Orbital-Engineered Spin Asymmetry and Multifunctionality in Eu-Activated CaAlSiN$_3$: A First-Principles Roadmap to Optical-Thermoelectric Fusion

Rare-earth-doped nitride phosphors are promising materials for solid-state lighting and photonic applications due to their thermal stability, sharp emission lines, and strong UV-blue absorption. In this work, we present a first-principles density functional theory (DFT) study, using the GGA+U approach, of pristine and Eu3+-doped CaAlSiN3 at doping levels of 8.5% and 17%. Electronic structure calculations show that Eu incorporation introduces localized 4f states within the band gap, leading to band-gap narrowing and enabling red photoluminescence through the 5D0 -> 7F2 transition. Spin-polarized density of states and spin density mapping confirm the magnetic nature of Eu3+, while charge density, Bader analysis, and electron localization function (ELF) indicate mixed ionic-covalent bonding and charge transfer from Eu to neighboring N and Al atoms, stabilizing the doped lattice. Optical spectra, including dielectric function, absorption, refractive index, and reflectivity, reveal red-shifted absorption edges and enhanced visible-range light-matter interactions, consistent with experimental red to near-infrared emission. Formation energy analysis confirms the thermodynamic feasibility of Eu substitution, while elastic constants and Pugh's ratio indicate mechanical robustness and ductility. Thermoelectric transport properties, obtained using WIEN2k and BoltzTraP, suggest that moderate Eu3+ doping improves the power factor and reduces lattice thermal conductivity through disorder scattering. These results establish Eu-doped CaAlSiN3 as a stable and efficient red-emitting phosphor for white light-emitting diodes (WLEDs) and provide theoretical insights for crystal site engineering in advanced optoelectronic materials.