  Density functional theory (DFT) and DFT corrected for on-site Coulomb
interactions (DFT+U) calculations are presented on Aluminium doping in bulk
TiO$_2$ and the anatase (101) surface. Particular attention is paid to the
mobility of oxygen vacancies throughout the doped TiO$_2$ lattice, as a means
by which charge compensation of trivalent dopants can occur. The effect that Al
doping of TiO$_2$ electrodes has in dye sensitised solar cells is explained as
a result of this mobility and charge compensation. Substitutional defects in
which 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 in
exothermic defect formation which maintain charge neutrality. Nudged elastic
band calculations have been performed to investigate the formation of these
clustered defects in the (101) surface by oxygen vacancy diffusion, with the
resulting potential energy surface suggesting energetic gains with small
diffusion barriers. Efficiency in- creases observed in dye sensitised solar
cells as a result of aluminium doping of TiO$_2$ electrodes are investigated by
adsorbing the tetrahydroquinoline C2-1 chromophore on the defective surfaces.
Adsorption on the clustered extrinsic Al3+ and intrinsic oxygen vacancy defects
are found to behave as if adsorbed on a clean surface, with vacancy states not
present, while adsorption on the oxygen vacancy results in a down shift of the
dye localised states within the band-gap and defect states being present below
the conduction band edge. Aluminium doping therefore acts as a benign dopant
for 'cleaning' TiO$_2$ through oxygen vacancy diffusion.
