Absence of confinement in ( SrTiO 3 ) / ( SrTi 0.8 Nb 0.2 O 3 ) superlattices

The reduction of dimensionality is considered an efficient pathway to boost the performances of thermoelectric materials. Quantum confinement of the carriers is expected to induce large Seebeck coefficients $(S)$ and it also suppresses the thermal conductivity by increasing the phonon scattering processes. However, quantum confinement in superlattices is not always easy to achieve and needs to be carefully validated. In the past decade, large values of $S$ have been measured in $({\mathrm{SrTiO}}_{3})$/$({\mathrm{SrTi}}_{0.8}{\mathrm{Nb}}_{0.2}{\mathrm{O}}_{3})$ superlattices [H. Ohta et al., Nat. Mater. 6, 129 (2007); Y. Mune et al., Appl. Phys. Lett. 91, 192105 (2007)]. In the $\ensuremath{\delta}$-doped compound, the reported $S$ was almost six times larger than that of the bulk material. This huge increase has been attributed to the two-dimensional carrier confinement in the doped regions. Here, we demonstrate that the experimental data are well explained quantitatively assuming delocalized electrons in both in-plane and growth directions. Moreover, we rule out the confined electron hypothesis whose signature would be the suppression of the Seebeck coefficient. This strongly suggests that the presupposed confinement picture in these superlattices is unlikely.