Critical enhancement of thermoelectric properties with doping-induced second-order ferroelectric transition in ${\mathrm{BaTiO}}_3$

Doping a conventional ferroelectric insulator can yield intriguing changes in its electronic transport properties, in particular when a polar-to-nonpolar transition occurs. In this work, we study the effect of electron doping on the resistivity and Seebeck coefficient of the prototypical ferroelectric ${\mathrm{BaTiO}}_3$, which undergoes a tetragonal-to-cubic second-order phase transition at a critical doping concentration. The transport properties are computed using two first-principles methods: (1) The constant relaxation time approximation and (2) the fully ab initio variational approach considering explicitly electron-phonon coupling. We show that the doping effect on the transport properties is manifold, via upshift of the Fermi level, variation of the band structure (tetragonal towards cubic), and phonon softening around the transition point, which causes nonmonotonic changes of the resistivity and Seebeck coefficient, especially the anomalies close to the transition point. Results of the two methods are compared, and the effect of temperature is also discussed.

Figure 1

DFT-predicted structural evolution of ${\mathrm{BaTiO}}_3$ as a function of electron-doping concentration. (a) Tetragonality (c/a ratio) and volume of the unit cell. The inset shows the unit-cell structure of the T phase. (b) Atomic positions taking Ba as reference.

Figure 2

CRTA-calculated transport properties of ${\mathrm{BaTiO}}_3$ as a function of electron-doping concentration at room temperature (300 K). The in-plane, out-of-plane, and diagonal-average of (a) the electrical conductivity divided by a constant relaxation time, and (b) the Seebeck coefficient; (c) Electronic density of states (DOS) N and (d) derivative of $\ln N\left(\epsilon \right)$ with respect to energy at the Fermi level.

Figure 3

Calculated electronic band structure and the corresponding Fermi surface of ${\mathrm{BaTiO}}_3$ at electron-doping concentrations of (a) 0.02 e/f.u., (b) 0.06 e/f.u., and (c) 0.12 e/f.u. Zero energy is set at the bottom of the conduction band. The red dashed line denotes the Fermi energy.

Figure 4

Calculated phonon-dispersion curves and phonon linewidths of ${\mathrm{BaTiO}}_3$ at doping concentrations of (a) 0.06 e/f.u., (b) 0.09 e/f.u., (c) 0.10 e/f.u., and (d) 0.12 e/f.u. The red broadening shows the phonon linewidths and the blue dots denote the softening optical modes at Γ point.

Figure 5

VA-calculated transport-related properties of ${\mathrm{BaTiO}}_3$ as a function of doping concentration. (a) EPC strength $\lambda$ (black solid line) and the overall transport EPC strength ${\lambda }_{\mathrm{tr}}$ (red solid line). (b) The in-plane, out-of-plane, and diagonal-average of the transport EPC strength ${\lambda }_{\text{tr}}$, (c) the electrical resistivity, and (d) the Seebeck coefficient.

Figure 6

VA-calculated transport properties as a function of temperature of ${\mathrm{BaTiO}}_3$ for selected doping concentrations near the T-to-C transition, i.e., 0.10 e/f.u., 0.11 e/f.u., and 0.12 e/f.u. The in-plane and out-of-plane components of (a) the electrical resistivity and (b) the Seebeck coefficient.