Energetics and optical properties of carbon impurities in rutile TiO₂

Titanium dioxide is one of the most promising materials for many applications such as photovoltaics and photocatalysis. Non-metal doping of TiO₂ is widely used to improve the photoconversion efficiency by shifting the absorption edge from the UV to visible-light region. Here, we employ hybrid density-functional calculations to investigate the energetics and optical properties of carbon (C) impurities in rutile TiO₂. The predominant configurations of the C impurities are identified through the calculated formation energies under O-poor and O-rich growth conditions. Under the O-poor condition, we find that C occupying the oxygen site (C_O) is energetically favorable for Fermi-level values near the conduction band minimum (n-type TiO₂), and acts as a double acceptor. Under the O-rich condition, the C_i-V_Ti complex is energetically favorable, and is exclusively stable in the neutral charge state. We also find that interstitial hydrogen (H_i) can bind to C_O, forming a C_O-H_i complex. Our results suggest that C_O and C_O-H_i are a cause of visible-light absorption under oxygen deficient growth conditions.