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Density functional theory (DFT) and DFT corrected for on-site Coulombinteractions (DFT+U) calculations are presented on Aluminium doping in bulkTiO$_2$ and the anatase (101) surface. Particular attention is paid to themobility of oxygen vacancies throughout the doped TiO$_2$ lattice, as a meansby which charge compensation of trivalent dopants can occur. The effect that Aldoping of TiO$_2$ electrodes has in dye sensitised solar cells is explained asa result of this mobility and charge compensation. Substitutional defects inwhich one Al3+ replaces one Ti4+ are found to introduce valence band holes,while intrinsic oxygen vacancies are found to introduce states in the band-gap.Coupling two of these substitutional defects with an oxygen vacancy results inexothermic defect formation which maintain charge neutrality. Nudged elasticband calculations have been performed to investigate the formation of theseclustered defects in the (101) surface by oxygen vacancy diffusion, with theresulting potential energy surface suggesting energetic gains with smalldiffusion barriers. Efficiency in- creases observed in dye sensitised solarcells as a result of aluminium doping of TiO$_2$ electrodes are investigated byadsorbing the tetrahydroquinoline C2-1 chromophore on the defective surfaces.Adsorption on the clustered extrinsic Al3+ and intrinsic oxygen vacancy defectsare found to behave as if adsorbed on a clean surface, with vacancy states notpresent, while adsorption on the oxygen vacancy results in a down shift of thedye localised states within the band-gap and defect states being present belowthe conduction band edge. Aluminium doping therefore acts as a benign dopantfor 'cleaning' TiO$_2$ through oxygen vacancy diffusion.

Intrinsic Oxygen Vacancy and Extrinsic Aluminium Dopant Interplay: A Route to the Restoration of Defective TiO$_2$