First-principles investigation of Pd-based Kesterites for optoelectronic and photovoltaic applications

First-principles investigation of Pd-based Kesterites for optoelectronic and photovoltaic applications | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article First-principles investigation of Pd-based Kesterites for optoelectronic and photovoltaic applications Ihsan Ullah, Imad Khan This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-8933098/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 4 You are reading this latest preprint version Abstract In this article, we report a first-principles study of the structural, electronic, optical and photovoltaic properties of the earth abundant quaternary Kesterites Cu 2 PdSnSe 2 (CPTSe) and Cu 2 PdSnS 4 (CPTS). Electronic structure calculations were performed using density functional theory within the full-potential linearized augmented plane wave (FP-LAPW) method. The generalized gradient approximation (GGA) and Hubbard U correction (GGA+U) along with mBJ (TB-mBJ+U) were employed to accurately account for exchange-correlation effects and electrons localization. The calculated band structures revealed that both materials are direct band gap semiconductors with gaps of 1.11 eV (CPTSe) and 1.40 eV (CPTS). The density of states (DOS) shows that the valence band maximum is dominated by Cu-3d, S/Se-p, while the conduction band minimum is primarily composed of Sn-p, Sn-s and Se-p orbital, further the inclusion of Hubbard potential U shifts the localized states below the Fermi level and improving electronic stability. Optical calculations indicate strong visible light absorption (>10 4 cm -1) , high dielectric constants and favorable refractive indices, demonstrating efficient light harvesting and low optical losses. Device simulations of the (FTO/WS 2 /CPT(Se/S)/Spiro-MeOTAD/Mo) architecture were performed using SCAPS-1D. The CPTSe/CPTS based device achieve an open circuit voltage (V oc ) of 0.95/1.34 V, a high short-circuit current density (J sc ) of 25.05/15.58 mAcm -2 and a fill factor (FF) 0f 86.21/87.82 %, resulting in a power conversion efficiency (PCE) of 20.61/18.34 %. The enhanced performance is attributed to reduce antisite defects, improved cation ordering and optimized alignment. These results established Pd-based Kesterites as promising sustainable absorber materials for high efficient photovoltaic applications. Quaternary chalcogenides Earth abundant Non-toxic Efficient eco-friendly Optical materials Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 Figure 9 Figure 10 Figure 11 1. Introduction The depend on fossil fuels is a major contributor of global warming due to increased carbon dioxide (CO 2 ) emissions, which trap outgoing radiation and intensifying the green house effect [ 1 – 5 ]. Despite their environmental impact and finite nature, fossil fuels still account for nearly 80% of global energy consumption, underscoring the urgency of transitioning toward sustainable energy systems [ 6 – 8 ]. In response to rising global electricity demand and the objectives of the 21st -century green energy agenda, renewable energy technologies have become a critical research focus; however, many alternatives such as wind, geothermal and thermoelectric systems remain geographically constrained. In contrast, solar energy is abundant and universally available, and its direct conversion into electricity via photovoltaic (PV) technology particularly through advances in nano-materials based absorbers offer a scalable, environmentally benign, and efficient pathway for large-scale renewable power generation [ 9 ]. Photovoltaic (PV) technology has emerged as a promising alternative to conventional energy sources, such as fossil fuels, offering significant potential to address global energy demands and environmental challenges like greenhouse gas (GHG) emissions, cost, and climate change [ 10 , 11 ]. Since past decade the worldwide PV-based solar panel installation rate has been expanded rapidly, driven largely by significant reduction in module costs and rising efficiencies of the solar cell. PV technology stands out for being green, renewable, scalable, and increasingly affordable, giving it a strong edge over nonrenewable and even some renewable energy sources in terms of accessibility and sustainability. These advantages position solar cell technology as a central pillar in the global transition toward zero GHG emissions and emphasize their potential in the development of next generation energy conversion technologies with strong commercialization prospects [ 12 – 15 ]. Solar cell industry has seen three generational stages. The conventional first generation is based on single and polycrystalline silicon (Si) achieving power conversion efficiency (PCE) of 25% and long lifetime (25–30 year) [ 16 ]. Limitations of the first generation include high production cost, energy intensive fabrication, low optical absorption due to indirect band gap and thick absorber layer (180–300 µm) [ 17 ]. Thin-film solar cells based on amorphous Si (a-Si), CdTe and Cu(In,Ga)Se 2 (CIGS) contribute the second generation. These materials are lightweight, flexible, adaptable substrates suitable for portable application and achieved PEC in the range 10–21% [ 16 ]. On the downside this generation has low efficiencies, reliance on scarce or toxic elements (In, Te, Cd), shorter lifespan and limiting large scale commercialization [ 16 ]. The third-generation known as emerging solar cells includes perovskite solar cells (PSC), dye synthesized solar cells (DSSC), organic photovoltaic (OPV), hybrid (organic and inorganic) solar cells, quantum dot solar cells (QDSC) and Kesterite solar cells (KSC) [ 17 ]. The advantages of this emerging generation include low-cost fabrication, high PCEs, tunable properties and compatible with flexible substrates. However, most of these materials have stability issues, scalability challenges and toxicity (Pb in perovskites) [ 17 ]. The prerequisites for an ideal solar cell material include strong optoelectronic properties (such as high optical absorption, suitable direct band gap (1.5 eV), higher charge carrier mobility, low-binding energy), long term stability, high PCE, excellent flexibility and reliability, availability, low-toxicity, low cost fabrication, and longer lifetime [ 18 ]. Organic-inorganic lead halide perovskites have received remarkable attention due to their interesting physical properties and rapidly achieved high efficiencies (~ 27%), but suffer from poor environmental stability (degrading when exposed to moisture, oxygen, light, and heat) and toxicity due the presence of lead which are major bottlenecks for their commercialization [ 19 , 20 ]. Therefore, the search for sustainable and environmentally benign absorber materials has shifted toward quaternary semiconducting materials with the general formula A 2 BCD 4 (A = Cu, Ag, K, Li; B = Zn, Cd, Pd, Ni, Mg; C = Sn, Pb, Ge, Si and D = S, Se, Te), whom structure is the derivative of chalcopyrite CuInS 2 . The substitution of two indium (In) atoms with zinc (Zn) and tin (Sn) atoms yield quaternary semiconductors that preserved favorable optoelectronic features of chalcopyrites while offering broader compositional flexibility [ 21 ]. This family of quaternary semiconductor compounds are known as Kesterite and has attracted significant attention, with Cu 2 ZnSnS 4 /Se 4 are of special interest due to their suitable direct band gap (~ 1.5 eV), higher charge carrier mobility, low-binding energy, long term stability, excellent flexibility and reliability, low-toxicity, low-cost fabrication, longer lifetimes and earth-abundant constituents [ 22 – 24 ]. Their environmentally friendly composition and compatibility with established CIGS device architectures and fabrication processes further strengthen their potentials for scalable thin film photovoltaic, making them one of the most promising candidates for solar energy conversion [ 25 ]. As members of the broader A 2 BCD 4 family of quaternary semiconductors, compounds such as Cu 2 ZnGeS 4 , and Cu 2 ZnSn(S, Se) 4 (CZTSSe) exhibit tunable direct band gaps having range of 1.0-2.5 eV, enabling band gap engineering via S/Se alloying to achieve the optimal 1.0-1.6 eV for single-junction photovoltaic devices [ 26 – 30 ]. Beyond PV, Kesterite-based compounds have also been investigated for thermoelectric, water splitting, CO 2 reduction and non-linear optical applications due to their versatile optoelectronic properties [ 31 – 35 ]. Structurally, both experimental studies and theoretical calculations confirm that tetragonal phase is the most stable crystal structure [ 36 ]. Kesterite thin films can be synthesized using vacuum-based methods such as co-evaporation and sputtering, which provide compositional control but are limited by poor scalability and high cost. In contrast non-vacuum approaches including sol-gel, spray pyrolysis, electro deposition, nano-crystal inks along with emerging methods like microwave-assisted solvothermal and chemical vapor deposition (CVD) are more attractive for large-scale, low-cost fabrication with improved crystal quality [ 37 ]. Since the first Kesterite solar cell was reported in 1997 with a PCE of only 0.66% [ 38 ], the PCE of Kesterite-based devices has steadily increased, reaching a current record of 15.8% [ 39 ]. However they remain far below CIGS and halides perovskites largely due to limited research attention compared to halides perovskites and silicon, as well as non-radiative recombination losses arising from intrinsic defects, cation disorder, and grain boundaries [ 40 ]. Yet Kesterite remain highly attractive due to their earth-abundant, non-toxic and stable composition. Advance in defect passivation, interface engineering, and composition engineering using computational simulations could provide a strong platform for the development of stable, scalable, and sustainable Kesterite photovoltaic while unlocking further efficiency improvements [ 41 – 44 ]. Among these strategies, a key strategy for tuning the optoelectronic performance of such materials is cation substitution within the Kesterite material Cu 2 ZnSnX 4 at B-site has been shown to be highly effective in modifying band gap characteristics and enhancing light absorption behavior make them attractive for photovoltaic applications. Such as replacement of Sn with Ge to form Cu 2 ZnGe(S,Se) 4 (CZGX) enables band gap tunings for tandem integration and offers superior optoelectronic properties [ 45 ], while cation at Cu/Zn sites substitution reduces disorder and defect formation. Similarly the replacement of zinc (Zn) with palladium (Pd) has led to the development of Cu 2 PdSnX 4 (X = S, Se) (CPTX). This Pd substation reduces the formation of antisite defect by lowering their formation energy, thereby promoting greater cationic ordering within the crystal lattice [ 46 ]. The incorporation of Pd also leads to favorable band gap tuning within the optimal range of 1.0-1.4 eV, while also enhancing the absorption coefficient- both of which are important parameters for efficient solar energy conversion [ 46 ]. Moreover, these Pd-based chalcogenides retain the advantages of being non-toxic and composed of relatively stable constituents, positioning them as promising absorber layers for environmentally benign and stable thin-film solar cells. Notably, they have been successfully synthesized experimentally via a microwave-assisted solvothermal method [ 46 , 47 ]. Despite these potential, Pd- substituted systems remain insufficiently explored from a theoretical perspective. To date, only experimental studies found on the synthesis and characterization of Cu 2 PdSnSe 4 (CPTSe) and its sulfide analogue Cu 2 PdSnS 4 (CPTS). Consequently, a comprehensive first-principles understanding of the electronic and optical properties of both CPTSe and CPTS remain lacking. In this work, density functional theory (DFT) calculations are employed to systematically investigate the structure, electronic and optical properties of Cu 2 PdSnX 4 (X = S/Se) (CPTX). This study provides a detailed theoretical analysis of experimentally reported CPTX. The results offer fundamental insights into their electronic band structure and optical response, thereby supporting the rational design of Pd-based absorber materials for high performance photovoltaic devices. 2. Computational Detail In this study, first-principles calculations were performed using WIEN2K computational code, based on DFT [ 48 ]. Specially, the full potential linearized augmented plane-wave method and its extension incorporation local orbital (FP-LAPW + lo) are used [ 49 ]. This method is recognized for its high accuracy in describing the all electron behavior of crystalline solids and is particularly suitable for systems with complex electronic structures [ 48 ]. The structural optimization of the investigated compounds were carried out using generalized gradient approximation (GGA), to treat the exchange-correlation functional [ 50 ]. GGA generally provides improved prediction for structural parameters, but tends to underestimates the band gaps of semiconductors. To address this issue, the Tran-Blaha modified Becke-Johnson (TB-mBJ) potential has been adopted, offering significantly more reliable predictions of electronic and optical properties [ 51 ]. mBJ improves band gap accuracy by using kinetic-energy density to better approximate the exchange potential. For atoms possessing localized d and f orbitals, on-site Coulomb interactions were incorporated within the GGA + U formalism to adequately capture strong electron correlation effects, which are often underestimated in conventional DFT approaches [ 52 ]. The separation energy between core and valence states was set to 7.0 Ry to ensure an accurate treatment of core electrons. Appropriate muffin-tin radii were selected to prevent sphere overlap and to achieve basis set convergence, with values of 2.22 bohr for Cu, 2.25 bohr for Pd, 2.34 bohr for Sn and 1.90 bohr for S and 2.04 for Se atoms. The plane-wave cutoff in the interstitial region was defined by R MT K max = 7.0, where R MT corresponds to the smallest muffin-tin radius among the atomic species, while Fourier expansion of the charge density was truncated at G max = 12. Brillouin zone integrations were performed using k-point mesh 1000 to ensure convergence of total energy and electronic properties. Self-consistent field (SCF) calculations were converged to within 10 − 4 Ry in total energy. To properly treat for on-site coulombic interactions, particularly for localized Cu-3d states and Pd-4d states, a Hubbard U correction was applied within the GGA + U formalism. The Hubbard potential was applied to d-orbital of Cu and Pd separately. The choice of U = 6 and 2 eV was selected for Cu-d and Pd-d orbital respectively after testing U values in range of 0 to 8 eV. In different research articles U value is optimize for Cu-d state near six 6 eV. The value of 6 eV for Cu-d and 2 eV for Pd-d is selected in term of band gap comparison [ 53 ], which showed that the band gap calculated using mBJ + U closely matches experimental observations [ 46 ]. Finally, the PCE of the Kesterite-based absorbers were simulated using the Solar Cell Capacitance Simulator in one Dimension (SCAP-ID), thereby linking the first-principles results with realistic device-level performance predictions [ 54 ]. This tool is widely recognized for simulating solar cell characteristics by solving semiconductor equations, such as Passion’s equation, continuity equation and drift diffusion equation under illumination conditions [ 55 ]. 3. Results and discussion 3.1 Structural Properties Both compounds crystallize in the tetragonal Kesterite structure with space group I-4 (No. 82) [ 46 ]. The optimized unit cell structure of Cu 2 PdSnX 4 (X = Se, S) is illustrated in Fig. 1 . In this structure, the cation sub-lattice is composed of alternating Cu-Sn and Cu-Pd tetrahedral layers along xy plane, creating a tetrahedral coordinate framework. Due to the layered cation arrangement, Cu-S/Se bonding environments differ slightly between Pd-Cu and Sn-Cu containing layers, resulting in small variations in the local atomic bonding within the crystal structure [ 56 ]. Inside the Kesterite unit cell, Cu atoms occupy two distinct Wyckoff positions, 2a (0, 0, 0) and 2c (0, 1/2, 3/4), Pd atoms are located at the 2d (0, 1/2, 1/4) site, and Sn atoms occupy the 2b (0, 0, 1/2) position. The anions (S/Se) are located at the 8g (x, y, z) sites, forming tetrahedral coordination around the cations. The equilibrium lattice parameters were obtained by fitting the calculated total energy as a function of unit cell volume to the Murnaghan equation of states [ 57 ] as shown in Fig. 2 . The minimum total energies were found to be -48485.401Ry for CPTSe and − 32245.394 Ry for CPTS. In the optimized structural parameters of CPTX, the calculated lattice parameters of CPTSe are a = b = 5.6815 Ǻ and c = 11.041 Ǻ, where for CPTS, the calculated lattice parameters are a = b = 5.4510 Ǻ and c = 10.5216 Ǻ. CPTSe exhibits larger lattice parameters, reflecting the larger ionic radius of Se. The calculated lattice parameters of CPTSe and CPTS are in good agreement with the reported experimental values [ 46 , 47 ], and iso-structure compounds [ 45 , 58 ] and are summarized in Table 1 . Table 1 Calculated and experimental lattice parameter, anion S/Se atomic positions and bond length for CPTX (X = Se/S) Kesterite crystallographic phases. Compound CPTSe CPTS CZGSe CZGS a = b (Å) 5.6815(5.7061) c 5.4510/5.409 5.71 a /5.58 b 5.38 a /5.28 b c 11.042(11.0712) 10.5216/10.808 11.11 b 10.51 b c/2a 0.9717(0.9701) 0.965 0.987 a 0.974 a Bulk modulus (GPa) 91.56 89.64 X 0.23348 0.23533 0.24276 a 0.24799 a Y 0.24026 0.24224 0.25331 a 0.25684 a Z 0.12998 0.12899 0.124945 a 0.12328 a Cu1-X 2.3907 2.2988/2.320 d 2.4501 a 2.3315 a Cu2-X 2.3957 2.2973/2.323 2.4287 a 2.3100 a Pd-X 2.4419 2.3409/2.326 2.4986 a 2.3650 a Sn-X 2.5653 2.4373/2.398 2.4762 a 2.3014 a a) Ref.67 b) Ref.45 c) Ref. 46 d) Ref. 47 The bond lengths of CPTSe and CPTS compounds were calculated and are summarized in Table 1 . In CPTSe, the calculated bond length for Cu1-Se is 2.3907 Ǻ, for Cu2-Se is 2.3957 Ǻ, for Pd-Se is 2.4419 and for Sn-Se is 2.5653. In case of CPTS bond lengths are 2.2988Ǻ and 2.2973Ǻ for Cu1-S, and Cu2-S respectively, while 2.3409Ǻ and 2.4373Ǻ for Pd-S and Sn-S. The increase values in bond length of CPTSe compared to CPTS is due to larger ionic radius of Se. Furthermore, the observed trends are consistent with those reported for experimental CPTS only and iso-structural CZGSe and CZGS compounds, confirming the reliability and accuracy of the present structural optimization [ 47 , 59 ]. The values of the bulk modulus are predicted for first time for these compounds and the values are 91.56 GPa for CPTSe and 89.64 GPA for CPTS, indicating slightly higher stiffness in the CPTSe compound. 3.2 Electronic Properties The electronic band structures of Cu 2 PdSnX 4 (X = Se, S) were calculated using GGA, modified Becke-Johnson (mBJ) exchange potential, both with and without the Hubbard U correction (mBJ + U). The band structures were evaluated along the high-symmetry directions Г-H-N-Г-P in the irreducible Brillouin zone, with the Fermi level set to 0 eV as shown in Fig. 3 . Figure 3 (a) and 3(b) represent the band structures of CPTSe and CPTS respectively. The negative energy region corresponds to the valence band, while the positive energy region represents the conduction band. For both compounds, the valence and conduction band maximum and minimum are located at the Г point, indicating a direct band gap nature. Direct band gap semiconductors exhibit significantly higher optical absorption coefficients than indirect band gap materials, as electronic transitions from valence to conduction band occur without phonon assistance, enabling more efficient electron excitation [ 60 ]. GGA result of both compounds reveal zero band gaps thus show metallic nature and are list in Table 2 . Therefore, GGA + U was employed in the range of 0–8 eV and get a band gap value of 0.2 and 0.5 eV for CPTSe and CPTS respectively. Due to the underestimate results of GGA + U, the mBJ approximation were used and as result, the calculated band gaps are 0.4 eV for CPTSe and 0.8 eV for CPTS are obtained, which are also underestimated the experimentally reported values. Therefore the inclusion of on-site Coulomb interactions through the mBJ + U approach is applied as a result a band gap of 1.11 eV is obtained for CPTSe, in excellent agreement with experimental observations. An enhancement in the energy band gap is observed for CPTS, where mBJ + U predict a larger band gap (1.4 eV) compared to CPTSe as mention in Table 2 . The band gap calculated for CPTS using mBJ + U approach is underestimated the experimental optical band gap energy of 1.64 eV [ 47 ], but comparable with that of iso-structural compound. The band gap of CPTSe is comparable to that of silicon (1.12 eV). However, unlike silicon, which possesses an indirect band gap, CPTSe exhibits a direct band gap. This direct band gap nature enables stronger optical absorption and more efficient charge-carrier generation, making CPTSe a potentially superior photovoltaic absorber. Based on the direct and suitable band gap value, CPTSe is expected to achieve higher photovoltaic efficiency just like silicon. The smaller band gap of the Se-based compound relative to its S-based counterpart arises from the larger ionic radius and higher p-orbital energy of Se, which shifts the valence band upward. Our calculated results of band gap are also consistence with other iso-structure compound CZTSe and CZTS respectively and mention in Table 2 [ 45 , 58 ]. Table 2 Band gap values calculated through different potential and effective mass comparison of Cu₂PdSnX₄ (X = S, Se). Compound EXP. GGA (eV) TB-mBJ GGA + U mBJ + U m e *(mo) m h *(mo) E b (meV) Cu 2 PdSnSe 4 1.13 a 0 0.4 0.22 1.11 0.23 0.56 53 Cu 2 PdSnS 4 1.07/1.64 b 0 0.8 0.5 1.4 0.34 0.71 81 Cu 2 ZnGeSe 4 1.28 d 0.13 e 0.38 e 31 Cu 2 ZnSnS 4 1.5 c 0.22 e 0.60 e 52 a) Ref. 46 b) Ref.47 c) Ref.58 d) Ref 45 e) Ref 65 To further elucidate the electronic structure, the total and partial densities of states (DOS) for CPTSe were calculated and are shown in Fig. 4 within an energy range of -5 to 6 eV. The DOS results are consistent with the band structure analysis and provide insight into orbital contributions near the band edges. The valence band region close to the Fermi level is dominated by hybridized Cu-3d, S/Se-p and some contribution from Pd-d states, whereas the conduction band edge is primarily composed of Sn-p, Sn-s and Se-p orbital. These features reflect strong Pd hybridization within the tetragonal Kesterite lattice and confirm that the electronic states near the band gap are governed by the interaction between cation and anion orbital, consistent to other theoretical reports [ 59 ]. The same is observed for CPTS compound. The charge carrier mobility of CPTSe and CPTS were studied through the effective masses m*, together with the exciton binding energy (E b ). The effective masses at the conduction band minimum and valence band maximum were calculated from the band curvature using the formula $${\text{m}}^{\text{*}}=\frac{{\text{ћ}}^{2}}{\left[\frac{{\partial}^{2}{\epsilon}\left(\text{k}\right)}{\partial{\text{k}}^{2}}\right]}$$ 1 Where ε(k) represents the band-edge eigenvalue and k is the corresponding wave vector [ 61 ]. The calculated effective masses show that m h * > m e * for both CPTSe and CPTS, which is attributed to relatively flatter curvature of the valence band compared to the conduction band. The small values of m e * and m h * indicate high carrier mobility, consistence with the inverse dependence of electrical conductivity on effective mass [ 62 ]. In CPTS a slight increase in effective masses is observed compared to CPTSe, which correlates with the larger band gap induced by sulfur replacement. The exciton binding energy (E b ) was estimated using the Mott-Wannier model expressed as $${E}_{b}=\frac{\mu}{{{\epsilon}}_{1}^{2}\left(0\right)}\times{R}_{y}$$ 2 Where µ is reduced effective mass, ε 1 (0) is the static dielectric constant and Ry is the Rydberg energy [ 63 ]. The calculated E b values decrease from CPTS to CPTSe due to band gap narrowing and enhanced dielectric constant value. The relatively low exciton binding energies indicate efficient exciton dissociation and high free carrier density, which are essential for photovoltaic absorber materials [ 64 ]. Overall the combined low effective masses and moderate exciton binding energies confirm that CPTSe and CPTS exhibit favorable charge transport properties, making them promising candidates for high performance solar cell and optoelectronic applications. The calculated value are compared with iso-structure compound [ 65 ] and summarized in Table 2 . 3.3 Optical Properties The knowledge of optical properties of a material is crucial for designing photovoltaic, photonic and optoelectronic devices. In semiconductors, interband transitions of electrons from occupied valence band (VB) to unoccupied conduction band (CB) determine the optical response, which can be described in term of key parameters such as the complex dielectric function, ε(ω) = ε 1 (ω) + iε₂(ω), index of refractive n(ω), absorption coefficient α(ω) etc. These parameters are strongly influenced by the electronic structure, crystal symmetry and chemical composition. In this study, the optical properties of tetragonal Cu 2 PdSnX 4 (X = Se, S) were calculated using the Kramers-Kronig relations, Fermi-golden rule and Drude Model [ 66 – 68 ]. Owing to tetragonal symmetry, these compounds exhibit anisotropic optical behavior along transverse (perpendicular to z-axis) and longitudinal (parallel to z-axis) directions. The calculated real and imaginary parts of the dielectric function for CPTSe and CPTS along these directions are shown in Fig. 5 and Fig. 6 . Both ε 1 (ω) and ε 2 (ω) display similar energy dependent trends for the two polarizations axes with distinct features corresponding to their respective band gap energies. The real part of dielectric function, ε 1 (ω), describes the dispersive response of a material to an external electromagnetic field and governs the phase velocity of light propagation along different crystallographic directions. The static dielectric constant ε 1 (0) for CPTSe and CPTS are shown in Fig. 5 . CPTSe posses ε 1 (0) value 6.5 along xy-plane and 6.6 along z-axis perpendicular and parallel to the tetragonal c-direction. Similarly, for CPTS compound the value decrease to 6.2 and 6.3 in their respective axes, this decrease can be associated to the increase in band gap. For both CPTSe and CPTS, the z component is consistently larger than the x and y components, indicating optical anisotropy arising from the tetragonal crystal symmetry and layered cation arrangement. In the low-energy region, ε 1 (ω) increases monotonically and reaches a maximum within the photon energy range of approximately 1–2 eV, then declined interband electronic transitions. With increases photon energy, ε 1 (ω) decreases and crosses zero just above 8 eV, marking the screened plasma frequency, beyond which metallic-like reflection behavior occurs [ 69 ]. The higher static dielectric constant of CPTSe compared to CPTS follows the inverse band gap dependence predicted by the Penn model [ 70 ]. The fundamental parameter for evaluating optical properties is ε₂(ω), which describes the optical absorption arising from interband electronic transitions between occupied valence band and unoccupied conduction band. The optical band gaps (onset points) in the imaginary dielectric function plots in Fig. 6 for CPTSe and CPTS respectively are consistence with their electronic band gaps. Optical absorption started just beyond the optical gaps with maximum absorption occurs between 2 to 4 eV, corresponding to strong interband transitions near high-symmetry points of the brillouin zone. The absorption onset in ε₂(ω) coincides with the fundamental band gap indicating that the initial optical transitions arise from Cu-d and S/Se-p hybridized valence states to Sn-s and S/Se-p dominated conduction states. The position of the absorption edge shifts in accordance with the variation in band gap energy between CPTSe and CPTS. Enhanced ε₂(ω) intensity near the energies where ε 1 (ω) approaches zero indicated strong absorptive nature of CPTSe and CPTS in the visible and near-ultraviolet regions. The result of both compounds for dielectric function ε 1 (ω) and ε 2 (ω) are comparable with iso-structure compound Cu 2 NiSnS 4 [ 71 ] and Cu 2 GeSn(S/Se) 4 [ 72 ]. The optical properties of tetragonal CPTX were further analyzed through refractive index, which describe how light propagates through a material. The static refractive index, obtained from the zero-frequency limit of n(ω) is found to be approximately 2.6 for CPTSe and 2.5 for CPTS, indicating strong light-matter interaction in both compounds as shown in Fig. 7 . At low photon energies n(ω) remains nearly constant and then increase sharply with increasing photon energy, reaching a maximum value around 2.2 eV in the visible region. This trend reflects the inverse relationship between the refractive index and the electronic band gap and explains the slightly higher refractive index of the Se-based compound due to its smaller band gap. The results are comparable with iso-structure compound Cu 2 NiSnS 4 [ 71 ] and Cu 2 GeSn(S/Se) 4 [ 72 ]. The absorption coefficient α(ω), describes how strongly a material absorbs incident light and is an important parameter for evaluating its potential as a photovoltaic absorber. The calculated absorption spectra for CPTSe and CPTS are drawn in Fig. 8 , show high absorption coefficients near to 10 4 cm -1 in the visible energy range, which is a typical characteristic of direct band gap semiconductors and is favorable for thin film solar cell applications. For both compounds, the absorption onset occurs close to the fundamental band gap energy and increases rapidly with increasing photon energy. This strong absorption near the band edge is mainly due to direct electronic transitions between the valence and conduction bands. At higher photon energies, slight reductions in α(ω) appear due to transitions into less densely populated conduction band states. Overall, the high absorption coefficients in the visible region confirm that CPTSe and CPTS can efficiently absorb incident light within thin absorber layers, making them promising materials for photovoltaic applications. The results are comparable with iso-structural compound Cu 2 GeSn(S/S) 4 [ 72 ]. Overall, the DFT results indicate that CPTX posse’s strong optical absorption, favorable refractive index dispersion, high dielectric response and optical anisotropy confirming their strong potential for photovoltaic and photonic applications. 3.4 Photovoltaic Properties Based on the favorable optical properties, key photovoltaic (PV) parameters, including open-circuit voltage (V oc ), short circuit current density (J sc ), fill factor (FF) and PCE were evaluated using SCAPS-1D [ 54 ]. The simulated n-i-p (FTO/ETL/CPT(Se/S)/HTL/Mo) device architecture, schematically shown in Fig. 9 , consist of fluorine-doped tin oxide (FTO) as the transparent conductive layer (TCL), tungsten disulfide (WS 2 ) [ 73 ] as the electron transport layer (ETL), CPTSe or CPTS as the absorber layer, Spiro-MeOTAD [ 74 ] as the hole transport layer (HTL) and Mo as the rear electrode [ 75 ]. In this configuration, CPTS/CPTSe serves as the photoactive layer responsible for light absorption and electron-hole pair generation. The overall photovoltaic performance of thin-film solar cells is strongly governed by the appropriate selection of best absorber layer along with suitable ETL and HTL materials. The best absorber layer easily generates electron-hole pair, leading to the establishment of a potential difference across the device. The ETL facilitates efficient extraction and transport of photo-generated electrons from the absorber to the front electrode while simultaneously blocking holes, thereby suppressing interfacial recombination losses. Conversely, the HTL selectively extracts holes, prevent electron back-transfer and enhance charge collection efficiency at the rear contact [ 76 ]. WS 2 has emerged as a highly efficient ETL due to its favorable band alignment, high electron mobility and relatively high dielectric permittivity, which collectively facilitate efficient electron extraction and suppress interfacial recombination. Moreover, WS 2 exhibits excellent chemical stability avoids photo-catalytic degradation and does not require high temperature annealing, making it particularly advantageous for low-cost and stable photovoltaic device fabrication [ 73 ]. Similarly, Spiro-MeOTAD is employed as the HTL due to its suitable energy band gap alignment with CPTS absorber, high hole transport capability and proven effectiveness in high-efficiency photovoltaic devices [ 74 ]. The optimized HTL effectively suppresses interfacial recombination and ensures efficient hole transport toward the Mo back electrode. The optimized material parameters used in the SCAPS-1D simulations including layer thickness, band gap (E g ), electron affinity (χ), dielectric permittivity (ε r ), effective density of states (Nc, Nv), carrier nobilities (µ e , µ h ) and doping concentrations (ND, NA) are summarized in Table 3 . These parameters were selected based on reported experimental and simulated literature as well as DFT calculations to ensure physical reliability and consistency. Table 3 Simulated parameters for different layers, taking CPTX (X = Se/S) as the absorber layer. Parameters TCO ETL Compound HTL FTO WS 2 [ 65 ] CPTX Spiro-MeOTAD[ 66 ] Thickness (nm) 500 195 600 200 E g (eV) 3.5 1.8 1.1/1.4 3 Electron affinity (eV) 4.0 3.95 4.45/4.30 2.2 Dielectric Permittivity (ϵ r ) 9.0 13.6 6.5/6.2 3.0 Nc (cm − 3 ) 10 19 10 18 2.5/1.8×10 18 2.2 × 10 18 Nv (cm − 3 ) 10 19 10 18 4.12/3.0×10 18 1.8 × 10 19 µ e (cm 2 Vs − 1 ) 50 500 25/15 2.1 × 10 − 3 µ h (cm 2 Vs − 1 ) 50 500 25/15 2.16 × 10 − 3 N D (cm − 3 ) 10 15 7.25×10 18 0/0 0 N A (cm − 3 ) 0 0 10 16 /10 15 10 18 The calculated photovoltaic parameters and interface defect parameters between absorber/HTL and absorber/ETL are presented in Table 4 and Table 5 . The results indicate that CPTSe based solar cells, owing to their narrower band gap and enhanced light absorption in the visible and near-infrared regions, deliver a high short-circuit current density (J sc ) of 25.05 mA/cm − 2 , along with an open-circuit voltage (V oc ) of 0.95V and a fill factor (FF) of 86.21%, resulting in an overall simulated power conversion efficiency (PCE) of 20.61%. In contrast, CPTS-based solar cells, benefiting from their wider band gap, exhibit a high V oc of 1.34 V, a J sc of 15.58 mA/cm 2 , and a fill factor of 87.82%, are resulting a PCE of 18.34%, reflecting efficient charge extraction and reduced recombination losses. This complementary performance between CPTSe and CPTS absorbers is consistent with fundamental photovoltaic principles, wherein a decreasing band gap enhances photocurrent at the expense of open-circuit voltage, thereby demonstrating the strong photovoltaic potential of Pd-based Kesterite absorbers [ 77 ]. Table 4 J-V Characteristic parameters for CPTS Compounds Space group V oc (Volt) J sc mA/cm 2 FF % PCE % Cu 2 PdSnSe 4 I-4 (82) 0.95 25.05 86.21 20.61 Cu 2 PdSnS 4 1.34 15.58 87.82 18.34 Table 5 Interface defect parameter used in SCAP-1D simulations of CPTX. Parameter ETL/absorber Absorber absorber/HTL Type Of defect Neutral Neutral Neutral Energetic distribution Single Single Single Characteristic energy (eV) 0.1 0.1 0.1 Electron capture cross-section (cm 2 ) 1x10 − 15 1x10 − 15 1x10 − 15 Energy level w.r.t (eV) 0.65 0.60 0.65 Total defect density (cm − 3 ) 1x10 15 10 14 1x10 15 The simulated current voltage (J-V) characteristic under AM 1.5 G illuminations, shown in Fig. 10 , exhibit low series resistance and minimal recombination losses, indicating efficient carrier transport across the device interfaces. The high FF values further confirm efficient charge extraction at both the ETL/absorber and absorber/HTL interfaces. The quantum efficiency (QE) spectra presented in Fig. 11 demonstrate a strong photo-response throughout the visible region, confirming efficient photon absorption and carrier collection by both CPTS and CPTSe absorber. The gradual drop in QE at shorter wavelengths is attributed to transport-relate losses within the front contact and ETL layers. Overall, the high values of V oc , FF and PCE obtained for CPTS and CPTSe device indicate that Pd based Kesterite absorbsers perform better than conventional CZTS-based devices and effectively addressing the common Voc deficit in Kesterite solar cells. These findings highlight that Pd incorporation is an effective strategy for improving carrier transport, reducing mediated recombination and enhancing photovoltaic efficiency, thereby demonstrating the strong potential of CPTS and CPTSe as environmentally benign and high-performance thin film solar cells. Conclusions The structural, electron, optical and photovoltaic properties of Pd based Kesterites CPTSe and CPTS were investigated using first-principles calculations. The crystal structures were fully relaxed to determine the electronic and optical properties. In these materials, the Pd substitution at the Zn site stabilizes the lattice, suppresses secondary phase formation and reduces antisite defect concentrations particularly Cu-Pd defects. The calculations confirm that both CPTSe and CPTS are direct band gap semiconductors with band gaps of 1.11 eV and 1.4 eV respectively, falling within the optimal range for solar energy conversion. Optical analyses reveal strong visible light absorption (10 4 cm − 1 ), favorable dielectric constants and refractive indices, indicating efficient light harvesting and low optical losses. Device simulations of the (FTO/WS 2 /CPT(Se/S)/Spiro-MeOTAD/Mo) architecture were performed using SCAPS-1D. The CPTSe based device achieve an open circuit voltage (V oc = 0.95V), a high short-circuit current density (J sc = 25.05 mAcm − 2) and a fill factor (FF = 86.21%), resulting in a power efficiency (PCE) 20.61%. In contrast the CPTS-based device, benefiting from enhanced visible-light absorption and a wider band gap, delivers a higher V oc = 1.34V, J sc = 15.58 mAcm − 2 , FF = 87.82% and PCE 18.34%, highlighting complementary performance trends between the two Pd-based Kesterite absorbers. Device-level simulations demonstrate enhanced photovoltaic performance. Pd incorporation improves electron mobility, suppress defect and enhances cation ordering. These characteristics combined with favorable band gaps, strong optical absorption and enhanced structure stability, position Pd- based Kesterites as promising alternatives to conventional Zn based Kesterites for high efficiency, reliable, earth abundant, stable and sustainable thin film solar cells as well as other optoelectronic applications such as LEDs. Declarations Credit Authorship Contribution Statement Ihsan Ullah: Writing–original draft, Validation, Software, Investigation, Methodology. Imad Khan: Supervision, Project administration, Conceptualization, Writing–review & editing. Declaration Of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Data Availability Data will be made available on request. 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Khan","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAA6klEQVRIiWNgGAWjYBACNiCWbGxgYLA/3n7wAZDDw0e0FoYzZ5INQFrYiLEJouVGgpkEzBC8gE/s8MObM3fY5TE2JKRVfs2xk2FjYH746AY+h0mnGVtuPJNczMxw8Nht2W3JQIexGRvn4NWSYCb5sI05sY2xIe225DZmoBYeNmn8WtK/AbXUJ/YwM5gVS26rJ0ZLjpnkxrbDiTPYGMwYP247TJSWYsuZbccTN/DwJEszbjvOw8ZMwC/ys9M33uxtq07cIP/84Mef26rt+dmbHz7GpwUFMPOASWKVgwDjD1JUj4JRMApGwYgBAB83RvTNRVT4AAAAAElFTkSuQmCC","orcid":"","institution":"University of Malakand","correspondingAuthor":true,"prefix":"","firstName":"Imad","middleName":"","lastName":"Khan","suffix":""}],"badges":[],"createdAt":"2026-02-21 11:24:43","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-8933098/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-8933098/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":104977551,"identity":"92ebe962-8db6-444a-84ab-d937ff75a7db","added_by":"auto","created_at":"2026-03-19 12:32:05","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":590245,"visible":true,"origin":"","legend":"\u003cp\u003eCPTX(X=S/Se) crystal structure for (a) kesterite phase (Space group I-4) while (b) showing Sn/Pd at the center of tetrahedron and chalcogens (S/Se) at the corner of tetrahedron.\u003c/p\u003e","description":"","filename":"image1.png","url":"https://assets-eu.researchsquare.com/files/rs-8933098/v1/8ce5b0786471187ffeed31ac.png"},{"id":104977555,"identity":"af4c5160-13bc-4eda-b4f3-e2bc1dcf4dd7","added_by":"auto","created_at":"2026-03-19 12:32:06","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":324521,"visible":true,"origin":"","legend":"\u003cp\u003eTotal energy as a function of volume of CPTX (X=Se,S) in kesterite structure.\u003c/p\u003e","description":"","filename":"image2.png","url":"https://assets-eu.researchsquare.com/files/rs-8933098/v1/dd543da19e6e5e0512e1b3c7.png"},{"id":105034789,"identity":"c8bb6dcb-354c-49d2-8eac-2d31775b5a40","added_by":"auto","created_at":"2026-03-20 07:24:12","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":152347,"visible":true,"origin":"","legend":"\u003cp\u003eBand structure of CPTX (X=S, Se) (a) kesterite CPTSe and (b) kesterite CPTS systems.\u003c/p\u003e","description":"","filename":"image3.png","url":"https://assets-eu.researchsquare.com/files/rs-8933098/v1/5949b80bc7637a92932703d7.png"},{"id":104977549,"identity":"7e7fb655-cc7f-4810-b1e4-a4ca078251dc","added_by":"auto","created_at":"2026-03-19 12:32:05","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":256792,"visible":true,"origin":"","legend":"\u003cp\u003eTotal and partial densities of states (DOS) of CPTSe calculated using the mBJ+U.\u003c/p\u003e","description":"","filename":"image4.png","url":"https://assets-eu.researchsquare.com/files/rs-8933098/v1/95a2f5546e8fa8a17794038e.png"},{"id":104977553,"identity":"2f524e89-ef5e-49c8-9c6f-f6739ea571f9","added_by":"auto","created_at":"2026-03-19 12:32:05","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":15792,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eDielectric functions (Real ε\u003c/strong\u003e\u003csub\u003e\u003cstrong\u003e1\u003c/strong\u003e\u003c/sub\u003e\u003cstrong\u003e(ω) \u0026nbsp;of CPTX (X =Se, S)).\u003c/strong\u003e\u003c/p\u003e","description":"","filename":"image5.png","url":"https://assets-eu.researchsquare.com/files/rs-8933098/v1/79632f7268ed603efaf88d69.png"},{"id":105034928,"identity":"c9f0aa79-e64a-41c4-b030-17cfe856afc3","added_by":"auto","created_at":"2026-03-20 07:24:52","extension":"png","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":16918,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eDielectric functions imaginary part ε\u003c/strong\u003e\u003csub\u003e\u003cstrong\u003e2\u003c/strong\u003e\u003c/sub\u003e\u003cstrong\u003e(ω) \u0026nbsp;of CPTX (X =Se, S)).\u003c/strong\u003e\u003c/p\u003e","description":"","filename":"image6.png","url":"https://assets-eu.researchsquare.com/files/rs-8933098/v1/020e97140d7535a9c149e3df.png"},{"id":104977554,"identity":"bc0fca97-6e9c-4a29-bf5c-0e3319f3fcfa","added_by":"auto","created_at":"2026-03-19 12:32:05","extension":"png","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":13581,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eIndex of refraction n (ω) of CPTX (X= Se, S).\u003c/strong\u003e\u003c/p\u003e","description":"","filename":"image7.png","url":"https://assets-eu.researchsquare.com/files/rs-8933098/v1/e8b7d0c72682b85a16165ae8.png"},{"id":104977559,"identity":"82bffd22-8c6b-459c-aa6e-6c74e73b2f16","added_by":"auto","created_at":"2026-03-19 12:32:06","extension":"png","order_by":8,"title":"Figure 8","display":"","copyAsset":false,"role":"figure","size":17059,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eAbsorption coefficient α (ω) of CPTX (X= Se, S).\u003c/strong\u003e\u003c/p\u003e","description":"","filename":"image8.png","url":"https://assets-eu.researchsquare.com/files/rs-8933098/v1/2ed19db82ca77959b5ebda41.png"},{"id":104977552,"identity":"81b0a535-1fba-4df6-b5e9-2fb74146fcf9","added_by":"auto","created_at":"2026-03-19 12:32:05","extension":"png","order_by":9,"title":"Figure 9","display":"","copyAsset":false,"role":"figure","size":157233,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eIllustration of the simulated cell architecture of CPTX.\u003c/strong\u003e\u003c/p\u003e","description":"","filename":"image9.png","url":"https://assets-eu.researchsquare.com/files/rs-8933098/v1/053f0e6f9d87a31b7d20a664.png"},{"id":105035439,"identity":"9aa7ace0-7be0-4453-83ae-f480f28b8825","added_by":"auto","created_at":"2026-03-20 07:26:05","extension":"png","order_by":10,"title":"Figure 10","display":"","copyAsset":false,"role":"figure","size":97843,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eI-V curves of CPTX\u003c/strong\u003e\u003c/p\u003e","description":"","filename":"image10.png","url":"https://assets-eu.researchsquare.com/files/rs-8933098/v1/8519ef12df3ea30ddb3f88d4.png"},{"id":104977557,"identity":"299f6d0a-8af7-4efa-b9e6-f1fc4016f0d7","added_by":"auto","created_at":"2026-03-19 12:32:06","extension":"png","order_by":11,"title":"Figure 11","display":"","copyAsset":false,"role":"figure","size":78853,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eQuantum efficiency of CPTX\u003c/strong\u003e\u003c/p\u003e","description":"","filename":"image11.png","url":"https://assets-eu.researchsquare.com/files/rs-8933098/v1/7218d0ee5621afbedd737e47.png"},{"id":105562711,"identity":"ed2ffdcf-c88d-4ac3-9551-73b74c0d85af","added_by":"auto","created_at":"2026-03-27 12:44:17","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":2665667,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-8933098/v1/dca43e25-6087-43e9-8a20-8593d5d3b107.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"First-principles investigation of Pd-based Kesterites for optoelectronic and photovoltaic applications","fulltext":[{"header":"1. Introduction","content":"\u003cp\u003eThe depend on fossil fuels is a major contributor of global warming due to increased carbon dioxide (CO\u003csub\u003e2\u003c/sub\u003e) emissions, which trap outgoing radiation and intensifying the green house effect [\u003cspan additionalcitationids=\"CR2 CR3 CR4\" citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e]. Despite their environmental impact and finite nature, fossil fuels still account for nearly 80% of global energy consumption, underscoring the urgency of transitioning toward sustainable energy systems [\u003cspan additionalcitationids=\"CR7\" citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e]. In response to rising global electricity demand and the objectives of the 21st -century green energy agenda, renewable energy technologies have become a critical research focus; however, many alternatives such as wind, geothermal and thermoelectric systems remain geographically constrained. In contrast, solar energy is abundant and universally available, and its direct conversion into electricity via photovoltaic (PV) technology particularly through advances in nano-materials based absorbers offer a scalable, environmentally benign, and efficient pathway for large-scale renewable power generation [\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e]. Photovoltaic (PV) technology has emerged as a promising alternative to conventional energy sources, such as fossil fuels, offering significant potential to address global energy demands and environmental challenges like greenhouse gas (GHG) emissions, cost, and climate change [\u003cspan citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e, \u003cspan citationid=\"CR11\" class=\"CitationRef\"\u003e11\u003c/span\u003e]. Since past decade the worldwide PV-based solar panel installation rate has been expanded rapidly, driven largely by significant reduction in module costs and rising efficiencies of the solar cell. PV technology stands out for being green, renewable, scalable, and increasingly affordable, giving it a strong edge over nonrenewable and even some renewable energy sources in terms of accessibility and sustainability. These advantages position solar cell technology as a central pillar in the global transition toward zero GHG emissions and emphasize their potential in the development of next generation energy conversion technologies with strong commercialization prospects [\u003cspan additionalcitationids=\"CR13 CR14\" citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eSolar cell industry has seen three generational stages. The conventional first generation is based on single and polycrystalline silicon (Si) achieving power conversion efficiency (PCE) of 25% and long lifetime (25\u0026ndash;30 year) [\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e]. Limitations of the first generation include high production cost, energy intensive fabrication, low optical absorption due to indirect band gap and thick absorber layer (180\u0026ndash;300 \u0026micro;m) [\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e]. Thin-film solar cells based on amorphous Si (a-Si), CdTe and Cu(In,Ga)Se\u003csub\u003e2\u003c/sub\u003e (CIGS) contribute the second generation. These materials are lightweight, flexible, adaptable substrates suitable for portable application and achieved PEC in the range 10\u0026ndash;21% [\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e]. On the downside this generation has low efficiencies, reliance on scarce or toxic elements (In, Te, Cd), shorter lifespan and limiting large scale commercialization [\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e]. The third-generation known as emerging solar cells includes perovskite solar cells (PSC), dye synthesized solar cells (DSSC), organic photovoltaic (OPV), hybrid (organic and inorganic) solar cells, quantum dot solar cells (QDSC) and Kesterite solar cells (KSC) [\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eThe advantages of this emerging generation include low-cost fabrication, high PCEs, tunable properties and compatible with flexible substrates. However, most of these materials have stability issues, scalability challenges and toxicity (Pb in perovskites) [\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e]. The prerequisites for an ideal solar cell material include strong optoelectronic properties (such as high optical absorption, suitable direct band gap (1.5 eV), higher charge carrier mobility, low-binding energy), long term stability, high PCE, excellent flexibility and reliability, availability, low-toxicity, low cost fabrication, and longer lifetime [\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eOrganic-inorganic lead halide perovskites have received remarkable attention due to their interesting physical properties and rapidly achieved high efficiencies (~\u0026thinsp;27%), but suffer from poor environmental stability (degrading when exposed to moisture, oxygen, light, and heat) and toxicity due the presence of lead which are major bottlenecks for their commercialization [\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e, \u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e]. Therefore, the search for sustainable and environmentally benign absorber materials has shifted toward quaternary semiconducting materials with the general formula A\u003csub\u003e2\u003c/sub\u003eBCD\u003csub\u003e4\u003c/sub\u003e (A\u0026thinsp;=\u0026thinsp;Cu, Ag, K, Li; B\u0026thinsp;=\u0026thinsp;Zn, Cd, Pd, Ni, Mg; C\u0026thinsp;=\u0026thinsp;Sn, Pb, Ge, Si and D\u0026thinsp;=\u0026thinsp;S, Se, Te), whom structure is the derivative of chalcopyrite CuInS\u003csub\u003e2\u003c/sub\u003e. The substitution of two indium (In) atoms with zinc (Zn) and tin (Sn) atoms yield quaternary semiconductors that preserved favorable optoelectronic features of chalcopyrites while offering broader compositional flexibility [\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e]. This family of quaternary semiconductor compounds are known as Kesterite and has attracted significant attention, with Cu\u003csub\u003e2\u003c/sub\u003eZnSnS\u003csub\u003e4\u003c/sub\u003e/Se\u003csub\u003e4\u003c/sub\u003e are of special interest due to their suitable direct band gap (~\u0026thinsp;1.5 eV), higher charge carrier mobility, low-binding energy, long term stability, excellent flexibility and reliability, low-toxicity, low-cost fabrication, longer lifetimes and earth-abundant constituents [\u003cspan additionalcitationids=\"CR23\" citationid=\"CR22\" class=\"CitationRef\"\u003e22\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e]. Their environmentally friendly composition and compatibility with established CIGS device architectures and fabrication processes further strengthen their potentials for scalable thin film photovoltaic, making them one of the most promising candidates for solar energy conversion [\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eAs members of the broader A\u003csub\u003e2\u003c/sub\u003eBCD\u003csub\u003e4\u003c/sub\u003e family of quaternary semiconductors, compounds such as Cu\u003csub\u003e2\u003c/sub\u003eZnGeS\u003csub\u003e4\u003c/sub\u003e, and Cu\u003csub\u003e2\u003c/sub\u003eZnSn(S, Se)\u003csub\u003e4\u003c/sub\u003e (CZTSSe) exhibit tunable direct band gaps having range of 1.0-2.5 eV, enabling band gap engineering via S/Se alloying to achieve the optimal 1.0-1.6 eV for single-junction photovoltaic devices [\u003cspan additionalcitationids=\"CR27 CR28 CR29\" citationid=\"CR26\" class=\"CitationRef\"\u003e26\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e30\u003c/span\u003e]. Beyond PV, Kesterite-based compounds have also been investigated for thermoelectric, water splitting, CO\u003csub\u003e2\u003c/sub\u003e reduction and non-linear optical applications due to their versatile optoelectronic properties [\u003cspan additionalcitationids=\"CR32 CR33 CR34\" citationid=\"CR31\" class=\"CitationRef\"\u003e31\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR35\" class=\"CitationRef\"\u003e35\u003c/span\u003e]. Structurally, both experimental studies and theoretical calculations confirm that tetragonal phase is the most stable crystal structure [\u003cspan citationid=\"CR36\" class=\"CitationRef\"\u003e36\u003c/span\u003e]. Kesterite thin films can be synthesized using vacuum-based methods such as co-evaporation and sputtering, which provide compositional control but are limited by poor scalability and high cost. In contrast non-vacuum approaches including sol-gel, spray pyrolysis, electro deposition, nano-crystal inks along with emerging methods like microwave-assisted solvothermal and chemical vapor deposition (CVD) are more attractive for large-scale, low-cost fabrication with improved crystal quality [\u003cspan citationid=\"CR37\" class=\"CitationRef\"\u003e37\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eSince the first Kesterite solar cell was reported in 1997 with a PCE of only 0.66% [\u003cspan citationid=\"CR38\" class=\"CitationRef\"\u003e38\u003c/span\u003e], the PCE of Kesterite-based devices has steadily increased, reaching a current record of 15.8% [\u003cspan citationid=\"CR39\" class=\"CitationRef\"\u003e39\u003c/span\u003e]. However they remain far below CIGS and halides perovskites largely due to limited research attention compared to halides perovskites and silicon, as well as non-radiative recombination losses arising from intrinsic defects, cation disorder, and grain boundaries [\u003cspan citationid=\"CR40\" class=\"CitationRef\"\u003e40\u003c/span\u003e]. Yet Kesterite remain highly attractive due to their earth-abundant, non-toxic and stable composition. Advance in defect passivation, interface engineering, and composition engineering using computational simulations could provide a strong platform for the development of stable, scalable, and sustainable Kesterite photovoltaic while unlocking further efficiency improvements [\u003cspan additionalcitationids=\"CR42 CR43\" citationid=\"CR41\" class=\"CitationRef\"\u003e41\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR44\" class=\"CitationRef\"\u003e44\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eAmong these strategies, a key strategy for tuning the optoelectronic performance of such materials is cation substitution within the Kesterite material Cu\u003csub\u003e2\u003c/sub\u003eZnSnX\u003csub\u003e4\u003c/sub\u003e at B-site has been shown to be highly effective in modifying band gap characteristics and enhancing light absorption behavior make them attractive for photovoltaic applications. Such as replacement of Sn with Ge to form Cu\u003csub\u003e2\u003c/sub\u003eZnGe(S,Se)\u003csub\u003e4\u003c/sub\u003e (CZGX) enables band gap tunings for tandem integration and offers superior optoelectronic properties [\u003cspan citationid=\"CR45\" class=\"CitationRef\"\u003e45\u003c/span\u003e], while cation at Cu/Zn sites substitution reduces disorder and defect formation.\u003c/p\u003e \u003cp\u003eSimilarly the replacement of zinc (Zn) with palladium (Pd) has led to the development of Cu\u003csub\u003e2\u003c/sub\u003ePdSnX\u003csub\u003e4\u003c/sub\u003e (X\u0026thinsp;=\u0026thinsp;S, Se) (CPTX). This Pd substation reduces the formation of antisite defect by lowering their formation energy, thereby promoting greater cationic ordering within the crystal lattice [\u003cspan citationid=\"CR46\" class=\"CitationRef\"\u003e46\u003c/span\u003e]. The incorporation of Pd also leads to favorable band gap tuning within the optimal range of 1.0-1.4 eV, while also enhancing the absorption coefficient- both of which are important parameters for efficient solar energy conversion [\u003cspan citationid=\"CR46\" class=\"CitationRef\"\u003e46\u003c/span\u003e]. Moreover, these Pd-based chalcogenides retain the advantages of being non-toxic and composed of relatively stable constituents, positioning them as promising absorber layers for environmentally benign and stable thin-film solar cells. Notably, they have been successfully synthesized experimentally via a microwave-assisted solvothermal method [\u003cspan citationid=\"CR46\" class=\"CitationRef\"\u003e46\u003c/span\u003e, \u003cspan citationid=\"CR47\" class=\"CitationRef\"\u003e47\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eDespite these potential, Pd- substituted systems remain insufficiently explored from a theoretical perspective. To date, only experimental studies found on the synthesis and characterization of Cu\u003csub\u003e2\u003c/sub\u003ePdSnSe\u003csub\u003e4\u003c/sub\u003e (CPTSe) and its sulfide analogue Cu\u003csub\u003e2\u003c/sub\u003ePdSnS\u003csub\u003e4\u003c/sub\u003e (CPTS). Consequently, a comprehensive first-principles understanding of the electronic and optical properties of both CPTSe and CPTS remain lacking.\u003c/p\u003e \u003cp\u003eIn this work, density functional theory (DFT) calculations are employed to systematically investigate the structure, electronic and optical properties of Cu\u003csub\u003e2\u003c/sub\u003ePdSnX\u003csub\u003e4\u003c/sub\u003e (X\u0026thinsp;=\u0026thinsp;S/Se) (CPTX). This study provides a detailed theoretical analysis of experimentally reported CPTX. The results offer fundamental insights into their electronic band structure and optical response, thereby supporting the rational design of Pd-based absorber materials for high performance photovoltaic devices.\u003c/p\u003e"},{"header":"2. Computational Detail","content":"\u003cp\u003eIn this study, first-principles calculations were performed using WIEN2K computational code, based on DFT [\u003cspan citationid=\"CR48\" class=\"CitationRef\"\u003e48\u003c/span\u003e]. Specially, the full potential linearized augmented plane-wave method and its extension incorporation local orbital (FP-LAPW\u0026thinsp;+\u0026thinsp;lo) are used [\u003cspan citationid=\"CR49\" class=\"CitationRef\"\u003e49\u003c/span\u003e]. This method is recognized for its high accuracy in describing the all electron behavior of crystalline solids and is particularly suitable for systems with complex electronic structures [\u003cspan citationid=\"CR48\" class=\"CitationRef\"\u003e48\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eThe structural optimization of the investigated compounds were carried out using generalized gradient approximation (GGA), to treat the exchange-correlation functional [\u003cspan citationid=\"CR50\" class=\"CitationRef\"\u003e50\u003c/span\u003e]. GGA generally provides improved prediction for structural parameters, but tends to underestimates the band gaps of semiconductors. To address this issue, the Tran-Blaha modified Becke-Johnson (TB-mBJ) potential has been adopted, offering significantly more reliable predictions of electronic and optical properties [\u003cspan citationid=\"CR51\" class=\"CitationRef\"\u003e51\u003c/span\u003e]. mBJ improves band gap accuracy by using kinetic-energy density to better approximate the exchange potential. For atoms possessing localized \u003cem\u003ed\u003c/em\u003e and \u003cem\u003ef\u003c/em\u003e orbitals, on-site Coulomb interactions were incorporated within the GGA\u0026thinsp;+\u0026thinsp;U formalism to adequately capture strong electron correlation effects, which are often underestimated in conventional DFT approaches [\u003cspan citationid=\"CR52\" class=\"CitationRef\"\u003e52\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eThe separation energy between core and valence states was set to 7.0 Ry to ensure an accurate treatment of core electrons. Appropriate muffin-tin radii were selected to prevent sphere overlap and to achieve basis set convergence, with values of 2.22 bohr for Cu, 2.25 bohr for Pd, 2.34 bohr for Sn and 1.90 bohr for S and 2.04 for Se atoms. The plane-wave cutoff in the interstitial region was defined by R\u003csub\u003eMT\u003c/sub\u003eK\u003csub\u003emax\u003c/sub\u003e = 7.0, where R\u003csub\u003eMT\u003c/sub\u003e corresponds to the smallest muffin-tin radius among the atomic species, while Fourier expansion of the charge density was truncated at G\u003csub\u003emax\u003c/sub\u003e = 12. Brillouin zone integrations were performed using k-point mesh 1000 to ensure convergence of total energy and electronic properties. Self-consistent field (SCF) calculations were converged to within 10\u003csup\u003e\u0026minus;\u0026thinsp;4\u003c/sup\u003e Ry in total energy. To properly treat for on-site coulombic interactions, particularly for localized Cu-3d states and Pd-4d states, a Hubbard U correction was applied within the GGA\u0026thinsp;+\u0026thinsp;U formalism. The Hubbard potential was applied to d-orbital of Cu and Pd separately. The choice of U\u0026thinsp;=\u0026thinsp;6 and 2 eV was selected for Cu-d and Pd-d orbital respectively after testing U values in range of 0 to 8 eV. In different research articles U value is optimize for Cu-d state near six 6 eV. The value of 6 eV for Cu-d and 2 eV for Pd-d is selected in term of band gap comparison [\u003cspan citationid=\"CR53\" class=\"CitationRef\"\u003e53\u003c/span\u003e], which showed that the band gap calculated using mBJ\u0026thinsp;+\u0026thinsp;U closely matches experimental observations [\u003cspan citationid=\"CR46\" class=\"CitationRef\"\u003e46\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eFinally, the PCE of the Kesterite-based absorbers were simulated using the Solar Cell Capacitance Simulator in one Dimension (SCAP-ID), thereby linking the first-principles results with realistic device-level performance predictions [\u003cspan citationid=\"CR54\" class=\"CitationRef\"\u003e54\u003c/span\u003e]. This tool is widely recognized for simulating solar cell characteristics by solving semiconductor equations, such as Passion\u0026rsquo;s equation, continuity equation and drift diffusion equation under illumination conditions [\u003cspan citationid=\"CR55\" class=\"CitationRef\"\u003e55\u003c/span\u003e].\u003c/p\u003e"},{"header":"3. Results and discussion","content":"\u003cdiv id=\"Sec4\" class=\"Section2\"\u003e \u003ch2\u003e3.1 Structural Properties\u003c/h2\u003e \u003cp\u003eBoth compounds crystallize in the tetragonal Kesterite structure with space group I-4 (No. 82) [\u003cspan citationid=\"CR46\" class=\"CitationRef\"\u003e46\u003c/span\u003e]. The optimized unit cell structure of Cu\u003csub\u003e2\u003c/sub\u003ePdSnX\u003csub\u003e4\u003c/sub\u003e (X\u0026thinsp;=\u0026thinsp;Se, S) is illustrated in Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e. In this structure, the cation sub-lattice is composed of alternating Cu-Sn and Cu-Pd tetrahedral layers along xy plane, creating a tetrahedral coordinate framework. Due to the layered cation arrangement, Cu-S/Se bonding environments differ slightly between Pd-Cu and Sn-Cu containing layers, resulting in small variations in the local atomic bonding within the crystal structure [\u003cspan citationid=\"CR56\" class=\"CitationRef\"\u003e56\u003c/span\u003e]. Inside the Kesterite unit cell, Cu atoms occupy two distinct Wyckoff positions, 2a (0, 0, 0) and 2c (0, 1/2, 3/4), Pd atoms are located at the 2d (0, 1/2, 1/4) site, and Sn atoms occupy the 2b (0, 0, 1/2) position. The anions (S/Se) are located at the 8g (x, y, z) sites, forming tetrahedral coordination around the cations.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThe equilibrium lattice parameters were obtained by fitting the calculated total energy as a function of unit cell volume to the Murnaghan equation of states [\u003cspan citationid=\"CR57\" class=\"CitationRef\"\u003e57\u003c/span\u003e] as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e. The minimum total energies were found to be -48485.401Ry for CPTSe and \u0026minus;\u0026thinsp;32245.394 Ry for CPTS. In the optimized structural parameters of CPTX, the calculated lattice parameters of CPTSe are a\u0026thinsp;=\u0026thinsp;b\u0026thinsp;=\u0026thinsp;5.6815 Ǻ and c\u0026thinsp;=\u0026thinsp;11.041 Ǻ, where for CPTS, the calculated lattice parameters are a\u0026thinsp;=\u0026thinsp;b = 5.4510 Ǻ and c\u0026thinsp;=\u0026thinsp;10.5216 Ǻ. CPTSe exhibits larger lattice parameters, reflecting the larger ionic radius of Se. The calculated lattice parameters of CPTSe and CPTS are in good agreement with the reported experimental values [\u003cspan citationid=\"CR46\" class=\"CitationRef\"\u003e46\u003c/span\u003e, \u003cspan citationid=\"CR47\" class=\"CitationRef\"\u003e47\u003c/span\u003e], and iso-structure compounds [\u003cspan citationid=\"CR45\" class=\"CitationRef\"\u003e45\u003c/span\u003e, \u003cspan citationid=\"CR58\" class=\"CitationRef\"\u003e58\u003c/span\u003e] and are summarized in Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab1\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 1\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eCalculated and experimental lattice parameter, anion S/Se atomic positions and bond length for CPTX (X\u0026thinsp;=\u0026thinsp;Se/S) Kesterite crystallographic phases.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"5\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u003cem\u003eCompound\u003c/em\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eCPTSe\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eCPTS\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eCZGSe\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eCZGS\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003ea\u0026thinsp;=\u0026thinsp;b (\u0026Aring;)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e5.6815(5.7061)\u003csup\u003ec\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e5.4510/5.409\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e5.71\u003csup\u003ea\u003c/sup\u003e/5.58\u003csup\u003eb\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e5.38\u003csup\u003ea\u003c/sup\u003e/5.28\u003csup\u003eb\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003ec\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e11.042(11.0712)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e\u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003e10.5216/10.808\u003c/span\u003e\u003cspan address=\"10.5216/10.808\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e11.11\u003csup\u003eb\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e10.51\u003csup\u003eb\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003ec/2a\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.9717(0.9701)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.965\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.987\u003csup\u003ea\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.974\u003csup\u003ea\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eBulk modulus (GPa)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e91.56\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e89.64\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eX\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.23348\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.23533\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.24276\u003csup\u003ea\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.24799\u003csup\u003ea\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eY\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.24026\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.24224\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.25331\u003csup\u003ea\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.25684\u003csup\u003ea\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eZ\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.12998\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.12899\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.124945\u003csup\u003ea\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0.12328\u003csup\u003ea\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eCu1-X\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e2.3907\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e2.2988/2.320\u003csup\u003ed\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e2.4501\u003csup\u003ea\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e2.3315\u003csup\u003ea\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eCu2-X\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e2.3957\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e2.2973/2.323\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e2.4287\u003csup\u003ea\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e2.3100\u003csup\u003ea\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003ePd-X\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e2.4419\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e2.3409/2.326\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e2.4986\u003csup\u003ea\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e2.3650\u003csup\u003ea\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eSn-X\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e2.5653\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e2.4373/2.398\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e2.4762\u003csup\u003ea\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e2.3014\u003csup\u003ea\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003ctfoot\u003e \u003ctr\u003e\u003ctd colspan=\"5\"\u003ea) Ref.67\u003c/td\u003e\u003c/tr\u003e \u003ctr\u003e\u003ctd colspan=\"5\"\u003eb) Ref.45\u003c/td\u003e\u003c/tr\u003e \u003ctr\u003e\u003ctd colspan=\"5\"\u003ec) Ref. 46\u003c/td\u003e\u003c/tr\u003e \u003ctr\u003e\u003ctd colspan=\"5\"\u003ed) Ref. 47\u003c/td\u003e\u003c/tr\u003e \u003c/tfoot\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eThe bond lengths of CPTSe and CPTS compounds were calculated and are summarized in Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e. In CPTSe, the calculated bond length for Cu1-Se is 2.3907 Ǻ, for Cu2-Se is 2.3957 Ǻ, for Pd-Se is 2.4419 and for Sn-Se is 2.5653. In case of CPTS bond lengths are 2.2988Ǻ and 2.2973Ǻ for Cu1-S, and Cu2-S respectively, while 2.3409Ǻ and 2.4373Ǻ for Pd-S and Sn-S. The increase values in bond length of CPTSe compared to CPTS is due to larger ionic radius of Se. Furthermore, the observed trends are consistent with those reported for experimental CPTS only and iso-structural CZGSe and CZGS compounds, confirming the reliability and accuracy of the present structural optimization [\u003cspan citationid=\"CR47\" class=\"CitationRef\"\u003e47\u003c/span\u003e, \u003cspan citationid=\"CR59\" class=\"CitationRef\"\u003e59\u003c/span\u003e]. The values of the bulk modulus are predicted for first time for these compounds and the values are 91.56 GPa for CPTSe and 89.64 GPA for CPTS, indicating slightly higher stiffness in the CPTSe compound.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec5\" class=\"Section2\"\u003e \u003ch2\u003e3.2 Electronic Properties\u003c/h2\u003e \u003cp\u003eThe electronic band structures of Cu\u003csub\u003e2\u003c/sub\u003ePdSnX\u003csub\u003e4\u003c/sub\u003e (X\u0026thinsp;=\u0026thinsp;Se, S) were calculated using GGA, modified Becke-Johnson (mBJ) exchange potential, both with and without the Hubbard U correction (mBJ\u0026thinsp;+\u0026thinsp;U). The band structures were evaluated along the high-symmetry directions Г-H-N-Г-P in the irreducible Brillouin zone, with the Fermi level set to 0 eV as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e. Figure\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e(a) and 3(b) represent the band structures of CPTSe and CPTS respectively. The negative energy region corresponds to the valence band, while the positive energy region represents the conduction band. For both compounds, the valence and conduction band maximum and minimum are located at the Г point, indicating a direct band gap nature. Direct band gap semiconductors exhibit significantly higher optical absorption coefficients than indirect band gap materials, as electronic transitions from valence to conduction band occur without phonon assistance, enabling more efficient electron excitation [\u003cspan citationid=\"CR60\" class=\"CitationRef\"\u003e60\u003c/span\u003e].\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eGGA result of both compounds reveal zero band gaps thus show metallic nature and are list in Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e. Therefore, GGA\u0026thinsp;+\u0026thinsp;U was employed in the range of 0\u0026ndash;8 eV and get a band gap value of 0.2 and 0.5 eV for CPTSe and CPTS respectively. Due to the underestimate results of GGA\u0026thinsp;+\u0026thinsp;U, the mBJ approximation were used and as result, the calculated band gaps are 0.4 eV for CPTSe and 0.8 eV for CPTS are obtained, which are also underestimated the experimentally reported values. Therefore the inclusion of on-site Coulomb interactions through the mBJ\u0026thinsp;+\u0026thinsp;U approach is applied as a result a band gap of 1.11 eV is obtained for CPTSe, in excellent agreement with experimental observations. An enhancement in the energy band gap is observed for CPTS, where mBJ\u0026thinsp;+\u0026thinsp;U predict a larger band gap (1.4 eV) compared to CPTSe as mention in Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e. The band gap calculated for CPTS using mBJ\u0026thinsp;+\u0026thinsp;U approach is underestimated the experimental optical band gap energy of 1.64 eV [\u003cspan citationid=\"CR47\" class=\"CitationRef\"\u003e47\u003c/span\u003e], but comparable with that of iso-structural compound. The band gap of CPTSe is comparable to that of silicon (1.12 eV). However, unlike silicon, which possesses an indirect band gap, CPTSe exhibits a direct band gap. This direct band gap nature enables stronger optical absorption and more efficient charge-carrier generation, making CPTSe a potentially superior photovoltaic absorber. Based on the direct and suitable band gap value, CPTSe is expected to achieve higher photovoltaic efficiency just like silicon. The smaller band gap of the Se-based compound relative to its S-based counterpart arises from the larger ionic radius and higher p-orbital energy of Se, which shifts the valence band upward. Our calculated results of band gap are also consistence with other iso-structure compound CZTSe and CZTS respectively and mention in Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e [\u003cspan citationid=\"CR45\" class=\"CitationRef\"\u003e45\u003c/span\u003e, \u003cspan citationid=\"CR58\" class=\"CitationRef\"\u003e58\u003c/span\u003e].\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab2\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 2\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eBand gap values calculated through different potential and effective mass comparison of Cu₂PdSnX₄ (X\u0026thinsp;=\u0026thinsp;S, Se).\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"9\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c8\" colnum=\"8\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c9\" colnum=\"9\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eCompound\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eEXP.\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eGGA (eV)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eTB-mBJ\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eGGA\u0026thinsp;+\u0026thinsp;U\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003emBJ\u0026thinsp;+\u0026thinsp;U\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c7\"\u003e \u003cp\u003em\u003csub\u003ee\u003c/sub\u003e*(mo)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c8\"\u003e \u003cp\u003em\u003csub\u003eh\u003c/sub\u003e*(mo)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c9\"\u003e \u003cp\u003eE\u003csub\u003eb\u003c/sub\u003e(meV)\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eCu\u003csub\u003e2\u003c/sub\u003ePdSnSe\u003csub\u003e4\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1.13\u003csup\u003ea\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.22\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e1.11\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0.23\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0.56\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e53\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eCu\u003csub\u003e2\u003c/sub\u003ePdSnS\u003csub\u003e4\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1.07/1.64\u003csup\u003eb\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.8\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e1.4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0.34\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0.71\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e81\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eCu\u003csub\u003e2\u003c/sub\u003eZnGeSe\u003csub\u003e4\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1.28\u003csup\u003ed\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0.13\u003csup\u003ee\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0.38\u003csup\u003ee\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e31\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eCu\u003csub\u003e2\u003c/sub\u003eZnSnS\u003csub\u003e4\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1.5\u003csup\u003ec\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e0.22\u003csup\u003ee\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e0.60 \u003csup\u003ee\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e52\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003ctfoot\u003e \u003ctr\u003e\u003ctd colspan=\"9\"\u003ea) Ref. 46\u003c/td\u003e\u003c/tr\u003e \u003ctr\u003e\u003ctd colspan=\"9\"\u003eb) Ref.47\u003c/td\u003e\u003c/tr\u003e \u003ctr\u003e\u003ctd colspan=\"9\"\u003ec) Ref.58\u003c/td\u003e\u003c/tr\u003e \u003ctr\u003e\u003ctd colspan=\"9\"\u003ed) Ref 45\u003c/td\u003e\u003c/tr\u003e \u003ctr\u003e\u003ctd colspan=\"9\"\u003ee) Ref 65\u003c/td\u003e\u003c/tr\u003e \u003c/tfoot\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eTo further elucidate the electronic structure, the total and partial densities of states (DOS) for CPTSe were calculated and are shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig4\" class=\"InternalRef\"\u003e4\u003c/span\u003e within an energy range of -5 to 6 eV. The DOS results are consistent with the band structure analysis and provide insight into orbital contributions near the band edges. The valence band region close to the Fermi level is dominated by hybridized Cu-3d, S/Se-p and some contribution from Pd-d states, whereas the conduction band edge is primarily composed of Sn-p, Sn-s and Se-p orbital. These features reflect strong Pd hybridization within the tetragonal Kesterite lattice and confirm that the electronic states near the band gap are governed by the interaction between cation and anion orbital, consistent to other theoretical reports [\u003cspan citationid=\"CR59\" class=\"CitationRef\"\u003e59\u003c/span\u003e]. The same is observed for CPTS compound.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThe charge carrier mobility of CPTSe and CPTS were studied through the effective masses m*, together with the exciton binding energy (E\u003csub\u003eb\u003c/sub\u003e). The effective masses at the conduction band minimum and valence band maximum were calculated from the band curvature using the formula\u003cdiv id=\"Equ1\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ1\" name=\"EquationSource\"\u003e\n$${\\text{m}}^{\\text{*}}=\\frac{{\\text{ћ}}^{2}}{\\left[\\frac{{\\partial}^{2}{\\epsilon}\\left(\\text{k}\\right)}{\\partial{\\text{k}}^{2}}\\right]}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e1\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eWhere ε(k) represents the band-edge eigenvalue and k is the corresponding wave vector [\u003cspan citationid=\"CR61\" class=\"CitationRef\"\u003e61\u003c/span\u003e]. The calculated effective masses show that m\u003csub\u003eh\u003c/sub\u003e* \u0026gt; m\u003csub\u003ee\u003c/sub\u003e* for both CPTSe and CPTS, which is attributed to relatively flatter curvature of the valence band compared to the conduction band. The small values of m\u003csub\u003ee\u003c/sub\u003e* and m\u003csub\u003eh\u003c/sub\u003e* indicate high carrier mobility, consistence with the inverse dependence of electrical conductivity on effective mass [\u003cspan citationid=\"CR62\" class=\"CitationRef\"\u003e62\u003c/span\u003e]. In CPTS a slight increase in effective masses is observed compared to CPTSe, which correlates with the larger band gap induced by sulfur replacement. The exciton binding energy (E\u003csub\u003eb\u003c/sub\u003e) was estimated using the Mott-Wannier model expressed as\u003cdiv id=\"Equ2\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ2\" name=\"EquationSource\"\u003e\n$${E}_{b}=\\frac{\\mu}{{{\\epsilon}}_{1}^{2}\\left(0\\right)}\\times{R}_{y}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e2\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003eWhere \u0026micro; is reduced effective mass, ε\u003csub\u003e1\u003c/sub\u003e(0) is the static dielectric constant and Ry is the Rydberg energy [\u003cspan citationid=\"CR63\" class=\"CitationRef\"\u003e63\u003c/span\u003e]. The calculated E\u003csub\u003eb\u003c/sub\u003e values decrease from CPTS to CPTSe due to band gap narrowing and enhanced dielectric constant value. The relatively low exciton binding energies indicate efficient exciton dissociation and high free carrier density, which are essential for photovoltaic absorber materials [\u003cspan citationid=\"CR64\" class=\"CitationRef\"\u003e64\u003c/span\u003e]. Overall the combined low effective masses and moderate exciton binding energies confirm that CPTSe and CPTS exhibit favorable charge transport properties, making them promising candidates for high performance solar cell and optoelectronic applications. The calculated value are compared with iso-structure compound [\u003cspan citationid=\"CR65\" class=\"CitationRef\"\u003e65\u003c/span\u003e] and summarized in Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec6\" class=\"Section2\"\u003e \u003ch2\u003e3.3 Optical Properties\u003c/h2\u003e \u003cp\u003eThe knowledge of optical properties of a material is crucial for designing photovoltaic, photonic and optoelectronic devices. In semiconductors, interband transitions of electrons from occupied valence band (VB) to unoccupied conduction band (CB) determine the optical response, which can be described in term of key parameters such as the complex dielectric function, ε(ω) = ε\u003csub\u003e1\u003c/sub\u003e(ω) + iε₂(ω), index of refractive n(ω), absorption coefficient α(ω) etc. These parameters are strongly influenced by the electronic structure, crystal symmetry and chemical composition.\u003c/p\u003e \u003cp\u003eIn this study, the optical properties of tetragonal Cu\u003csub\u003e2\u003c/sub\u003ePdSnX\u003csub\u003e4\u003c/sub\u003e (X\u0026thinsp;=\u0026thinsp;Se, S) were calculated using the Kramers-Kronig relations, Fermi-golden rule and Drude Model [\u003cspan additionalcitationids=\"CR67\" citationid=\"CR66\" class=\"CitationRef\"\u003e66\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR68\" class=\"CitationRef\"\u003e68\u003c/span\u003e]. Owing to tetragonal symmetry, these compounds exhibit anisotropic optical behavior along transverse (perpendicular to z-axis) and longitudinal (parallel to z-axis) directions. The calculated real and imaginary parts of the dielectric function for CPTSe and CPTS along these directions are shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e and Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e. Both ε\u003csub\u003e1\u003c/sub\u003e(ω) and ε\u003csub\u003e2\u003c/sub\u003e(ω) display similar energy dependent trends for the two polarizations axes with distinct features corresponding to their respective band gap energies.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThe real part of dielectric function, ε\u003csub\u003e1\u003c/sub\u003e(ω), describes the dispersive response of a material to an external electromagnetic field and governs the phase velocity of light propagation along different crystallographic directions. The static dielectric constant ε\u003csub\u003e1\u003c/sub\u003e(0) for CPTSe and CPTS are shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e5\u003c/span\u003e. CPTSe posses ε\u003csub\u003e1\u003c/sub\u003e(0) value 6.5 along xy-plane and 6.6 along z-axis perpendicular and parallel to the tetragonal c-direction. Similarly, for CPTS compound the value decrease to 6.2 and 6.3 in their respective axes, this decrease can be associated to the increase in band gap. For both CPTSe and CPTS, the z component is consistently larger than the x and y components, indicating optical anisotropy arising from the tetragonal crystal symmetry and layered cation arrangement. In the low-energy region, ε\u003csub\u003e1\u003c/sub\u003e(ω) increases monotonically and reaches a maximum within the photon energy range of approximately 1\u0026ndash;2 eV, then declined interband electronic transitions. With increases photon energy, ε\u003csub\u003e1\u003c/sub\u003e(ω) decreases and crosses zero just above 8 eV, marking the screened plasma frequency, beyond which metallic-like reflection behavior occurs [\u003cspan citationid=\"CR69\" class=\"CitationRef\"\u003e69\u003c/span\u003e]. The higher static dielectric constant of CPTSe compared to CPTS follows the inverse band gap dependence predicted by the Penn model [\u003cspan citationid=\"CR70\" class=\"CitationRef\"\u003e70\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eThe fundamental parameter for evaluating optical properties is ε₂(ω), which describes the optical absorption arising from interband electronic transitions between occupied valence band and unoccupied conduction band. The optical band gaps (onset points) in the imaginary dielectric function plots in Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e6\u003c/span\u003e for CPTSe and CPTS respectively are consistence with their electronic band gaps. Optical absorption started just beyond the optical gaps with maximum absorption occurs between 2 to 4 eV, corresponding to strong interband transitions near high-symmetry points of the brillouin zone. The absorption onset in ε₂(ω) coincides with the fundamental band gap indicating that the initial optical transitions arise from Cu-d and S/Se-p hybridized valence states to Sn-s and S/Se-p dominated conduction states. The position of the absorption edge shifts in accordance with the variation in band gap energy between CPTSe and CPTS. Enhanced ε₂(ω) intensity near the energies where ε\u003csub\u003e1\u003c/sub\u003e(ω) approaches zero indicated strong absorptive nature of CPTSe and CPTS in the visible and near-ultraviolet regions. The result of both compounds for dielectric function ε\u003csub\u003e1\u003c/sub\u003e(ω) and ε\u003csub\u003e2\u003c/sub\u003e(ω) are comparable with iso-structure compound Cu\u003csub\u003e2\u003c/sub\u003eNiSnS\u003csub\u003e4\u003c/sub\u003e [\u003cspan citationid=\"CR71\" class=\"CitationRef\"\u003e71\u003c/span\u003e] and Cu\u003csub\u003e2\u003c/sub\u003eGeSn(S/Se)\u003csub\u003e4\u003c/sub\u003e [\u003cspan citationid=\"CR72\" class=\"CitationRef\"\u003e72\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eThe optical properties of tetragonal CPTX were further analyzed through refractive index, which describe how light propagates through a material. The static refractive index, obtained from the zero-frequency limit of n(ω) is found to be approximately 2.6 for CPTSe and 2.5 for CPTS, indicating strong light-matter interaction in both compounds as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e7\u003c/span\u003e. At low photon energies n(ω) remains nearly constant and then increase sharply with increasing photon energy, reaching a maximum value around 2.2 eV in the visible region. This trend reflects the inverse relationship between the refractive index and the electronic band gap and explains the slightly higher refractive index of the Se-based compound due to its smaller band gap. The results are comparable with iso-structure compound Cu\u003csub\u003e2\u003c/sub\u003eNiSnS\u003csub\u003e4\u003c/sub\u003e [\u003cspan citationid=\"CR71\" class=\"CitationRef\"\u003e71\u003c/span\u003e] and Cu\u003csub\u003e2\u003c/sub\u003eGeSn(S/Se)\u003csub\u003e4\u003c/sub\u003e [\u003cspan citationid=\"CR72\" class=\"CitationRef\"\u003e72\u003c/span\u003e].\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThe absorption coefficient α(ω), describes how strongly a material absorbs incident light and is an important parameter for evaluating its potential as a photovoltaic absorber. The calculated absorption spectra for CPTSe and CPTS are drawn in Fig.\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e8\u003c/span\u003e, show high absorption coefficients near to 10\u003csup\u003e4\u003c/sup\u003e cm\u003csup\u003e-1\u003c/sup\u003e in the visible energy range, which is a typical characteristic of direct band gap semiconductors and is favorable for thin film solar cell applications. For both compounds, the absorption onset occurs close to the fundamental band gap energy and increases rapidly with increasing photon energy. This strong absorption near the band edge is mainly due to direct electronic transitions between the valence and conduction bands. At higher photon energies, slight reductions in α(ω) appear due to transitions into less densely populated conduction band states. Overall, the high absorption coefficients in the visible region confirm that CPTSe and CPTS can efficiently absorb incident light within thin absorber layers, making them promising materials for photovoltaic applications. The results are comparable with iso-structural compound Cu\u003csub\u003e2\u003c/sub\u003eGeSn(S/S)\u003csub\u003e4\u003c/sub\u003e [\u003cspan citationid=\"CR72\" class=\"CitationRef\"\u003e72\u003c/span\u003e]. Overall, the DFT results indicate that CPTX posse\u0026rsquo;s strong optical absorption, favorable refractive index dispersion, high dielectric response and optical anisotropy confirming their strong potential for photovoltaic and photonic applications.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec7\" class=\"Section2\"\u003e \u003ch2\u003e3.4 Photovoltaic Properties\u003c/h2\u003e \u003cp\u003eBased on the favorable optical properties, key photovoltaic (PV) parameters, including open-circuit voltage (V\u003csub\u003eoc\u003c/sub\u003e), short circuit current density (J\u003csub\u003esc\u003c/sub\u003e), fill factor (FF) and PCE were evaluated using SCAPS-1D [\u003cspan citationid=\"CR54\" class=\"CitationRef\"\u003e54\u003c/span\u003e]. The simulated n-i-p (FTO/ETL/CPT(Se/S)/HTL/Mo) device architecture, schematically shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig9\" class=\"InternalRef\"\u003e9\u003c/span\u003e, consist of fluorine-doped tin oxide (FTO) as the transparent conductive layer (TCL), tungsten disulfide (WS\u003csub\u003e2\u003c/sub\u003e) [\u003cspan citationid=\"CR73\" class=\"CitationRef\"\u003e73\u003c/span\u003e] as the electron transport layer (ETL), CPTSe or CPTS as the absorber layer, Spiro-MeOTAD [\u003cspan citationid=\"CR74\" class=\"CitationRef\"\u003e74\u003c/span\u003e] as the hole transport layer (HTL) and Mo as the rear electrode [\u003cspan citationid=\"CR75\" class=\"CitationRef\"\u003e75\u003c/span\u003e]. In this configuration, CPTS/CPTSe serves as the photoactive layer responsible for light absorption and electron-hole pair generation.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThe overall photovoltaic performance of thin-film solar cells is strongly governed by the appropriate selection of best absorber layer along with suitable ETL and HTL materials. The best absorber layer easily generates electron-hole pair, leading to the establishment of a potential difference across the device. The ETL facilitates efficient extraction and transport of photo-generated electrons from the absorber to the front electrode while simultaneously blocking holes, thereby suppressing interfacial recombination losses. Conversely, the HTL selectively extracts holes, prevent electron back-transfer and enhance charge collection efficiency at the rear contact [\u003cspan citationid=\"CR76\" class=\"CitationRef\"\u003e76\u003c/span\u003e].\u003c/p\u003e \u003cp\u003eWS\u003csub\u003e2\u003c/sub\u003e has emerged as a highly efficient ETL due to its favorable band alignment, high electron mobility and relatively high dielectric permittivity, which collectively facilitate efficient electron extraction and suppress interfacial recombination. Moreover, WS\u003csub\u003e2\u003c/sub\u003e exhibits excellent chemical stability avoids photo-catalytic degradation and does not require high temperature annealing, making it particularly advantageous for low-cost and stable photovoltaic device fabrication [\u003cspan citationid=\"CR73\" class=\"CitationRef\"\u003e73\u003c/span\u003e]. Similarly, Spiro-MeOTAD is employed as the HTL due to its suitable energy band gap alignment with CPTS absorber, high hole transport capability and proven effectiveness in high-efficiency photovoltaic devices [\u003cspan citationid=\"CR74\" class=\"CitationRef\"\u003e74\u003c/span\u003e]. The optimized HTL effectively suppresses interfacial recombination and ensures efficient hole transport toward the Mo back electrode.\u003c/p\u003e \u003cp\u003eThe optimized material parameters used in the SCAPS-1D simulations including layer thickness, band gap (E\u003csub\u003eg\u003c/sub\u003e), electron affinity (χ), dielectric permittivity (ε\u003csub\u003er\u003c/sub\u003e), effective density of states (Nc, Nv), carrier nobilities (\u0026micro;\u003csub\u003ee\u003c/sub\u003e, \u0026micro;\u003csub\u003eh\u003c/sub\u003e) and doping concentrations (ND, NA) are summarized in Table\u0026nbsp;\u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e3\u003c/span\u003e. These parameters were selected based on reported experimental and simulated literature as well as DFT calculations to ensure physical reliability and consistency.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab3\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 3\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eSimulated parameters for different layers, taking CPTX (X\u0026thinsp;=\u0026thinsp;Se/S) as the absorber layer.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"5\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\" morerows=\"1\" rowspan=\"2\"\u003e \u003cp\u003eParameters\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eTCO\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eETL\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eCompound\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eHTL\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eFTO\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eWS\u003csub\u003e2\u003c/sub\u003e[\u003cspan citationid=\"CR65\" class=\"CitationRef\"\u003e65\u003c/span\u003e]\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eCPTX\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eSpiro-MeOTAD[\u003cspan citationid=\"CR66\" class=\"CitationRef\"\u003e66\u003c/span\u003e]\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eThickness (nm)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e500\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e195\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e600\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e200\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eE\u003csub\u003eg\u003c/sub\u003e (eV)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e3.5\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e1.8\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e1.1/1.4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e3\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eElectron affinity (eV)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e4.0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e3.95\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e4.45/4.30\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e2.2\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eDielectric Permittivity (ϵ\u003csub\u003er\u003c/sub\u003e)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e9.0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e13.6\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e6.5/6.2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e3.0\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eNc (cm\u003csup\u003e\u0026minus;\u0026thinsp;3\u003c/sup\u003e)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e10\u003csup\u003e19\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e10\u003csup\u003e18\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e2.5/1.8\u0026times;10\u003csup\u003e18\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e2.2 \u0026times; 10\u003csup\u003e18\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eNv (cm\u003csup\u003e\u0026minus;\u0026thinsp;3\u003c/sup\u003e)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e10\u003csup\u003e19\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e10\u003csup\u003e18\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e4.12/3.0\u0026times;10\u003csup\u003e18\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e1.8 \u0026times; 10\u003csup\u003e19\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u0026micro;\u003csub\u003ee\u003c/sub\u003e (cm\u003csup\u003e2\u003c/sup\u003eVs\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e50\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e500\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e25/15\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e2.1 \u0026times; 10\u003csup\u003e\u0026minus;\u0026thinsp;3\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e\u0026micro;\u003csub\u003eh\u003c/sub\u003e (cm\u003csup\u003e2\u003c/sup\u003eVs\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e50\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e500\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e25/15\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e2.16 \u0026times; 10\u003csup\u003e\u0026minus;\u0026thinsp;3\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eN\u003csub\u003eD\u003c/sub\u003e (cm\u003csup\u003e\u0026minus;\u0026thinsp;3\u003c/sup\u003e)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e10\u003csup\u003e15\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e7.25\u0026times;10\u003csup\u003e18\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0/0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eN\u003csub\u003eA\u003c/sub\u003e(cm\u003csup\u003e\u0026minus;\u0026thinsp;3\u003c/sup\u003e)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e10\u003csup\u003e16\u003c/sup\u003e/10\u003csup\u003e15\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003e10\u003csup\u003e18\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eThe calculated photovoltaic parameters and interface defect parameters between absorber/HTL and absorber/ETL are presented in Table\u0026nbsp;\u003cspan refid=\"Tab4\" class=\"InternalRef\"\u003e4\u003c/span\u003e and Table\u0026nbsp;\u003cspan refid=\"Tab5\" class=\"InternalRef\"\u003e5\u003c/span\u003e. The results indicate that CPTSe based solar cells, owing to their narrower band gap and enhanced light absorption in the visible and near-infrared regions, deliver a high short-circuit current density (J\u003csub\u003esc\u003c/sub\u003e) of 25.05 mA/cm\u003csup\u003e\u0026minus;\u0026thinsp;2\u003c/sup\u003e, along with an open-circuit voltage (V\u003csub\u003eoc\u003c/sub\u003e) of 0.95V and a fill factor (FF) of 86.21%, resulting in an overall simulated power conversion efficiency (PCE) of 20.61%. In contrast, CPTS-based solar cells, benefiting from their wider band gap, exhibit a high V\u003csub\u003eoc\u003c/sub\u003e of 1.34 V, a J\u003csub\u003esc\u003c/sub\u003e of 15.58 mA/cm\u003csup\u003e2\u003c/sup\u003e, and a fill factor of 87.82%, are resulting a PCE of 18.34%, reflecting efficient charge extraction and reduced recombination losses. This complementary performance between CPTSe and CPTS absorbers is consistent with fundamental photovoltaic principles, wherein a decreasing band gap enhances photocurrent at the expense of open-circuit voltage, thereby demonstrating the strong photovoltaic potential of Pd-based Kesterite absorbers [\u003cspan citationid=\"CR77\" class=\"CitationRef\"\u003e77\u003c/span\u003e].\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab4\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 4\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eJ-V Characteristic parameters for CPTS\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"6\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c5\" colnum=\"5\"\u003e\u003c/div\u003e \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c6\" colnum=\"6\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eCompounds\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eSpace group\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eV\u003csub\u003eoc\u003c/sub\u003e (Volt)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eJ\u003csub\u003esc\u003c/sub\u003e mA/cm\u003csup\u003e2\u003c/sup\u003e\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eFF %\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003ePCE %\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eCu\u003csub\u003e2\u003c/sub\u003ePdSnSe\u003csub\u003e4\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eI-4 (82)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.95\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e25.05\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e86.21\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e20.61\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eCu\u003csub\u003e2\u003c/sub\u003ePdSnS\u003csub\u003e4\u003c/sub\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e1.34\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e15.58\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e87.82\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e18.34\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab5\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 5\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eInterface defect parameter used in SCAP-1D simulations of CPTX.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"4\"\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c1\" colnum=\"1\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c2\" colnum=\"2\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c3\" colnum=\"3\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c4\" colnum=\"4\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eParameter\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eETL/absorber\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eAbsorber\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eabsorber/HTL\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eType Of defect\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eNeutral\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eNeutral\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eNeutral\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eEnergetic distribution\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eSingle\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eSingle\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eSingle\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eCharacteristic energy (eV)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.1\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.1\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eElectron capture cross-section (cm\u003csup\u003e2\u003c/sup\u003e)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1x10\u003csup\u003e\u0026minus;\u0026thinsp;15\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e1x10\u003csup\u003e\u0026minus;\u0026thinsp;15\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e1x10\u003csup\u003e\u0026minus;\u0026thinsp;15\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eEnergy level w.r.t (eV)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e0.65\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e0.60\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.65\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eTotal defect density (cm\u003csup\u003e\u0026minus;\u0026thinsp;3\u003c/sup\u003e)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1x10\u003csup\u003e15\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e10\u003csup\u003e14\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e1x10\u003csup\u003e15\u003c/sup\u003e\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003cp\u003eThe simulated current voltage (J-V) characteristic under AM 1.5 G illuminations, shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig10\" class=\"InternalRef\"\u003e10\u003c/span\u003e, exhibit low series resistance and minimal recombination losses, indicating efficient carrier transport across the device interfaces. The high FF values further confirm efficient charge extraction at both the ETL/absorber and absorber/HTL interfaces.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThe quantum efficiency (QE) spectra presented in Fig.\u0026nbsp;\u003cspan refid=\"Fig11\" class=\"InternalRef\"\u003e11\u003c/span\u003e demonstrate a strong photo-response throughout the visible region, confirming efficient photon absorption and carrier collection by both CPTS and CPTSe absorber. The gradual drop in QE at shorter wavelengths is attributed to transport-relate losses within the front contact and ETL layers. Overall, the high values of V\u003csub\u003eoc\u003c/sub\u003e, FF and PCE obtained for CPTS and CPTSe device indicate that Pd based Kesterite absorbsers perform better than conventional CZTS-based devices and effectively addressing the common Voc deficit in Kesterite solar cells. These findings highlight that Pd incorporation is an effective strategy for improving carrier transport, reducing mediated recombination and enhancing photovoltaic efficiency, thereby demonstrating the strong potential of CPTS and CPTSe as environmentally benign and high-performance thin film solar cells.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e"},{"header":"Conclusions","content":"\u003cp\u003eThe structural, electron, optical and photovoltaic properties of Pd based Kesterites CPTSe and CPTS were investigated using first-principles calculations. The crystal structures were fully relaxed to determine the electronic and optical properties. In these materials, the Pd substitution at the Zn site stabilizes the lattice, suppresses secondary phase formation and reduces antisite defect concentrations particularly Cu-Pd defects. The calculations confirm that both CPTSe and CPTS are direct band gap semiconductors with band gaps of 1.11 eV and 1.4 eV respectively, falling within the optimal range for solar energy conversion. Optical analyses reveal strong visible light absorption (10\u003csup\u003e4\u003c/sup\u003e cm\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e), favorable dielectric constants and refractive indices, indicating efficient light harvesting and low optical losses. Device simulations of the (FTO/WS\u003csub\u003e2\u003c/sub\u003e/CPT(Se/S)/Spiro-MeOTAD/Mo) architecture were performed using SCAPS-1D. The CPTSe based device achieve an open circuit voltage (V\u003csub\u003eoc\u003c/sub\u003e = 0.95V), a high short-circuit current density (J\u003csub\u003esc\u003c/sub\u003e= 25.05 mAcm\u003csup\u003e\u0026minus;\u0026thinsp;2)\u003c/sup\u003e and a fill factor (FF\u0026thinsp;=\u0026thinsp;86.21%), resulting in a power efficiency (PCE) 20.61%. In contrast the CPTS-based device, benefiting from enhanced visible-light absorption and a wider band gap, delivers a higher V\u003csub\u003eoc\u003c/sub\u003e = 1.34V, J\u003csub\u003esc\u003c/sub\u003e= 15.58 mAcm\u003csup\u003e\u0026minus;\u0026thinsp;2\u003c/sup\u003e, FF\u0026thinsp;=\u0026thinsp;87.82% and PCE 18.34%, highlighting complementary performance trends between the two Pd-based Kesterite absorbers. Device-level simulations demonstrate enhanced photovoltaic performance. Pd incorporation improves electron mobility, suppress defect and enhances cation ordering. These characteristics combined with favorable band gaps, strong optical absorption and enhanced structure stability, position Pd- based Kesterites as promising alternatives to conventional Zn based Kesterites for high efficiency, reliable, earth abundant, stable and sustainable thin film solar cells as well as other optoelectronic applications such as LEDs.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e\u003cstrong\u003eCredit Authorship Contribution Statement\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eIhsan Ullah:\u003c/strong\u003e Writing\u0026ndash;original draft, Validation, Software, Investigation, Methodology. \u003cstrong\u003eImad Khan:\u003c/strong\u003e Supervision, Project administration, Conceptualization, Writing\u0026ndash;review \u0026amp; editing.\u0026nbsp;\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eDeclaration Of Competing Interest\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eData Availability\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eData will be made available on request.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003e\u0026nbsp;Funding Declaration\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003e\u003cem\u003eThe authors declare that no funding was received for this work\u003c/em\u003e\u003cstrong\u003e\u003cem\u003e\u0026nbsp;\u003c/em\u003e\u003c/strong\u003e\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003eJones MW, Peters GP, Gasser T, Andrew RM, Schwingshackl C, G\u0026uuml;tschow J, Le Quere C (2023) National contributions to climate change due to historical emissions of carbon dioxide, methane, and nitrous oxide since 1850. \u003cem\u003eScientific Data\u003c/em\u003e 10:155 \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1038/s41597-023-02041-1\u003c/span\u003e\u003cspan address=\"10.1038/s41597-023-02041-1\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eVoumik LC, Ridwan M, Rahman MH, Raihan A (2023) An investigation into the primary causes of carbon dioxide releases in Kenya: Does renewable energy matter to reduce carbon emission? \u003cem\u003eRenewable Energy Focus\u003c/em\u003e 47:100491 \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1016/j.ref.2023.100491\u003c/span\u003e\u003cspan address=\"10.1016/j.ref.2023.100491\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eWhiteside M, Herndon JM (2023) Humic-like substances (HULIS): Contribution to global warming and stratospheric ozone depletion. \u003cem\u003eEuropean Journal of Applied Sciences\u003c/em\u003e 11:325\u0026ndash;346 \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.14738/aivp.112.14363\u003c/span\u003e\u003cspan address=\"10.14738/aivp.112.14363\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eAakko-Saksa PT, Lehtoranta K, Kuittinen N, J\u0026auml;rvinen A, Jalkanen JP, Johnson K, Jung H, Ntziachristos L, Gagn\u0026eacute; S, Takahashi C, Karjalainen P (2023) Reduction in greenhouse gas and other emissions from ship engines: Current trends and future options. \u003cem\u003eProgress in Energy and Combustion Science\u003c/em\u003e 94:101055 \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1016/j.pecs.2022.101055\u003c/span\u003e\u003cspan address=\"10.1016/j.pecs.2022.101055\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eWeart SR (2023) Are there simple models of global warming? \u003cem\u003eThe Physics Teacher\u003c/em\u003e 61:516\u0026ndash;518 \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://doi.org/10.1119/5.0128940\u003c/span\u003e\u003cspan address=\"10.1119/5.0128940\" targettype=\"DOI\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eAndrews SS (2023) Matter waves. 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Electronic structure calculations were performed using density functional theory within the full-potential linearized augmented plane wave (FP-LAPW) method. The generalized gradient approximation (GGA) and Hubbard U correction (GGA+U) along with mBJ (TB-mBJ+U) were employed to accurately account for exchange-correlation effects and electrons localization. The calculated band structures revealed that both materials are direct band gap semiconductors with gaps of 1.11 eV (CPTSe) and 1.40 eV (CPTS). The density of states (DOS) shows that the valence band maximum is dominated by Cu-3d, S/Se-p, while the conduction band minimum is primarily composed of Sn-p, Sn-s and Se-p orbital, further the inclusion of Hubbard potential U shifts the localized states below the Fermi level and improving electronic stability. Optical calculations indicate strong visible light absorption (\u0026gt;10\u003csup\u003e4\u003c/sup\u003e cm\u003csup\u003e-1)\u003c/sup\u003e, high dielectric constants and favorable refractive indices, demonstrating efficient light harvesting and low optical losses. Device simulations of the (FTO/WS\u003csub\u003e2\u003c/sub\u003e/CPT(Se/S)/Spiro-MeOTAD/Mo) architecture were performed using SCAPS-1D. The CPTSe/CPTS based device achieve an open circuit voltage (V\u003csub\u003eoc\u003c/sub\u003e) of 0.95/1.34 V, a high short-circuit current density (J\u003csub\u003esc\u003c/sub\u003e) of 25.05/15.58 mAcm\u003csup\u003e-2 \u003c/sup\u003eand a fill factor (FF) 0f 86.21/87.82 %, resulting in a power conversion efficiency (PCE) of 20.61/18.34 %. The enhanced performance is attributed to reduce antisite defects, improved cation ordering and optimized alignment. These results established Pd-based Kesterites as promising sustainable absorber materials for high efficient photovoltaic applications.\u003c/p\u003e","manuscriptTitle":"First-principles investigation of Pd-based Kesterites for optoelectronic and photovoltaic applications","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2026-03-19 12:31:56","doi":"10.21203/rs.3.rs-8933098/v1","editorialEvents":[{"type":"communityComments","content":0},{"type":"decision","content":"Revision requested","date":"2026-03-04T08:57:19+00:00","index":"","fulltext":""},{"type":"editorAssigned","content":"","date":"2026-03-03T10:20:45+00:00","index":"","fulltext":""},{"type":"checksComplete","content":"","date":"2026-03-03T10:17:53+00:00","index":"","fulltext":""},{"type":"submitted","content":"Journal of Molecular Modeling","date":"2026-02-21T11:09:31+00:00","index":"","fulltext":""}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"journal-of-molecular-modeling","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":false,"externalIdentity":"jmmo","sideBox":"Learn more about [Journal of Molecular Modeling](https://www.springer.com/journal/894)","snPcode":"894","submissionUrl":"https://submission.nature.com/new-submission/894/3","title":"Journal of Molecular Modeling","twitterHandle":"","acdcEnabled":true,"dfaEnabled":true,"editorialSystem":"em","reportingPortfolio":"Springer Hybrid","inReviewEnabled":true,"inReviewRevisionsEnabled":false}}],"origin":"","ownerIdentity":"89e1ef6d-63d0-43fa-8aef-6a4755e3c86f","owner":[],"postedDate":"March 19th, 2026","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"under-review","subjectAreas":[],"tags":[],"updatedAt":"2026-05-14T14:24:13+00:00","versionOfRecord":[],"versionCreatedAt":"2026-03-19 12:31:56","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-8933098","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-8933098","identity":"rs-8933098","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}