Lattice expansion and local lattice distortion in Nb- and La-doped SrTiO3 single crystals investigated by x-ray diffraction and first-principles calculations

Electron-doped $\mathrm{SrTi}{\mathrm{O}}_{3}$ (where the dopant can be Nb or La) has been widely investigated for both its fundamental interest in condensed matter physics and for industrial applications. Its electronic properties are closely related to the Ti-O bonding states in the $\mathrm{SrTi}{\mathrm{O}}_{3}$ crystal. To further develop and control these properties, it is crucial to understand the factors controlling the change in lattice parameters and local lattice distortion upon doping with various atoms. Herein, we report the changes in lattice parameters and local lattice distortion in Nb- and La-doped $\mathrm{SrTi}{\mathrm{O}}_{3}$ single crystals, investigated by in-plane x-ray diffraction and first-principles calculations. The lattice parameter of Nb- and La-doped $\mathrm{SrTi}{\mathrm{O}}_{3}$ single crystals increased with dopant concentration. The broad intensities around the Bragg peak observed in the in-plane x-ray-diffraction experiments indicated that the local lattice expansion and contraction, or local lattice distortions, in the crystal were caused by the dopant atoms. First-principles calculations similarly showed that the lattice expansion and local lattice distortions in the $\mathrm{SrTi}{\mathrm{O}}_{3}$ crystals were caused by doped Nb and La atoms. Atoms surrounding Schottky pairs of O and Sr vacancies were displaced both away from and towards the vacancies, resulting in a reduction in the lattice expansion of donor-doped $\mathrm{SrTi}{\mathrm{O}}_{3}$. Donor atoms and Schottky pairs thus play an important role in determining the lattice parameters of $\mathrm{SrTi}{\mathrm{O}}_{3}$ crystals. These fundamental structural analyses provide a useful basis to further investigate the electronic conductivity of electron-doped $\mathrm{SrTi}{\mathrm{O}}_{3}$.