The effect of metal substitution in CsSnI3 perovskites with enhanced optoelectronic and photovoltaic properties

Non-toxic lead-free halide metal perovskites have gained significant interest in photovoltaic and optoelectronic device applications. In this manuscript, we have studied the structural, electronic, mechanical, and optical properties of eco-friendly cubic CsSn1−xCuxI3, (x = 0, 0.125, 0.25, 0.5, 1) perovskites applying first-principles pseudopotential-based density functional theory (DFT). Cu-doped CsSnI3 has a large impact on the band gap energy viz. the transition of direct band gap towards the indirect band gap. The mechanical properties demonstrate that the pristine and Cu-doped CsSnI3 samples are mechanically stable and their ductility is enhanced by Cu doping. The mechanical stability and ductility favors the suitability of pure and Cu-doped samples in the thin film industry. The absorption edge of Cu-doped CsSnI3 moves towards the lower energy region in comparison with their pure form. In addition, the high dielectric constant, high optical absorption, and high optical conductivity of Cu-doped CsSnI3 materials suggests that the studied materials have a broad range of applications in optoelectronic devices, especially solar cells. A combined analysis of the structural, electronic, mechanical and optical properties suggests that CsSn1−xCuxI3, (x = 0, 0.125, 0.25, 0.5, 1) samples are a suitable candidate for photovoltaic as well as optoelectronic device applications.


Introduction
In the last decades, lead-free metal halide perovskites have been used in versatile applications like photovoltaics, light-emitting diodes, lasers, and optoelectronics because of their outstanding electronic and optical properties. [1][2][3][4][5] Practical applications of metal halide, CsSnI 3 perovskites have increased to a large scale owing to their unique optoelectronic properties including large tunable direct band gap with high light absorption potential, outstanding charge carrier mobility, low recommendation rate, strong optical absorption, and high dielectric constant. [6][7][8][9][10][11] The well-known chemical formula of a metal halide is ABX 3 , where A refers to a cation, B represents a divalent material and X stands for a halogen anion. 12,13 The cubic CsSnI 3 perovskite is composed of corner-sharing SnI 6 octahedral which forms a three dimensional network, where the A-site cations reside in the 12-fold coordinated voids to preserve charge neutrality. In the recent years, the efficiency of perovskite solar cells has increased considerably from 3.8% to over 22% due to intense efforts on the optimization of perovskite layers. CsPbX 3 (X ¼ halide ions) are outgoing as a member of promising light emitters due to small size, tunable band gaps from the violet to near-infrared and immensely narrow full width at half-maximum. [14][15][16][17][18] A large number of researchers are avoiding lead halide perovskite material due to toxicity and searching new metal halide perovskites for applications in optoelectronic and photovoltaic. Roknuzzaman et al. reported that metal cubic structure perovskites CsBX 3 (B ¼ Sn, Ge, and X ¼ Br, Cl, I) samples have better applications for an optoelectronic especially solar cell in compared to lead halide perovskites CsPbX 3 (X ¼ Br, Cl, I). 19 In recent years, metal halide perovskites fulll optoelectronic demands in the commercial market. Due to mixing halide ions with perovskites materials, improve material stability, tunable band gap and enhanced photoluminescence properties. Metals doped halide perovskites like MAPbI 3Àx Br x , MAPbBr 3Àx Cl x , MA 0.15 FA 0.85 Pb (I 0.85 Br 0. 15 ) and Cs 0.17 FA 0.83 Pb (I 0.6 Br 0.4 ) have been greatly improved structural, electrical, optical properties. [20][21][22] Metals substitution doping with single halide CsBX 3 (B ¼ Sn, Ge, and X ¼ Br, Cl, I) perovskites are used in solar cell devices due to faster electrons transport occurred within cation and divalent materials. In spite of breakthroughs, CsSnI 3 metal halides have no use in device applications, because of their poor stability. For increasing device efficiency, researchers are trying to improve the instability of the perovskite light absorber. 23,24 Lead-free cesium tin halide, (CsSnI 3 ) is highly desirable for device application especially solar cells. CsSnX 3, (X ¼ Br, Cl, I) perovskites are promising candidates, especially CsSnI 3 due to the semiconductor properties. 25,26 Lead free-metal halide CsSnI 3 has direct band gap energy of 0.44 eV, while the Cu-doped CsSnI 3 samples have a large impact on band gap energy due to reducing the electronic band gap energy. The maximum valence band and the minimum conduction bands are staying at the same k-points in the Brillouin zone, which is indicating the pure CsSnI 3 sample has direct band gap nature. 8,24 The CsSn 1Àx Cu x I 3 , (x ¼ 0.125, 0.25, 0.5, 1) samples have indirect band gap energy of 0.59 eV for CsSn 0.875 Cu 0.125 I 3 , 0.48 eV for CsSn 0.75 Cu 0.25 I 3 , 0.42 eV for CsSn 0.5 Cu 0.5 I 3 and 0.29 eV for CsCuI 3 . Notable, 100% Cu-doped CsSnI 3 sample has indirect band gap energy, with 0.29 eV, reduced the band gap approximately 48.2% from pristine CsSnI 3 sample. In case of Cu-doped CsSnI 3 sample, the band gap energy is transferred towards direct to indirect due to intra-band and inter-band transition that occurred in the CsSnI 3 lattice network. Raman and Hossain attempted to substitute metals at the G-site of CsGeCl 3 halide to simply improve the absorption over the range of solar energy. 25 Transition metal Ni-doping in CsGeCl 3 increases its band gap energy and shrinkage the optical absorption due to the Moss-Burstein effect. [27][28][29] In this manuscript, we are addressing the effects of Cu-doped CsSnI 3 for optoelectronic and photovoltaic applications. We have applied density functional theory (DFT) to calculate electronic, mechanical, and optical properties. A combined analyzed manifested that Cu-doped CsSnI 3 is a potential candidate material for applications in photovoltaic and optoelectronic devices, especially solar cells.

Theoretical methodology
The theoretical simulations of lead-free metal halide CsSn 1Àx -Cu x I 3 , (x ¼ 0, 0.125, 0.25, 0.5, 1) samples were studied using pseudo-potential density functional theory (DFT) simulations of the supercell approach. In this manuscript, 2 Â 2 Â 2 supercell model is constructed for all simulations. The supercell of CsSnI 3 contains 40 atoms including eight Cs atoms, eight Sn atoms, and 24 I atoms. All of the calculations in this study were performed by material studio 8.0 based on density functional theory. 27,30 For geometry optimizations, we employed general gradient approximation (GGA) exchange-correlation function, while the Perdew-Burke-Ernzerhof (PBE) 31 was selected to conduct the simulation to gain the electronic behaviors in the sample and exact formation energy. The cutoff energy of the plane wave basis set was used at 700 eV for pristine and Cudoped CsSnI 3 samples. We have employed 10 Â 10 Â 10 gamma centered k-points for pure and Cu-doped CsSnI 3 samples. A scissor value (0.68 eV) was applied for the calculations of absorption, conductivity, and dielectric function. A scissor value (0.68 eV), a disparity, between theoretical (0.59 eV) and experimental (1.27 eV) band gap of CsSnI 3 . The crystal structure is completely optimized through a change in k-points and cut-off energy and nally, we have found ground state energy in the studied samples. The lattice parameters and coordinates are varying in time under the Broyden-Fletcher-Goldfarb-Shanno (BFGS) algorithm method. 32 The unit cell parameters and atomic relaxations were accomplished by the residual forces under 0.03 eV A À1 . With the CASTEP code, the  properties are calculated by using the nite-strain theory. 33,34 Stress tensor has six stress components s ij for each strain d j applied to the unit cell.

Structural properties and phase stability
The cubic metal halide CsSnI 3 perovskites have space group Pm 3m (no. 221). In the unit cell, Cs atoms are located on the face-centered position (0 0 0) fractional coordinates, the Sn atoms occupy the body-centered position with fractional coordinates (0.5 0.5 0.5) and I atom located on the face-centered positions with fractional coordinates (0 0.5 0.5). In supercell structures, the simulated equilibrium lattice parameter a, and unit cell volume, V, are well-matched with experimental as well as theoretical published results. Fig. 1(a-d) shows the cubic structures 2 Â 2 Â 2 supercell of pure and Cu-doped CsSnI 3 . The cell volume and lattice parameters are decreased with Cu doping concentrations due to lattice strain occurred in random directions.
Phase stability is more essential for materials. To be stable, the materials have to fulll some special criteria. Firstly, for mechanical stability, a material must have full-lled elastic moduli conditions. The second one is phase stability. In a single halide perovskites material, phase stability is calculated by the tolerance equation. 35 where, R A , R B, and R X are represented for the ionic radius of A, B, and I atoms. For stability, the tolerance factor range must be lying in between 0.813 to 1.107. Table 1. Shows that pure and Cu-doped CsSnI 3 samples full ll phase stability conditions. In the case of 100% Cu-doped CsSnI 3 sample, the stability is increased compared to pure CsSnI 3 sample. Xiao Feng et al. reported that the CsSnI 3 sample has poor stability and can't be suitable for devices. 24 Notably, the Cudoped CsSnI 3 samples have increased phase stability. To gain phase stability, we have employed the Shannon ionic radius. Finally, we concluded that the Cu-doped CsSnI 3 samples may have potential applications for device purpose.
The formation enthalpy is calculated by the following equations 36,37 For an un-doped system, For doped system Herein, Cu doping concentrations are varying as x ¼ 0.125, 0.25, 0.5, 1. In eqn (2) and (3), E s (Cs), E s (Sn), E s (Cu), and E s (I) are the energy of Cs, Sn, Cu, and I atoms, respectively, whereas E tot (-CsSn 1Àx Cu x I 3 ) represents the unit cell, total energy, and N is the number of atoms in the unit cell. Herein, we have calculated formation energy to see thermodynamic stable nature's of pure and Cu-doped CsSnI 3 samples. The formation enthalpy values are presented in Table 1. Moreover, the calculated formation enthalpy (Table 1) shows negative values for both pure and Cudoped CsSnI 3 halides, which is conrming their thermodynamic stability.

Electronic properties
To see the electronic behaviors of pure and Cu-doped CsSnI 3 perovskite, we have simulated the electronic band energy along with high symmetry points. The calculated band energy structures are shown in Fig. 2(a-f). The simulated band structures of the pure CsSnI 3 have direct band gap of 0.44 eV, where the maximum valence band and minimum conduction bands are staying at similar k-points. The single cell band gap has small difference from the supercell structure (eight times) band gap. Note that band gap values for unit cell are 0.442 eV and 2 Â 2 Â 2 supercells of CsSnI 3 for 0.445, which suggesting the good convergence of the orbital uctuations. 20 It is seen that the simulated band gap value underestimates the experimentally calculated band gap values of 1.27 eV. 40 Several researchers reported that the hybrid potential HSC (Heyd-Scuseria-Ernzerhof) methods are perfect for exact band gap measurements, although this potential is not t for estimate samples. 13,19 The experimental calculated band gap value differs from the theoretical band gap due to the limitations of GGA method. However, our work focuses only on the reduction of electrical band gap of Cu-doped CsSnI 3 and ignores the band gap error for the GGA method. The present band gap energy values are good in agreement with other publication. 40 It is noteworthy that Cudoped CsSnI 3 samples appear in intermediate states.
The valence energy states are expanded into the higher energy region due to the valence band into the Fermi level can cross the transition of electrons from the valence band to the  Table 2 along with previously published theoretical and experimental results. The calculated band structure suggests that the pattern of the band gap is affected by the Cudoping concentrations. The total density of states (TDOS) and partial density of states (PDOS) of pure and Cu-doped CsSnI 3 samples are presented in Fig. 3(a-f). As shown in the partial density of states gure the valence band is mostly composed of Cu-3d and I-6s orbital with a small contribution of Cs-6s and Cs-3p states. The high energy band is mainly dominated by Cu-3d orbital with a small contribution of Cs-6s and Cs-5p electrons. The band structure identies that the difference between valences band maximum to the conduction band minimum in a sample. The TDOS shape of Cu-doped CsSnI 3 becomes broader than that of pure CsSnI 3 , which indicates that the electronic non-locality is more because of the reduction of crystal symmetry. 41 The conduction band energy is mostly attributed to the Cu atom due to CB shis towards the lowest energy states. A at peak is seen in the conduction band because Cu-3d states are generated by new dopants energy states. It is observed from Cu-doped CsSnI 3 samples, the impurity energy states appear in the partial density of states. This intermediate state appears electronic band structure, which is essential for electrons transition between conduction bands to valence bands.   QðaÞ Here, P mv represents an element of the density matrix and S mv (k) is the overlap matrix. The overlap population between two atoms a and b can be expressed using the following equation 44 Noticeably, the Mulliken effective charges of the individual Cs, Sn, I, and Cu atoms are found to be reasonably smaller than their formal ionic charges, which are +1, +4, À1, and +2, respectively.
To see the difference between Mulliken effective charge and formal ionic radius, we have applied the Shannon ionic radius. The difference between Mulliken effective charges and formal ionic radius indicates that the CsSn 1Àx Cu x I 3 (x ¼ 0, 0.125, 0.25, 0.5, 1) samples have mixed ionic and covalent bonds ( Table 3).
The effective valence charge is reduced with Cu-doping concentrations. The level of covalence Cu-doped CsSnI 3 reduced due to the effect of on-site Coulomb interaction. The positive value of bond population refers to the high degree of covalence, whereas the small bond population identies a high degree of ionicity in the covalence bond. 45 Moreover, the simulated bond populations of Cu-I are found to be higher than the Sn-I. The bond length is decreased in pristine CsSnI 3 compared to Cu-doped CsSnI 3 due to ionic radius mismatch between Sn and Cu atoms.
To see the charge distribution and bonding nature of pristine and Cu-doped CsSnI 3 , we analyzed charge density distribution and presented it in Fig. 4(a-e). Spherical shape charge distribution exists in the pure and Cu-doped CsSnI 3 . Sn and Cu atoms are bonded covalently with the I atom. The electron clouds around Sn, Cu, and I atoms are distorted towards, which indicating the covalent bond natures. Fig. 4 shows the almost similar charge distribution and bonding character of pure and Cu-doped CsSnI 3 perovskites.
Photo-catalytic is an essential parameter to identify the device efficiency of optoelectronic and photovoltaic applications. Tin-based halides CsSnI 3 have more response to photocatalytic materials. Cu-doped CsSnI 3 samples, photo-catalytic activity tends to increase in comparation to pristine CsSnI 3 . Charge carrier mobility transition samples have more photocatalytic activities efficiency. In this paper, we found that the    Fig. 5. It gives the inuence of the separation of photo-generated electron-hole pairs, as well as favors in migration of photo-excited carriers and processing photocatalysis. Cu-doped CsSnI 3 samples introduction of new dopant energy levels that effectively changes the band gap energy of the photo-catalyst. This work would be suitable for optoelectronic and photovoltaic device applications.

Mechanical properties
The three independent elastic moduli for pure and Cu-doped CsSnI 3 perovskites are simulated by the nite strain theory. 43,46 The single and polycrystalline elastic properties are simulated via CASTEP code material studio 8.0 and tabularized in Tables 4 and 5. The simulated polycrystalline properties for CsSnI 3 are good to coincide with the previously published paper. 34 For cubic symmetry criteria, the simulated elastic modulus of pure and Cu-doped CsSnI 3 compound should satisfy the following conditions: 44,47 C 11 + 2C 12 > 0, C 44 > 0 and C 11 À C 44 > 0. The simulated elastic modulus for pure and Cudoped CsSnI 3 full led the mechanical stability criteria, which indicating that pristine and Cu-doped CsSnI 3 samples are mechanically stable. The quantity C 12 -C 44 , is dened as Cauchy pressure, 45,48 which identies the brittle/ductile nature of a sample. The simulated Cauchy pressure is positive values, which ensures that the pristine and Cu-doped CsSnI 3 samples are ductile natures (Fig. 6). The evaluated bulk modulus, shear modulus, Young's modulus, Pugh's ratio, and Poisson's ratio of the pure and Cudoped CsSnI 3 samples are presented in Table 5. The bulk modulus values are identied that pure and Cu-doped CsSnI 3 samples are exible and so. Therefore, these metal halide perovskites can easily be made into a suitable thin lm for optoelectronic applications especially for solar cells. Bulk modulus to shear modulus ratio (B/G) is called Pugh's ratio and Poisson's ratio both can identify the ductility/brittleness nature of a material. 49,50 The critical value of Pugh's and Poisons distinguish the brittle materials from ductile ones. If the Pugh's (0.26) and Poisson's ratio (1.75) values are higher than critical values, then the sample is said to be in ductile types, otherwise, it is brittle types. The ductile nature is tended to reduce with Cudoping concentrations. Cauchy pressure predicted that pristine and Cu substitution doped CsSnI 3 samples are ductile in nature. It can be seen from single and polycrystalline; elastic properties (Tables 4 and 5) are changed with Cu-doping concentrations. Notable, the single elastic properties of Cu-    doped CsSnI 3 samples are nearly similar with pristine CsSnI 3 sample. The mechanical stability and ductility natures imply that the pure and Cu-doped CsSnI 3 samples are perfect for the thin lms industry.

Optical properties
To understand the optical behaviors, we simulated optical absorption (a), conductivity (s), and dielectric constant (3) for pristine and Cu-doped CsSnI 3 samples. The complex dielectric function is given by the following equations. 51 Here, 3 1 (u), i3 2 (u) and N represents the real and imaginary part of the dielectric constant and complex refractive index respectively. The complex dielectric function is expressed by the following equations 52 Where, the symbol u, e, U, and u refer the phonon frequency, electronic charge, unit cell volume, and unit volume along the polarization of the incident electric eld.
To see optical nature, we used photon energy, E, 0 to 20 eV. In this manuscript, the Gaussian smearing of 0.5 eV was used for all simulations. The optical properties calculation were taken in the {100} plane orientation. A scissor value is applied of 0.68 eV, which is the disparity between experimental and theoretical band gap energy.
The simulated absorption spectra of pristine and Cu-doped CsSnI 3 are presented in Fig. 7(a and b). The optical absorption coefficient a(u) gives the information about the amount of light entrance with a particular wavelength into solid materials. 28 It also gives information about solar spectrum energy which is most important for devices application, especially for solar cells. First, absorption peak is more essential for device applications. The absorption spectra were taken in the range of 100-800 nm to investigate the optical behavior in the UV-vis. and visible wave length (l) range. Accordingly, the absorption spectra are shied to the lower energy region (redshi) compared to pure and Cu-doped CsSnI 3 . The absorption spectra conrmed that Cu has a large inuence on the band gap energy and nally decreased the band gap. The absorption band is shied towards the lower energy region due to Sn and Cu ions created defect energy of Cu 3d and Sn 4d orbitals.
Stronger optical absorption spectra identify increase photovoltaic efficiency. Hence the band gap energy transferred towards the visible region and the maximum absorption peak occurred in the UV region, which indicates that the pure and Cu-doped CsSnI 3 samples are potential candidates for the optoelectronics industry. The absorption spectra threshold energy is signicantly higher than the simulated band gap, which is indicating that the CsSnI 3 sample has direct band gap nature and reverses at Cu-doped CsSnI 3 samples. The rst absorption peak stay at 1.0-4.5 eV energy regions, which demonstrated that pure and Cu-doped CsSnI 3 samples are perfect for photoelectric device applications. The simulated optical conductivity (s) are presented in Fig. 7(c). The optical conductivity is an essential parameter for identifying how the amount of electromagnetic wave response in a substance. Moreover, the optical conductivity (s) refers to the number of photons that pass through the substance. The optical conductivity and absorption spectra have a similar structure, as presented in Fig. 7(a-c), due to the escape of electron and photon from the valence band to the conduction band when it absorbs energy. The optical conductivity of Cu-doped CsSnI 3 occurs at lower energy compared with pristine CsSnI 3 . Optical conductivity at low energy of Cu-doped CsSnI 3 perovskites makes them potential candidate materials for applications in optoelectronic especially solar cells devices. Optical conductivity results conrm that Cu-doped CsSnI 3 samples have a low band gap compared with their pristine CsSnI 3 . The dielectric function gives information about the amount of electromagnetic radiation response in a solid substance. 53 The imaginary part of the dielectric function (3 2 ) is similar to electron excitation. Notable, the rst peak of the imaginary part of the dielectric function (3 2 ) occurs at <1.5 eV, at Cu-doped CsSnI 3 samples, which indicates that the intra-band transition has occurred and vice versa at pure CsSnI 3 . The overall optical properties recommend that Cudoped CsSnI 3 is perfect for optoelectronic especially solar cell applications.

Conclusions
In this work, we have applied the density functional theory (DFT) simulations to calculate structural, electronic, mechanical, and optical properties of pure and Cu-doped CsSnI 3 samples. The structural parameters lattice constants a, and cell volumes, V are well-matched with previously published work. The simulated band structure reveals that the pure CsSnI 3 sample has a direct band gap nature semiconductor. In the case of Cu-doped CsSnI 3 samples, the band gap energy transferred towards direct to indirect. The Pugh's and Poisson's ratio refers that the pure and Cu-doped CsSnI 3 samples are to be fabricated easily in the thin lms industry. The absorption edge is transferred to the lower energy regions with Cu-doping concentrations. The dielectric properties manifested that inter-band transferred towards the intra-band due to changes of the band gap energy at Cu-doped samples. A combined evaluation of the structural, electronic, mechanical, and optical properties recommend that eco-friendly CsSn 1Àx Cu x I 3 (x ¼ 0, 0.125, 0.25, 0.5, 1) perovskite is a suitable candidate materials for photovoltaic and optoelectronic device applications.