Size effects on thermoelectricity in a strongly correlated oxide

We investigated size effects on thermoelectricity in thin films of a strongly correlated layered cobaltate. At room temperature, the thermopower is independent of thickness down to 6 nm. This unusual behavior is inconsistent with the Fuchs-Sondheimer theory, which is used to describe conventional metals and semiconductors, and is attributed to the strong electron correlations in this material. On the other hand, the resistivity increases below a critical thickness of $\sim$30 nm, as expected. The temperature-dependent thermopower is similar for different thicknesses but the resistivity shows systematic changes with thickness. Our experiments highlight the differences in thermoelectric behavior of strongly correlated and uncorrelated systems when subjected to finite-size effects. We use the atomic-limit Hubbard model at the high-temperature limit to explain our observations. These findings provide new insights into decoupling electrical conductivity and thermopower in correlated systems.

Figure 1

(a) Out-of-plane x-ray diffraction pattern for BSCO film on YSZ. Inset: Comparison of the rocking curves for the substrate and the film. (b) Pole figure scan for the (116) plane of BSCO. The four peaks at $\phi$ $=$ 45${}^{\circ }$, 135${}^{\circ }$, 225${}^{\circ }$, and 315${}^{\circ }$ correspond to the substrate YSZ (111). The corresponding 2$\theta$ value for the scan is 29.75${}^{\circ }$. (c) Pole figure scan for the (11 14) plane of BSCO. The four peaks at $\phi$ $=$ 0${}^{\circ }$, 90${}^{\circ }$, 180${}^{\circ }$, and 270${}^{\circ }$ correspond to the substrate YSZ (2 2 0). The corresponding 2$\theta$ value for the scan is 50.46${}^{\circ }$.

Figure 2

Thickness-dependent thermopower and resistivity of thin films of BSCO measured at room temperature. Thicknesses of the films range from 6 to 170 nm. The resistivity of the films was calculated by dividing the measured sheet resistance by the measured thickness. The actual resistivity can be estimated only after considering the thickness of the dead layer present in these films, which we show in Fig. 3, but the overall trend remains the same.

Figure 3

Sheet carrier density and Hall mobility as a function of thickness at room temperature. Top: The sheet carrier density data were an excellent fit for a straight line with a small offset in thickness, $\sim$4 nm. Bottom: The thermopower and actual resistivity as a function of the thickness, with the surface scattering fits clearly showing the deviation for the thermopower data. The surface scattering model used the mean free path estimated from the resistivity data and typical values for the energy-dependent scattering term, 0.1 and 0.2.[7] The actual resistivity of the films is calculated accounting for the dead layer.

Figure 4

Temperature-dependent thermopower for films of thickness 115, 88, 16, and 15 nm. The films showed very similar temperature dependences over the measured temperature range. Inset: Magnetic field dependence of thermopower for an 88-nm film at 20 K with the field applied along the temperature gradient. The calculated spin-entropic contribution to the thermopower is shown as the solid (red) line.

Figure 5

Temperature-dependent resistivity for films of different thicknesses. At the bulk limit, the films show the characteristic metal-insulator transition with a transition temperature of $\sim$100 K. As the thickness is decreased the transition temperature increases, and below 23 nm, the films remain insulating up to 300 K.