An investigation was made of the doping of bulk rutile TiO2 with trivalent cations, Al, Ga and In, using DFT, DFT corrected for on-site Coulomb interactions (DFT+U, with U on oxygen 2p states) and hybrid DFT (the screened exchange HSE06 exchange correlation functional) in an effort to better understand the performance of DFT in describing such fundamental doping scenarios and to analyse the process of charge compensation with these dopants. With all dopants, DFT delocalizes the oxygen hole polaron that results from substitution of Ti with the lower valence cation. DFT also finds an undistorted geometry and does not produce the characteristic polaron state in the band gap. DFT+U and hybrid DFT both localize the polaron, and this was accompanied by a distortion to the structure around the oxygen hole site. DFT+U and HSE06 both give a polaron state in the band gap. The band gap underestimation present in DFT+U means that the offset of the gap state from both the valence and the conduction band cannot be properly described, while the hybrid DFT offsets should be correct. An investigation was made of  dopant charge compensation by formation of oxygen vacancies. Due to the large number of calculations required, DFT+U was used for these studies. It was found that the most stable oxygen vacancy site had either a very small positive formation energy or was negative, so under typical experimental conditions, anion vacancy formation will compensate for the dopant.

Charge Compensation in Trivalent Cation Doped Bulk Rutile TiO2. Iwaszuk, A., Nolan, M.: Journal of Physics - Condensed Matter, 2011, 23[33], 334207