First-principles investigations on the mechanical, thermal, electronic, and optical properties of the defect perovskites Cs2SnX6 (X = Cl, Br, I)
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Huang Hai-Ming, Jiang Zhen-Yi, Luo Shi-Jun. First-principles investigations on the mechanical, thermal, electronic, and optical properties of the defect perovskites Cs2SnX6 (X = Cl, Br, I). Chinese Physics B, 2017, 26(9): 096301 
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First-principles investigations on the mechanical, thermal, electronic, and optical properties of the defect perovskites Cs2SnX6 (X = Cl, Br, I)
† Corresponding author. E-mail:
Project supported by the National Natural Science Foundation of China (Grant Nos. 51572219 and 11447030), the Natural Science Foundation of Shaanxi Province of China (Grant No. 2015JM1018), and Graduate’s Innovation Fund of Northwest University of China (Grant No. YJG15007).
Abstract
The mechanical properties, thermal properties, electronic structures, and optical properties of the defect perovskites Cs2SnX6 (X = Cl, Br, I) were investigated by first-principles calculation using PBE and HSE06 hybrid functional. The optic band gaps based on HSE06 are 3.83 eV for Cs2SnCl6, 2.36 eV for Cs2SnBr6, and 0.92 eV for Cs2SnI6, which agree with the experimental results. The Cs2SnCl6, Cs2SnBr6, and Cs2SnI6 are mechanically stable and they are all anisotropic and ductile in nature. Electronic structures calculations show that the conduction band consists mainly of hybridization between the halogen p orbitals and Sn 5s orbitals, whereas the valence band is composed of the halogen p orbitals. Optic properties indicate that these three compounds exhibit good optical absorption in the ultraviolet region, and the absorption spectra red shift with the increase in the number of halogen atoms. The defect perovskites are good candidates for probing the lead-free and high power conversion efficiency of solar cells.
1. Introduction
Perovskites compounds, especially pure inorganic and inorganic/organic halides, such as CsSnI3, methyl ammonium lead iodide CH3NH3PbI3, and formamidinium lead iodide HC(NH2)2PbI3, have been proved to be some of the most promising materials in solar cells.[1–3] The ABX3 type halide-based hybrid perovskites, where A is a metal atom or molecular cation, B is Sn or Pb, and X is a halide atom (Cl, Br, or I), are attracting an increasing amount of attention for applications due to advantageous optical properties and high power conversion efficiency.[4–10] Since Miyasaka et al.[11] pioneered the incorporation of the hybrid organic–inorganic perovskite halides CH3NH3PbI3 into solar cells, the power conversion efficiency of this kind of solar cell increased from the begging of 3.8% to the current 20.1% in a few years.[12] However, the presence of toxic elements and instabilities of these perovskites halides greatly limit their widespread applications in efficient field-effect transistors light-emitting diodes, and photovoltaic devices.[13–17] Therefore, looking for non-toxic, environmentally friendly, and high conversion efficiency of new perovskite-type solar cell materials has become a current research hotspot.
Recently, Falaras et al.[18] reported three defect perovskites compounds Cs2SnX6 (X = Cl, Br, I). They found Cs2SnCl6, Cs2SnBr6, and Cs2SnI6 are all direct band gap semiconductors and can be used in dye-sensitized solar cells. They also found these three compounds are air-stable, and the dye-sensitized solar cells based on Cs2SnI6 hole-transporting materials present a power conversion efficiency of 4.23% at 1 sun illumination. Neilson et al.[19] pointed out that the greatest advantage of this kind of defect perovskites is that the Cs2SnX6 compounds contain Sn4+ rather than Sn2+ in the B-site, which makes it more stable under exposure to air and moisture. However, Xiao[20] and colleagues indicated the real valence state of Sn in Cs2SnI6 is +2 rather than +4. Although there are different opinions about the valence state of Sn cations in the defect perovskites compounds, it does not prevent the researchers from doing theoretical and experimental investigations on the new lead-free perovskite solar cell materials.[21–23]
The mechanical and thermal properties of perovskite are important for practical applications in solar cells. On the one hand, the absorption performances of perovskite solar cell strongly rely on the crystallinity and stress state of the perovskite layer.[24] On the other hand, as very important thermal parameters, the Debye temperature and melting temperature are related to the bond strength, which is important for the preparation of solar cell devices. Therefore, it is essential to study the mechanical and thermal properties of perovskite type solar cell materials. In this paper, we study the structural, mechanical, thermal, electronic and optical properties of the defect perovskites Cs2SnX6 (X = Cl, Br, I) by first-principles calculations. Our findings shed light on the key properties that are hard to measure experimentally and probing the lead-free solar cells materials.
2. Computational details
First-principles calculations were carried out to study various physical properties of the defect perovskites by using the Vienna ab initio simulation package (VASP).[25] Generalized gradient approximation (GGA) of Perdew–Burke–Ernzerh (PBE) was used to describe the exchange-correlation functional.[26] It is well known that PBE usually underestimates the band-gap, which will result in unreasonable optic properties. In order to overcome this predicament, band gap correction was considered by using range separated hybrid functional (HSE06),[27] which can give improved approximate results to match with experimental data. The electronic configurations: 6s1 for Cs, 5s25p2 for Sn, 3s23p5 for Cl, 4s24p5 for Br, and 5s25p5 for I were used in calculations. The plane wave cut-off energy was set to 450 eV. A mesh of 9×9×9 k-points was used for calculating the electronic, mechanical, thermal, and optic properties. The convergence tolerances of the energy and the force are 1.0 × 10−6 eV and 1.0 × 10−2 eV/Å, respectively.
3. Results and discussion
3.1. Structural properties
Cs2SnX6 chemical composition presents the cubic antifluorite phase with the space group Fm-3m in cubic structure as shown in Fig.
 | Fig. 1. (color online) Crystal structure of the defect perovskites Cs2SnX6 (X = Cl, Br, I). Thick blue lines represent the unit cell edges. |
 | Table 1.
Optimized lattice constants (Å) of Cs2SnX6 (X = Cl, Br, I). Experimental and other theoretical values are included. . |
One can observe that the optimized lattice constants of Cs2SnCl6 are almost the same as those of the experimental results. However, there is a slight deviation for Cs2SnBr6 and for Cs2SnI6, respectively. This slight deviation does not affect further research. On the whole, there is a good agreement between the optimized lattice constants and the experimental findings and available theoretical data. Furthermore, one can see that the lattice constants increase in the order from Cs2SnCl6 to Cs2SnBr6 to Cs2SnI6. The phenomenon is due mainly to the size differences between the univalent anion Cl−, Br−, and I−.
3.2. Mechanical properties
It is known that first-principles methods are often used to calculate reliable elastic properties of solid materials. The criterions for mechanical stability of cubic crystals are given by[33]
 |
Table
| Table 2.
Calculated elastic properties Cij, shear anisotropy factor A, bulk modulus B, shear modulus G, Pough’s ratio B/G, Frantesvich ratio G/B, Young’s modulus Y, Poisson’s ratio υ, Kleinman parameter ξ, Debye temperature ΘD, and melting temperature Mt for Cs2SnX6 (X = Cl, Br, I). . |
Using the elastic constants, some mechanical properties including shear anisotropy factor (A), bulk modulus (B), shear modulus (G), Pough’s ratio (B/G), Frantesvich ratio (G/B), Young’s modulus (Y), Poisson’s ratio (υ) and Kleinman parameter (ξ) are also calculated and presented in Table
Young’s modulus Y is an important parameter in showing the stiffness of a solid material. The larger the Young’s modulus, the stiffer the solid material will be. From Table
3.3. Thermal properties
where h represents Plank’s constant, k is the Boltzman constant, n is the number of atoms per molecule, NA is the Avogadro number, ρ is the density of the solid, and M represents the molecular weight. The average sound velocity Vm was calculated by[33,36]
where vt and vl are the transverse and longitudinal sound velocity, respectively, which is calculated by[37]
Debye temperature ΘD is a fundamental parameter for materials’ thermodynamic properties, and it is closely related to specific heat, bond strength, elastic constants, and melting temperature.[35] ΘD can be predicted by the average sound velocity Vm according to[33,36]
 |
 |
 |
 |
The calculated Debye temperatures of Cs2SnX6 (X = Cl, Br, I) are also listed in Table
The Deby temperature corresponds to the highest frequency of the lattice vibration, which is actually a reflection of the strongest bonding of the crystal. Recently, Kumar et al.[38] obtained a linear relation between Deby temperature and melting temperature for II–VI and III–V semiconductors. In general, for the same compound, a larger Debye temperature means a higher melting temperature.[39] The melting temperature Mt of Cs2SnX6 can be calculated by elastic constants C11 according to the following expression:[33,40]
 |
Calculated melting temperatures are also shown in Table
3.4. Electronic properties
Density of states and band structures calculations predict the direct band gaps at the Г point for Cs2SnCl6, Cs2SnBr6 and Cs2SnI6. The results are consistent with the ones of other investigators.[18,22] Band gap values, as obtained by PBE and HSE06 using the optimized lattice constants, are listed in Table
| Table 3.
Calculated band gap (eV) of Cs2SnX6 (X = Cl, Br, I) using the PBE and HSE06 functional. Experimental and other theoretical values are also included. . |
Figures
 | Fig. 2. (color online) (a) Band structures, (b) total and orbital-projected densities of states for Cs2SnCl6 based on the HSE06. |
 | Fig. 3. (color online) (a) Band structures, (b) total and orbital-projected densities of states for Cs2SnBr6 based on the HSE06. |
 | Fig. 4. (color online) (a) Band structures, (b) total and orbital-projected densities of states for Cs2SnI6 based on the HSE06. |
3.5. Optic properties
where ω is the angular frequency, and ε1(ω) and ε2(ω) are the real and the imaginary parts of the complex dielectric function, respectively.
The optical properties of a semiconductor material are closely related to their electronic band structures; it is usually obtained from the dielectric function by the formula that is given by[41,42]
 |
The dielectric functions of Cs2SnCl6, Cs2SnBr6, and Cs2SnI6 with changes in photon energy were calculated up to 20.0 eV and shown in Figs.
 | Fig. 5. (color online) Real part of the dielectric function for the defect perovskites Cs2SnX6 (X = Cl, Br, I). |
 | Fig. 6. (color online) Imaginary part of the dielectric function for the defect perovskites Cs2SnX6 (X = Cl, Br, I). |
The imaginary dielectric function ε2(ω) gives some important information on the multifarious interband transitions between the valence and conduction bands. The imaginary part for Cs2SnCl6 exhibits five major absorption peaks at 3.80, 5.19, 7.50, 9.49, and 15.23 eV. The five major absorption peaks of Cs2SnBr6 are located at 2.32, 3.74, 6.54, 8.65, and 15.05 eV. The five major absorption peaks of Cs2SnI6 are located at 0.90, 2.30, 4.98, 7.26, and 14.63 eV. These peaks are associated with the transition from valence bands to conduction ones. The lower energy peaks are relative to the electronic transition between the Cl-3p, Br-4p, and I-5p states in the upper valence bands and the Sn-5s states in conduction bands.
In addition to the real and imaginary components of the dielectric functions, the refractive index n(ω), extinction coefficient k(ω), absorption coefficient α(ω), reflectivity coefficient R(ω), optical conductivity κ(ω) and energy loss function L(ω) are calculated and plotted in Fig.
 | Fig. 7. (color online) Refractive index n(ω), extinction coefficient k(ω), absorption coefficient α(ω), reflectivity coefficient R(ω), optical conductivity κ(ω) and energy loss function L(ω) of the defect perovskites Cs2SnX6 (X = Cl, Br, I). |
| Table 4.
Static refractive index, static reflectivity, maximum refractive index and maximum reflectivity for Cs2SnX6 (X = Cl, Br, I). . |
The absorption coefficient can be further calculated according to the refractive index and extinction coefficient. From Fig.
| Table 5.
The positions (eV) of the characteristic peaks and the absorption edges in the absorption spectrum for Cs2SnX6 (X = Cl, Br, I). . |
The static reflectivity R(0) and the maximum reflectivity of the title compounds are listed in Table
The optical conductivity, which is decided by refractive index and absorption coefficient, is usually used to investigate the optical response of material. From Fig.
The energy loss function is an important parameter in describing the energy loss when electrons pass through a dielectric. The function is directly relative to the real and imaginary components of dielectric functions, and the peak of the loss function is associated with plasma oscillation. Figure
4. Conclusion
Employing the first-principles method within the PBE and HSE06 functional, we carried out a comprehensive study on the structural, mechanical, thermal, electronic, and optical properties of the defect perovskites Cs2SnCl6, Cs2SnBr6, and Cs2SnI6. The results indicate that the optimized lattice parameters are in good agreement with the available theoretical and experimental data. These three compounds are mechanically stable and they are all anisotropic and ductile in nature. Calculated Debye temperature and melting temperature decrease from Cs2SnCl6 to Cs2SnBr6 to Cs2SnI6. Density of states and band structures indicate direct band gaps for all the defect perovskites Cs2SnX6, which accords with other theoretical investigations. Orbital-projected DOSs indicate that the contribution to the conduction band mainly originates from the halogen p orbitals hybridized with Sn 5s orbitals, whereas the contribution to the valence band is consisted of the halogen p orbitals. Some parameters, which are closely related to optical properties such as dielectric functions, refractive index, extinction coefficient, absorption coefficient, reflectivity coefficient, optical conductivity, and energy loss function, are studied theoretically for the first time. The results indicate that these three materials exhibit good optical absorption in the ultraviolet region, and the absorption spectra red shift with the increase of the number of halogen atoms. In conclusion, these three defect perovskites are good candidates for probing the lead-free and high-power conversion efficiency of solar cells materials owing to their stable mechanical properties and excellent optical absorption in the ultraviolet region.
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