Investigating the Influence of Exchange-correlation Effects and the Hubbard Term on the Electronic Bands of Defected Cu2o: a Dft Study

Abstract

This study investigates the structural and electronic properties of defected Cu2O using density functional theory (DFT) within the Quantum Espresso package, incorporating plane wave and pseudopotential methods. The analysis includes three exchange-correlation functionals: Perdew-Burke-Ernzerhof (PBE), Perdew-Burke-Ernzerhof revised for solids (PBEsol), and local density approximation (LDA), with and without the Hubbard term (U=8.5 eV for Cu and O). The study reveals that PBE and PBEsol underestimate the experimental lattice constant 'b' while PZ-LDA provides values closer to the experimental data. The lattice parameters for PBEsol (b = 7.6940 Å) and PZ-LDA (b = 7.7006 Å) were observed to deviate from the initial lattice parameter (b = 8.5040 Å). Bond distances, such as Cu-O and O-O, are overestimated across all functionals, with PBE yielding the highest values (Cu-O = 1.9082 Å, O-O = 3.8027 Å) compared to PZ-LDA (Cu-O = 1.9077 Å, O-O = 3.8018 Å) and PBEsol (Cu-O = 1.8652 Å, O-O = 3.7406 Å). The Cu-Cu bond distance showed a modulated pattern with LDA underestimating these values (Cu-Cu = 3.1776 Å). Bond angles in the structure also varied, with angles such as Cu5∠O11∠Cu6, Cu5∠O11∠Cu7, and Cu6∠O11∠Cu7 showing significant deviations across functionals. The inter-atomic distances at the vacant site also exhibited noticeable changes post-relaxation, particularly with PBEsol and LDA, where the distances between Cu atoms such as Cu11 to Cu21 (2.4855 Å), Cu06 to Cu16 (2.4855 Å), and Cu06 to Cu11 (2.6653 Å) differed from the initial values (3.006 Å). The inclusion of the Hubbard term notably impacted the band structure, improving the band gap values for all functionals. The Fermi energy (eV) for PBE (1.97 eV), PBEsol (1.05 eV), and LDA (1.27 eV) showed varied deviations. The study highlights the Jahn-Teller distortion effect, particularly at the Cu-Cu bond length at the oxygen vacant site, and underscores the importance of Cu 3dxz, 3dyz, and O 2s orbital hybridization in forming the defected Cu2O band gap. The research therefore, underscores the necessity of accounting for exchange-correlation effects and the Hubbard term in accurately modeling defected Cu2O, contributing to a deeper understanding of its electronic properties and guiding future doping investigations.