K₃Ti₂Cl_9−xBr_x: structurally stable lead-free perovskites as permissive absorbers for solar cell and visible-light photocatalysis

Abstract

The toxicity issues with lead-based perovskite solar cells sparked interest in lead-free alternatives, such as K₃Ti₂Cl_9−xBr_x (x = 0, 3, 6, and 9), which are environmentally friendly. The optical, structural, and electrical properties of K₃Ti₂Cl_9−xBr_x (x = 0, 3, 6, and 9) are investigated using density-functional theory in this study to assess their potential as absorber materials for solar cells. Phonon dispersion is used to determine the dynamical stability of these perovskites in addition to their formation energy, which further provides evidence regarding their stability. The TB-mBJ indicates its direct bandgap along the M–M direction and indirect bandgap at the M–K direction and lie within the ideal range for photoelectric conversion. The SCAPS-1D program is employed to identify the optimal solar cell designs that integrate various ETLs and HTLs. The structure with the highest power conversion efficiency out of the fifty four configurations examined is FTO/WS₂/K₃Ti₂Cl_9−xBr_x (x = 0, 3, 6 and 9)/CuI, provides the highest performance with an efficiency of 19.11, 24.68, 25.25 and 29.00%, FF of 82.14, 81.53, 80.09 and 62.07%, V_oc of 1.30, 1.29, 1.25 and 1.35 V and J_sc of 17.84, 23.42, 25.88 and 27.00 mA cm⁻² with the addition of recombination effect. Additionally, the effect of thickness, defect density, series and shunt resistance is also examined. Photocatalytic analysis shows that all of these compounds are capable of converting H₂O to O₂ and H₂. In the same way that the compounds under study may reduce N₂ to NH₃, they can likewise reduce CO₂ to CH₄OH and CH₄. In comparison to other materials, these compounds have an effective efficiency for reducing CO₂ and N₂ and their photocatalytic efficiency for water splitting is higher than the intended value for industrial applications. Future research should focus on developing lead-free, totally inorganic perovskite photovoltaics and photocatalysts with enhanced photovoltaic and photocatalytic performance. Such materials could have uses in photocatalysis, especially in visible light-driven processes like water splitting, CO₂ reduction, and N₂ fixation and are highly promising for use in photovoltaics and high-performance optoelectronics because they all have absorbers with strong visible-light absorption, a large PCE, and a high quantum efficiency.

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1 Introduction

The breakthrough power conversion efficiencies (PCEs) of Pb-based halide perovskites have garnered a lot of interest.^1,2 On the other hand, concern about Pb's considerable toxicity has a negative impact on ecosystems and living things, as well as slows down the commercialization of perovskite solar cells (PSCs).³ This is why creating perovskite materials that are free of lead is becoming a higher priority for the perovskite community. Several potential replacements to Pb that meet these criteria include halides based on Sn and Ge, double perovskites, and halides that are similar to perovskites but have lower toxicity and better optoelectrical characteristics.^3–6 Although Sn/Ge-based halides have appealing characteristics and a structure similar to Pb, their instability resulting from quick oxidation in ambient conditions is a serious constraint.^7,8

The more stable double perovskites (A₂BB'X₆) have been used despite having a larger band gap than Pb-based halides.^9,10 A new class of group-VA trivalent metal cation based perovskite halides (A₃B₂X₉) with an electronic configuration comparable to that of Pb-based perovskites and environmentally pleasant photovoltaic device candidates and display better thermodynamic stability.^11,12 The electrical characteristics of Sb-based halides can be affected by the halide components, like Bi-based perovskite compounds that have the same problems as double perovskites. There are inherent issues with the MA₃Sb₂I₉ is poor carrier transport and an indirect bandgap value over 2.2 eV.¹³ The mixed halide MA₃Sb₂I_9−xCl_x¹⁴ with theoretical direct bandgap values ranging from 1.8 eV to 2.2 eV, allows for improved carrier mobility and transport when iodine is mixed with chlorine. 2D perovskite-like solar cells based on Sb still have unsatisfactory PCEs due to disordered growth, poor film shape, and uncontrolled halide components.^15,16

Research into mixed Bi based Cs₃Bi₂I_9−xBr_x has also focused on its potential in photovoltaics and photodetection comparatively as Sb based compounds.¹⁷ In their study, Yu et al. documented a thorough investigation of the I/Br solid solution. They utilized spin coating to create thin films with end-members and intermediate mixed compositions, which were then utilized in PSCs. Although the statistics demonstrate that Bi-based phases are quite stable, the power conversion efficiencies (PCEs) are very low; the compound with the best performance, Cs₃Bi₂I₆Br₃, achieved 1.15%.¹⁷ Liu et al.¹⁸ investigated the photodetection capabilities of Cs₃Bi₂Br_9−xI_x films with different values of x. The Cs₃Bi₂I₆Br₃ composition showed the most promising results, with a photosensitivity of 4.1 × 10¹ at zero bias, a responsiveness of 15 mA W⁻¹, and a detectivity of 4.6 × 10⁵ Jones.¹⁹ In this particular instance, remarkable environmental stability is noticed over 96% of the initial value even after 100 days. So far, all the evidence that has been reported pertains to recent research that suggests that layered perovskites made of Bi have potential for future exploration and use in various technologically significant areas. This is supported by the interest in tunable Cs₃Bi₂(Cl_1−xI_x)₉ halide perovskites.

Recently titanium in halides comparatively to Bi have taken instruct due to an interesting property of their ability to create compounds with varying valences. Solid state processes were used to produce K₃Ti₂Cl₉ and K₃Ti₂Br₉ single crystals by Schroeder et al.²⁰ The larger anions and smaller cations crating the deviance from the idealized geometry. During symmetry reductions in K₃Ti₂Cl₉ and K₃Ti₂Br₉, the [Ti₂X₉]³⁻ units are rotated. For optimal outcomes, this rotation is a geometrical requirement.

Conversely the efficiency of photo-to-current conversion is restricted due to the low band gap of most perovskite semiconductors. Not only that, but they are also not suitable for use as stable photodetector materials due to their toxicity and inconsistent performance. Thus, perovskites based on titanium halide are presented as a more sustainable and environmentally friendly option for photodetection due to their extensive band gap, in order to address these important concerns. Modulating the photo response properties can probably be achieved more effectively using band gap tenability, which involves adjusting the ratio of halide ions. For the photocatalysis and solar cell application, it would be most intriguing to examine these less-studied Ti-based perovskites. A common method for modifying or altering semiconductor materials' optoelectronic and photophysical characteristics is alloying or modification. In the current study the K₃Ti₂Cl_9−xBr_x (x = 0, 3, 6 and 9) have been studied to understand the Cl/Br allying and its impact on their physical properties.

2 Computational detail

This computational study used the WIEN2k software package's Full-Potential Linearized Augmented Plane Wave (FP-LAPW) approach²¹ to determine the material characteristics that are desired. In order to accurately calculate the density of states (DOS) and explain optical and electrical properties, the Trans-Blaha modified Becke-Johnson (TB-mBJ) method²² was used. The generalized gradient approximation (GGA)²³ an exchange–correlation potential were used for structural property calculations. A number of FP-LAPW basis functions were investigated, with RMT spheres set to 8 as an example. The muffin-tin spheres had their spherical harmonics magnified to L_max = 11, and their Fourier-expanded charge densities were capped at G_max = 12 (a.u.). For self-consistent field calculations, convergence was defined as a total energy variation less than or equal to 0.0001 Ry. The energy–volume curve was fitted using the Birch–Murnaghan equation of state,²⁴ which allowed the estimation of equilibrium lattice parameters. To further understand the possible optoelectronic applications of the chosen crystalline materials, their optical behavior was investigated using the dielectric function.²⁵ The photocatalytic performance of these compounds are calculated using Mullikan electronegativity method²⁶ and the solar to energy conversion efficiency is calculated by the formula²⁷ The variables J_sc, ΔG, η_F, and P_in represent the current density, Gibbs free energy, faradaic efficiency and input power and the η_F is assumed to be one, the upper limit in this equation. Analytical determination of ΔG is made using the conversion reaction for water splitting, CO₂ reduction, and N₂ fixation.

The study of PV performance, including J_sc, V_oc, FF, and PCE of the designed solar cells are investigated and modeled by employing the SCAPS simulation software.²⁸ A light power of 1000 W m⁻² spectrum is employed for the simulations, which were conducted at 300 K and the simulation parameters are given in Table 1 and 2 correspondingly.^29,30

Table 1 Simulation parameters for different layers taking K₃Ti₂Cl_9−xBr_x (x = 0, 3, 6, 9) perovskite as absorber layer

Parameters	FTO	WS2 (ref. 29)	K3Ti2Cl9^[calculated]	K3Ti2Cl6Br3^[calculated]	K3Ti2Cl3Br6^[calculated]	K3Ti2Br9^[calculated]	CuI^29
Thickness (nm)	300	180	900	900	900	900	150
Eg (eV)	3.5	1.80	1.86	1.64	1.56	1.51	3.10
χe (eV)	4.0	3.95	4.0	4.0	4.0	4.0	2.14
ε1 (eV)	9.0	13.6	2.486	2.89	3.22	3.28	6.50
Nc (cm^−3)	2.02 × 10^19	1 × 10^18	4.85 × 10^17	8.87 × 10^15	1.47 × 10^16	2.25 × 10^15	2.8 × 10^19
Nv (cm^−3)	1.8 × 10^19	2.4 × 10^19	2.13 × 10^18	1.14 × 10^18	1.50 × 10^18	6.11 × 10^17	1 × 10^19
VTh,e (cm s^−1)	10^7	10^7	4.34 × 10^7	0.96 × 10^8	0.98 × 10^8	1.48 × 10^7	10^7
VTh,h (cm s^−1)	10^7	10^7	2.65 × 10^7	3.27 × 10^7	2.98 × 10^7	4.02 × 10^6	10^7
µe (m^2 V s^−1)	2 × 10^1	100	80.05	183.31	258.19	495.44	100
µh (m^2 V s^−1)	1 × 10^−1	100	144.34	251.11	168.17	254.60	43.9
ND (cm^−3)	10^15	0	0	0	0	0	1 × 10^18
NA (cm^−3)	0	10^18	10^14	10^14	10^14	10^14	0
NT (cm^−3)	10^15	10^15	10^15	10^15	10^15	10^15	10^15

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Table 2 Simulation parameters of interface layer

Interfaces	ETL/absorber	Absorber/HTL
Type of defect	Neutral	Neutral
Cross section for electron (cm^2)	1 × 10^−15	1 × 10^−15
Cross section for hole (cm^2)	1 × 10^−15	1 × 10^−15
Energetic distribution	Single	Single
Reference of defect energy level	Above the highest Ev	Above the highest Ev
Energy level with respect to Ev (eV)	0.6	0.65
Characteristic energy (eV)	0.1	0.1
Total density (cm^−3)	1 × 10^15	1 × 10^15

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3 Results and discussion

3.1 Structural properties

In the current study, the compounds K₃Ti₂Cl_9−xBr_x (x = 0, 3, 6 and 9) have a hexagonal crystal with space group P6₃/m (no. 176) and belong to K₃W₂Cl₉ type crystal is shown in Fig. 1. In these perovskite-related structures the monovalent cations K as large as the halide anions Cl and Br and have a K : Cl or Br is of 1 : 3. Ti cations fill the octahedral spaces created by anions in hexagonal sequences but are absent in cubic sequences. Separate face-sharing octahedra [Ti₂Cl₉ or Br₉] are the most noticeable structural element in these compounds and therefore these compounds are of great interest due to Ti–Ti interactions owing to the proximity of the Ti atom.

Fig. 1 Crystal structure and optimized ground state energies versus c/a ratio of the K₃Ti₂Cl_9−xBr_x (x = 0, 3, 6 and 9) halide perovskites.

The total energy was determined by plotting it against the c/a ratio in order to study the structural behavior and analyze its ground-state characteristics. To find their optimum ground state lattice constants, all these compounds were subjected to single-point computations. The Birch–Murnaghan equation of state is used to determine the optimized lattice constants (a and c).³¹ The actual lowest ground state of the compound is represented by the minimum energy E₀, and their structural stability is enhanced by the negative energy values. The optimized structural parameters are shown in Table 3. The changes in cell characteristics from Cl to Br are in line with the cations' increasing ionic radii. As a contrast to Br, Cl has a smaller ionic radius. Both the cell size trend and the ionic sizes of these cations are in excellent agreement. Fig. 1 shows the optimization curve for all these compounds, and the lowering of energy value from Cl-based to Br-based compounds suggests increased structural stability. On the other hand, the tolerance and octahedral factors for these compounds are also calculated and found to be in the stable range for these compounds.³² In addition, the formation enthalpy (H_f) is computed in order to evaluate the formation feasibility. Their structural stability is further confirmed by the negative formation energies, which indicate that the production of these compounds is energetically satisfactory.³³ The studied compounds show negative formation energies, which indicates these compounds are energetically favorable, according to the computed values in Table 3.

Table 3 Calculated lattice constants, c/a ratio, ground state energy, formation enthalpy, bond lengths, bond angels and band gap, Mulliken electronegativity CBM and VBM potentials of the K₃Ti₂Cl_9−xBr_x (x = 0, 3, 6, 9) compounds

Parameters	K3Ti2Cl9 (exp.)^20	K3Ti2Cl6Br3	K3Ti2Cl3Br6	K3Ti2Br9 (exp.)^20
a (Å)	7.128 (7.073, 7.052)	7.17	7.28	7.387 (7.429, 7.406)
c (Å)	17.430 (17.544, 17.491)	17.68	17.84	18.295 (18.382, 18.330)
c/a	2.48 (2.50)	2.46	2.45	2.38 (2.47)
E0 (Ry)	−30631.254	−56311.7500	−82029.6252	−107747.297
Τ	1.01	1.00	0.998	0.992
µ	0.334	0.325	0.317	0.301
Hf (Ry)	−0.224	−0.252	−0.272	−0.287
Eg (eV)	1.861, 1.861	1.643, 1.648	1.567, 1.577	1.512, 1.519
For direct nature
	0.229me	0.060me	0.131me	0.037me
	0.127me	0.084me	0.153me	0.072me
For indirect nature
	0.209me	0.100me	0.071me	0.100me
	0.187me	0.073me	0.109me	0.193me
Eb (meV)	66.28	10.63	8.78	3.18
a* (Å)	33.15	273.22	254.95	784.08
χcom	5.313	5.263	5.214	5.166
ECB	−0.056	−0.06	−0.015	−0.038
EVB	1.783	1.633	1.544	1.471

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On the other hand for specialized device performance, it is essential to evaluate a material's dynamic stability. This has been accomplished by working with the WIEN2k using the Phonopy code.³⁴ Theoretically, when the basic unit cell of a material contains n atoms, the resulting phonon spectrum will show 3n different branches.³⁵ Three of the peaks on this spectrum are directly related to acoustic phonon modes, and the other 3n-3 peaks are directly related to optical phonon modes. A material's intrinsic physical qualities and behavior can be understood by using this concept, which sheds light on the complex connection between the atomic make-up of a material's unit cell and the unique vibrational modes exhibited by its individual atoms. The materials under study have a basic unit cell structure with 14 atoms, which causes them to exhibit 42 different vibrational modes, as illustrated in Fig. 2. The three curves that show the lowest frequencies at the Γ point depict the acoustic branch lattice waves, which are in the frequency range of sound waves. The remaining 39 curves among the 42 represent the lattice waves of the optical branch. The figure illustrates that phonon dispersion curves for all compounds are above zero and does not found imaginary frequencies, which further confirms the stability of the under study compounds. Based on this finding, it may be concluded that these materials have dynamically stable materials. In addition, the phonon dispersion curves do not include imaginary frequencies indicating that the materials under study are not prone to phase transitions or structural distortions at the analyzed pressure and temperature conditions. Based on these results, it appears that these materials are dynamically stable for use in high-performance devices.

Fig. 2 Phonon dispersion curves of the K₃Ti₂Cl_9−xBr_x (x = 0, 3, 6 and 9) halide perovskites.

3.2 Electronic properties

To fully grasp the potential of K₃Ti₂Cl_9−xBr_x (x = 0, 3, 6 and 9) compounds in optoelectronic and solar cell applications, a systematic understanding of their electronic band structure is essential. The electronic behavior of the under study compounds are explained with the help of total density of states (DOS) estimated via GGA and mBJ revealed in Fig. 3, which reveals that the densities do not overlap at the Fermi level and do not encompass the VB to the CB indicate the semiconductor nature of these compounds through mBJ, while the GGA indicates their metallic nature. In order to further validate the electronic nature of the compounds, their TDOS is also calculated by applying Hubbard U with GGA, SOC and HSE06 and given in Fig. S1. The obtained results also indicate the semiconductor nature of these compounds with minor changes in their band gaps accordingly.

Fig. 3 Total DOSs and partial DOSs of the K₃Ti₂Cl_9−xBr_x (x = 0, 3, 6 and 9) halide perovskites.

Fig. 4 shows the electronic band structure for K₃Ti₂Cl_9−xBr_x (x = 0, 3, 6 and 9) respectively. The horizontal dashed line shows the Fermi level at 0 eV. The electronic band structure is computed over the representative directions of high symmetry k-points (Γ–M–K–Γ–A) in the first Brillouin zone for K₃Ti₂Cl_9−xBr_x (x = 0, 3, 6 and 9) perovskite as depicted in Fig. 4. The band gap (E_g) of K₃Ti₂Cl_9−xBr_x (x = 0, 3, 6 and 9) compound, with mBJ functional is determined over the high-symmetry k-lines in the first Brillouin zone, indicating its direct bandgap of 1.861, 1.648 and 1.577 eV along the M–M direction and 1.519 eV along the Γ–Γ direction and indirect E_g of 1.861, 1.643, and 1.567 eV at the M–K direction and 1.512 eV at the Γ–M direction. The difference among the direct and indirect E_g is 0.00, 0.005, 0.01 and 0.007 eV accordingly in these compounds are of unique character and both the direct and indirect E_g of the K₃Ti₂Cl_9−xBr_x (x = 0, 3, 6 and 9) semiconductor is associated with the absorption span in the visible light, which may yield a PV quantum effect in inter-bands with better efficiency.³⁶ A similar effect of electronic transition via atomic doping is also reported for double perovskites.^37,38

Fig. 4 Electronic band structure of the K₃Ti₂Cl_9−xBr_x (x = 0, 3, 6 and 9) halide perovskites.

Moreover, the projected density of states (PDOS) on s, p, d states of K, Cl, Br and Ti atoms respectively for K₃Ti₂Cl_9−xBr_x (x = 0, 3, 6 and 9) perovskites are computed. As plotted in Fig. 3, the PDOS results reveal four regions of energy states of the studied compounds. The plot displays two portions of valence bands (VB) that range between −5.5 eV and EF. The major portion of PDOS of the various s, p, and d states of K, Cl, Br and Ti atomic elements participated in the VB. Remarkably, the two sections situated upward the EF in the positive range of energy states are delineated by the conduction bands (CB). The lowest valence states that are mainly assisted by a sharp spectral peak of Cl and Br-p states are around −5.5 to 1 eV and are overlapped with a small contribution of d orbitals of the Ti atom. A significant hybridization of Ti-d state occur with the Cl and Br-p states that participate to form the valence states edge. The next section is composed of a weak assistance of states of the Ti element centered at about −1 to 0 eV. On the other hand the CB is composed of the Ti-d state in the two sections from E_g to 2 eV and from 3 to 4 eV respectively.

3.3 The effective mass, exciton binding energy and radius

Diffusion length, electrical conductivity, carrier mobility, and effective mass of charge carriers are the fundamental variables that have a direct impact on the transport properties of semiconductors. The curvature of the electronic band diagram around the VBM and CBM, respectively, is used to compute the effective mass of holes and electrons for K₃Ti₂Cl_9−xBr_x (x = 0, 3, 6 and 9). Band topologies with relatively distributed valence bands around the EF are shown in Fig. 4. This suggests that the is lower than the , which is beneficial for effective charge transfer, as specified in Table 3. The values of for the K₃Ti₂Cl_9−xBr_x (x = 0, 3, 6 and 9) compounds are 0.229 m_e, 0.100 m_e, 0.071 m_e and 0.037 m_e, while the is 0.127 m_e, 0.073 m_e, 0.109 m_e and 0.072 m_e, as shown in Table 3. This indicates the compounds with the lowest effective mass and the highest carrier mobility and are consistent with the effective masses for electrons and holes reported for isotropic compounds.^39,40

It is expected that K₃Ti₂Cl_9−xBr_x (x = 0, 3, 6 and 9) compounds, which have lighter effective masses and lower E_g, will have higher light absorption and increased carrier mobility, as a result of the equilibrium between the two variables controlling their transport properties. Consequently, K₃Ti₂Cl_9−xBr_x (x = 0, 3, 6 and 9) might be the best which would make it a viable option for SCs and optoelectronic applications. Additionally, the exciton radius (a*) and exciton binding energy (E_b) are determined for these compounds to study their excitonic properties. An estimated value of E_b for these compounds are 66.28, 10.63, 8.78 and 3.18 meV component respectively show in Table 3. Table 3 also displays a* these compounds, which are 33.15, 273.22, 254.95 and 784.08 Å respectively. From Table 3, it is clear that the a* is increasing with decreases E_b. The photogenerated electron and hole charge carriers have a larger a* and a lower exciton E_b, which are advantageous for SC applications since they interact less and disintegrate faster. The compounds under investigation show outstanding potential as SC and photocatalytic materials because of their remarkable E_g, electron mobility, reduced effective mass, decreased exciton energy, and increased exciton radius as a Pb-free alternative.

3.4 Optical properties

Since the semiconducting compounds with direct band gaps, are optically active materials, it is crucial to provide a detailed explanation of their optical characteristics. The dielectric function ε(ω), which represents the polarization of light response to the material, serves to determine the corresponding optical characteristics. ε(ω) composed of two components, the real and imaginary. The imaginary component ε₂(ω) of the dielectric function is simulated using the joint DOS along the first-Brillouin zone, whereas the real part ε₁(ω) is connected to the imaginary component via the Kramers–Kronig relation.⁴¹ Both ε₁(ω) and ε₂(ω) components are useful for computing all the important optical constants, including reflectivity coefficient R(ω), the refractive index n(ω), and the optical absorption coefficient α(ω), and so forth.

The peak values of ε₁(ω) show the materials' noticeable optical characteristics in the visible and ultraviolet region. This is in agreement with Penn's hypothesis, which postulates that static polarization and the E_g are inversely related.⁴² The static ε denoted as SDF is represented by the expression (ε₁(0)) at zero frequency. SDF for K₃Ti₂Cl₉ is 2.48, 2.89 for K₃Ti₂Cl₆Br₃, 3.22 for K₃Ti₂Cl₃Br₆ and for K₃Ti₂Br₉ is 3.28 respectively as visible in Fig. 5. As can be seen in Fig. 5, a peaking of the spectra for K₃Ti₂Cl_9−xBr_x (where x = 0, 3, 6, and 9) occurred at 2.97, 3.36, 3.33, and 2.95 eV, respectively, after the zero frequency. After reaching their peak, the spectra progressively decline until they drop below zero. When this happens, the compounds lose their dielectric nature and start behaving more like metals.

Fig. 5 Real part of dielectric function of the K₃Ti₂Cl_9−xBr_x (x = 0, 3, 6 and 9) halide perovskites.

The imaginary part ε₂(ω) of dielectric function representing light absorption and energy dissipation is shown in Fig. 6. It can be seen that at the beginning ε₂(ω) is zero so light absorption is zero after that the light absorption starts at the E_g value. After the E_g value the ε₂(ω) reaches its greatest value at particular photon intensities. These peaks show possible light-energy absorptions that result in interband transitions.

Fig. 6 Imaginary part of dielectric function of the K₃Ti₂Cl_9−xBr_x (x = 0, 3, 6 and 9) halide perovskites.

The optical absorption coefficient describes the amount of light absorbed when the electromagnetic radiation with sufficient photon energy is incident upon the material. Electrons will absorb photons in the valence band of a semiconducting material with energies exceeding the band gap, thereby transiting to the conduction band. The efficiency of SC possesses an essential reliance on the details of the VB and CB edges. Fig. 7 exhibits the absorption coefficient spectrum for these compounds. As shown in Fig. 7, the absorption edge starts at an energy value approximately at the band gap. It is illustrated in Fig. 7, that the maximal peak features appear in the energy range between 9.5 and 13.95 eV for these compounds. The absorption coefficient reveals that the compounds have a much larger optical absorption coefficient exceeding 10⁴ cm⁻¹ in the visible spectrum, which could serve as an appealing characteristic for SC applications.⁴³ This can make this semiconductor perfect, as a light-absorbing material beneficial for the thin-film PV devices.

Fig. 7 Absorption of the K₃Ti₂Cl_9−xBr_x (x = 0, 3, 6 and 9) halide perovskites.

The linear optical response from VBs to the lowest CBs is delineated via the reflectivity. As is apparent, the reflectivity spectrum of the stannite structure is depicted in Fig. 8. The occurrence of a prominent peak is around 13.95 eV for these compounds. The static spectral components of the optical reflectivity R(0) are 5.0, 6.7, 8.1 and 8.3% for K₃Ti₂Cl_9−xBr_x (x = 0, 3, 6 and 9) compound.

Fig. 8 Reflectivity of the K₃Ti₂Cl_9−xBr_x (x = 0, 3, 6 and 9) halide perovskites.

Refractive index n(ω) measures the transparency and has an essential impact on devices such as SCs.⁴⁴ The optical characteristic of a material whose n(ω) is dependent on the direction of light propagation and polarization is referred to as birefringence.⁴⁵ The orientation of the crystalline lattice with respect to the incident light determines whether the optically anisotropic materials interact with light through their crystallographically different axes. A notable feature n(0) the static n(ω) for these compounds is 1.57, 1.70, 1.79 and 2.36 shown in Fig. 9. The refractive index spectrum versus the photon energy increases and then decreases with a few oscillations (at high photon energies).

Fig. 9 Refractive index of the K₃Ti₂Cl_9−xBr_x (x = 0, 3, 6 and 9) halide perovskites.

To quantify a material's absorption and scattering properties extinction coefficient k(ω) for these compounds is also calculated and shown in Fig. 10. A stronger absorption of light is indicated by higher values of k(ω). After E_g value the k(ω) grows and achieves a maximum value at 4.79 to 5.89, 10.21 to 11.63 and at 13.56 eV correspondingly for K₃Ti₂Cl_9−xBr_x (x = 0, 3, 6 and 9) compounds, indicating that these compounds outstandingly absorb and poorly transmit in this range. Fig. 10 also shows that all compounds exhibit strong absorption in the visible range which make them efficient for solar cell applications.

Fig. 10 Excitation coefficient of the K₃Ti₂Cl_9−xBr_x (x = 0, 3, 6 and 9) halide perovskites.

3.5 Simulation and modelling of solar cell

The optimization of the electrical parameters of the solar cells investigated in this study is carried out using the SCAPS-1D. The cell structure is shown in Fig. 11 and the input parameters of the different layers are in Table 1 and Table S1 to S3 while the input parameters of the interface defect layers in Table 2.

Fig. 11 Schematic solar cell model of the K₃Ti₂Cl_9−xBr_x (x = 0, 3, 6 and 9) halide perovskites.

Fig. 12 Effect of absorber thickness on the PV parameters of the K₃Ti₂Cl_9−xBr_x (x = 0, 3, 6 and 9) halide perovskites.

3.5.1 ETL and HTL optimization. The aim is to design the suitable solar cell with the best electrical parameters and PV characteristics.⁴⁶ Here, several HTLs and ETLs are incorporated in order to produce all the feasible combinations of solar cell devices. All the input data of different ETLs and HTLs respectively are collected and given in Tables S1 to S3 which are employed in SCAPS simulations for different FTO/ETL/K₃Ti₂Cl_9−xBr_x (x = 0, 3, 6 and 9)/HTL structures.

This study examines the effects of some selected HTLs, such as CFTS CuO₂, CuI, CuSCn, MoO₃, NiO, rGO, PEDOT:PSS and P3HT, K₃Ti₂Cl_9−xBr_x (x = 0, 3, 6 and 9) as the absorbers, some selected ETLs, such as the TiO₂, Li doped TiO₂, ZnO, Al doped ZnO, C₆₀, IGZO, PCBM, SnO₂, WS₂ as ETL, PCBM-PCPB, PCBM-SnS₂ and TiO₂-SnO₂ as hybrid ETL and Cu as the back contact to examine the PV performance parameters of the K₃Ti₂Cl_9−xBr_x (x = 0, 3, 6 and 9)-based solar cells. Here, fifty four combinations of ETL/K₃Ti₂Cl_9−xBr_x (x = 0, 3, 6 and 9)/HTL heterojunction structures are designed. The PV characteristics of the various designed solar cells by considering all combinations of HTLs and ETLs and their PV characteristics, are given in Tables 4–6. From the tables it is well noticeable that among all the K₃Ti₂Cl_9−xBr_x (x = 0, 3, 6 and 9)-based solar cell structures, the WS₂/K₃Ti₂Cl_9−xBr_x (x = 0, 3, 6 and 9)/CuI configuration with CuI HTL and WS₂ ETL provides the highest performance with an efficiency of 18.52, 24.16, 25.25 and 29.34%, FF of 81.36, 81.63, 79.78 and 79.58%, V_oc of 1.28, 1.29, 1.25 and 1.35 V and J_sc of 17.77, 22.87, 25.29 and 27.00 mA cm⁻² indicating WS₂ and CuI as the best ETL and HTL for these absorbers.

Table 4 Simulation parameters of CuI as HTL with different ETL for K₃Ti₂Cl_9−xBr_x (x = 0, 3, 6, 9) perovskite as absorber layer

HTL	ETL	Absorber	Voc (V)	JC (mA cm^−2)	FF (%)	PCE (%)
CuI	TiO2	K3Ti2Cl9	1.147	16.00	76.48	14.04
		K3Ti2Cl6Br3	1.10	22.40	76.73	18.99
		K3Ti2Cl3Br6	1.04	24.88	74.02	19.30
		K3Ti2Br9	1.00	26.61	72.53	19.37
	Li-TiO2	K3Ti2Cl9	1.17	16.20	74.89	14.30
		K3Ti2Cl6Br3	1.10	22.76	77.57	19.56
		K3Ti2Cl3Br6	1.04	25.23	75.63	19.86
		K3Ti2Br9	0.99	26.97	74.47	19.95
	ZnO	K3Ti2Cl9	1.16	16.30	75.94	14.39
		K3Ti2Cl6Br3	1.11	22.76	76.24	19.28
		K3Ti2Cl3Br6	1.05	25.23	73.71	19.54
		K3Ti2Br9	1.00	26.96	72.32	19.62
	Al-ZnO	K3Ti2Cl9	1.16	16.32	76.38	14.51
		K3Ti2Cl6Br3	1.12	22.61	77.18	19.61
		K3Ti2Cl3Br6	1.06	25.22	74.39	20.00
		K3Ti2Br9	1.02	26.95	73.00	20.11
	WS2	K3Ti2Cl9	1.28	17.77	81.36	18.52
		K3Ti2Cl6Br3	1.29	22.87	81.63	24.16
		K3Ti2Cl3Br6	1.25	25.29	79.76	25.25
		K3Ti2Br9	1.35	27.00	79.58	29.34
	PCBM	K3Ti2Cl9	1.16	16.31	78.25	14.86
		K3Ti2Cl6Br3	1.11	22.71	77.33	19.52
		K3Ti2Cl3Br6	1.04	25.17	75.21	19.82
		K3Ti2Br9	1.00	26.89	73.92	19.91

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Table 5 Simulation parameters of CuI as HTL with different ETL for K₃Ti₂Cl_9−xBr_x (x = 0, 3, 6, 9) perovskite as absorber layer

HTL	ETL	Absorber	Voc (V)	JC (mA cm^−2)	FF (%)	PCE (%)
CuI	SnO2	K3Ti2Cl9	1.16	16.33	76.42	14.50
		K3Ti2Cl6Br3	1.11	22.72	77.27	19.59
		K3Ti2Cl3Br6	1.03	25.19	75.80	19.69
		K3Ti2Br9	1.09	21.76	78.37	18.71
	IGZO	K3Ti2Cl9	1.15	16.31	75.19	14.21
		K3Ti2Cl6Br3	1.06	22.76	75.22	18.22
		K3Ti2Cl3Br6	0.99	25.23	72.85	18.28
		K3Ti2Br9	0.94	26.96	71.29	18.25
	PCBM-PCPB	K3Ti2Cl9	1.17	16.31	76.66	14.70
		K3Ti2Cl6Br3	1.12	22.71	74.70	19.07
		K3Ti2Cl3Br6	1.05	25.17	72.13	19.24
		K3Ti2 Br 9	1.01	26.89	70.55	19.22
	TiO2-SnO2	K3Ti2Cl9	1.15	16.26	76.81	14.47
		K3Ti2Cl6Br3	1.11	22.64	77.39	19.58
		K3Ti2Cl3Br6	1.06	25.11	74.73	19.94
		K3Ti2Br 9	1.06	25.11	74.71	20.06

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Table 6 Simulation parameters of WS₂ as ETL with different HTL for K₃Ti₂Cl_9−xBr_x (x = 0, 3, 6, 9) perovskite as absorber layer

HTL	ETL		Voc (V)	JC (mA cm^−2)	FF (%)	PCE (%)
CFTS	WS2	K3Ti2Cl9	0.34	19.37	46.58	3.12
		K3Ti2Cl6Br3	0.34	24.26	45.25	3.81
		K3Ti2Cl3Br6	0.34	26.37	44.75	4.09
		K3Ti2Br9	0.77	17.79	75.54	12.24
Cu2O		K3Ti2Cl9	1.20	16.98	78.45	16.03
		K3Ti2Cl6Br3	1.11	22.76	77.27	19.64
		K3Ti2Cl3Br6	1.04	25.20	75.65	19.94
		K3Ti2Br9	0.99	26.92	74.43	20.04
CuSCn		K3Ti2Cl9	0.91	17.79	75.54	12.24
		K3Ti2Cl6Br3	0.91	22.73	73.70	15.25
		K3Ti2Cl3Br6	0.90	25.21	73.83	16.80
		K3Ti2Br9	0.89	26.96	74.29	17.92
MoO3		K3Ti2Cl9	1.18	16.72	78.64	15.53
		K3Ti2Cl6Br3	1.0	22.76	78.48	19.37
		K3Ti2Cl3Br6	1.04	25.20	75.91	19.95
		K3Ti2Br9	1.32	21.57	82.65	23.62
NiO		K3Ti2Cl9	1.05	17.81	78.25	14.68
		K3Ti2Cl6Br3	1.03	22.85	77.71	18.34
		K3Ti2Cl3Br6	1.02	25.29	75.97	19.63
		K3Ti2Br9	1.00	27.00	73.86	20.01
rGO		K3Ti2Cl9	0.84	17.24	68.46	9.99
		K3Ti2Cl6Br3	0.85	22.56	67.53	13.00
		K3Ti2Cl3Br6	0.85	25.04	67.33	14.42
		K3Ti2Br9	0.85	26.76	67.56	15.40
PEDOT:PSS		K3Ti2Cl9	0.91	25.17	77.81	20.57
		K3Ti2Cl6Br3	0.92	23.39	74.93	6.15
		K3Ti2Cl3Br6	0.92	25.34	74.97	17.53
		K3Ti2Br9	0.92	26.98	74.85	18.66
P3HT		K3Ti2Cl9	0.64	17.85	68.12	8.92
		K3Ti2Cl6Br3	0.64	22.8v	67.79	10.03
		K3Ti2Cl3Br6	0.64	25.24	67.57	11.06
		K3Ti2Br9	0.64	26.96	67.03	11.71

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3.5.2 Effect of absorber layer thickness on the performance of the devices. Device performance, material consumption, and cost are all impacted by thickness. The ideal thickness of the absorber in solar cell devices is determined by balancing absorption and recombination; this allows for effective charge collection.⁴⁷ These devices are simulated to determine the best range of absorber layer thickness for K₃Ti₂Cl_9−xBr_x (x = 0, 3, 6 and 9). Throughout the course of the simulation, the absorber layer's thickness was adjusted between 200 nm and 2000 nm. Parameters, including J_sc and η are found to rise as the absorber thickness is raised, according to the simulation findings displayed in tables S4 to S7. A high absorption coefficient causes an increase in the formation of electron–hole pairs as a result of the absorption of more photons with longer wavelengths, which happens when the thickness is raised. On the other hand the V_oc and FF shown an increasing nature for K₃Ti₂Cl₉ and decreasing nature for other absorbers is due to reduced interfacial recombination and high photon absorption and behaves in the opposite nature for other absorbers. Additionally, FF follows the same trends due to the lower and higher series resistance. A thickness of approximately 1500 nm seems to be adequate to attain a good efficiency due to the slower growth rate of device efficiency, which is enough to absorb the majority of incident photons.

3.5.3 Influence of the density of defects on the K₃Ti₂Cl_9−xBr_x (x = 0, 3, 6 and 9) absorber layer. Defect states in the bulk material and the interface have a substantial impact on the optoelectronic characteristics of semiconductor compounds in thin films.⁴⁸ In this stage, we quantitatively analyzed the impact of defect states on the performance of solar cells. We adjusted the defect density from 10¹⁰ cm⁻³ to 10¹⁷ cm⁻³, while keeping all other input values constant. The variations in V_oc, J_sc, FF, and η in relation to the density of neutral defects are shown in Fig. 13 and Tables S8 to S11. When the defect density is less than 10¹² cm⁻³, the total cell performance is constant. However, when N_t increases, the performance drops significantly. The efficiency of K₃Ti₂Cl_9−xBr_x (x = 0, 3, 6 and 9) is merely 18.54 to 25.70% when the defect density is 10¹⁰ cm⁻³. An increase in defect density results in a decrease in the diffusion length of electrons and holes and the addition of a recombination carrier to the absorber layer, both of which have a direct impact on efficiency.

Fig. 13 Effect of accepter carrier concentration on the PV parameters of the K₃Ti₂Cl_9−xBr_x (x = 0, 3, 6 and 9) halide perovskites.

3.5.4 Effect of doing acceptor carrier concentration on device performance. There are a number of variables that influence SC performance, but doping is among the most important.⁴⁸ Fig. 14 and Tables S8 to S11 displays the change in cell characteristics as a function of the absorber layer's acceptor carrier concentration (N_A), with doping levels ranging from 10¹⁰ to 10²⁰ cm⁻³. Up to 10¹⁵ cm⁻³ the J_sc is almost constant and then decreases due to an increase in free charge recombination. Additionally, all the other cell parameters are increasing as a function of the N_A. The overall efficiency of the SC is enhanced as the acceptor concentration increases since cell characteristics like FF and V_oc also increase. V_oc increases as the concentration of acceptor doping increases because the hole's Fermi energy level falls.

Fig. 14 Effect of defect density on the PV parameters of the K₃Ti₂Cl_9−xBr_x (x = 0, 3, 6 and 9) halide perovskites.

3.5.5 A device's efficiency as a function of series and shunt resistance. The device's performance is heavily affected by the series and shunt resistance. While in a perfect solar cell the series and shunt resistances would be infinite and zero respectively but in reality they would have an effect. The resistance in series is comprised of the bulk layers, electrodes and charge generation's interface resistance.⁴⁹ In contrast, shunt resistance is the obstacle that cells with faulty states face when trying to arise from recombination. A higher shunt resistance is indicative of a less faulty state.⁴⁹ Its performance is impacted by the SC's imperfection. The effect of series and shunt resistance on the cell's photovoltaic characteristics is seen in Fig. 15, 16 and Tables S12 to S15 respectively. From 0 to 10 Ω cm², the fill factor and efficiency diminish as the series resistance increases. Be that as it may, V_oc and J_sc are unchanging. At 0 Ω cm², the maximum value of efficiency is 19.12, 24.70, 25.58 and 29.54% and reduce 16.15, 19.11, 19.41 and 22.45% respectively while the maximum value of FF in the range of 79.24 to 82.16% and then reduces accordingly with rises in R_s. One possible explanation for the drop in FF as series resistance increases is a decline in maximum output power.

Fig. 15 Effect of series resistance on the PV parameters of the K₃Ti₂Cl_9−xBr_x (x = 0, 3, 6 and 9) halide perovskites.

Fig. 16 Effect of shunt resistance on the PV parameters of the K₃Ti₂Cl_9−xBr_x (x = 0, 3, 6 and 9) halide perovskites.

Fig. 16 show the effect of shunt resistance (R_sh) on the PV parameters of these compounds set from 101 to 108 Ω cm². All the PV parameters increase up to certain value and then become constant as the R_sh rises. FF rises as R_sh rises because SC's power output improves due to less leakage current. The data shown above indicate that the device's J_sc are unaffected by shunt resistance. It follows that the study showed that the PCE of the SC can be further improved by raising shunt resistance and lowering series resistance. In addition, there appears to be a saturation point beyond which the variation of efficiency and FF with shunt resistance no longer increases.

3.5.6 Effect of recombination on the device's performance. The recombination rate and its impact on the cell's performance are determined by considering the radiative and Auger recombination coefficients.⁵⁰ The recombination parameters for the absorbers are shown in Table 8. Similarly, the radiative coefficients (B_r) for these compounds are 1.76 × 10⁻⁹, 1.51 × 10⁻⁹, 1.27 × 10⁻⁹ and 1.05 × 10⁻⁹ photons cm³ s⁻¹ and the non-radiative Auger recombination is also taken in to account and optimized for these compounds both for holes and electrons in the range from 10⁻²⁹ to 10⁻³¹ cm⁶ s⁻¹ to evaluate its effect on the SC parameters for these absorbers. The PV parameters after applying the recombination coefficients are given in Table 9 in addition to parameters obtained through 900 and 1500 nm thickness. From the table it is clear that recombination slightly effect the PV parameters indicating the good optimization of the solar cell design.

Table 7 Calculated solar to chemical efficiency for the K₃Ti₂Cl_9−xBr_x (x = 0, 3, 6, 9) compounds

Parameters	ΔG Product (V)	K3Ti2Cl9	K3Ti2Cl3Br6	K3Ti2Cl3Br6	K3Ti2Br9	For other materials
η (H2O → H2)	1.23	21.89%	28.13%	31.10%	33.21%	2.07% (ref. 57),11.5% (ref. 58), 17% (ref. 59)
η (CO2 → CH4)	0.24	4.27%	5.48%	6.06%	6.48%
η (CO2 → CH4OH)	0.39	6.94%	8.91%	9.86%	10.53%
η (N2 → NH3)	0.10	1.78%	2.28%	2.25%	2.70%	1.48% (ref. 60), 0.24% (ref. 61)

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Table 8 Radiative and Auger recombination parameters of the K₃Ti₂Cl_9−xBr_x (x = 0, 3, 6 and 9) compound

Parameters	K3Ti2Cl9	K3Ti2Cl6Br3	K3Ti2Cl3Br6	K3Ti2Br9
Radiative coefficient (Br cm^3 s^−1)	1.76 × 10^−9	1.51 × 10^−9	1.27 × 10^−9	1.05 × 10^−9
Auger coefficient for electron (Cn cm^6 s^−1)	10^−29 to 10^−31	10^−29 to 10^−31	10^−29 to 10^−31	10^−29 to 10^−31
Auger coefficient for hole (Cp cm^6 s^−1)	10^−29 to 10^−31	10^−29 to 10^−31	10^−29 to 10^−31	10^−29 to 10^−31

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Table 9 Simulation parameters for initial configuration, after thickness optimization and with recombination coefficients for K₃Ti₂Cl_9−xBr_x (x = 0, 3, 6 and 9) perovskite as absorber layer

Parameters	K3Ti2Cl9	K3Ti2Cl6Br3	K3Ti2Cl3Br6	K3Ti2Br9
Initial configuration after EHL and HTL optimization
Thickness (nm)	900	900	900	900
ETL	WS2	WS2	WS2	WS2
HTL	CuI	CuI	CuI	CuI
Voc (V)	1.28	1.29	1.25	1.35
Jsc (mA cm^−2)	17.77	22.87	25.29	27.00
FF (%)	81.36	81.63	79.76	79.58
PCE (%)	18.52	24.16	25.25	29.34
After thickness optimization
Thickness (nm)	1500	1500	1500	1500
Voc (V)	1.30	1.29	1.23	1.34
JC (mA cm^−2)	17.84	23.42	25.88	27.67
FF (%)	82.16	81.53	79.92	60.15
PCE (%)	19.12	24.70	25.58	29.54
With calculated recombination coefficients
Thickness (nm)	1500	1500	1500	1500
Voc (V)	1.30	1.29	1.23	1.31
JC (mA cm^−2)	17.84	23.42	25.88	27.00
FF (%)	82.14	81.53	80.09	62.07
PCE (%)	19.11	24.68	25.51	29.00

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The J–V characteristics of K₃Ti₂Cl_9−xBr_x (x = 0, 3, 6 and 9)-based solar cell WS₂/K₃Ti₂Cl_9−xBr_x (x = 0, 3, 6 and 9)/CuI configuration with the addition of recombination effect is shown in Fig. 17 provides the highest performance with an efficiency of 19.11, 24.68, 25.51 and 29.00%, FF of 82.14, 81.53, 80.09 and 62.07%, V_oc of 1.30, 1.29, 1.23 and 1.35 V and J_sc of 17.84, 23.42, 25.88 and 27.00 mA cm⁻² indicating WS₂ and CuI as the best ETL and HTL for these absorbers. On the other hand WS₂ also acts as a good ETL for the isotropic compound.^51,52

Fig. 17 J–V curve of the optimized K₃Ti₂Cl_9−xBr_x (x = 0, 3, 6 and 9) halide perovskites.

The EQE form Fig. 18 for K₃Ti₂Cl_9−xBr_x (x = 0, 3, 6 and 9) absorber ranges from 11.88 to 57.60% at 4.1 eV, reaches 99.38 to 99.02 and 100% between 3.44-2.38 eV and then drops to 43.21% at 1.82 eV for K₃Ti₂Cl₉, for K₃Ti₂Cl₆Br₃ to 55.51% at 1.65 eV, for K₃Ti₂Cl₃Br₆ to 50.60% at 1.56 eV and reduces for K₃Ti₂Br₉ up to 22.88% at 1.51 eV. In the visible light range, the device transforms photons into practical electricity with relative ease. Nevertheless, the QE begins to fall as the energy falls and the wavelengths grow longer. A key component in determining the photovoltaic properties, especially the PCE, is the control of electron flow to minimize energy losses produced by the HTL.

Fig. 18 EQE curve of the optimized K₃Ti₂Cl_9−xBr_x (x = 0, 3, 6 and 9) halide perovskites.

3.5.7 Band structure. The energy band diagram for the simulated K₃Ti₂Cl_9−xBr_x (x = 0, 3, 6 and 9) based device employing CuI as the HTL and WS₂ as the ETL is shown in Fig. 19. Based on observations, lead-free PSCs with band gaps between 1.3 to 2.15 eV produce superior photovoltaic results. Our computed device meets this requirement, with an E_g of 1.86 to 1.51 eV for the K₃Ti₂Cl_9−xBr_x (x = 0, 3, 6 and 9) absorbers and improved PV performance. In addition, it is crucial to ensure that the band gaps of the HTL, ETL, and absorber layers are properly matched in order to avoid charge recombination and maximize carrier extraction from the interfaces of different layers within the device structure. This is accomplished by taking into account the valence band offset (VBO) between the HTL and absorber layer and the conduction band offset (CBO) between the ETL and absorber layer. As a result of the electron affinity of the ETL, HTL, and absorber layers, the barrier height at interfaces created by photo-generated carriers determines the value of CBO and VBO. A tiny positive value for VBO and a negative value for CBO can improve PSC performance, since a high VBO will impede hole conduction from the absorber to the HTL and a negative VBO will enhance carrier recombination. A spike at the perovskite/ETL interface while the perovskite/HTL shows the cliff is shown in Fig. 19 as their CBO becomes positive and VBO becomes negative.⁵³ In this case, E_c, E_v, E_n and E_p stand for the energy levels of the conduction band, valence band, and Fermi level in n-type and p-type materials, respectively. The band structure shows the alignment of the VB between the HTL and the absorber layer, as well as the alignment of the CB between the ETL and the absorber layer.

Fig. 19 Band structure of the K₃Ti₂Cl_9−xBr_x (x = 0, 3, 6 and 9) halide perovskites.

3.6 Photocatalytic properties

Photocatalytic reactions can only occur in materials with superior optical and electrical properties. Crystals with optimum bandgap (E_g), band edge levels (BEL), optical absorbance (GA), and effective carrier masses (ECM) may be able to split water photocatalytically. The most important thing is that each of these perovskites has an appropriate E_g between 1.5 and 3.0 eV.

The Mulliken electronegativity technique is used to study the photocatalytic properties of these 2D perovskites in order to determine their water-splitting potential. Estimates of the ECB and EVB are derived respectively. The geometric mean of an electronegativity, represented by χ, is 5.31, 5.26, 5.21 and 5.16 eV for K₃Ti₂Cl_9−xBr_x (x = 0, 3, 6 and 9) is a crucial component in figuring out an electron's electrical characteristics and free energy.⁵⁴ For these semiconductor materials to effectively split water photocatalytically, their VBM and CBM must be larger than or equal to the redox potential of H*/H₂ (0 V against NHE).⁵⁵ CO₂ and N₂ can also be reduced photocatalytically using these methods. These materials have oxygen potentials (EVB) greater than 1.23 V and hydrogen redox potentials (ECB) lower than 0 V and are feasible for photocatalytic water splitting, as shown in Fig. 20, when exposed to visible light. In addition, as shown in Fig. 20, the EVB of all perovskites is more negatively correlated with CO₂ reduction, which can photo-reduce CO₂ more easily than CO₂/CH₄OH, and CO₂/CH₄. Similarly, when evaluating N₂, it can photo-reduce to NH₃. Therefore, the compounds are feasible under ideal conditions at PH = 0, in assessing oxygen, splitting water, decreasing CO₂ and fixing nitrogen, in that order. The reduction products, however, should be used with consideration and treated accordingly to ensure that they do not harm the environment.

Fig. 20 Band edges of the K₃Ti₂Cl_9−xBr_x (x = 0, 3, 6 and 9) halide perovskites compared to the redox potentials of the water-splitting reaction, CO₂ reduction and N₂ fixation photo degradation processes at normal hydrogen electrode (NHE) scale at pH = 0.

Furthermore Table 7 displays the computed solar to chemical efficiency (STC) and the value of J_sc is displayed in Fig. 12, both of which are used to assess the photocatalytic performance of these compounds. The compounds in consideration have η (H₂O → H₂) values of 21.89, 28.13, 31.10 and 33.21% respectively, which exceed the 10% threshold value for commercial usage⁵⁶ and two-dimensional compounds.^57–59

In the same way, the η values for CO₂ → CH₄ is 4.27, 5.48, 6.06 and 6.48%, for CO₂ → CH₄OH is 6.94, 8.91, 9.86 and 1.53% and η for N₂ → NH₃ are 1.78, 2.28, 2.25 and 2.70% respectively. The reported values for these compounds are significantly higher than the other 2D materials' reported values of 0.24% and 1.48%.^60,61

Anion substitution consistently improves photocatalytic activity when compared to pure K₃Ti₂Cl₉, according to the computed solar-to-chemical efficiencies. The η values for water splitting, carbon dioxide reduction, and nitrogen fixation are greater in K₃Ti₂Cl_9−xBr_x (x = 0, 3, 6 and 9) compared to other 2D materials that have been reported. Additionally, for hydrogen evolution, they surpass the 10% industrial benchmark. Cation disorder-induced changes to the electronic structure are responsible for this enhancement; they lead to better charge separation and stronger light absorption, which in turn boost reaction efficiencies in various reduction pathways.

4 Conclusions

These halide K₃Ti₂Cl_9−xBr_x (x = 0, 3, 6 and 9) perovskites are studied structurally and optoelectronically using the FPLAPW method in the DFT domain with GGA and TB-mBJ potentials. The structural parameters computed by WIEN2k match the experimental data to a tee. According to band structure TDOS and PDOS computations, all of these compounds have a direct band gap of 1.861, 1.648, 1.577, 1.519 eV along M–M symmetry and an indirect band gap of 1.861, 1.643, 1.567 and 1.512 eV at the M–K symmetry. Optoelectronic devices and SC applications are ideal for these compounds because of their visible-light optical dynamics. The SCAPS-1D program is employed to identify the optimal solar cell designs that integrate various ETLs and HTLs. The structure with the highest power conversion efficiency out of the fifty four configurations examined is FTO/WS₂/K₃Ti₂Cl_9−xBr_x (x = 0, 3, 6 and 9)/CuI, providing the highest performance with an efficiency of 19.11, 24.68, 25.25 and 29.00%, FF of 82.14, 81.53, 80.09 and 62.07%, V_oc of 1.30, 1.29, 1.25 and 1.35 V and J_sc of 17.84, 23.42, 25.88 and 27.00 mA cm⁻² with the addition of the recombination effect. On the other hand, the effect of thickness, defect density, series and shunt resistance is also examined. Photocatalytic analysis shows that all of these compounds are capable of converting H₂O to O₂ and H₂. In the same way that the compounds under study may reduce N₂ to NH₃, they can likewise reduce CO₂ to CH₄OH and CH₄. In comparison to other materials, these compounds have an effective efficiency for reducing CO₂ and N₂ and their photocatalytic efficiency for water splitting is higher than the intended value for industrial application. The findings of this study paves the way for lead-halide-free, entirely inorganic perovskite photovoltaics and photocatalysts. Such materials would exhibit enhanced photovoltaic and photocatalytic performance and could be used in various fields such as optoelectronics, photovoltaics, and photocatalysis, especially those involving visible light-driven processes like water splitting, CO₂ reduction, and N₂ fixation.

Author contributions

Shahid Mehmood handle the formal analysis, research techniques and writing (first draft). Shah Rukh Khan performs the investigation, research data collection, methodology and writing (first draft). Shaimaa A. M. Abdelmohsen involved in leading the initial idea and design of the research manages projects, providing guidance and oversight to the research team. Meznah M. Alanazi supervise the work, provide resources and software and validate the work. Hanan Al Ghamdi handles data visualization, validation, editing and review. Mohamed Mousa is managing, cleaning and organizing research data.

Conflicts of interest

The authors stated that they have no competing interest.

Data availability

The data supporting this article have been included as part of the supplementary information (SI). Supplementary information: numerical data for the optimization of different parameters of K₃Ti₂Cl_9−xBr_x-based solar cells. See DOI: https://doi.org/10.1039/d6ra01597b.

Acknowledgements

The research was funded by the Deanship of Scientific Research and Libraries at Princess Nourah bint Abdulrahman University through the Research Funding Program, Grant No. (FRP-2025-47).

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