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(Color online) Primitive unit cell of the anatase crystal. and represent the bond lengths (bond angle) between Ti and O atoms. In N(C)-doped , the substitutional site of N (C) for O is marked (X). The , , and directions are , , and , respectively.
Calculated band structure of the anatase crystal along high-symmetry lines of the irreducible Brillouin zone. The valence-band maximum is taken as the energy zero. The inset shows the Brillouin zone for the tetragonal Bravais lattice.
Caculated band structure of (a) N-doped and (b) C-doped . The energy zero represents the Fermi level. The values in (a) and (b) denote the energy difference between the lowest band and the highest band.
Charge characters of (a) the state (b) the state, (c) the state, and (d) the state at the point of the Brillouin zone. The charge densities of (a) and (b) [(c) and (d)] were obtained from undoped [doped] . The plot for (a) is drawn in the horizontal plane containing Ti, while those for (b), (c), and (d) are in the vertical plane containing the impurity atom. Contour spacings are .
Optimized structural parameters for the anatase crystal compared with those of FLAPW calculationsa and experiment.b
Atomic displacements of the N (C) atom in N(C)-doped relative to the position of the O atom in undoped .
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