first-principles investigation of erbium doping and intrinsic defects on the structural and electronic properties of silicon dioxide

Rare-earth-doped silica (sio₂) nanostructures have great potential for optoelectronics but little is known about the atomic-scale processes controlling their electrical behaviour in the presence of intrinsic defects and erbium (er) doping. in order to close this gap, this work uses the density functional theory with generalized gradient approximation (dft-gga), a first-principles density functional theory, to analyse the structural and electrical changes in er-doped sio₂ and its defective forms. er was used to replace si atoms in three doping concentration models of 2.08%, 4.17%, and 6.25%, for silicon vacancies (siv) and oxygen vacancies (ov), which were added to evaluate defect-mediated effects. lattice expansion proportionate to er concentration was found by structural optimisation, which was driven by er–o bonds of 2.1 – 2.3 å and larger ionic radius 2.45 å and 1.46 å for si. thermodynamic stability was demonstrated by formation energies ranging from -0.675 to -0.724 ev/atom, where lower energy configurations were preferred by increased er content. er 4f, which derives the impurity states near the conduction band, is responsible for the transition to a direct band gap. the band structure calculations show moderate er doping at 4.17%, which shows sio₂’s indirect band gap of 5.32 ev to the doped indirect band gap of 5.98 ev and direct band gap of 5.01 and 5.08 ev. due to dopant interactions changing of the host matrix, the gap unexpectedly extended to 5.89 ev at 6.25% er concentration. oxygen and silicon vacancies further modulated electronic properties, introducing deep donor levels and reducing the gap of ov  to 3.89 ev and  siv to 4.21 ev formation energy albeit at significant energetic costs. density of states analysis highlighted hybridization between er 4f and 5d orbitals and host o 2p and si 3p states, enabling tailored band engineering. this work establishes a theoretical framework linking er doping and defects to tunable electronic properties in sio₂, offering insights for designing high-efficiency optoelectronic materials.