Electronic structure in the band gap of lightly doped ${\mathrm{SrTiO}}_3$ by high-resolution x-ray absorption spectroscopy

The electronic structure of lightly Nb-doped ${\mathrm{SrTiO}}_3$ has been investigated using high resolution x-ray absorption spectroscopy (XAS). Below the O $1s$ threshold, XAS spectra show two features due to empty states whose energy positions match with those of the $3d$ photoemission spectra in the band gap energy region of the parent undoped ${\mathrm{SrTiO}}_3.$ Similar features are also observed in lightly La-doped ${\mathrm{SrTiO}}_3.$ These features exhibit systematic temperature dependence, which is well explained by the Fermi-Dirac distribution function. This indicates that the two features in the band gap are real bulk states such as simple donor states.