Sb2Br9 and Cs3Sb2I9, respectively. In contrast, the lattice constant in the c-direction decreases from 9.49 to 7.77 Å , 9.97 to 8.05 Å and 10.61 to 8.43 Å for Cs3Sb2Cl9, Cs3Sb2Br3 and Cs3Sb2I3, respectively. The decrease in lattice constant indicated that the continuous pressure induced a contraction of the unit cell. S. Idrissi et al. reported that the changes in the lattice constant cause a shrinkage in the bandgap energies [36]. Both lattice constants and bandgaps calculated in this paper for Cs3Sb2X9 had the same variation trend. Figure 3d showed the change in unit cell volume, which indicated that the volume of Cs3Sb2X9 gradually decrease. As the pressure increases, the interatomic distance decreases, leading to gradual shrinkage in both lattice constant and unit cell volume [36]. This trend follows the similar behavior as the change in lattice constants, decreasing rapidly at first and then gradually slowing down. The reason is that as the space between atoms decreases, the repulsive forces between atoms become stronger, resulting in more difficult to compress [37]. To explain the shrinking bandgap and lattice constant of the Cs 3 Sb 2 X 9 under pressure, we also calculated the relation between the bond length and the pressure. As shown in Figure 4a, two different bond lengths, L 1 and L 2 , are defined as the short and long Sb-X bonds, respectively. The bond lengths were obtained using the VESTA. Figure 4bd presented bond length as a function of pressure for Cs 3 Sb 2 X 9 . The bond lengths of Cs 3 Sb 2 Cl 9 , Cs 3 Sb 2 Br 9 and Cs 3 Sb 2 I 9 increase in order without pressure, which can be explained by the increase in the atomic radius of halogen atoms [28]. Both short and long Sb-X bond lengths decrease with pressure, indicating that Cs 3 Sb 2 X 9 are compressed under the pressure. The variation range in short bond L 1 of the Cs 3 Sb 2 X 9 is 2.53-2.34, 2.69-2.44 and 2.92-2.56 Å, respectively. The long bond L 2 varies in the range of 2.84-2.45, 2.98-2.54 and 3.18-2.66 Å, respectively. The theoretically calculated bond lengths of Cs 3 Sb 2 X 9 under the pressure from 0-40 GPa are shown in Supplementary Materials Table S5. The previous work also showed that the electronic structure of Cs 3 Sb 2 X 9 was strongly affected by the Sb-X bond length [19,38]. In addition, L 1 and L 2 rapidly decrease at first and then slowly, which means that the increasing proximity of adjacent [Sb 2 X 9 ] 3− polyhedra leads to electrostatic interactions becoming strong under high pressure [19]. As the pressure increases, the Sb and X orbitals gradually overlap, and the electronic band dispersion increases as the Sb-X bond contracts. As a result, the CBM gradually decreases towards the Fermi energy level, and the VBM starts to rise simultaneously [17]. As a result, the narrowing of the bandgap at high pressure is presented. Combined with the above analysis, the reduction in bond length leads to a shrinkage in the lattice constant and further reduces the bandgap.
To explain the shrinking bandgap and lattice constant of the Cs3Sb2X9 under pressure, we also calculated the relation between the bond length and the pressure. As shown in Figure 4a, two different bond lengths, L1 and L2, are defined as the short and long Sb-X bonds, respectively. The bond lengths were obtained using the VESTA. Figure 4b-d presented bond length as a function of pressure for Cs3Sb2X9. The bond lengths of Cs3Sb2Cl9, Cs3Sb2Br9 and Cs3Sb2I9 increase in order without pressure, which can be explained by the increase in the atomic radius of halogen atoms [28]. Both short and long Sb-X bond lengths decrease with pressure, indicating that Cs3Sb2X9 are compressed under the pressure. The variation range in short bond L1 of the Cs3Sb2X9 is 2.53-2. 34 Table S5. The previous work also showed that the electronic structure of Cs3Sb2X9 was strongly affected by the Sb-X bond length [19,38]. In addition, L1 and L2 rapidly decrease at first and then slowly, which means that the increasing proximity of adjacent [Sb2X9] 3− polyhedra leads to electrostatic interactions becoming strong under high pressure [19]. As the pressure increases, the Sb and X orbitals gradually overlap, and the electronic band dispersion increases as the Sb-X bond contracts. As a result, the CBM gradually decreases towards the Fermi energy level, and the VBM starts to rise simultaneously [17]. As a result, the narrowing of the bandgap at high pressure is presented. Combined with the above analysis, the reduction in bond length leads to a shrinkage in the lattice constant and further reduces the bandgap.  The density of states (DOS) represents the number of electrons in the unit energy range. Much information can be obtained from a DOS diagram, such as VBM, CBM and the contribution of each orbital to the total density of states. Therefore, we calculated DOS of Cs 3 Sb 2 X 9 with and without pressure to help us further understand the band structures. Here, the electronic configurations of 5s 2 5p 6 6s for Cs, 5s 2 5p 3 for Sb, 3s 2 3p 5 for Cl, 4s 2 4p 5 for Br and 5s 2 5p 5 for I are considered as valence electrons. As shown in Figure 5a-c, the partial density of states (DOS) indicates that the VBM of the Cs 3 Sb 2 X 9 mainly originates from Sb-5s and X-p, while the CBM is dominated by both Sb-5p and X-p. DFT analysis indicates that these results are consistent with the previous reports [28]. and CBM move towards the Fermi energy level and eventually overlap (for Cs 3 Sb 2 Br 9 and Cs 3 Sb 2 I 9 ). When the valence and conduction bands become overlapped, the material changes from semiconductor to metal, which is consistent with the previous work [39]. Additionally, according to Figure 2a-d, the conduction band dropped by 1.71 eV and the valence band rose by 0.386 eV for Cs 3 Sb 2 I 9 . Thus, the conduction band plays a major role in the narrowing of the bandgap. The electrons that make up the conduction band are mainly provided by Sb-5p and X-p and the strong anti-bonding interaction between the two electrons [17].
of Cs3Sb2X9 with and without pressure to help us further understand the band structures. Here, the electronic configurations of 5s 2 5p 6 6s for Cs, 5s 2 5p 3 for Sb, 3s 2 3p 5 for Cl, 4s 2 4p 5 for Br and 5s 2 5p 5 for I are considered as valence electrons. As shown in Figure 5a-c, the partial density of states (DOS) indicates that the VBM of the Cs3Sb2X9 mainly originates from Sb-5s and X-p, while the CBM is dominated by both Sb-5p and X-p. DFT analysis indicates that these results are consistent with the previous reports [28]. Figure 5d-f showed the total density of states under different pressures. As the pressure increases, both VBM and CBM move towards the Fermi energy level and eventually overlap (for Cs3Sb2Br9 and Cs3Sb2I9). When the valence and conduction bands become overlapped, the material changes from semiconductor to metal, which is consistent with the previous work [39]. Additionally, according to Figure 2a-d, the conduction band dropped by 1.71 eV and the valence band rose by 0.386 eV for Cs3Sb2I9. Thus, the conduction band plays a major role in the narrowing of the bandgap. The electrons that make up the conduction band are mainly provided by Sb-5p and X-p and the strong anti-bonding interaction between the two electrons [17]. The absorption coefficient of perovskite is significant for photoelectric and photovoltaic applications, such as solar cells, lasers and detectors. The optical absorption coefficient of perovskite is usually expressed by the complex dielectric function, i.e., ε(ω) = ε1(ω) + iε2(ω), where ω is the frequency of the incident light and ε1(ω) and ε2(ω) are the real and imaginary parts of the complex dielectric function, respectively. Generally, ε1(ω) and ε2(ω) are used to describe the refractive and absorption behavior, respectively, which are given by the following equations [39,40]: The absorption coefficient of perovskite is significant for photoelectric and photovoltaic applications, such as solar cells, lasers and detectors. The optical absorption coefficient of perovskite is usually expressed by the complex dielectric function, i.e., ε(ω) = ε 1 (ω) + iε 2 (ω), where ω is the frequency of the incident light and ε 1 (ω) and ε 2 (ω) are the real and imaginary parts of the complex dielectric function, respectively. Generally, ε 1 (ω) and ε 2 (ω) are used to describe the refractive and absorption behavior, respectively, which are given by the following equations [39,40]: where P is the principal value of the integral, V represents a unit volume, e is the electron charge, p represents the momentum transition matrix, and kn and kn are the wave functions of the conduction band and valence band, respectively. The absorption coefficient, α, can be obtained by calculating the real and imaginary parts of the dielectric function [40]: The high pressure influences the band structure, bandgap energy and the nature of the bonding of the band structure; these changes will further influence the optical absorption of Cs 3 Sb 2 X 9 . Figure 6a-c showed the absorption spectra of Cs 3 Sb 2 X 9 as a function of photon energy at different pressures. One can see that the absorption edge shifts towards lower energies (redshift) with increasing the pressure, which is consistent with the variation of the bandgap under the pressure shown in Figure 2. The redshift of the absorption edge for CsSnCl 3 with increasing pressure was also mentioned in a previous report by Jakiul Islam et al. [37]. Supplementary Materials Figure S3 showed the optical properties calculated using the HSE06 hybrid exchange-correlation function and employing a dense 5 × 5 × 5 k-point grid. The same variation trend is obtained for both PBE and HSE06. As the pressure increases, the gap between the conduction band and the valence band decreases or even overlaps, which facilitates the transport of carriers and thus enhances light absorption. In Figure 6a, the absorption peaks of Cs 3 Sb 2 Cl 9 are concentrated in the ultraviolet region and can theoretically be used as an alternative material for sterilizing surgical equipment [41], whereas in Figure 6c, the absorption spectra of Cs 3 Sb 2 I 9 fully covered the visible region and can be used in the field of solar cells [42].
tions of the conduction band and valence band, respectively. The absorption coefficient, α, can be obtained by calculating the real and imaginary parts of the dielectric function [40]: The high pressure influences the band structure, bandgap energy and the nature of the bonding of the band structure; these changes will further influence the optical absorption of Cs3Sb2X9. Figure 6a-c showed the absorption spectra of Cs3Sb2X9 as a function of photon energy at different pressures. One can see that the absorption edge shifts towards lower energies (redshift) with increasing the pressure, which is consistent with the variation of the bandgap under the pressure shown in Figure 2. The redshift of the absorption edge for CsSnCl3 with increasing pressure was also mentioned in a previous report by Jakiul Islam et al. [37]. Supplementary Materials Figure S3 showed the optical properties calculated using the HSE06 hybrid exchange-correlation function and employing a dense 5 × 5 × 5 k-point grid. The same variation trend is obtained for both PBE and HSE06. As the pressure increases, the gap between the conduction band and the valence band decreases or even overlaps, which facilitates the transport of carriers and thus enhances light absorption. In Figure 6a, the absorption peaks of Cs3Sb2Cl9 are concentrated in the ultraviolet region and can theoretically be used as an alternative material for sterilizing surgical equipment [41], whereas in Figure 6c, the absorption spectra of Cs3Sb2I9 fully covered the visible region and can be used in the field of solar cells [42]. The integral values of light absorption are shown in Table 2. The integral value for the absorption spectra gradually increases with the pressure. Supplement Table S6 shows the integral value of the absorption coefficient calculated using HSE06 algorithms, and the The integral values of light absorption are shown in Table 2. The integral value for the absorption spectra gradually increases with the pressure. Supplement Table S6 shows the integral value of the absorption coefficient calculated using HSE06 algorithms, and the same regularity is obtained for both algorithms, which indicates that the pressure is beneficial for light absorption. As the pressure increases, the bandgap gradually decreases and approaches the ideal bandgap value, resulting in an increase in the light absorption of the material. Therefore, pressure can be used as an efficient and unpolluted method to adjust bandgap energies and enhance the absorption coefficient of Cs 3 Sb 2 X 9 in order to develop its applications, such as solar cells, LEDs, lasers and other photovoltaic devices.

Conclusions
To summarize, we have systematically investigated the electronic structure, DOS and optical properties of lead-free Cs 3 Sb 2 X 9 (X = Cl, Br, and I) under high pressure. Both bandgap energy and bond length of Sb-X rapidly decreased at first and then became slow with the pressure, which was led by the enhancement of the interactions of the atoms. The strong anti-bonding between Sb-5p and X-p caused a substantial downward shift of the conduction band and a slight upward shift of the valence band, resulting in a reduction or disappearance of the bandgap. The bandgap of Cs 3 Sb 2 I 9 can be adjusted in the range of 1.55 to −0.20 eV under pressure from 0 to 40 GPa. In addition, DOS showed that the VBM of Cs 3 Sb 2 X 9 was dominated by Sb-5s and Cl-3p, Br-4p and I-5p states, and the CBM originated from Sb-5p and X-p states. Moreover, it was found that as the pressure increases, the absorption edge shifts towards lower energy, and the light absorption coefficient increases, which is consistent with the decrease of the bandgap energy. Therefore, the high-pressure treatment can reversibly tune the bandgap and optical properties of Cs 3 Sb 2 X 9 , providing a new method for the design of the photovoltaic and photoelectronic devices.
Supplementary Materials: The following are available online at https://www.mdpi.com/article/10 .3390/nano12172982/s1, Table S1: Optimized the atomic coordinates without high pressure. Figure  S1: Calculated Gibbs free energy as a function of pressure. Figure Table S2: Calculated lattice parameters a, b, c, and bandgap energy E g of Cs 3 Sb 2 Cl 9 ; Table S3: Calculated lattice parameters a, b, c, and bandgap energy E g of Cs 3 Sb 2 Br 9 ; Table S4: Calculated lattice parameters a, b, c, and bandgap energy E g of Cs 3 Sb 2 I 9 ; Table S5: Calculated bond length of Cs 3 Sb 2 X 9 ; Figure S4: Optical properties are calculated by HSE06 functional for Cs 3 Sb 2 Cl 9 (a), Cs 3 Sb 2 Br 9 (b), and Cs 3 Sb 2 I 9 (c); Table S6: Integrating absorption coefficient of Cs 3 Sb 2 X 9 calculated using HSE06.