Calculation of carrier-concentration-dependent effective mass in Nb-doped anatase crystals of TiO2

The calculated optical effective masses of electrons, both orthogonal and parallel to the tetragonal axis of the crystal, are reported as a function of carrier concentration in Nb-doped anatase. The calculation is based on the band structure, obtained by density functional theory in the generalized gradient approximation or by using the HSE06 screened hybrid functional. The anisotropy of the crystal and the nonparabolicity of the bands both have been taken into account. It has been found that in the concentration range relevant for transparent conductive oxide applications, the effective mass is determined by several branches of the conduction band, leading to a complicated dependence on the carrier concentration. The form of the function obtained with HSE06 is in line with experiment. The strong anisotropy in the effective mass is confirmed, and very large values are predicted along the tetragonal axis for high carrier concentrations.