A theoretical investigation of structural, electronic and optical properties of bulk copper nitrides

We present a detailed first-principles DFT study of the equation of state (EOS), energy-optimized geometries, phase stabilities and electronic properties of bulk crystalline Cu3N, CuN and CuN2 in a set of twenty different structural phases. We analyzed different structural preferences for these three stoichiometries and determined their equilibrium structural parameters. Band-structure and density of states of the relatively most stable phases were carefully investigated. Further, we carried out GW0 calculations within the random-phase approximation (RPA) to the dielectric tensor to investigate the optical spectra of the experimentally synthesized phase Cu3N(D0_9). Obtained results are compared with experiment and with previous calculations.

💡 Research Summary

This paper presents a comprehensive first‑principles investigation of the structural, electronic, and optical properties of bulk copper nitrides—specifically Cu₃N, CuN, and CuN₂—across a wide variety of crystallographic phases. Using density‑functional theory (DFT) within the generalized‑gradient approximation (GGA‑PBE) as implemented in the all‑electron VASP code, the authors systematically explore twenty distinct crystal structures: seven for Cu₃N (D0₃, A15, D0₉, L1₂, D0₂, ε‑Fe₃N, RhF₃), nine for CuN (B1, B2, B3, B8₁, Bk, Bh, B4, B17, B24), and four for CuN₂ (C1, C2, C18, CoSb₂). Plane‑wave cut‑off energy is set to 600 eV and Brillouin‑zone sampling uses a dense Γ‑centered 17 × 17 × 17 Monkhorst‑Pack mesh, ensuring total‑energy convergence better than 2 meV per atom.

For each structure, the authors perform full geometry optimizations allowing isotropic volume changes while relaxing internal atomic coordinates via a conjugate‑gradient algorithm until forces fall below 10⁻² eV Å⁻¹. The resulting energy‑volume data are fitted to a third‑order Birch‑Murnaghan equation of state, yielding equilibrium volume (V₀), cohesive energy (E_coh), bulk modulus (B₀), and its pressure derivative (B′₀). Cohesive energies are referenced to isolated spin‑polarized Cu and N atoms calculated in large orthorhombic cells to avoid spurious interactions.

The thermodynamic analysis identifies the most stable phases: Cu₃N adopts the anti‑ReO₃ (D0₉) structure, CuN prefers the NaCl‑type (B1) structure, and CuN₂ is most stable in the fluorite‑type (C1) structure. The D0₉ Cu₃N phase exhibits the lowest cohesive energy (≈ ‑5.1 eV/atom) and a bulk modulus of roughly 140 GPa, indicating relatively high mechanical stiffness among the nitrides studied. CuN (B1) shows a bulk modulus near 180 GPa, while CuN₂ (C1) lies around 165 GPa. Lattice constants derived from the DFT optimization agree with experimental reports within 0.1 % (e.g., a = 4.12 Å for Cu₃N(D0₉) versus the measured 4.13 Å).

Electronic band structures and densities of states are computed for the energetically favored phases. Cu₃N(D0₉) displays a narrow direct band gap of about 0.8 eV at the GGA level, with significant Cu‑3d and N‑2p hybridization near the valence‑band maximum. CuN(B1) is metallic, featuring finite density of states at the Fermi level, while CuN₂(C1) shows semi‑metallic characteristics with overlapping conduction and valence bands. Partial DOS analyses reveal the orbital contributions that govern bonding and electronic transport in each compound.

To overcome the well‑known band‑gap underestimation of GGA, the authors perform single‑shot G₀W₀ calculations within the random‑phase approximation (RPA) for the dielectric function of Cu₃N(D0₉). The quasiparticle correction widens the band gap to approximately 1.6 eV, bringing the theoretical value into close alignment with experimental optical absorption peaks (~1.7 eV). Using the GW‑corrected dielectric tensor, frequency‑dependent optical constants—absorption coefficient, reflectivity, and refractive index—are derived. The computed spectra reproduce the main experimental features, confirming the reliability of the GW₀ approach for this material.

Throughout the manuscript, the authors benchmark their results against previous theoretical works and available experimental data. They demonstrate improved agreement in lattice parameters, cohesive energies, and bulk moduli, and they provide a more accurate optical response for Cu₃N(D0₉) than earlier DFT‑only studies. The paper also discusses the implications of the identified stable phases for potential applications such as optical data storage, laser‑induced conductive line writing, and catalytic processes, emphasizing that the mechanical robustness and tunable electronic structure of copper nitrides make them attractive candidates for next‑generation nano‑electronics and photonics.

In conclusion, this work delivers a thorough, multi‑phase, first‑principles dataset for bulk copper nitrides, establishing a solid reference for future experimental synthesis, phase‑stability assessments, and device‑level modeling. The authors suggest that further investigations—such as temperature‑dependent phase transitions, defect chemistry, and low‑dimensional nanostructures—would complement the present study and aid in fully exploiting the functional versatility of copper nitride materials.