MID-GAP STATES IN DEFECTIVE ANATASE TiO2 : A DENSITY FUNCTIONAL THEORY STUDY PLUS A HUBBARD TERM (DFT+U)

Abstract

Motivated by the performance of reduced Titania in various important applications including photo-catalysis, photo-voltaics and CO2 reduction in hydrocarbon fuels, a systematic study of the structural properties and the electronic band structure characteristics of intrinsic point defects in the bulk TiO2 beginning with well established rutile then anatase was performed. All the calculations were performed within the density functional theory using an on-site Coulomb term, U=5.3 eV, and a plane wave basis set as implemented in the Quantum ESPRESSSO computer code. A comparison with the DFT results was also done. Non-relativistic norm-conserving pseudo-potentials were used to describe the core-valence interactions with GGA-PBE being chosen for the exchange-correlation functional. The systems were modeled using 48-atoms and 96- atoms super-cells for rutile and anatase, respectively. The calculated lattice parameters for the pristine cells were compared with those of other studies and found to be in good agreement with them, differing only by -1.40% to +3.42%. A direct band gap of 2.89 eV along the Γ high symmetry direction was observed in rutile while an indirect band gap of 3.01 eV from Γ-Z high symmetry points was observed in anatase TiO2. A direct band gap of 3.11 eV was also observed along Γ in anatase. The presence of isolated intrinsic point defects, both Schottky and Frenkel within the perfect cells led to the alteration of both bond lengths and angles. The largest of these distortions occurred in the presence of Frenkel defects with OF and TiF causing changes in the equatorial Ti-O bond length of between -11.2% and 12.3%, respectively, in rutile and -8.9% and 8.0%, respectively, in anatase. This was accompanied by changes in Ti-O-Ti bond angle ranging from of 143.490-131.410 and 99.930-88.860 for OF and TiF , respectively, in rutile and 152.390- 176.050 and 103.810-93.590, respectively, in anatase. As a result, the electronic band structures were equally altered. The presence of OV and OI in rutile resulted to defect states located 0.75 eV below the CB edge and 0.64 eV above the VB edge, respectively. TiV led to formation of defect states located 0.62 eV above the VB edge while TiI led to quadruple defect states located 0.83 eV & 1.17 eV above the VB edge and others located 0.93 eV & 0.56 eV below the CB edge. The presence of OF caused defect states located 0.203 eV below the CB edge while TiF caused defect states located 0.801 eV above the the VB edge. In anatase, the presence of OV and OI resulted to defect level states located 0.735 eV below the CB edge and 0.646 eV above the VB edge, respectively. Similarly, TiV and TiI led to the formation of defect states located 0.805 eV above the VB edge and 1.22 eV below the CB edge. On the other hand, OF caused defect states located 0.297 eV below the CB edge while TiF caused defect states located 0.718 eV above the the VB edge. The origin of the observed defect states in both phases of TiO2 are the O−2p and Ti−3d orbitals. The contribution of Ti−3d orbitals is dominant in all the considered defects except in OF where O−2p orbitals dominates. These features were confirmed by a plot of density of states differences. The calculated defect formation energies (DFEs) for the phases of TiO2 showed that the formation of OI is the most favoured while OV is the most difficult to form. Additionally, it is easier to displace an atom within a crystal than to remove it all together. Since the band-gap of materials determines the overall behavior and performance of devices made from them, this study suggests that native point defects in anatase TiO2 do indeed contribute to desired electronic properties of this material of interest for various industrial applications.