First-principles investigation of the electronic, optical, and mechanical properties of β-Si3N4 using rSCAN meta-GGA and DFT-D4 dispersion correction

A first-principles study of the electronic, optical, and mechanical properties of hexagonal β-Si 3 N 4 has been conducted within the framework of density functional theory (DFT) using the plane-wave-based CASTEP code, the rSCAN meta-generalized gradient approximation (meta-GGA) exchange–correlation functional, and the DFT-D4 dispersion correction. The present study aims to investigate the relationship between Si–N bonding characteristics and the electronic, optical, and mechanical properties of β-Si 3 N 4 . The calculations were performed using a 1200 eV plane-wave cutoff, a 4 × 4 × 9 Monkhorst–Pack k-point mesh, and strict convergence criteria. Structural validation shows good agreement with available experimental measurements and previously reported theoretical results, indicating the consistency of the adopted computational framework. The calculated electronic structure reveals a wide weakly indirect band gap of 5.029 eV, with the valence-band maximum located near the Γ–A direction and the conduction-band minimum at Γ. Density-of-states analyses reveal strong Si–N orbital hybridization and the insulating nature of β-Si 3 N 4 . The calculated dielectric constant and refractive index are 3.636 and 1.907, respectively. Optical analysis reveals a weak pre-edge feature at 4.11 eV and a primary absorption onset at 5.29 eV, followed by strong ultraviolet absorption with polarization-dependent maximum absorption peaks occurring at approximately 17.46 eV for E ⊥ c [100] and 17.79 eV for E ∥ c [001]. The electron energy-loss spectrum shows an evident peak at 24.28 eV, indicating a strong collective electronic excitation associated with the bulk electronic response. The calculated elastic constants satisfy the Born stability criteria of mechanical stability for hexagonal crystals, giving C 11 = 454.91 GPa, C 33 = 584.78 GPa, and C 44 = 108.50 GPa. The Hill-averaged elastic moduli yield B = 263.02 GPa, G = 135.26 GPa, and E = 346.40 GPa, while the directional Young’s modulus along the c-axis reaches 539.19 GPa, indicating pronounced elastic anisotropy. Overall, the combined electronic, optical, and mechanical results identify β-Si 3 N 4 as a wide-bandgap dielectric ceramic with potential applications in high-temperature structural components, ultraviolet optical systems, electrical insulation, and microelectronic protection technologies.