Hypothesis

In order to enhance total PF of 2DES, two-dimensionality should be enhanced. Use of longer λ D should be effective if the electron carriers are confined within a defined thickness layer (Fig. 1). Very recently, we observed a steep decrease in m*/m e at x ~ 0.3 in SrTiO 3 –SrNbO 3 solid solution system, SrTi 1−x Nb x O 3 (x is ranging from 0.05 to 0.9; Fig. 2)19. The ratio x of SrTi 1−x Nb x O 3 can be divided into two regions, region A (x is <0.3) and region B (x is >0.3). The origin of the two regions is most likely due to the difference in the overlap population between the Ti 3d and Nb 4d orbitals (r Ti3d is 48.9 pm and r Nb4d is 74.7 pm)20. We calculated λ D values of SrTi 1−x Nb x O 3 using the Eq. (2). The λ D value in region B is ~5.3 nm, which is 27% longer than that in region A (~4.1 nm). One can expect that S-enhancement factor in region B is much higher than that in region A because of higher two-dimensionality. Therefore, we hypothesized that SrTi 1−x Nb x O 3 -based 2DES can be used to clarify the effectiveness of 2DES to enhance PF experimentally.

Fig. 1 Thermoelectric effect of a 2D electron system. a Schematic illustration of thermoelectric Seebeck effect in a 2DES. A thermoelectric power output (S·ΔT·I) can be obtained when ΔT is introduced. b The hypothesis that a 2DES with longer de Broglie wavelength (λ D ) shows a larger enhanced factor of thermopower Full size image

Fig. 2 SrTiO 3 –SrNbO 3 solid solution: a model system having two different λ D . x-dependent effective mass (m*/m e , white symbols) and λ D (gray symbols) for SrTi 1 − x Nb x O 3 solid solutions. m*/m e exerts a decreasing tendency with x, resulting in an increased λ D . Sharp changes in both m*/m e and λ D are detected around x = 0.3 due to the conduction band transition from Ti 3d to Nb 4d. The properties of SrTi 1 − x Nb x O 3 solid solutions can be divided into two regions based on the conduction bands (Ti 3d → region A and Nb 4d → region B). Inset: schematic illustrations of conduction electrons at regions A and B. At region B, λ D is ∼5.3 nm, while it is ∼4.1 nm at region A Full size image

We fabricated [N uc SrTi 1−x Nb x O 3 |11 uc SrTiO 3 ] 10 superlattices (N is ranging from 1 to 12, x is ranging from 0.2 to 0.9) by a pulsed laser deposition (PLD) technique on insulating (001) LaAlO 3 (pseudo-cubic perovskite, the lattice parameter, a is 3.79 Å) single-crystal substrates using dense ceramic disks of a SrTiO 3 –SrNbO 3 mixture and SrTiO 3 single crystal as the targets. The thicknesses of different layers were monitored in situ using the intensity oscillation of the reflection high-energy electron diffraction (RHEED) spots. (See Experimental Section.) High-resolution X-ray diffraction (XRD) measurements revealed that the resultant superlattices were heteroepitaxially grown on (001) LaAlO 3 with cube-on-cube epitaxial relationship with superlattice structure. Atomically smooth surfaces with stepped and terraced structure were observed by an atomic force microscopy (AFM).

Microstructure and electronic structure

Figure 3a summarizes the atomic arrangements of the [1 uc SrTi 0.4 Nb 0.6 O 3 |11 uc SrTiO 3 ] 10 superlattice. Rather bright bands are observed near each SrTi 0.4 Nb 0.6 O 3 layer in the Cs-corrected high-angle annular dark-field scanning transmission electron microscopy (HAADF-STEM) image. In the magnified image, the #4 atom in the B-site column is brighter than the nearby atoms. However, there is no obvious difference in the A-site column, indicating Nb substitution occurs for the #4 atom in the B-site column. The electron energy loss spectroscopy signal of #4 is broader than that of the nearby atoms, implying the coexistence of Ti4+/Ti3+ in the SrTi 0.4 Nb 0.6 O 3 layers21. Therefore, in our superlattice fabrication, Nb ions are successfully confined into 1 uc of SrTi 0.4 Nb 0.6 O 3 layers22.

Fig. 3 Experimental and theoretical analyses of the 2DES. a Cross-sectional HAADF-STEM image of the [1 uc SrTi 0.4 Nb 0.6 O 3 |11 uc SrTiO 3 ] 10 superlattice. Layer stacking sequence is also shown. Rather bright bands are seen near each SrTi 0.4 Nb 0.6 O 3 layer. In the magnified image, the #4 atom in the B-site column is brighter than the nearby atoms, whereas no obvious difference is observed in the A-site column. EELS spectrum of #4 is broader than that of nearby atoms, indicating the coexistence of Ti4+/Ti3+ in the SrTi 0.4 Nb 0.6 O 3 layers. b The calculated partial DOS of Nb 4d or Ti 3d in the [1 uc SrNbO 3 |10 uc SrTiO 3 ] superlattice. The Fermi energy (E F ) is located on the higher-energy side of the conduction band minimum for the first and second nearest neighbor (Ti first NN and Ti second NN). SrTiO 3 layers together with 1 uc SrNbO 3 layer (Nb) suggest that the electron carriers can seep from the SrTi 1 − x Nb x O 3 layers into the SrTiO 3 layers Full size image

In order to clarify the 2DES formation, the electronic band structures of the [1 uc SrNbO 3 |10 uc SrTiO 3 ] superlattices were calculated based on the projector-augmented wave (PAW) method (Fig. 3b). The E F is located on the higher-energy side of the conduction band minimum for the first and second nearest-neighbor SrTiO 3 layers (Ti first NN and Ti second NN) together with the 1 uc SrNbO 3 layer (Nb). The electron carriers can seep from the SrNbO 3 layers into the SrTiO 3 layer. Delugas et al.23 have also predicted theoretically that for lower Nb substituted samples, it is much easier for the electrons, especially in the d xz and d yz bands, to spread out to the neighboring SrTiO 3 layers, reducing the two-dimensionality. However, as the Nb content increases, the minimum thickness of the barrier layer may be reduced to 5 uc in the SrNbO 3 case. There is no doubt that the electron diffusion cannot be removed thoroughly in superlattice structure, but diffusion effects can be effectively suppressed by the high Nb substitution. From the band calculation, 2DES in our work is mainly confined to the 1 uc SrTi 1−x Nb x O 3 layers and should contribute to the S enhancement.

In order to further confirm the superlattice structure, we measured the κ of the [1 uc SrTi 0.4 Nb 0.6 O 3 |11 uc SrTiO 3 ] 10 superlattice along the cross-plane direction by time-domain thermal reflectance (TDTR) method. The total κ could be suppressed to ~3.3 W m−1 K−1, similar to the minimum value of CaTiO 3 /SrTiO 3 -based superlattices (κ ~ 3.2 W m−1 K−1) reported by Ravichandran et al.24. From these results, we judged that our [N uc SrTi 1−x Nb x O 3 |11 uc SrTiO 3 ] 10 superlattices (N is ranging from 1 to 12, x is ranging from 0.2 to 0.9) are appropriate for us to clarify the effectiveness of 2DES to enhance PF.

Thermoelectric properties

The electrical conductivity (σ), carrier concentration (n), and Hall mobility (μ Hall ) of the superlattices were measured at room temperature by a conventional d.c. four-probe method with a van der Pauw geometry. S was measured at room temperature by creating a temperature difference (ΔT) of ~4 K across the film using two Peltier devices. Figure 4a summarizes the n-dependent S of [N uc SrTi 1−x Nb x O 3 |11 uc SrTiO 3 ] 10 superlattices (N is ranging from 1 to 12, x = 0.2, 0.3, and 0.8) along with bulk (~100-nm-thick SrTi 1−x Nb x O 3 films, x = 0.2, 0.3, and 0.8, respectively) values for comparison. The bulk S for x = 0.2 was −143 μV K−1, x = 0.3 was −73 μV K−1, and x = 0.8 was −19 μV K−1. The n value was measured based on the total thickness of the 2DES, which includes the insulating SrTiO 3 layers. All the 2DES samples show enhanced thermopower (−S) with a reduced N. Compared to the bulk samples at a similar n, a much higher −S is observed in superlattices as N is reduced below 3 uc.

Fig. 4 Two-dimensionality of 2DES: a key to enhance thermopower. a Plots of thermopower of the 2DESs, [N uc SrTi 1 − x Nb x O 3 |11 uc SrTiO 3 ] 10 superlattices (x = 0.2, 0.3, and 0.8), versus the carrier concentration (n). Compared to bulk values (gray squares), all the 2DESs show an enhanced −S as N is reduced under 3 uc. b Enhancement factors in –S (S 2DES /S Bulk ) for three sets of 2DESs. For x = 0.2 and 0.3 2DESs, the highest S 2DES /S Bulk values are obtained at N = 1, which are 4 and 5, respectively, while that of x = 0.8 can reach 10 Full size image

To confirm the increasing two-dimensionality with x, the S-enhancement factors (S 2DES /S Bulk ) were plotted versus the N values (Fig. 4b). For 2DES with x = 0.2 and 0.3, the highest S 2DES /S Bulk values are around 4 and 5, respectively, whereas that for the x = 0.8 counterpart is ~10. As hypothesized, the enhanced S 2DES /S Bulk should stem from the increasing λ D with x. In our experiment, S 2DES /S Bulk for the x = 0.2 and 0.3 2DESs are saturated around 11 uc, which is consistent with λ D in region A (~4.2 nm indicated by dashed line λ DA ). As λ D increases in region B, the saturation position for the x = 0.8 2DES has a thickness larger than the λ D (~5.2 nm indicated by dashed line λ DB ). As a result, a significantly enhanced two-dimensionality is achieved in the x > 0.3 region B, which fits well with our hypothesis and suggests that region B has the potential to further enhance the thermoelectric PF.

Based on the conclusions above, we have enhanced the thermoelectric PF in [1 uc SrTi 1−x Nb x O 3 |11 uc SrTiO 3 ] 10 superlattices by adjusting x between 0.2 and 0.9. Figure 5 summarizes the n dependences of the thermoelectric properties of [1 uc SrTi 1−x Nb x O 3 |11 uc SrTiO 3 ] 10 superlattices at room temperature along with the reported bulk values for comparison19. Following the bulk values, σ increases almost linearly with n (Fig. 5a), indicating that n dominates σ. In the SrTi 1−x Nb x O 3 system, carriers are mostly due to Nb substitution. The high n also induces a highly Nb substituted region with a superiority in σ. However, σ for the superlattices remains lower than the bulk value due to the coexistence of 11 uc SrTiO 3 insulating layers.

Fig. 5 Double enhancement of the thermoelectric power factor in a 2DES. Carrier concentration dependences of a electrical conductivity (σ), b Hall mobility (μ Hall ), c thermopower (−S), and d power factor [PF (S2·σ)] of [1 uc SrTi 1 − x Nb x O 3 | 11 uc SrTiO 3 ] 10 2DESs (x is ranging from 0.2 to 0.9) at room temperature. Similar to the trends in the bulk values, σ increases almost linearly with n. μ Hall for lower x samples (x ≤ 0.5) fluctuates around 3–5 cm2 V−1 s−1, while that for higher x ones (x ≥ 0.6) is ~6 cm2 V−1 s−1. Slope of –S versus log n for bulk SrTi 1 − x Nb x O 3 is –198 μV K−1, which is ∼1.5 times lower than –300 μV K−1 for the 2DESs. Double enhancement of PF is seen in x = 0.6 (5.1 mW m−1 K−2 at n ∼ 8 × 1020 cm−3). Since the PF values are scattered due to the rather large distribution of μ Hall (3–6 cm2 V−1 s−1), we calculated PFs using the relationship between S and n (c) at constant μ Hall (6 cm2 V−1 s−1). The optimized PF of the 2DES should be ~5 mW m−1 K−2 at n ∼ 8 × 1020 cm−3, which doubles that of bulk SrTi 1 − x Nb x O 3 (PF ∼ 2.5 mW m−1 K−2 at n ∼ 2 × 1021 cm−3) Full size image

μ Hall for lower x of 2DESs (x ≤ 0.5) fluctuates around 3–5 cm2 V−1 s−1, while for higher x 2DESs (x ≥ 0.6) values are ~6 cm2 V−1 s−1 (Fig. 5b). Usually, μ Hall is controlled by the conduction band of materials along with the effects of crystal defects such as impurities and grain boundaries. In the bulk samples, μ Hall sharply increases due to the transition of the conduction band from Ti 3d to Nb 4d as x increases into the highly Nb substituted region19. This pattern is also observed in the superlattice counterparts. A higher μ Hall (≥6 cm2 V−1 s−1) is observed in samples with x ≥ 0.6 than that for x ≤ 0.5 (3–5 cm2 V−1 s−1). Compared to the bulk samples, all the superlattices exert a much lower μ Hall , which may result from an insufficient crystal quality or electron diffusion into the pure SrTiO 3 barrier layers. Regardless, a conduction band transition from Ti 3d to Nb 4d is recognized in our superlattice systems. Due to the high overlapping population of the Nb 4d orbital, a superior electron transport property is realized in higher x of 2DES.

Figure 5c plots the S values for all the superlattices versus n along with the reported bulk values19. The solid line depicts the overall tendency. In the diagram, the superlattices have a significantly enhanced –S compared to bulk samples at similar n values. As indicated by the solid lines, the experimental points for 2DES and bulk show different slopes of –300 and –200 μV K−1 per decade, respectively. The relationship between –S and n eff can be expressed by Eq. (3)

$$- S = - k_{\mathrm{B}}{\mathrm{/}}e\cdot {\mathrm{ln}}\,10\cdot A\cdot \left( {{\mathrm{log}}\,{\it{n}} + B} \right),$$ (3)

where k B is the Boltzmann constant and e is an electron charge. A and B are the parameters that depend on the type of materials and their electronic band structures. Bulk shows a 3D electronic band structure with a parabolic shaped DOS near E F , where the A value = 1 and the slope reflects a constant value of −k B /e·ln10 (−198 μV K−1). On the other hand, the slope of the 2DESs may reach −300 μV K−1 per decade, indicating that the A value = 1.5. Therefore, the 2DESs work well to enhance the S even for the whole superlattice, including SrTiO 3 insulating layers.