Insights into the Characteristic Gap Level and n-Type Conductivity of Rutile TiO₂ from the Hybrid Functional Method

Abstract

Using the Heyd–Scyseria–Ernzerhof (HSE) hybrid functional in the framework of the density functional theory (DFT), we probe the insight into the characteristic gap level and n-type conductivity of the intrinsic rutile TiO2. Thermodynamic and kinetic investigations have been conducted to elaborate the favorability for the formation of the possible n-type defects and unintentional impurities in rutile TiO2. Results show that oxygen vacancy is clearly identified to induce a deep localized state inside the forbidden energy region through localizing two excess electrons at two Ti4+ ions along the [001] direction and reducing them into Ti3+ ions, accounting for the characteristic gap level observed experimentally. The eg orbital composition of this gap level offers an accountable explanation of the experimentally measured ferromagnetism in TiO2–x , while the electron transition from this characteristic level is contributable to the photocatalytic behaviors and visible photoluminescence of slightly reduced TiO2. Also, unintentional incorporation of hydrogen substitution for oxygen acts as a shallow donor, providing a consistent explanation of the n-type conductivity in TiO2. The fundamental understanding of these characteristic properties and the associated functionalities would be essential to improving and expanding the practical applications of TiO2-based materials and devices.

Donors and polaronic absorption in rutile TiO2 single crystals

“…Thus, H i is likely to be the main donor in N 2 -annealed samples even though these samples exhibit a lower [H i ] than as-received samples. However, first-principles calculations by Han et al 84 predict H O , rather than H i , is the main H-related donor in rutile TiO 2 , which is in contrast to the calculations by Bjørheim et al 69 The LVM due to H O occurs typically at lower wavenumbers where the crystal is opaque to IR light, which prevents its observation in our measurements. Therefore, our data do not allow us to completely exclude the possibility that the electrical conductivity increase is due, at least partially, to the formation of H O .…”

Ab Initio Prediction of the Redox Potentials of 3d Transition Metals Embedded in a Semiconducting Host Lattice

“…12,[76][77][78][79] Moreover, conclusions from theoretical predictions on the depth of defects are sometimes conflicting between shallow and deep nature. 7,9,11,14,15,74,80 In that context, the thermodynamic stability of rutile TiO2 synthesized under different atmospheres was reinvestigated. To do so, 10 competitive phases (i.e., Ti, O2, Ti6O, Ti3O, Ti2O, TiO, Ti2O3, Ti3O5, Ti4O7 and Ti5O9) were considered in relation with the experimental Ti-O phase diagram, 81 while previous reported DFT studies took into account only 3 (i.e., Ti, O2 and Ti2O3).…”

“…To do so, 10 competitive phases (i.e., Ti, O2, Ti6O, Ti3O, Ti2O, TiO, Ti2O3, Ti3O5, Ti4O7 and Ti5O9) were considered in relation with the experimental Ti-O phase diagram, 81 while previous reported DFT studies took into account only 3 (i.e., Ti, O2 and Ti2O3). 7,9,15 The hcp-Ti(s) and O2(g) phases were used to set the chemical potential references 0 and 0 , respectively. We emphasize the fact that the actual study only focuses on the rutile TiO2 phase and neglects the competition with other stable (i.e., brookite and anatase) and metastable (i.e., columbite, ramsdellite, bronze, hollandite) phases of titania. )…”

“…Regarding the electronic properties, this wide band gap material belongs to the transparent semiconducting oxide's family. Point defects have already been widely investigated for the rutile TiO2 phase through experimental and theoretical studies, [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15] even if some conflicting points are still a matter of debate within the community such as the exact nature of the dominant defect or the depth of donor levels for oxygen vacancies.…”

“…Formation energies and charge transition levels of intrinsic defects have been carefully detailed through the use of density functional theory. [7][8][9][10][11]53,15 However, authors often did not consider extrinsic dopants. Regarding the impurities, most of articles report energy level positions determined through the analysis of densities of states.…”