Insights into the Characteristic Gap Level and n-Type Conductivity of Rutile TiO ₂ from the Hybrid Functional Method

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 TiO ₂ . 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 TiO ₂ . 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 Ti ⁴⁺ ions along the [001] direction and reducing them into Ti ³⁺ ions, accounting for the characteristic gap level observed experimentally. The e _g orbital composition of this gap level offers an accountable explanation of the experimentally measured ferromagnetism in TiO _2-x , while the electron transition from this characteristic level is contributable to the photocatalytic behaviors and visible photoluminescence of slightly reduced TiO ₂ . Also, unintentional incorporation of hydrogen substitution for oxygen acts as a shallow donor, providing a consistent explanation of the n-type conductivity in TiO ₂ . The fundamental understanding of these characteristic properties and the associated functionalities would be essential to improving and expanding the practical applications of TiO ₂ -based materials and devices.