Electronic band structure and thermoelectric properties of SrTiO$_3$, BaTiO$_3$ and CaTiO$_3$: ab initio approach

The calculations of Seebeck's coefficient, conductivity and power functions for the electron-doped SrTiO$_3$, BaTiO$_3$ and CaTiO$_3$ compounds have been performed depending on temperature and current carrier concentration by employing ab initio method based on the electron density functional theory, on the Frohlich's approach for the electron-phonon interaction and on the theory of Boltzmann–Onsager for the thermoelectric properties. The calculated Seebeck's coefficient and conductivity correspond to experimental data. It is shown that for SrTiO$_3$ and BaTiO$_3$ the dependencies of power functions on the carrier concentration have maxima in the range of (200–250) $\cdot$ 10$^{19}$ cm$^{-3}$ at any temperature, while for CaTiO$_3$ the maxima are typical only at temperatures below 500 K. The temperature dependencies of the power function also confirm that such carrier concentration range is favorable for achieving high values of the SrTiO$_3$ figure of merit, while the maximally possible carrier concentration is necessary for optimal CaTiO$_3$ figure of merit.