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The conduction band of a 48-atom supercell with no dopants (black dotted line), with one substitutional NbTi (blue dashed line) or one TaTi (red solid line) atom, as calculated by the HSE06 functional. The bands have been aligned based on the average electrostatic potential far from the defect, and the zero of the energy scale has been set to the bottom of the CB in the perfect crystal. The horizontal lines show the position of the Fermi level.
Orthogonal (a) and parallel (b) optical effective mass of Nb-doped (blue) and Ta-doped (red) anatase, calculated by the PBE (dashed lines) and HSE06 (solid lines) functionals. The circles represent values calculated from the band structure of the respective supercells. The lines are extrapolations assuming no change in the bands for small concentration changes.
Formation energy Ef (eV) of Nb and Ta dopants in anatase calculated with PBE (HSE06) at two different concentrations.
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