First principle study on the Structural and Electronic Properties of Lead-Free Double Halide Perovskite Cs 2 InSbCl 6

The structural and electronic characteristics of Cs 2 InSbCl 6 were investigated using first principle density functional theory (DFT) within local density approximation (LDA) and generalized gradient approximation (GGA) as implemented in the Quantum ESPRESSO package. A supercell with 40 atoms was used in carrying out the calculations, using the optimized lattice parameters of the Cs 2 InSbCl 6 (a = b = c =11.342 Ǻ). The findings revealed that Cs 2 InSbCl 6 is a direct band gap material with gaps of 0.74 eV and 0.99 eV for LDA/PZ and GGA/PBE respectively, in which the GGA/PBE gap shows consistency within the literature range. The calculated densities of states highlight the contributions of the constituent atoms within the valence and the conduction bands.


I. INTRODUCTION
erovskites have unique features which make them suitable for application as photovoltaic absorbers [1].These include high absorption coefficients, long carrier diffusion length, low exciton binding energy, tunable band gap, and low processing cost etc.[2][3][4][5][6].Due to the environmental hazard and the toxicity of lead-based perovskite, there is a tremendous effort towards developing Lead-free halide perovskite with improved chemical stability under heat, extended light exposure and humid ambient air.Reference [7] presented a systematic first-principle calculations study of double perovskite, A2M + M 3+ X6 with potentially superior photovoltaic performance.Where A is an organic or inorganic component, M + and M 3+ are metal atoms, and X is a halogen atom with band gaps spanning the solar range.They found two In+-based compounds, Cs2InSbCl6 and Cs2InBiCl6 to have direct optical band gaps of 1.02 eV and 0.91 eV, respectively.And the materials have high theoretical solar cell efficiencies comparable to that of CH3NH3PbI3 [7].This report has constituted an important step forward in the design of environmentally friendly perovskite solar cells [8].
Researchers often use the first principle study to model or simulate the electron/hole effective masses, theoretical absorption spectra, carrier mobilities, and energy band gap of materials for technological application [9].Density functional theory (DFT), a modelling tool has been widely employed for simulating the electronic structures of many-body systems using atomic-scale quantum mechanics [1].The accuracy of DFT calculations highly depends on the exchange-correlation functionals used.A range of exchange-correlation functionals are available in DFT computations, including Local density approximation (LDA) and generalized gradient approximation (GGA); both have a qualitative impact on the final output.However, this does not rule out the possibility of issues with unexpected cancellations between the exchange-correlation constituents of LDA/PZ and GGA/PBE which may result in unphysical electron self-interactions [10].This submission P causes both the LDA/PZ and GGA/PBE functionals to significantly underestimate solid band gaps by 30-100% [11].Despite there being several studies on the properties of leadfree halide perovskite, only very few literatures are available for choosing various DFT exchange-correlation functionals and the different pseudopotential methods for accurate calculations of the structure and properties of lead-free halide perovskites, Cs2InSbCl6.
In this work, we investigate and focus mainly on the calculations of crystal structure, lattice parameters, bond length, band structure, density of states (DOS) and partial density of state (PDOS) for Cs2InSbCl6 using the various DFT functionals and pseudopotential methods.The purpose of this study is to present the DFT calculations and performance of various exchange-correlation functionals in predicting the structural and electronic properties of the lead-free halide perovskite, Cs2InSbCl6.

II. COMPUTATIONAL METHOD
We began with the crystal parameters and atomic positions of Lead-free halide perovskite compound Cs2InSbCI6 obtained from the Material Projects online database.Cs2InSbCI6 is a face-centred cubic (FCC) belonging to the space group Fm-3m [12].A supercell of 40 atoms was used in the course of this work.A plane-wave (PW) pseudo potential technique as implemented in the Quantum ESPRESSO simulation package within the framework of DFT was used throughout the work.The GGA in the Perdew, Burke, Ernzerhof (PBE) and the LDA in the Perdew Zunger (PZ) [13] was used as the exchange-correlation functionals independently [14].The Maxfessel-Paxton smearing method was employed for the integrals.The structural parameters (lattice parameters and internal atomic coordinate) were optimized and fully relaxed using Broyden-Fletcher-Goldfarb-Shanno (BFGS) quasi-Newton algorithm.60 and 240 Ry were set for the convergence test of the kinetic energy cut-off for wave function and charge densities respectively.The Monkhorst-pack-point mesh sampling of Brillouin zone integration was set as 6 × 6 × 6 and a denser k-point mesh of 12 × 12 × 12 for density of state (DOS).10 −7 was set as the convergence threshold for self-consistent-field (SCF) iteration.The value of pressure, P, in (1) which was used to calculate the bulk modulus of the material was obtained from the output file of the SCF calculation.

A. Structural properties
The crystal lattice parameters (Å) calculated within LDA/PZ and GGA/PBE functionals compared to available literature data results for Cs2InSbCI6 are listed in Table I.The relative deviation between the calculated parameters is also listed to show the performance and diversity in the crystal parameters.
Table I.Crystal lattice parameters (a), relative deviation, average bond length, bulk modulus (B0), calculated by different DFT functionals in this work compared with available literature data results for Cs2InSbCl6.
The crystal lattice parameters calculated within LDA/PZ and GGA/PBE are 11.28Å and 11.3421Å respectively.Compared with the available literature value [15], a relative deviation of -0.3534% and 0.195% was noticed for DFT-LDA and DFT-GGA respectively.These deviations may be due to unphysical electron self-interactions [10].The lattice parameter calculated within GGA/PBE has the least relative deviation compared with the literature data.Fig. 1(a) and (b) show the crystal structure of cubic perovskite within LDA/PZ and GGA/PBE respectively.It shows that the material crystallizes in the cubic Fm ̅ -3m space group.The average bond length for both LDA/PZ and GGA/PBE is listed in Table 1.From Fig. 1, Cs¹⁺ is bonded to twelve equivalent Cl¹⁻ atoms.It forms a CsCl12 cuboctahedron that shares twelve comparable corners of CsCl12 cuboctahedron, six equivalent faces with CsCl12 cuboctahedron, six equivalent faces with InCl6 octahedral, and six equivalent faces with SbCl6 octahedral.The average Cs-Cl bond lengths are 2.8382 Å in the case of LDA/PZ and 2.9474 Å for GGA/PBE.Similarly, the In¹⁺ is bonded to six equivalent Cl¹⁻ atoms which form InCl6 octahedral that share corners with six equivalent SbCl6 octahedral and eight equivalent faces with CsCl12 cuboctahedron.The average In-Cl bond length is 2.5360 Å in the case of LDA/PZ and 2.4655 Å for GGA/PBE.Sb³⁺ is bonded to six equivalent Cl¹⁻ atoms to form SbCl6 octahedral that share corners with six equivalent InCl6 octahedral and eight equivalent faces with CsCl12 cuboctahedron.The cornersharing octahedral is not tilted.The average Sb-Cl bond lengths are 3.7234 Å in the case of LDA/PZ and 4.1218Å for GGA/PBE.Finally, the Cl¹⁻ is found to be bonded in a clear distorted linear geometry to four equivalents Cs¹⁺, one In¹⁺, and one Sb³⁺ atom.

B. Electronic properties
The results of the band structure calculated by the different DFT functionals and various plane-wave pseudo potential methods for Cs2InSbCI6 are presented in Table II.The relative deviation between the calculated bands is also listed to show the performance and diversity in the band structure.
Table II.The band gap (in eV) calculated by the different DFT functionals in this work compared with available literature data results for Cs2InSbCl6.
The value of the bandgap is frequently underestimated by LDA/PZ and GGA/PBE [17].The electronic band gap was calculated employing the two approximations for eventual comparison.The band structure was calculated in the high symmetrical direction of the Brillouin zone (X-Г-W-Г-L) within the LDA/PZ and GGA/PBE.These are presented in Fig. 2(a) and 2(b) for LDA/PZ and GGA/PBE respectively.The zero-energy level was set to coincide with Fermi energy.The band structure of the two approximations reveals that Cs2InSbCl6 exhibits semiconductor behaviour.Both the LDA/PZ and GGA/PBE have their conduction band minimum and a valence band maximum coinciding at the Г-point of the Brillouin zone.This indicates that the compound is a direct bandgap material.The plot reveals that the compound has a bandgap of 0.74 eV and 0.99 eV within LDA/PZ and GGA/PBE respectively, the GGA/PBE result is in better agreement with the value of 0.98 eV obtained by [16] and most recently 1.02eV obtained by [15].However, they both underestimate the obtained value [17], evidently because of its simplistic form, which isn't flexible enough to regenerate exchange-correlation energy accurately.
The DOS indicates how the material's energy gap behaves.It provides information on the number of possible states in the system, as well as the number of permissible electrons (hole) states per volume at a certain energy level.It's a crucial instrument for evaluating energy distributions and carrier concentrations in semiconductors [18].Fig. 3(a) and 3(b) show the DOS within DFT-LDA and DFT-GGA respectively.It shows that there is an energy range below and above Fermi's level (0 ).The higher peaks are located at the valence band, as shown.This suggests that there are a lot of electrons in that energy level.Finally, the DOS supports the material's gap nature, with an energy gap of 0.74  for DFT-LDA and 0.99  for DFT-GGA with more electrons in the conduction band.
The partial density of state (PDOS) is the relative contribution of a particular atom/orbital to the total DOS.It provides details about the origin of bands both in the valence and conduction bands.
Fig. 4 shows the graph of the PDOS which indicates that the valence band maximum (VBM) is contributed from the Cs-5s orbital.The Cs-5p orbital is associated with the contribution in the conduction band while the Cs-6s have a contribution to both valence and conduction band.The conduction band maximum (CBM) is contributed by the transition In-4d orbital.The In-5s orbital contributed to the conduction band while the In-5p orbital contributed to both the valence and conduction band.The Sb-5s and 5p orbital have most of their contribution to the conduction band.The Cl-5s orbital contributed to both the valence and the conduction band while the Cl-3s had most of its contribution to the conduction band.

IV. CONCLUSION
Quantum ESPRESSO package runs the different DFT calculation methods on the crystal structure and electronic properties of lead-free double halide perovskite Cs2InSbCl6 within LDA/PZ and GGA/PBE.The calculated lattice constant, bond length, energy band structure, DOS and PDOS show that GGA/PBE exchange-correlation functional is the best combination of all the density functional methods and pseudo potential in predicting the structural and electronic properties of the lead-free double halide perovskite Cs2InSbCI6.