Semiconductor to metallic transition under induced pressure in Cs2AgBiBr6 double halide perovskite: a theoretical DFT study for photovoltaic and optoelectronic applications

Inorganic double halide perovskites have a wide range of applications in low-cost photovoltaic and optoelectronic devices. In this manuscript, we have studied their structural, electronic, mechanical and optical properties using density functional theory (DFT) simulations. In this work, hydrostatic pressure is induced from 0 to 50 GPa. Disordered Ag and Bi atoms have a large impact on band gap energy; in this case, the indirect band gap is transferred towards a direct band gap. We have seen that pressure-driven samples have transformed a band energy semiconductor into a metallic one. Under the induced hydrostatic pressure, the covalent bond is transformed into a metallic bond and the bond lengths are reduced. Meanwhile, pressure-induced samples enhance symmetry breaking in [AgBr6]5− and [BiBr6]3− octahedra, which reduces the density of states of the Fermi surface and lowers the total energy. The mechanical behaviors demonstrated that the studied materials are mechanically stable as well as ductile and their ductile nature is enhanced by the driving pressure. The absorption peak is shifted towards the low energy region with increased hydrostatic pressure. The absorptivity and dielectric constant values are also increased with driving pressure. Phase transformed double halide perovskites triggered by outside stimuli produce several outstanding materials properties, giving great scope for a broad range of applications. This type of pristine and disordered double halide perovskite with pressure-driven semiconductor-to-metal phase transition samples may have potential applications in optoelectronic and photovoltaic devices.


Introduction
In recent years, lead-free double halide perovskites have been considered promising candidates for versatile applications in low-cost photovoltaic and optoelectronic devices because of their unique electronic and optical properties. [1][2][3][4][5] Practical applications of inorganic halide perovskites have increased to a large scale, such as a light emitting diodes (LEDs), lasers, radiation detectors, and solar cells. Pb-based hybrid halide perovskites have superior and exceptional photovoltaic properties due to their suitable direct band gap, high absorption coefficients, effective masses of valence electrons and holes, defect tolerance, and carrier diffusion length. [6][7][8] In spite of breakthroughs, Pb based hybrid halides will have no use in the long term, because of their toxic impact on the environment. 9 There is a great challenge for a materials scientist to nd out the stable nature of a non-toxic double metal halide for low-cost optoelectronic device applications beyond all these restrictions. The well-known chemical formula of a double metal halide is A 2 M + M 3+ X 6 , where A is CH 3 NH 3 + or Cs + , M + (Na + , Cu + or Ag + ) is a monovalent cation, M 3+ (Bi 3+ , Sb 3+ or In 3+ ) is a trivalent cation, and X (Cl À , Br À or I À ) is a halide. In recent years, a new class of double halide perovskite has led to a new generation that provides potential applications in optoelectronic devices. 10,11 Bi-based organic and inorganic double halides are used in solar cell devices due to the ion's migration easily occurring within monovalent and trivalent cations. Lead free-halide Cs 2 AgBiBr 6 is an indirect gap semiconductor with a band gap of 1.93 eV, while (Ag, Bi) disorder has a large impact on the band gap energy. 12 The disordered (Ag, Bi) of Cs 2 AgBiBr 6 is found to have a direct band gap of nearly 0.44 eV. Herein, we have applied variable pressure on the band structure of Cs 2 -AgBiBr 6 , based on rst-principles simulations. The Ag 4delectron orbitals mainly dominate the band gap energy. In the disordered sample, Ag-3d and Bi-6p orbital electrons have undergone hybridization owing to the reduced band gap energy. The valence band maximum (VBM) and the conduction band minimum (CBM) lie at several k-points in the Brillouin zone. This is essential for understanding the pressure-dependent real space charge distribution at different k-point energies. Applying a hydrostatic pressure to a material can easily tune the material's various properties. 13-15 L. Wang et al. reported on the inuence of lead halide perovskite CH(NH 2 ) 2 PbBr 3 and found that the structural phase is changed at 2.2 GPa. 16 Pressuredependent samples undergo band-gap energy shrinkage and the electron orbits move toward the electric eld. As a result, the bonding energy is changed within the octahedral state, which mostly affects the boundary conditions of the electronic wave functions and brings about a reduced band gap energy. We have investigated whether the absorption peak is red shied or blue shied due to the distortion occurring within [AgBr 6 ] 5À and [BiBr 6 ] 3À octahedral states under induced pressure. In particular, the quenched absorption peak of the double halide Cs 2 -AgBiBr 6 was slightly blue-shied compared to the primary peak under zero pressure conditions. 17 In this manuscript, we are researching the effects of (Ag, Bi) disorder and pressure induced in Cs 2 AgBiBr 6 for optoelectronic and photovoltaic applications, applying density functional theory (DFT) via investigating the electronic, mechanical and optical properties. A combined characterization implies that Cs 2 BiAgBr 6 is a potential material for applications in photovoltaic and optoelectronic devices, especially solar cells and photocatalytic activity.

Theoretical methodology
All the density functional theory (DFT) simulations were performed using plane-wave-based CASTEP code, a module of the studio 8.0 package. 18,19 The non-spin polarized Perdew-Burke-Ernzerhof (PBE) functional within the general gradient approximation (GGA) method was chosen to describe the exchange-correlation potential and projector augmented-wave (PAW) pseudopotentials. [20][21][22] We used the simulations of pristine and disordered Cs 2 AgBiBr 6 in 4 Â 4 Â 4 gamma-centered (G) k-points. 5s 2 5p 6 6s 1 for Cs, 4d 10 5s 1 for Ag, 6s 2 6p 3 for Bi, and 4s 2 4p 5 for Br were some of the valence band electronic congurations used in these partial density of states (PDOS) calculations. The unit cell structure was constructed into a 1 Â 1 Â 1 supercell model for all simulations. 23 In these calculations, the cutoff energy was chosen as 420 eV. A scissor value (0.25 eV), a disparity between the theoretical values (1.91 eV) and the experimental values (2.16 eV) in the band gap of the Cs 2 AgBiBr 6 were used for the absorption and dielectric function property calculations. 24,25 The studied sample was entirely optimized by reducing the total energy, internal forces, and external stresses, varying the constant lattice parameters and internal coordinates simultaneously by applying the Broyden-Fletcher-Goldfarb-Shanno (BFGS) algorithm. The unit cell structure and atomic relaxations were accomplished so that the residual forces were below 0.03 eVÅ À1 . Within the CASTEP code, the elastic modulus C ij is simulated by nite-strain theory [26][27][28] and the consequence of external stresses. The stress tensor has six stress parameters s ij for each strain d j employed on the unit cell. The lattice dynamic properties such as phonon dispersion were calculated by employing the nite displacement supercell approach.

Results and discussion
3.1. Structural aspect and phase stability   fractional coordinates (0.2513 0 0). In our case, the samples have two octahedral sites AgBr 6 and BiBr 6 . We calculated the tolerance factor from the equation . The corresponding range of stable structure is 0.81 < t < 1.0. Within this range, the octahedral factor is identied as m¼ (R B / + R B // )/2R X , and the stability of the structure lies in the range 0.81 < m < 1.0. 29 To obtain the structural stability, we applied the Shannon ionic radius. For Cs 2 -BiAgBr 6 with bromide halide, we calculated (m, t) ¼ (0.41, 0.92), which is identied with standard halide perovskites.
The simulated lattice parameters a and the corresponding unit cell volume V 0 with previously published experimental and theoretical results of Cs 2 AgBiBr 6 are presented inTable 1. We conducted a DFT simulation driving various hydrostatic pressures from 0 to 50 GPa for Cs 2 AgBiBr 6 . Under ambient pressure, the simulated theoretical lattice parameters in this work are considered a good t with previously published theoretical work. The DFT-based calculated lattice parameter is slightly higher than the experimental nding, which is a limitation of the GGA approach. The lattice parameter and unit cell volume are changed under driving hydrostatic pressure and are displayed in Fig. 2. From Fig. 2, it is conrmed that the values of lattice parameters and unit cell volumes are decreased by applying various hydrostatic pressures due to the space between lattice vacancies and the bond lengths being reduced. As a result, repulsive phenomena between atoms have become more robust, increasing the difficulty of crystal compression under an applied pressure.

Electronic properties
The band energy calculation was carried out at hydrostatic pressure to study pressure-induced band structure variation in Cs 2 AgBiBr 6 . The present band gap energy values are in good agreement with those in other manuscripts. [32][33][34][35] The simulated band structure is shown in Fig. 3. A hybrid potential like HSE (Heyd-Scuseria-Ernzerhof) may be a better estimate for exact  band gap measurements. But it does not t for some samples. Thus, it is still challenging to search for the appropriate potential to predict the theoretical electronic band gap for the estimated samples. However, the main aim of this research is to investigate indirect to direct band gap conversion, and semiconductor to metal phase transformation due to ordered and disordered systems and the band gap limitation is ignored for the GGA approach. We have seen that the bottom of the conduction band (CB) and the top of the valence band (VB) are located at dissimilar (R 4 G) k-points.
In our samples, the calculated electrical band gap energy is lower than the absorption spectra threshold energy, which indicates that the ordered samples have an indirect band gap nature and the opposite is found for disordered samples. The indirect nature semiconductor is an effective candidate for photovoltaic applications. The indirect band sample identies that the electron cannot move directly from the high energy states in the valence band to the lower energy state in the conduction band, without undergoing any changes in k-point energy. These dissimilar k-points indicated that the structure of Cs 2 AgBiBr 6 was an indirect band gap semiconductor and the value of the band gap was decreased under induced pressure. Under induced pressure, there was band-gap shrinkage and orbital movement towards the electric eld (EF). For a 50 GPa pressure-induced sample, as presented in Fig. 3, electronic localization began to decrease the band gap across the Fermi level. Aer an increase in the induced pressure the sample ultimately achieved a metallic band nature. The band structure results conrmed that Ag-Bi disorder has a greater impact on the band gap energy. Fig. 3(b) shows that the maximum conduction band and the minimum valence band are lying at the same k-point energy, which indicates that the band structure is a direct semiconductor in nature.
In the band structure, energy is shied towards the lower energy region owing to Bi and Ag ions creating defect energies of Br 4p and Bi 6s orbitals. Band gap shiing and phase transition samples may be suitable for a broad range of applications. The total density of states (TDOS) and partial density of states (PDOS) of Cs 2 AgBiBr 6 are presented in Fig. 4. From the TDOS and PDOS in the gure the valence band energy is mainly composed of Ag-4d and Br-6s orbitals with little contribution from Cs-6s and Cs-3p states. The high energy band is mainly attributed to the Ag-4d orbital with a small contribution from Cs-6s and Cs-5p electrons.
The band structures have been inuenced by the hydrostatic pressure, and the maximum conduction band (CB) of Cs 2 -AgBiBr 6 has been enhanced downward into the minimum valence band (VB). As shown in Fig. 3(a), the band gap energy of the studied samples decreases from 1.37 eV to zero when the hydrostatic pressure reaches 50 GPa. Lead-free double halide perovskites, Cs 2 AgBiBr 6 , have displayed great potential applications in photocatalytic devices. Herein, the (Ag, Bi) disorder has a large impact on the band gap energy, transforming the indirect band gap towards the direct band gap. Moreover, the indirect band gap energy creates phonon energy in the material due to producing heat energy and nally decreasing the device's suitability for optoelectronic device applications.
To be stable, natural gain in a material needs to full some criteria. Firstly, for mechanical stability, a sample must full a set of elastic moduli conditions. For the studied sample, this will be discussed in section 3.3. The second criterion is dynamic stability. For dynamic stability in a sample the crystal lattice must be invariable. The second condition is that there should be no so phonon modes in the phonon dispersion. This condition implies that so phonon modes are manifested in a set of atoms moving from a high to a low crystal symmetry structure, which means that the sample has an unstable nature. So phonon modes have an imaginary (negative) frequency. In the case of a dynamically stable crystal, all phonon frequencies must have positive values. To see the nature of the stability, we analyzed the phonon dispersion curves. It is clear that an imaginary frequency is found at the W, L, K, and X points whose phonon dispersion curves are shown below zero frequency, indicating unstable modes. Consequently, no imaginary frequency is found at the G point, indicating a stable nature (Fig. 5).
In this manuscript, we have investigated the thermodynamic stability at varying temperatures of the studied sample under 50 GPa pressure. Thermodynamic properties like enthalpy H, free energy F and entropy S at nite temperature were calculated via phonon modes. The vibration contribution to the free energy is derived as follows 36 where g (u) is the phonon density of states and k B is the Boltzmann constant. Fig. 6 shows the temperature-dependent thermodynamic properties. It can be seen from the gure that the enthalpy and free energy increased temperature while the entropy decreases with an increase in temperature. Fig. 6 also shows that when the temperature approaches zero, three terms (H, F and S) approach zero, which agrees with the third law of thermodynamics. Fig. 7 shows the temperature dependence of the Debye temperature and heat capacity derived from the phonon mode for Cs 2 AgBiBr 6 under 50 GPa pressure. It can be seen that heat capacity approaches the Dulong-Petit limit at high temperature. We predicted that our studied samples would have phase stability under 50 GPa pressure.
The indirect electrical band gap of pure Cs 2 AgBiBr 6 shows a longer lifetime of photo-excited electrons and holes than direct electrical band gap semiconductors due to the direct separation of photo-generated electrons from the CB to the VB of a semiconductor not being possible. Fig. 8 represents the photocatalytic activity. The excited electrons from the valance band (VB) are injected into the conduction band (CB), which decreases the gap energy in disordered Cs 2 AgBiBr 6 lead-free double metal halide perovskite. It shows the impact of the isolation of photo-generated electron-hole pairs, and favors the migration of photoexcited carriers and processing photocatalysis. The disordered sample with new dopant energy levels practically mitigates the band gap energy of the photocatalyst. 37 The work would be suitable for photocatalytic activity applications. Now we discuss the pressure-driven charge density and Ag-Br and Bi-Br bond length evaluation in Cs 2 AgBiBr 6 . From Fig. 9, we can see that pressure-induced on Ag-Br and Bi-Br, bond lengths decrease with increased driving pressure, due to ionic radii overlapping with each other. Another reason that the interoctahedral Ag-Br and Bi-Br bond lengths are changed is due to the crystal defects that have occurred with Ag and Bi atoms. The bond length changes with respect to driving pressure, which is easily understood from the viewpoint of the stiffness of the octahedra.  Without pressure, the intra-octahedral Ag-Br and Bi-Br bonds are considerably stronger due to the relatively weak van der Waals forces of the former Ag-Br and Bi-Br bonds. However, under a pressure of 50 GPa the Ag and Bi atoms exhibit weak bonds. Meanwhile, in pressure-induced samples symmetry breaking is occurring in [AgBr 6 ] 5À and [BiBr 6 ] 3À octahedra, which is manifested as a reduction in the density of states of the Fermi surface and thus lowers the total energy. The bond length of Ag-Br is decreased when the structure is converted from ordered (2.87Å) to disordered (2.82Å) Cs 2 AgBiBr 6 . The tendency of the bond length to shrink in the disordered systems can cause the band gap energy to shi from indirect to direct. In the case of pressure-driven samples, the Ag-Br bond length is decreased with respect to induced pressure, and nally, the samples are converted from semiconductor to metal.
We have researched the electronic charge density (eÅ À3 ) distribution in our sample. In the studied samples, sphericalshaped charge densities overlap with each other. Fig. 10 represents the electronic charge density of Cs 2 AgBiBr 6 . The color map on the right-hand side of Fig. 10 shows the total charge density. The charge density separation map identies that a covalent bond is present in the pure sample. The Bi and Ag atoms have formed a covalent bond at the site with the maximum charge density that exhibits strong electron localization. Under pressure, the bonding charge densities have increased because of the decreasing interatomic distances. As a result of the electric charge, aggregation is increased by driving pressure.

Mechanical properties
The elastic tensor properties are essential parameters for understanding the mechanical nature of crystal-solids. Cubic structure crystals like pressure-induced Cs 2 AgBiBr 6 have three independent elastic moduli C ij ; these are C 11 , C 12 , and C 44 . The simulated elastic parameters are listed in Table 2. The mechanical stability of a crystal can be satised with its elastic constants using Born criteria. For a cubic system, the estimated compound, to be mechanically stable, should satisfy the conditions: 34,35 C 11 + 2C 12 > 0, C 44 > 0, C 11 À C 44 > 0 for high symmetry. Additionally, the cubic crystal stability condition: C 12 < B < C 11 is also fullled by the title compound. Elastically isotropic cubic crystals should satisfy the conditions, 2C 44 ¼ C 11 À C 12 . The elastic moduli C 12 and C 44 are different quantities and (C 12 À C 44 ) is denoted the Cauchy pressure 36,38 and is distributed as an elementary instrument for computing many phenomena in crystalline solids. In solid samples, Cauchy pressure values with positive and negative signs indicate a metallic or covalent bond nature, respectively. Our studied samples have the positive Cauchy pressure that indicates that the studied sample shows ductile behavior. Moreover, some special mechanical characteristics of the title sample can be    Table 3. The Young's modulus value E determines the resistance in the opposite direction to the longitudinal tension. It can be seen from Table 3 that the elastic constants increase with an increase in the pressure up to 50 GPa; as a result, the bulk modulus increases. Pugh used the bulk to shear modulus value ratio (B/G) (brittle/ductile) to identify defects in crystal solids. 39,40 According to this idea, ductile materials have a B/G ratio higher than the critical value of 2.46, which is distributed as a broad line between the brittle and ductile natures in crystalline solid samples. A material will exhibit a ductile nature, if its Pugh's ratio has a value greater than the broader line value shown in Fig. 11. To compute Pugh's ratio (ductile/brittle), the failure mode in crystal solids and Poisson's value v are applied fruitfully for engineering purposes. In a crystalline solid sample, ductile or brittle natures are identied with a critical range of v ¼ 0.32. 41 It is shown from Table 4 that Cs 2 AgBiBr 6 is ductile and by employing a pressure up to 50 GPa, this ductility enhances Cs 2 AgBiBr 6 as a potential component for device fabrication. For the cubic structured Cs 2 AgBiBr 6 , the maximum and minimum values of Y, G, and v are analyzed with the help of the ELATE suit program. 42 The maximum and minimum Y, G, and v values showed in another way that the sample is isotropic in nature; the crystal is anisotropic in nature. The movement of the spherical shape identies the rate of elastic anisotropy level of the solids. Table 4

Optical properties
Optical properties, like the absorption spectrum, the real and imaginary parts of optical conductivity, and the dielectric function are shown in Fig. 12. In all of the simulations in this manuscript, a Gaussian smearing of 0.5 eV is used. The optical properties simulation results were taken in the {100} plane orientation. A scissor value is used of 0.25 eV for all optical property simulations. The energy range used was 0-20 eV. The absorption spectra were taken in the UV-vis, and visible wavelength (l) range 100-600 nm. The optical absorption a(u) determines the entrance of light at wavelength (l) into a solid sample. 43 The rst absorption peak in the energy range of approximately 3.95 eV is more important for device applications. We have seen that Cs 2 AgBiBr 6 has a strong absorption spectrum lying in the visible wavelength (nm) area. The rst and second absorption peaks are present in the ranges of approximately at 150 and 180 nm, respectively. The optical absorption intensities are apparently increased due to their large band gaps compared to pristine and pressure-induced samples. The absorption spectra output is blue-shied, and a strong absorption edge is situated at nearly 150 nm. For pressureinduced samples, the key absorption edge is red-shied and it develops in a lower energy region and increases in intensity. The light absorption spectra of perovskite materials are strongly dependent on the electronic structures. A stronger optical absorption implies an improved photovoltaic performance. Hence the band gap energy was transferred towards the visible region and the maximum absorption peak occurred in the UV-  region, which indicates that the studied samples are potential candidates for the optoelectronics industry. The optical conductivity (1/f s ) is a fundamental parameter for identifying the electromagnetic response of a material. 44 In another explanation, the optical conductivity implies the amount of photons passed through the samples. It exposes the electrical conductivity when a sample is placed in a strong electric eld and it connects the current density to the electric eld for natural frequencies. The optical conductivity and electrical conductivity improve with rising photon absorption. It can be seen that the real part vanishes at approximately 12.5 eV, indicating that the sample has an optically anisotropic nature. The optical conductivity has similar features to absorption spectra, as presented in Fig. 12(a), owing to the escape of free carriers from the balance band to the conduction band when it absorbs energy. The amount of electromagnetic radiation response in a sample needs to be understood from the complex dielectric function. 45 The imaginary part of the dielectric function (3 2 ) corresponds to electron excitation. The rst peak of the imaginary part of the dielectric function (3 2 ) occurs at <1.5 eV due to the intra-band transitions within the Bi 6p and Ag 3d orbital bands. In the spectrum the most essential quantity is the zero-frequency limit 3 1 (0), which is the electronic portion of the static dielectric constant. From the real part of the dielectric constant, it is clear that 3 1 (u) increases with induced pressure. The 3 1 (0) for a pressure-induced sample starts rising from a zero frequency, reaches its maximum peak, then starts to reduce, and in given energy ranges it drops below zero. In these areas, the incident photon beam is totally attenuated. 46 A combined study of the optical properties of pressure-induced and disordered materials is suitable for optoelectronic and photovoltaic device applications.

Conclusions
In conclusion, we have applied DFT to calculate the phase stability, and electronic, mechanical, and optical properties of Cs 2 AgBiBr 6 double halide perovskites. The simulated structural parameters a and V decreased with an increase in hydrostatic pressure in pristine Cs 2 AgBiBr 6 samples due to the space of lattice vacancies being reduced. The indirect band energy is transferred to the direct band energy in the case of the structure being converted from ordered to disordered. We have also seen that pressure-driven samples have transformed from semiconductor phase to metallic behavior. With pressure, the Ag-Br and Bi-Br bond lengths are changed due to the crystal defects occurring with Ag and Bi atoms. Meanwhile, in hydrostaticpressure driven samples, symmetry breaking is occurring in [AgBr 6 ] 5À and [BiBr 6 ] 3À octahedra due to a reduction in the density of states and band gap energy. The charge density map conrmed that the covalent bond is present in the pure sample. With increasing pressure, the covalent bond is converted into a metallic bond. The mechanical behaviors demonstrated that perovskite double halide compounds are mechanically stable. Their ductile nature is enhanced with an increase in driving pressure. The elastic anisotropy behaviors showed that pressure-driven samples will be suitable for applications by the scientic community. For the optical properties, we saw that the absorptivity and dielectric constant values also increased with an increase in driving pressure. Phase transferred double halide perovskite materials have provided great scope for a broad range of applications. A combined study suggests that the pressure-induced samples are suitable for optoelectronic devices, especially solar and photovoltaic applications.

Conflicts of interest
There are no conicts to declare.