Supported data and manuscript "Orbital-engineered spin asymmetry and multifunctionality in Eu-activated CaSiO3: a first-principles roadmap to optical-thermoelectric fusion"

Orbital-engineered spin asymmetry and multifunctionality in Eu-activated CaSiO 3 : a first-principles roadmap to optical-thermoelectric fusion Muhammad Tayyab a , Faiq Umar a , Sikander Azam a,b,* , Qaiser Rafiq a , Rajwali Khan c,** , Muhammad Tahir Khan d,e,*** , Vineet Tirth f,g , Ali Algahtani f,h a Department of Basic Sciences, Riphah International University, Islamabad 42000, Pakistan b University of West Bohemia, New Technologies – Research Centre, 8 Univerzitní, Pilsen 306 14, Czech Republic c National Water and Energy Center, United Arab Emirates University, Al Ain 15551, United Arab Emirates d School of Computer Science and Technology, Zhejiang Normal University, Jinhua, China e Key Laboratory of Urban Rail Transit Intelligent Operation and Maintenance Technology & Equipment of Zhejiang Province, College of Engineering, Zhejiang Normal University, Jinhua, China f Mechanical Engineering Department, College of Engineering, King Khalid University, Abha 61421 Aseer, Saudi Arabia g Centre for Engineering and Technology Innovations, King Khalid University, Abha 61421 Aseer, Saudi Arabia h Research Center for Advanced Materials Science (RCAMS), King Khalid University, Guraiger, Abha 61413 Aseer, Saudi Arabia ARTICLE INFO Keywords: Eu-doped CaAlSiN 3 Red phosphor materials GGA +U calculations Photoluminescence mechanisms Density functional theory (DFT) ABSTRACT Rare-earth-doped nitride phosphors have emerged as critical materials for solid-state lighting and photonic devices due to their high thermal stability, narrow emission bandwidths, and strong absorption in the UV-blue range. In this study, we present a comprehensive density functional theory (DFT) investigation, incorporating GGA +U formalism, of pristine and Eu 3+ -doped CaAlSiN 3 with doping concentrations of 8.5 % and 17 %. The electronic structure calculations reveal that Eu doping introduces localized 4f states within the band-gap, reducing the band-gap and enabling efficient red photo luminescence (PL) through the 5 D 0 → 7 F 2 transition. Analysis of the spin-resolved density of states and spin density confirms the magnetic nature of Eu 3+ , with a net magnetic moment arising from the unpaired 4f 6 electrons. Charge density, Bader analysis, and Electron Localization Function (ELF) plots demonstrate the mixed ionic-covalent bonding nature and confirm the charge transfer from Eu to the neighboring N and Al atoms, stabilizing the doped lattice. Optical properties, including the dielectric function ( ε 1 and ε 2 ), absorption coefficient, refractive index, and reflectivity, were evaluated, revealing significant redshifts in the absorption edge and enhanced light-matter interaction in the visible spectrum upon Eu doping. These changes are consistent with experimental PL emission in the red–NIR region. The formation energy calculations confirm the thermodynamic feasibility of Eu incorporation, while elastic constant evaluation and Pugh’s ratio suggest excellent mechanical stability and ductility of both pristine and doped systems. Thermoelectric transport coefficients were evaluated using WIEN2k coupled with BoltzTraP, revealing that moderate Eu 3+ substitution optimizes the power factor while Eu-induced disorder reduces the lattice thermal conductivity. This multi-scale theoretical analysis validates Eu-doped CaAlSiN 3 as a robust and efficient red-emitting phosphor suitable for white light-emitting diodes (WLEDs), offering predictive insights into its structure–property relationships. The study establishes a firm theoretical foundation for crystal site engineering strategies in phosphor materials for advanced optoelectronic applications. Introduction In the pursuit of energy-efficient lighting technologies, phosphorconverted white light-emitting diodes (pc-WLEDs) have emerged as a prominent replacement for traditional lighting sources, owing to their longevity, reduced energy consumption, and superior color rendering * Corresponding author at: Department of Basic Sciences, Riphah International University, Islamabad 42000, Pakistan. ** Corresponding author. *** Corresponding author at: School of Computer Science and Technology, Zhejiang Normal University, Jinhua, China. E-mail addresses: [email protected] (S. Azam), [email protected] (R. Khan), [email protected] (M.T. Khan), [email protected] (V. Tirth), [email protected] (A. Algahtani). Contents lists available at ScienceDirect Results in Physics journal homepage: www.elsevier.com/locate/rinp https://doi.org/10.1016/j.rinp.2025.108440 Received 14 August 2025; Received in revised form 4 September 2025; Accepted 16 September 2025 Results in Physics 77 (2025) 108440 Available online 17 September 2025 2211-3797/© 2025 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license ( http://creativecommons.org/licenses/by/4.0/ ). performance. A key component in pc-WLEDs is the phosphor material, which governs the spectral properties and thermal stability of the emitted light. Among the various phosphor hosts, CaAlSiN 3 has gained significant attention as a red-emitting nitride material due to its excellent thermal resistance, chemical robustness, and wide optical bandgap that ensures minimal self-absorption losses [1,2]. Recent first-principles investigations on perovskites and related oxides have demonstrated how crystal-site substitution can tailor structural stability, electronic correlations, optical activity, and even magnetism [3–9], motivating our present study on Eu 3+ site engineering in CaAlSiN 3 . CaAlSiN 3 is a robust nitridosilicate whose covalent [AlN 4 ]/[SiN 4 ] network and wide gap provide an ideal host for Eu 2+ activation, yielding intense, thermally stable red emission central to solid-state lighting. The near-isovalent Eu 2+ → Ca 2+ substitution enables clean doping without extrinsic compensators, while the strong crystal field affords fine control of Eu-5d–N-2p level alignment. These attributes, together with the material’s thermal/chemical stability, make CaAlSiN 3 :Eu 2+ an excellent model to explore how orbital-level engineering couples spin asymmetry with optical responses, aligning directly with our goal of optical–magnetic fusion in a technologically relevant host. The introduction of rare-earth (RE 3+ ) ions, such as Eu 3+ , into the CaAlSiN 3 host lattice is a well-established strategy to achieve strong red emission via intra-4f transitions, particularly the 5 D 0 → 7 F_J transitions that result in sharp, intense luminescence bands in the red and near-infrared regions [10,11]. However, the incorporation of Eu 3+ affects not only the photoluminescence properties but also leads to significant changes in the electronic structure, magnetic behavior, lattice dynamics, and thermomechanical response of the host material. These changes are complex and dependent on dopant concentration and local coordination, necessitating a comprehensive theoretical investigation. To this end, Density Functional Theory (DFT), augmented with the Hubbard U correction (GGA +U), provides a powerful framework to accurately model the localized 4f states of Eu 3+ and their interaction with the host matrix. This approach enables in-depth analysis of band structure modifications, density of states (DOS), and charge transfer dynamics, which directly influence luminescence mechanisms and nonradiative recombination paths [12,13]. In this study, pristine, 8.5 %, and 17 % Eu-doped CaAlSiN 3 systems are investigated to understand the evolution of optoelectronic and structural properties with doping. The band structure analysis reveals a progressive narrowing of the bandgap and the emergence of Eu-4f midgap states with increasing dopant content, which is consistent with enhanced red emission and potential quantum efficiency improvements. The DOS and PDOS projections clearly identify the role of Eu-f states near the Fermi level and their hybridization with N-2p orbitals. The impact of doping is further corroborated by ELF and Bader charge studies, which show charge localization and altered bonding environments near the dopant sites—critical for understanding emission quenching or enhancement phenomena [14,15]. Furthermore, spin-polarized calculations indicate a significant magnetic moment per Eu 3+ ion (~7 μ B), attributable to unpaired 4f electrons. At higher doping levels (17 %), weak ferromagnetic ordering is observed, opening avenues for multifunctional luminescent-magnetic materials suitable for spin-LEDs or magneto-optical applications [15]. These findings are supported by spin density plots and the separation of up and down electronic states in the calculated electronic structures. In terms of mechanical stability, we assess the elastic constants, bulk modulus, shear modulus, Young’s modulus, Poisson’s ratio, and Pugh’s ratio, revealing a marginal increase in ductility with moderate Eu doping. This is crucial for device integration, especially under thermomechanical stress. Formation energies indicate the thermodynamic feasibility of Eu substitution at Ca sites, while the unit cell volume expansion aligns with the larger ionic radius of Eu 3+ compared to Ca 2+ . To evaluate dynamical stability and thermal robustness, phonon density of states (Phonon-DOS) calculations are performed. The absence of imaginary modes confirms structural stability, while the vibrational entropy and heat capacity profiles suggest favorable thermal management capabilities. This is especially important for high-power LED applications where temperature-driven efficiency degradation is a concern [11,14]. Eu-doped CaAlSiN 3 (the nitridosilicate analogue CaAlSiN 3 : Eu 2+ ) demonstrates a unique convergence of properties. The wide-gap framework (4.5–5.5 eV) retains semiconducting character while hosting Eu-derived 4f states, ensuring charge localization without metallization. The Eu 2+ ion contributes a half-filled 4f 7 shell, producing strong exchange-driven spin polarization—a rare phenomenon in wide-gap semiconductors. The rigid tetrahedral network provides thermal and chemical robustness, accounting for the minimal thermal quenching observed in Eu-based phosphors. Moreover, the Eu 2+ 4f 6 5d 1 → 4f 7 transitions are parity-allowed, leading to intense optical absorption/ emission and strong light–matter coupling. This synergy of band gap, spin asymmetry, robustness, and optical strength underpins the multifunctional potential of Eu-doped CaSiO 3 /CaAlSiN 3 for integrated optical devices. The optical response, analyzed through dielectric function components ε 1 ( ω ) and ε 2 ( ω ), refractive index, absorption coefficient, reflectivity, and energy loss function (ELF), demonstrates a redshift in absorption edge and enhanced near-UV to visible transitions due to Eu-f state involvement. These transitions align with the expected f–f emission characteristics of Eu 3+ and match well with experimental PL trends reported for CaAlSiN 3 :Eu systems [10]. While direct prediction of photoluminescence (PL) from DFT is nontrivial, we approximate transition energies using ΔSCF calculations and align defect-related DOS features with known experimental PL peaks. These estimations suggest efficient emission channels and minimal non-radiative loss in the 8.5 % Eu-doped sample—a balance between luminescence intensity and structural integrity. Lastly, beyond optoelectronic functionality, understanding the thermoelectric response of CaAlSiN 3 and its Eu 3+ -doped variants is crucial, since rare-earth substitution simultaneously alters carrier concentrations and phonon scattering, offering a route to balance high electrical performance with low lattice thermal conductivity. Overall, this work offers a holistic, first-principles investigation into the electronic, magnetic, optical, structural, and thermodynamic properties of Eu-doped CaAlSiN 3 , contributing valuable insights toward the rational design of next-generation phosphor materials for efficient, stable, and tunable LED applications. Computational methodology All calculations were performed using the full-potential linearized augmented plane wave (FP-LAPW) method as implemented in the WIEN2k code [16]. Calculations were performed with the WIEN2k FPLAPW all-electron code because Eu-activated CaAlSiN 3 (see Fig. 1) combines ionic bonding with localized Eu-4f states. The FP-LAPW framework avoids pseudopotential transferability issues by treating core and valence electrons on equal footing and by using a full potential (no shape approximation), which is advantageous for accurately resolving f-level positions, crystal-field splittings, and band dispersions that underpin the spin-asymmetric orbital physics reported here. This method is based on density functional theory (DFT) and allows accurate treatment of core, semicore, and valence electrons with full relativistic effects. For the exchange–correlation functional, we employed the generalized gradient approximation (GGA) in the Perdew-BurkeErnzerhof (PBE) parameterization [17]. To properly account for the strong Coulombic interactions in the localized 4f orbitals of Eu 3+ ions, the GGA +U approach was adopted using the rotationally invariant formulation of Dudarev et al. (1998) [18]. A value of U =6.5 eV was applied to the Eu-4f orbitals, consistent with prior studies on rare-earthdoped nitride phosphors [19,20]. The plane-wave cutoff parameter RMTKmax was set to 7.0, and the muffin-tin radii (RMT) were selected to avoid overlap: typically 2.4 a.u. for Eu, 1.9 a.u. for N, 2.0 a.u. for Ca, and 1.8 a.u. for Si and Al. The M. Tayyab et al. Results in Physics 77 (2025) 108440 2 Brillouin zone integration was carried out using a Monkhorst-Pack kpoint mesh of 12 ×12 ×8 for structural optimization and DOS calculations, ensuring energy convergence within 10 −5 Ry. The structural optimization of pristine CaAlSiN 3 and the Eu-doped supercells (8.5 % and 17 %) was performed by minimizing the total energy and atomic forces using the PORT algorithm until the forces were below 1 mRy/a.u.. Supercells were constructed to simulate different Eu concentrations by substituting one or two Ca atoms with Eu in a 2 ×2 × 2 supercell, corresponding to ~8.5 % and ~17 % doping, respectively. Eu concentration was set to ~8.5 and 17 % on the Ca sublattice (one Eu per eight Ca sites in a 2 ×2 ×2 supercell). This level preserves a dilute/ semidilute local environment while keeping periodic image interactions small enough to isolate the local Eu–N crystal field, which governs the 4f–5d optical center. It also provides a tractable platform for fully converged FP-LAPW (WIEN2k) GGA +U +SOC calculations together with optic analyses. At higher Eu contents, reduced Eu–Eu separation is expected to enhance energy-transfer pathways and alloy scattering, promoting concentration quenching and band broadening; only beyond a geometry-dependent site-percolation threshold would Eu form a connected network capable of impurity-band transport, which lies above the composition studied here. Our analysis therefore targets the technologically relevant pre-percolative regime, where local crystal-field engineering of Eu 2+ coexists with host-dominated transport. The electronic band structure and density of states (DOS), including partial DOS (PDOS), were computed with and without spin-polarization to explore the influence of Eu 4f states and spin asymmetry. For optical property calculations, the momentum matrix elements were evaluated within the random phase approximation (RPA) using the optic module of WIEN2k. The real and imaginary parts of the complex dielectric function ε ( ω ) were calculated, and from these, secondary properties such as absorption coefficient, refractive index, reflectivity, and energy loss function were derived. Charge density and Electron Localization Function (ELF) were visualized using the WIEN2k’s LAPW5 and ELF modules. The ELF was evaluated on 2D planes slicing through the Eu and surrounding N/Al atoms to identify localized bonding features and f-electron confinement. Bader charge analysis was performed using the WIEN2WANNIER and Critic2 interfacing tools to evaluate the oxidation states and charge transfer mechanisms between Eu and the host matrix. The magnetic properties were explored by computing the total magnetic moment and plotting the spin density distributions for each doping level. For thermodynamic stability, we calculated the phonon density of states (Phonon-DOS) using PHONOPY interfaced with WIEN2k, using the finite displacement method on relaxed supercells. From the phonon calculations, we derived vibrational entropy, heat capacity, and checked for imaginary frequencies to confirm dynamical stability. To predict photoluminescence (PL) behavior, the DOS alignment and possible defect-related transitions were analyzed. For more accurate excited-state transition energies, we carried out ΔSCF calculations, where the total energy difference between the excited and ground-state configurations was evaluated by simulating the occupation of Eu 4f states, a technique successfully applied in literature for rare-earth PL modeling [10,21]. Transport properties including the Seebeck coefficient, electrical conductivity, and electronic thermal conductivity were calculated using the BoltzTraP code interfaced with WIEN2k. All simulations converged with high accuracy, and the results are benchmarked against existing experimental and theoretical findings. Results and discussion Structural analysis The host compound CaAlSiN 3 crystallizes in the orthorhombic Cmc2 1 space group, consisting of a rigid three-dimensional framework of corner-sharing [AlN 4 ] and [SiN 4 ] tetrahedra charge-balanced by interstitial Ca 2+ ions. This highly covalent network is well known for its exceptional chemical and thermal stability, making it a robust matrix for rare-earth activation. To investigate the impact of Eu 3+ substitution, we performed full structural relaxations for both pristine and Eu-doped models. After relaxation, the average Ca–N bond length in pristine CaAlSiN 3 is 2.48 Å, whereas substitution with Eu enlarges the local environment to an average Eu–N distance of 2.54 Å, yielding Δr ≈0.06 Å. This elongation arises from the ionic radius mismatch (Eu 3+ slightly larger than Ca 2+ ) and introduces local strain in the [AlN 4 ]/[SiN 4 ] tetrahedral network. Despite these distortions, the substitution remains thermodynamically accessible, with formation energies in the range of ~1–2 eV depending on chemical potential conditions, confirming the feasibility of Eu 3+ incorporation. Moreover, the calculated elastic constants continue to satisfy all Born stability criteria, indicating preserved global mechanical robustness of the host lattice. Importantly, these local distortions are not merely structural but also functional. The Eu-induced lattice relaxation enhances the crystal-field splitting of the Eu-5d states by ~0.2–0.3 eV, which rationalizes the predicted red-shift in emission and the strengthened oscillator strength in the optical spectra. Thus, Eu 3+ incorporation in CaAlSiN 3 not only maintains the mechanical and thermodynamic integrity of the host but also establishes a direct coupling between lattice strain and optical activity. This site-engineering effect forms the structural basis for the enhanced red emission and magneto-optical properties discussed in the following sections. Electronic properties Band structure The calculated electronic band structures of pristine and Eu-doped Fig. 1. Crystal structure of CaAlSiN 3 :Eu 2+ viewed along the [0 1 0] direction. Ca/Eu atoms are shown as large green/red spheres, Al/Si atoms are depicted within corner-sharing tetrahedra, and N atoms as small grey spheres. The figure highlights the Eu 2+ substitution at the Ca 2+ site and its coordination environment. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.) M. Tayyab et al. Results in Physics 77 (2025) 108440 3 CaAlSiN 3 (at 8.5 % and 17 % doping levels) provide profound insights into the influence of rare-earth doping on the electronic configuration of this red-emitting phosphor host (see Fig. 2). The undoped CaAlSiN 3 band structure, as shown in the first figure, demonstrates a clear semiconducting behavior with an indirect bandgap. The valence band maximum (VBM) is located between the Γ and H points, while the conduction band minimum (CBM) lies near the N point. The bandgap is appreciably large, in the range of approximately 3.5–4.0 eV, consistent with earlier reports [22,23], which characterized CaAlSiN 3 as a robust host for red phosphors due to its wide gap, high thermal stability, and ability to accommodate a variety of activator ions. Upon substitutional doping with Eu 3+ at 8.5 %, significant changes in the band structure are observed. In the spin-polarized calculations using GGA +U (with U applied to the Eu-4f orbitals), the up-spin and down-spin channels display distinct behaviors. In the up-spin channel, a set of narrow impurity bands appears just below the conduction band edge and in proximity to the Fermi level (E F ), reducing the effective bandgap. These flat bands are characteristic of localized 4f states introduced by Eu 3+ , as previously shown for other Eu-activated hosts like Eu:YAG and Eu:BaLa 2 ZnO 5 [24,25]. The down-spin channel retains a relatively broader bandgap but also shows defect-related states near E_F. The emergence of midgap states indicates a partial hybridization between the host lattice orbitals (mainly N 2p and Al/Si sp 3 ) and Eu 4f states. At 17 % Eu doping, these effects become more pronounced. In the upspin projection, the impurity 4f states move closer to the valence band maximum, in some regions merging with it. This signifies stronger interaction and overlap with the valence states, suggesting enhanced charge carrier localization and the possible formation of recombination centers. The down-spin channel at this doping level reveals a slight broadening of the 4f-derived states, accompanied by narrowing of the effective bandgap, which now approaches a nearly semimetallic limit, although the material retains its semiconducting nature overall. These observations imply that increasing Eu content enhances spin polarization and introduces more defect-related levels, potentially leading to concentration quenching if the activator density exceeds the percolation threshold. The transition from pristine to doped configurations also leads to a shift from an indirect to a more direct-like bandgap behavior, especially in the spin-polarized cases. This is evidenced by the minimal difference in energy between the VBM and CBM at the Γ point, particularly in the up-spin direction. Such a transition has implications for radiative recombination efficiency: direct transitions enhance the likelihood of photon emission, which is critical for phosphor performance in solidstate lighting. The physics of the system is governed by the localized nature of the Eu 4f orbitals, which do not contribute to broad band dispersion but rather manifest as flat bands. These localized levels serve as discrete energy levels that can participate in intra-4f transitions (e.g., 3 H 6 → 3 F 4 , 3 H 4 , 1 G 4 ), responsible for the characteristic blue (~480 nm) and nearinfrared (~800 nm, 1470 nm) emissions of Eu 3+ [26,27]. The presence of such transitions, together with the observed electronic structure modifications, confirms that Eu 3+ -doped CaAlSiN 3 can act as a multifunctional phosphor emitting across the visible and NIR spectrum, complementing red-emitting Eu 2+ phosphors for white LED devices. Furthermore, our results align with prior theoretical and experimental findings where rare-earth doping introduces localized defect levels and modifies host band structures. For instance, Zhang et al. (2018) [28] showed in Eu-doped CaAlSiN 3 that Eu 5d levels tend to lie near the CBM, while 4f levels remain deeper in the bandgap. In contrast, Eu 3+ 4f levels occupy positions closer to E F , enabling alternative recombination pathways and multi-wavelength emission. Additionally, the difference in spin-up and spin-down band structures reinforces the importance of treating f-electron systems with spin-polarized DFT +U to capture the correct ground-state properties. The observed band structure evolution—from a clean wide-gap semiconductor in the pristine phase to a defect-tuned and spinpolarized system with narrowed gap and intermediate impurity states Fig. 2. Electronic band structure of (a) pristine, (b and c) 8.5 % Eu-doped, and (d and e) 17 % Eu-doped CaAlSiN 3 using GGA +U. Bandgap narrowing and the appearance of flat f-states near the Fermi level are visible upon doping, supporting f–f transition activation for red emission. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.) M. Tayyab et al. Results in Physics 77 (2025) 108440 4 in the doped phases—reflects the potential of crystal site engineering in tuning the optoelectronic landscape of CaAlSiN 3 . These tunable properties make Eu-doped CaAlSiN 3 not only suitable for color-mixing in LEDs but also a promising material for NIR and dual-mode lighting applications. In summary, Eu doping at moderate levels (8.5 %) introduces discrete impurity states and moderate bandgap narrowing with potential for blue-NIR dual emission. At higher doping (17 %), the impurity states become more influential, leading to enhanced hybridization and strong spin-polarization, with implications for carrier dynamics and emission efficiency. The choice of doping concentration must therefore balance emission intensity, color purity, and potential quenching. These insights, supported by GGA +U-calculated band structures, establish a solid foundation for rational design of rare-earth-doped nitrides for nextgeneration phosphor-converted white LEDs and multi-band optical devices. Density of states (DOS) and partial DOS (PDOS) The total density of states (TDOS) and partial density of states (PDOS) for pristine and Eu-doped CaAlSiN 3 at 8.5 % and 17 % doping levels reveal critical insights into the underlying electronic structure modifications induced by rare-earth substitution (see Fig. 3). From the TDOS plots, the pristine CaAlSiN 3 (black line) shows a clean semiconducting behavior, with a well-defined bandgap between the valence band maximum (VBM) and conduction band minimum (CBM), both characterized by distinct π and σ bonding interactions primarily arising from the hybridization between nitrogen 2p and the Al/Si 3p states. The lower part of the valence band consists of deeper bonding states (mostly σ -type), while the upper valence band near the Fermi level comprises antibonding π states with broader dispersion, consistent with previous literature reports on this red-emitting host matrix [24,25]. Upon doping CaAlSiN 3 with Eu 3+ at 8.5 % concentration (red curve), new sharp states appear just below the Fermi level, centered around −1.8 eV. These are attributed to the partially filled Eu 4f orbitals, which are characteristically narrow due to their localized nature and minimal overlap with neighboring orbitals. In the PDOS projection for 8.5 % Eu doping, the Eu-f states (shown in bright cyan in the element-resolved plot and explicitly in the orbital-resolved f-PDOS plot) exhibit a dominant, nearly delta-function-like peak within the valence band. This indicates that the Eu 4f orbitals are non-bonding and do not significantly hybridize with the host matrix, maintaining their atomic-like character. Additionally, the Eu 4f states are entirely spin-polarized, contributing only to the majority (up) or minority (down) channel depending on the magnetic configuration, as seen in the slight asymmetry between spin channels in the TDOS. As we increase the Eu concentration to 17 % (green curve in TDOS), the intensity and influence of the Eu-derived 4f states increase significantly. In the corresponding PDOS (bottom two plots), we observe an enhancement of the Eu-f peak at roughly the same energy (−1.8 eV), though its broadening slightly increases. This indicates enhanced Eu–Eu interaction and a partial overlap of localized states at higher doping, though the f orbitals remain mostly localized. Moreover, a subtle shift in the Fermi level toward the valence band is observed, suggesting increased carrier localization and a narrowing of the effective bandgap. This doping-induced narrowing is typical in rare-earth-doped phosphors and has been observed in similar hosts, such as Eu-doped Sr 2 Si 5 N 8 and BaAlSiN 3 , where high doping levels distort the host lattice and shift band edges [22,29]. From a bonding perspective, the partial DOS for Ca, Al, Si, and N atoms remains largely unchanged in both 8.5 % and 17 % Eu-doped systems compared to the pristine host, except for slight redistribution of intensity around the −4 to 0 eV range. This suggests that the fundamental framework of π and σ bonding (particularly the N–Al and N–Si interactions) is preserved, and the Eu dopant occupies substitutional Ca 2+ sites without significantly altering the covalent framework. This agrees with previous structural and spectroscopic studies indicating that Eu 3+ prefers Ca 2+ substitution due to similar ionic radii and that the host lattice accommodates the dopant with minimal local distortion [30]. The orbital-resolved PDOS (dand f-states of Eu) confirms that the Eu-d states are minor contributors to the total electronic density near the Fermi level, lying mainly in the conduction band region and hence not actively participating in optical transitions. On the other hand, the fstates, which dominate near −1.8 eV, are optically active and correspond to intra-4f transitions such as 5 D 0 → 7 F_J (J =0,1,2,3…), responsible for the red emission (~610–620 nm) that characterizes CaAlSiN 3 :Eu 2+ phosphors. Although the present simulation uses Eu 3+ , the electronic structure reflects the energetic placement of f states consistent with both valence states depending on charge compensation [27,31]. The narrow, high-intensity 4f peak demonstrates that radiative transitions are possible from these localized states, which supports the photoluminescent behavior of Eu-doped CaAlSiN 3 . Importantly, as Eu concentration increases, the sharpness of the 4f peaks is slightly reduced, suggesting an onset of dopant–dopant interaction or concentration quenching. This is consistent with experimental reports that indicate optimal emission intensity at moderate doping levels (~5–10 %), with degradation in quantum efficiency at higher concentrations due to energy transfer to killer centers [32]. Spin polarization analysis confirms that Eu-doping introduces magnetic asymmetry, with the 4f electrons occupying predominantly one spin channel. In both 8.5 % and 17 % cases, the upand down-spin channels display distinct features, particularly in the Eu-PDOS. This spin-dependent behavior reflects the open-shell nature of Eu 3+ (4f 6 configuration) and supports the necessity of spin-polarized GGA +U treaEuent to capture the correct electronic structure. Inclusion of the U parameter (typically ~6 eV for Eu 4f states) ensures proper separation of occupied and unoccupied f levels, avoiding their artificial delocalization, which is common in plain GGA calculations. Altogether, the DOS and PDOS plots validate that Eu doping introduces new electronic states within the bandgap region, maintains the integrity of the host bonding network, and enables optical transitions through f-electron excitation pathways. The placement of Eu-f states well below the conduction band minimizes thermal ionization and enhances radiative recombination probability, reinforcing the suitability of Eu-doped CaAlSiN 3 as a robust red phosphor for white LEDs. The evolution from pristine to 8.5 % and then 17 % Eu doping illustrates a classic case of impurity-level engineering for photonic functionality. Charge density/bader charge analysis The charge density and Bader charge analysis provide critical insights into the redistribution of electron density upon doping CaAlSiN 3 with Eu ions at different concentrations (8.5 % and 17 %). This analysis offers a quantitative assessment of how the substitution of Ca2 + with Eu3 + alters the local bonding environment, influences oxidation states, and modifies the material’s electronic landscape. In the pristine CaAlSiN 3 system, Bader charge analysis shows that Ca atoms typically retain a charge close to +1.64 e, consistent with their formal oxidation state of +2. The Al atoms exhibit Bader charges of approximately +2.35 e, while Si atoms are around +3.17 e. Nitrogen atoms, being highly electronegative, pull significant electron density toward themselves, exhibiting average Bader charges close to −1.64 e. This configuration affirms the strongly ionic nature of the Ca–N and moderately covalent Al–N and Si–N bonds that form the tetrahedral and octahedral motifs within the host lattice. Upon substitution with Eu at 8.5 % doping (i.e., Ca 0 . 915 Eu 0 . 085 AlSiN 3 ), the Bader charge on the Eu atom is found to be approximately +2.26 e. This value is somewhat lower than the expected formal oxidation state of +3, implying that the Eu ion does not completely lose three electrons to the surrounding lattice. Instead, it forms partially covalent bonds, especially with neighboring nitrogen atoms, which now gain slightly more negative charge, averaging around −1.68 e compared to −1.64 e in the pristine system. This modest increase in nitrogen M. Tayyab et al. Results in Physics 77 (2025) 108440 5 (a) (b) Fig. 3. Total and partial density of states (DOS) for (a) pristine, (b) 8.5 %, and (c) 17 % Eu-doped CaAlSiN 3 . Eu-4f states are clearly observed in the gap region, indicating active photoluminescence centers and charge localization effects. M. Tayyab et al. Results in Physics 77 (2025) 108440 6 charge and reduction in Eu’s positive charge indicate a degree of hybridization and electron sharing between the Eu-4f states and the N-2p orbitals. The deviation from purely ionic bonding is characteristic of rare-earth-doped nitride hosts and is consistent with earlier reports on phosphor systems doped with Eu, Tb, or Eu, where partial covalency enables sharper emission transitions and influences the radiative recombination efficiency [22,30]. When the doping concentration is increased to 17 % (Ca 0 . 83 Eu 0 . 17 AlSiN 3 ), the Bader charge on Eu decreases further to approximately +2.14 e (see Table 1). This reduction signifies an increasing overlap and interaction among Eu ions at higher concentrations. Due to reduced inter-Eu distance, the f-electron cloud slightly delocalizes, resulting in enhanced charge back-donation from the nitrogen ligands. In addition, the increased presence of Eu 3+ leads to a more prominent polarization effect, with the neighboring N atoms pulling more electron density, showing Bader charges up to −1.70 e. These subtle but measurable shifts reflect how doping concentration governs the local chemical environment and alters the charge transfer pathways, affecting the energy landscape and potentially introducing non-radiative decay channels if the interaction becomes too strong [32]. From a charge density isosurface perspective, the pristine CaAlSiN 3 displays clear spherical charge distribution around the Ca atoms, characteristic of ionic bonds, while more directional, lobed distributions are visible around Al and Si atoms due to their covalent character. Upon doping, the Eu atom introduces a highly localized charge accumulation in the 4f orbital region, which, while remaining largely non-bonding, shows slight distortion due to surrounding nitrogen atoms. At 17 % doping, these isosurfaces begin to overlap between neighboring Eu atoms, which is a sign of emerging dopant–dopant interaction, a precursor to concentration quenching, a well-known limitation in luminescent materials [28]. The spin-resolved charge densities are also noteworthy. Eu 3+ has a 4f 12 configuration, resulting in significant spin polarization. The majority (spin-up) channel exhibits higher electron density near the Eu site, while the minority (spin-down) channel is largely depleted. This asymmetry is reflected in the spin-polarized Bader charges, with the upspin states contributing over 90 % of the localized 4f electron density. The preservation of this magnetic character is essential for the blue and near-infrared f–f transitions that characterize Eu 3+ ions, as they originate from spin-allowed intra-4f transitions such as 3 H 6 → 3 F 4 and 3 H 4 → 3 H 6 , responsible for emission at ~480 nm and ~800 nm, respectively [28,33]. The partially covalent environment provided by the CaAlSiN 3 host stabilizes these transitions while minimizing non-radiative relaxation pathways. Compared to Eu-doped CaAlSiN 3 , the Eu-doped system maintains more distinct f-state localization and less pronounced charge delocalization, which is beneficial for NIR emission applications. While Eu 2+ ions show broad-band red emission due to 4f 6 5d 1 → 4f 7 transitions, Eu 3+ ions support sharp line emission due to forbidden 4f–4f transitions. The charge analysis confirms that Eu 3+ maintains its oxidation state and localized nature even at higher doping levels, although signs of interaction begin to emerge beyond 10 %, as noted in both computational and experimental studies on similar nitride hosts [26]. The following table summarizes the Bader charge values for key atomic species across pristine and doped configurations: In summary, Bader charge analysis confirms that Eu substitutes into the Ca site, retains its trivalent oxidation state, and engages in moderate charge transfer with neighboring nitrogen atoms. As doping increases, the bond polarization and local electron redistribution become more pronounced, subtly influencing the optical and magnetic behavior of the system. The GGA +U approach is crucial in accurately capturing the localization of Eu 4f electrons and ensuring physically meaningful charge density distribution, without which the delicate balance between ionic and covalent contributions would be incorrectly modeled. These findings align well with spectroscopic and photoluminescent results from similar rare-earth-doped nitrides and affirm the potential of Eudoped CaAlSiN 3 in blue/NIR-emitting devices and high-efficiency phosphor-converted LEDs. Electron localization function (ELF) The Electron Localization Function (ELF) is a powerful quantum mechanical descriptor that offers insight into the spatial distribution and localization of electrons within a crystal. For complex oxynitride or nitride-based phosphors such as CaAlSiN 3 , the ELF plays a critical role in understanding both the bonding characteristics and the behavior of localized f-electrons introduced by rare-earth dopants like Eu 3+ . In the present investigation, ELF was computed using the GGA +U functional to accurately capture the correlation effects associated with Eu 4f orbitals. The analysis was performed for three configurations: pristine CaAlSiN 3 , 8.5 % Eu-doped CaAlSiN 3 , and 17 % Eu-doped CaAlSiN 3 . In the pristine CaAlSiN 3 structure, the ELF contour plot revealed a moderate level of localization around nitrogen atoms, primarily due to their high electronegativity and the strong covalent bonding they form with neighboring Ca, Al, and Si atoms. The distribution of ELF values in the pristine lattice shows a symmetrical spread with maximal localization near N atoms, confirming the hybrid ionic-covalent character of the bonding in the host matrix. The absence of 4f electrons in the pristine system results in a relatively smooth and delocalized ELF surface, devoid of any sharp peaks or confined lobes that are typical of f-electron localization. Upon introducing 8.5 % Eu into the CaAlSiN 3 matrix, the ELF plot exhibits significant changes (see Fig. 4), most notably the emergence of a distinct localization region centered around the Eu atom. This localization arises due to the strong on-site Coulomb interactions within the partially filled Eu 4f orbitals, which are poorly screened and do not participate actively in bonding but remain spatially confined. These electrons exhibit nonbonding character, forming sharp peaks in the ELF plot in the immediate vicinity of the Eu site. Compared to the pristine lattice, the bonding environment around the Eu ion becomes more anisotropic, reflecting the lower symmetry introduced by doping and the localized nature of the f-electron cloud. Furthermore, an increase in ELF intensity is observed between Eu and adjacent nitrogen atoms, suggesting a weak but non-negligible interaction that influences both electronic transitions and energy transfer mechanisms. At a higher doping level of 17 % Eu, the ELF localization around Eu becomes even more pronounced. The peaks are sharper and more intense, indicating a greater degree of electron confinement. This behavior is consistent with the increase in Eu–N interactions, as more nitrogen atoms come under the influence of nearby Eu 3+ ions. Additionally, this higher doping concentration leads to a stronger perturbation of the host lattice, as reflected in the ELF distribution, where the spatial localization extends beyond the immediate coordination sphere of the Eu atom. This may enhance nonradiative relaxation pathways in certain regions while simultaneously increasing the probability of radiative f–f transitions at specific Eu sites. These subtle changes in electron localization also affect the luminescent quantum efficiency of the material, which is a key parameter in designing efficient phosphor materials for white LEDs. From a physics standpoint, the observed evolution in ELF with increasing Eu content underscores the interplay between structural Table 1 Bader charge analysis results showing charge transfer between Eu and surrounding atoms. The oxidation state of Eu stabilizes around +2.4 to +2.6, confirming partial ionicity. Atom type Pristine CaAlSiN 3 8.5 % Eu-doped 17 % Eu-doped Ca +1.64 e +1.61 e +1.59 e Al +2.35 e +2.36 e +2.37 e Si +3.17 e +3.19 e +3.21 e N−1.64 e −1.68 e −1.70 e Eu —+2.26 e +2.14 e M. Tayyab et al. Results in Physics 77 (2025) 108440 7 distortion, electronic localization, and bonding anisotropy. In the GGA +U framework, the Hubbard U parameter applied to the Eu 4f states ensures that the strong Coulomb repulsion among localized electrons is adequately captured, which is crucial for systems where crystal field splitting and spin–orbit coupling play significant roles in determining optical behavior. The f-electrons in Eu 3+ , being highly localized and shielded by the filled 5 s and 5p orbitals, exhibit minimal hybridization with valence states but are highly sensitive to the surrounding electrostatic field, thus modifying ELF in a localized fashion. Although the current focus is on Eu doping, these insights directly extend to Tm 3+ -doped CaAlSiN 3 as well. Eu 3+ ions, which also possess partially filled f-orbitals, introduce similar localized features in ELF. However, unlike Eu 3+ , which commonly emits in the red spectral region ( 5 D 0 → 7 F 2 transitions), Tm 3+ offers sharp emission lines in the blue ( 1 D 2 → 3 F 4 ) and near-infrared regions ( 3 H 4 → 3 F 4 ), making it uniquely suited for dual-color and NIR phosphor applications. The ELF localization associated with Eu doping is expected to be even more pronounced, particularly under the influence of spin–orbit coupling, which splits the 4f manifold into distinct J-levels. The difference in ELF patterns between Eu 3+ dopant would be governed by their ionic radii, electronic configurations, and local site symmetry. Literature reports on RE-doped CaAlSiN 3 systems confirm that electron localization plays a central role in dictating emission properties. The Li et al. (2021) and Liu et al. (2020) [34,35] have shown through both experimental photoluminescence and theoretical DFT calculations that enhanced localization due to rare-earth doping improves the internal quantum efficiency by suppressing nonradiative losses and increasing radiative recombination rates. Additionally, comparing our ELF plots with those reported by Zhang et al. (2018) [36] for RE-doped nitrides confirms that the local bonding environment and the degree of f-electron localization are critical parameters influencing not only electronic structure but also thermal quenching resistance and color purity. As such, our results validate the design principle that judicious crystal-site engineering via rare-earth doping can tailor electron localization for optimizing optical output in phosphor materials. The ability to spatially resolve ELF differences between pristine, 8.5 %, and 17 % Eu-doped CaAlSiN 3 underscores the material’s versatility and potential for next-generation solid-state lighting technologies. Optical properties Dielectric function. Below is a detailed expert-level discussion of the optical properties of pristine, 8.5 % Eu-doped, and 17 % Eu-doped CaAlSiN 3 based on the provided real ( ε 1 ( ω )) and imaginary ( ε 2 ( ω )) dielectric function plots. The analysis addresses their physical implications, electron transition mechanisms, and relevance to LED phosphor performance using the GGA +U methodology. The real part of the dielectric function, ε 1 ( ω ) (see Fig. 5), describes the polarization response of the material to an external electric field and directly relates to its refractive index and optical dispersion. For pristine CaAlSiN 3 , ε 1 ( ω ) begins with a modest static value around 5 at zero energy and increases gradually, reaching a broad maximum near 6.8 eV. This behavior indicates a typical wide band gap dielectric response with low polarizability in the low-energy regime. Upon doping with 8.5 % Eu (Ca 0 . 925 Eu 0 . 085 AlSiN 3 ), ε 1 ( ω ) shows a significant increase in amplitude, peaking at ~11.2 around 5.8 eV. For 17 % Eu (Ca 0 . 83 Eu 0 . 17 AlSiN 3 ), the curve becomes even more prominent, showing a further increase in the static dielectric constant and shifting of the maximum toward 5.5 eV. This enhancement in ε 1 ( ω ) implies increased polarizability due to Eu 3+ substitution, which arises from the strong localization of the 4f orbitals and increased oscillator strength from transitions involving Eu 4f to the conduction band. This increase in ε 1 suggests that Eu doping improves the refractive index and energy storage capacity in the electric field, which is crucial for efficient light harvesting and guiding in LED materials. The imaginary part of the dielectric function, ε 2 ( ω ) (see Fig. 4), represents the absorption characteristics and energy loss due to interband transitions. In the pristine CaAlSiN 3 , ε 2 ( ω ) starts near zero until (c) Fig. 4. Electron localization function (ELF) for (a) pristine, (b) 8.5 %, and (c) 17 % Eu-doped CaAlSiN 3 plotted along the [1 0 0] plane. Enhanced localization around Eu and bonding with N atoms confirms f-electron confinement and partial covalency. M. Tayyab et al. Results in Physics 77 (2025) 108440 8 about 3.8 eV, where the first significant optical absorption begins, peaking around 5.8 eV with a value of ~6.2. This indicates the onset of strong interband transitions from the top of the valence band (VB) to the bottom of the conduction band (CB). When 8.5 % Eu is introduced, the ε 2 ( ω ) curve shifts significantly. A sharp absorption edge appears around 3.2 eV, and the main peak shifts to ~5.6 eV with an increased intensity of ~13.2. This indicates that Eu doping introduces intermediate 4f states near the Fermi level, enabling transitions at lower photon energies. With 17 % Eu doping, ε 2 ( ω ) shows further broadening, and the peak shifts slightly toward lower energy (~5.4 eV), with a similar high amplitude. This broadening and redshift imply enhanced light absorption in the visible range, making the material more suitable for optoelectronic and photonic applications, particularly for white light generation through red emission. Physically, the strong peaks observed in ε 2 ( ω ) for the doped samples correspond to transitions involving Eu 4f states. Specifically, transitions from the N 2p-dominated valence band to the Eu 4f and Ca/Al/Si conduction band hybridized states enhance the optical response. The substitution of Ca 2+ with Eu 3+ leads to partial occupation of the Eu-f orbitals, contributing to the density of states near the conduction band minimum and reducing the effective optical band gap. This is consistent with the behavior expected in rare-earth-doped phosphors, where the localized 4f levels of Eu 3+ act as luminescent centers. The 4f 6 → 4f 6 transitions in Eu 3+ are parity forbidden but become partially allowed due to crystal field and vibronic coupling, enhancing the radiative recombination efficiency. The increase in optical absorption and dielectric response with increasing Eu concentration can be directly linked to enhanced f–f and f–d transitions. These transitions are particularly relevant in phosphors because the 4f electrons of Eu 3+ are shielded by outer 5 s and 5p electrons, resulting in sharp emission lines and stable excited states. While ε 2 ( ω ) provides direct insight into these interband absorptions, ε 1 ( ω ) reflects the dispersive properties which control light propagation in the host lattice. The increasing trend in both dielectric components with doping aligns with previous findings, such as those reported by Zhang et al. (2018) and Li et al. (2021) [37,38], who observed similar enhancements in CaAlSiN 3 :Eu 3+ and related nitrides. Spin-polarized calculations using GGA +U reveal that the spin-up and spin-down components are largely symmetric for pristine CaAlSiN 3 , confirming a non-magnetic ground state. However, upon Eu doping, due to the open 4f 6 configuration of Eu 3+ , the system exhibits spin polarization. The majority spin (spin-up) states for Eu contribute significantly near the Fermi level in ε 2 ( ω ), while minority spin (spindown) states are pushed deeper into the conduction band. This spin asymmetry is responsible for magnetic splitting of energy levels, which further enhances optical transitions by lifting degeneracies. This spinresolved feature is not only important for luminescence but also plays a role in circularly polarized emission, which has implications in chiral optoelectronics. Overall, Eu-doped CaAlSiN 3 exhibits a marked improvement in optical properties relevant for red-emitting phosphors used in white light LEDs. The enhanced ε 1 and ε 2 functions support stronger photon-matter interaction, improved absorption, and efficient emission in the visible range. This confirms that Eu 3+ is an effective dopant for tuning the optical behavior of CaAlSiN 3 , making it a promising candidate for nextgeneration solid-state lighting technologies. The optical behavior of CaAlSiN 3 and its Eu-doped counterparts was evaluated through key optical functions—namely, the absorption coefficient ( α ), refractive index (n), reflectivity (R), and energy loss function (L), which are plotted above. These properties are pivotal for understanding how Eu doping modifies the optoelectronic landscape of CaAlSiN 3 , especially in the context of luminescent and photonic applications such as LEDs and phosphors. Absorption coefficient ( α ( ω )). The absorption coefficient provides insights into how efficiently a material can absorb photons of different energies. From the plots, the pristine CaAlSiN 3 shows a relatively lower absorption intensity across the visible to UV range (see Fig. 6). However, when Eu is introduced at 8.5 % and further at 17 %, the absorption edge shifts toward lower energies (a redshift), and the magnitude of absorption increases significantly in the range of 4–12 eV. This enhancement is Fig. 5. Dielectric function real part ε 1 ( ω ) and imaginary part ε 2 ( ω ) for pristine, 8.5 %, and 17 % Eu-doped CaAlSiN 3 . The redshift in ε 2 peaks indicates strong optical transitions due to Eu-4f states aligned with the conduction band. Fig. 6. Absorption coefficient α ( ω ) showing redshift in absorption edge with increasing Eu doping. The introduction of mid-gap states enhances absorption in the visible and NIR region, making the material suitable for LED applications. M. Tayyab et al. Results in Physics 77 (2025) 108440 9