Composition-Dependent Plasmon-Enhanced Emission in Lead-Free Cs$_3$Cu$_2$X$_5$ Halides: A DFT--FDTD Study

Lead-free Cs$_3$Cu$_2$X$_5$ (X = Cl, Br, I) halides exhibit high photoluminescence quantum yields and excellent ambient stability, yet light-emitting devices based on these materials remain limited by poor optical outcoupling. In this work, we develop an integrated density functional theory (DFT) and finite-difference time-domain (FDTD) framework to establish quantitative links between halide composition, wavelength-dependent optical constants, and plasmonic enhancement. First-principles calculations are used to obtain composition-specific refractive index (n) and extinction coefficient (k) spectra, which are directly implemented into three-dimensional FDTD simulations of a complete PeLED stack incorporating Ag/SiO$_2$ core--shell nanostructures. Among the investigated compositions, Cs$_3$Cu$_2$Cl$_5$ demonstrates the strongest plasmonic response, achieving a 4.4$\times$ Purcell enhancement and 30\% light extraction efficiency (LEE) using optimized nanorods. The superior performance originates from its lower refractive index, which reduces dielectric screening and improves near-field coupling. Cs$_3$Cu$_2$Br$_5$ exhibits the highest spectral overlap ($J_{\mathrm{cos}} = 0.955$) but yields moderate extraction (26%) due to increased optical confinement. Cs$_3$Cu$_2$I$_5$ requires a nanosphere geometry and shows limited enhancement, with LEE restricted to 10%. Distance-ependent analysis reveals composition-specific optimal emitter--plasmon separations, ranging from 8--12 nm for Cs$_3$Cu$_2$Br$_5$ to approximately 15 nm for Cs$_3$Cu$_2$Cl$_5$. These results provide composition-dependent design guidelines for plasmon-enhanced lead-free PeLEDs and highlight the critical role of accurate optical constants in predictive device optimization.