Synergistically enhanced electrical transport properties of SrTiO₃via Fermi level regulation and modulation doping

Abstract

SrTiO₃ has gained wide attention as an oxide thermoelectric material due to its high Seebeck coefficient and excellent high-temperature thermal stability. However, its intrinsic insulatory properties hinder its development as a thermoelectric material. Herein, we synergistically improved the electrical transport properties of SrTiO₃ by increasing carrier concentration and maintaining high carrier mobility via Fermi level regulation and modulation doping through co-doping and compositing. Nb and La co-doping notably heightened the carrier concentration and regulated the Fermi level in the conduction band, resulting in an enhanced ZT value from that of an insulator in SrTiO₃ to 0.033 in Sr_0.875La_0.125Ti_0.85Nb_0.15O₃ at 923 K. The subsequent TiB₂ compositing simultaneously improved carrier concentration (4.82 × 10¹⁷ cm³) and afforded high carrier mobility (3.55 × 10⁴ cm² V⁻¹ S⁻¹) in the Sr_0.875La_0.125Ti_0.85Nb_0.15O₃ + 4% TiB₂ sample at 923 K. The combination of synergistically improved carrier concentration and retained high carrier mobility resulted in an enhanced power factor (11.04 μW cm⁻¹ K⁻² at 923 K), maximum ZT (0.23 at 923 K) and average ZT (0.15 at 473–923 K) in Sr_0.875La_0.125Ti_0.85Nb_0.15O₃ + 4% TiB₂ through co-doping and compositing, which matches those of many excellent SrTiO₃-based materials. Our study demonstrated that the thermoelectric properties of SrTiO₃ could be improved via synergistically enhanced electrical transport properties through Fermi level regulation and modulation doping via co-doping and compositing, which will inspire further research on SrTiO₃ and other oxide thermoelectric materials with mediocre electrical transport properties.

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Xiao Zhang

Dr Xiao Zhang is a postdoctoral research fellow at Beihang University, China. She received her Bachelor of Engineering Degree from the University of Science and Technology, Beijing, in 2013, and received her PhD Degree in Materials Science and Engineering from Beihang University in 2018. She worked at Chongqing University as a faculty staff from 2018 to 2020 before joining Beihang University for postdoctoral research in 2020. Her main research interests focus on thermoelectric materials and devices as well as thermal barrier coatings.

1. Introduction

With the need for green energy, thermoelectric materials have gained growing attention since they can convert heat (industrial waste heat, geothermal heat, etc.) into electricity.¹ The conversion efficiency of thermoelectric materials is determined by ZT, defined as , where S: Seebeck coefficient, σ: electrical conductivity, and κ: thermal conductivity.^2–5 Through advanced material design and regulatory strategies, the properties of thermoelectric materials have been rapidly developed in recent decades.^6,7 However, most traditional thermoelectric materials comprise expensive elements such as Te^2,8–10 and Ge^1,11 or toxic elements such as S^12,13 and Pb.^14–17 Moreover, the high-temperature resistance and oxidation resistance of traditional thermoelectric materials are mediocre. Therefore, oxide ceramics and oxygenated compounds have been developed for non-toxicity, oxidation resistance, low cost and easy synthesis, satisfying the needs of large-scale production and high-temperature service requirements.^18,19 Compared with other oxide materials, such as Ca₃Co₃O₉ and NaCo₂O₄, SrTiO₃ (STO) shows superior S and excellent thermal stability at high temperatures,^6,20–22 and its isotropic properties indicate good mechanical properties in practical applications and a difficulty in fracture in a specific direction, thus gaining more attention as an oxide thermoelectric material.^23,24

As shown in Fig. 1(a), SrTiO₃ has a cubic perovskite structure (Pm3m) and a lattice constant of 3.905 Å at room temperature. The valence band maximum (VBM) and conduction band minimum (CBM) are located at the R and Γ points, respectively, indicating that it is an indirect semiconductor with a large band gap of ∼1.8 eV (Fig. 1(b)). The VBM mainly originates from the O atom while the CBM mainly results from the Ti-d orbital. Obviously, the CBM is a triple degenerate point and a strong anisotropy of effective mass can be found in the Fermi surface, as shown in the right panel of Fig. 1(b). Additionally, the longitudinal (v_l) and shear (v_s) acoustic velocities, the average sound velocity (v_a) and other elastic properties shown in Table S2 (ESI†) correspond to a high κ for the pristine STO material.

Fig. 1 Structural characterization of SrTiO₃: (a) structure of the crystal and (b) the atomic orbital resolved electronic band structure. The triple degenerate CBM is located at the Γ point. The right panel shows the Fermi energy surface in the first-Brillouin zone with the isosurface level E_CBM + 0.05 for these three degenerate bands.

The energy band structure calculation results and the sound velocity measurements showed that the pristine STO material as an insulator has ultralow σ and high κ. Roy et al.²⁵ reported that the power factor (PF) for Nb-doped SrTiO₃ synthesized by spark plasma sintering (SPS) could reach 33.21 μW cm⁻¹ K⁻² at 1229 K. Li et al.^26,27 proved that La doping in STO-Nb (Nb-doped SrTiO₃) can not only introduce additional electrons to increase the carrier concentration (n) but also reduce the total energy of the STO-Nb system, effectively increasing the electron-doping efficiency. Besides, Ito et al.²⁸ found that TiB₂ could enhance the PF, resulting in a ZT_max value of ∼0.18 for the Sr_0.95Y_0.05TiO₃ + 5 mass% TiB₂ composite. These motivated us to explore the combined role of co-doping and compositing on the thermoelectric properties of STO.

In this work, we optimized the n of a pristine STO insulator by adjusting the Fermi level (E_F) to enter the conduction band through Nb-La co-doping. In order to further improve the electrical transport, we composited TiB₂, a high electrical conductivity boride, to introduce modulation doping in the STO matrix, synergistically improving n and maintaining high carrier mobility (μ). Therefore, the PF reached an ideal value in the entire investigated temperature range, with ∼11.04 μW cm⁻¹ K⁻² for Sr_0.875La_0.125Ti_0.85Nb_0.15O₃ + 4% TiB₂ at 923 K. Owing to the enhanced electrical transport over the broad temperature range, the Sr_0.875La_0.125Ti_0.85Nb_0.15O₃ + 4% TiB₂ sample reached a ZT_max of ∼0.23 at 923 K and an average ZT (ZT_ave) of ∼0.15 at 473–923 K, revealing the development potential of SrTiO₃ for high-temperature thermoelectric applications.

2. Results and discussion

As revealed in Fig. 2, the designed improvement strategy for the thermoelectric performance of STO is divided into two consecutive steps: co-doping and compositing. Firstly, STO was transformed from an insulator to a semiconductor by electron-doping: the B-site (Ti⁴⁺) was substituted by Nb⁵⁺ and the A-site (Sr²⁺) was substituted by La³⁺. The experimental results and electronic structure calculations both verify that the La–Nb co-doped STO polycrystal showed measurable σ at room temperature. Secondly, to further synergistically improve n and μ, we composited the optimized La–Nb co-doped STO with TiB₂ with excellent σ. Combining co-doping and compositing, the σ and thermoelectric performance accomplished a striking enhancement in a broad temperature range.

Fig. 2 Roadmap towards the high thermoelectric performance achieved in the SrTiO₃-based samples via co-doping and modulation doping.

2.1. Transforming STO from an insulator to a semiconductor through increasing carrier concentration via Nb-La co-doping

According to the XRD pattern shown in Fig. 3, the diffraction peaks of all the SrTi_1−xNb_xO₃ (x = 0.1, 0.125, 0.15, 0.175) samples matched with the standard PDF card (PDF#35-0734) of STO, indicating that STO-based polycrystals were successfully synthesized by the solid-state reaction (SSR) without any impurity phase. Since the ion radius of Nb⁵⁺ (0.64 Å) is slightly larger than that of Ti⁴⁺ (0.61 Å), the lattice constants (Fig. 3(b)) increased gradually with increase in doping content.

Fig. 3 SrTi_1−xNb_xO₃ (x = 0–0.175): (a) XRD patterns and (b) lattice constant.

Fig. 4 displays the thermoelectric properties of SrTi_1−xNb_xO₃, revealing the transformation from insulator to semiconductor at 473–923 K with room-temperature insulativity via Nb doping. The σ (Fig. 4(a)) of SrTi_1−xNb_xO₃ showed a positive correlation with temperature, and generally increased with increasing doping content. σ reached ∼1.9 S cm⁻¹ for the SrTi_0.85Nb_0.15O₃ sample at 923 K. Fig. 4(b) shows that the S values of all samples at 473–923 K are negative, indicating that STO can be transformed from an insulator to an n-type semiconductor via electron-doping. The absolute values of all S are greater than 280 μV K⁻¹, verifying the development potential of STO due to its high |S| in oxide thermoelectric materials.

Fig. 4 Thermoelectric performance of SrTi_1−xNb_xO₃ (x = 0–0.175): (a) σ; (b) S; (c) PF; (d) κ_tot; (e) κ_lat; (f) ZT.

The decrease of |S| (absolute value of the Seebeck coefficient) and increase of σ are both due to the increased n via electron-doping.²⁹ Benefiting from the improved σ, the PF of all samples (Fig. 4(c)) shows enhanced electrical transport properties at high temperatures. The total thermal conductivity (κ_tot) (Fig. 4(d)) of the Nb-doped samples is depressed compared with that of un-doped SrTiO₃ due to the enhanced phonon scattering after introducing defects via doping.^30,31 The small difference between κ_tot and κ_lat seen in Fig. 4(e) indicates that lattice vibration is the main mechanism of heat transfer in the SrTi_1−xNb_xO₃ polycrystal, and that the electrical properties of SrTi_1−xNb_xO₃ are still inferior. Connected with the simultaneously enhanced electrical transport and depressed thermal properties, the ZT_max value (Fig. 4(f)) of SrTi_1−xNb_xO₃ (x = 0.1, 0.125, 0.15, 0.175) increased from that of an insulator in undoped STO to ∼0.009 for SrTi_0.85Nb_0.15O₃ at 923 K, and the ZT_ave value (Fig. S2, ESI†) was ∼0.003 for SrTi_0.85Nb_0.15O₃ at 473–923 K.

Due to the inferior electrical properties and the room-temperature insulativity of SrTi_1−xNb_xO₃, La–Nb co-doping was introduced to further increase the electrical transport properties of SrTi_0.85Nb_0.15O₃ over a wide temperature range. The XRD patterns of Sr_1−yLa_yTi_0.85Nb_0.15O₃ (y = 0, 0.1, 0.125, 0.15) in Fig. 5(a) suggest that the La–Nb co-doped STO purity phase was synthesized. The measured band gap of Sr_1−yLa_yTi_0.85Nb_0.15O₃ (Fig. 5(b)) showed a slight increase compared with that of SrTi_0.85Nb_0.15O₃, consistent with the theoretical calculation, which will be discussed later.

Fig. 5 Structural characterization of Sr_1−yLa_yTi_0.85Nb_0.15O₃ (y = 0–0.15): (a) XRD patterns and (b) absorption coefficient from the Kubelka–Munk method.

The σ of the Sr_1−yLa_yTi_0.85Nb_0.15O₃ samples (Fig. 6(a)) increased with temperature, reflecting good semiconductor behavior and did not reach a peak value within the tested temperature range. Besides, the σ values of Sr_1−yLa_yTi_0.85Nb_0.15O₃ are significantly superior to those of SrTi_0.85Nb_0.15O₃. It is worth noting that the σ of all the La–Nb co-doped samples is measurable at room temperature. All the |S| values indicated that the samples are heavily doped semiconductors, almost linearly proportional to temperature (Fig. 6(b)). Meanwhile, the depressed |S| and enhanced σ for all the La–Nb co-doped samples indicates enhanced n through La and Nb co-doping. Therefore, the PF value (Fig. 6(c)) reached ∼0.9 μW cm⁻¹ K⁻² for the Sr_0.875La_0.125Ti_0.85Nb_0.15O₃ sample at 923 K. On account of the measured σ and S, we acquired the weighted mobility (μ_W) (Fig. 6(d)) of the La–Nb co-doped STO polycrystal. The μ_W of Sr_1−yLa_yTi_0.85Nb_0.15O₃ increased monotonously with increase in temperature, possibly due to the thermal activation of the grain boundary.^32,33

Fig. 6 Electrical transport properties of Sr_1−yLa_yTi_0.85Nb_0.15O₃ (y = 0–0.15): (a) σ; (b) S; (c) PF; (d) μ_W.

To further understand the doping effect of Nb and La in STO, first-principles calculations were conducted. Compared with the matrix of STO, the introduction of La or Nb can move the E_F into the conduction band, mainly due to the additional electrons introduced by Nb and La. As a result, the n obviously improved compared with that of pristine STO. It is worth noting that the E_F went further into the conduction band with La–Nb co-doping (Fig. 7(c)), and the band gap increased slightly, in accordance with the measured band gap outcome (Fig. 5(b)). Fig. 7(d) shows the corresponding total density of states (TDOS) of Sr₈Ti₈O₂₄, Sr₇LaTi₈O₂₄, Sr₇LaTi₇NbO₂₄ and Sr₇LaTi₇NbO₂₄, and a clear entrance of E_F into the conduction band in doped systems is observed. The TDOS at the E_F is non-zero regardless of La, Nb and La–Nb co-doping, indicating that the doped material has metallic conductivity.

Fig. 7 Electronic band structures and TDOS calculated for the SrTiO₃-based materials: (a) Sr₇LaTi₈O₂₄; (b) Sr₈Ti₇NbO₂₄; (c) Sr₇LaTi₇NbO₂₄; and (d) TDOS near the bottom of the conduction band.

As displayed in Fig. 8(a), the κ_tot for Sr_1−yLa_yTi_0.85Nb_0.15O₃ showed a negative correlation with La content in the tested temperature range, going from ∼3.33 W m⁻¹ K⁻¹ in SrTi_0.85Nb_0.15O₃ to ∼2.61 W m⁻¹ K⁻¹ of Sr_0.875La_0.125Ti_0.85Nb_0.15O₃ at 473 K. The decreased κ_tot is due to the intensive phonon scattering by the point defects due to the mass contrast and lattice local strain introduced by co-doping. Benefiting from the enhanced electrical properties and the weakened thermal transport, the ZT_max value reached ∼0.033 at 923 K (Fig. 8(b)).

Fig. 8 Thermoelectric transport properties of Sr_1−yLa_yTi_0.85Nb_0.15O₃ (y = 0–0.15): (a) κ_tot; (b) ZT.

2.2. Synergistically enhancing the electrical transport of La–Nb co-doped STO through modulation doping via compositing TiB₂

To further synergistically enhance the n and μ_W over the entire tested temperature range, we composited Sr_0.875La_0.125Ti_0.85Nb_0.15O₃ with TiB₂, which possesses excellent σ (1 × 10⁵ S cm⁻¹), high melting point (3498 K) and an oxidation resistance temperature in air of 1273 K.^34,35 This afforded an intermetallic compound with a hexagonal graphite-like two-dimensional network structure, where B and Ti atomic planes appear alternately.³⁶ As depicted in Fig. 9(a), the trend of σ with temperature shows that the semiconductor behavior gradually weakens and the metallic behavior gradually increases with increase in TiB₂ concentration (z% from 0% to 5%). Particularly, the σ of Sr_0.875La_0.125Ti_0.85Nb_0.15O₃ with 1% and 2% TiB₂ showed monotonic positive correlation with temperature, while the σ of the 3% TiB₂ composite increased first and then decreased, and the electrical properties of the 4% and 5% TiB₂ composites monotonously decreased with increasing temperature. Additionally, the S (Fig. 9(b)) decreased from ∼−212 μV K⁻¹ for Sr_0.875La_0.125Ti_0.85Nb_0.15O₃ to ∼−48 μV K⁻¹ for Sr_0.875La_0.125Ti_0.85Nb_0.15O₃ + 4% TiB₂ at room temperature, and from ∼−321 μV K⁻¹ for Sr_0.875La_0.125Ti_0.85Nb_0.15O₃ to ∼128 μV K⁻¹ for Sr_0.875La_0.125Ti_0.85Nb_0.15O₃ + 4% TiB₂ at 923 K, indicating the enhancement of electrical transport properties. Therefore, the PF (Fig. 9(c)) of all samples was enhanced over the whole temperature range under investigation, especially for the sample with 4% TiB₂ where it reaches the highest value of ∼11 μW cm⁻¹ K⁻² at ∼675 K. Fig. 9(d) shows that the introduction of TiB₂ could effectively increase the n and the μ_W, leading to optimization of the σ of STO. The synergic optimization of the μ_W and n may be due to modulation doping. The different carrier transport properties of three-dimensional modulation doping models and ordinary high-density doping are shown in Fig. 9(e and f). In regular doping, the high-density carrier concentration would reduce μ due to the increased ionized impurity scattering. Comparatively, modulation doping is composed of a high-density carrier concentration phase and a low-density carrier concentration phase, which could depress the ionized impurity scattering and enhance μ, synergistically improving n and retaining a high μ. The modulation doping method has already been utilized in many thermoelectric systems, such as SnSe,³⁷ BiCuSeO,³⁸ p-type SiGe,³⁹ P-type ZnSb,⁴⁰ and n-type TeSb₂.⁴¹

Fig. 9 Electrical transport properties for Sr_0.875La_0.125Ti_0.85Nb_0.15O₃ + z% TiB₂ (z = 0–5): (a) σ; (b) S; (c) PF; (d) n and μ. (e) Modulation-doped semiconductor and (f) regular doped semiconductor.

As shown in Fig. 10(a), the electric thermal conductivity (κ_ele) of Sr_0.875La_0.125Ti_0.85Nb_0.15O₃ + z% TiB₂ (z = 0–5) exhibited a significant increase with increasing TiB₂ content, going from ∼0 W m⁻¹ K⁻¹ in the Sr_0.875La_0.125Ti_0.85Nb_0.15O₃ sample to ∼1.72 W m⁻¹ K⁻¹ in the Sr_0.875La_0.125Ti_0.85Nb_0.15O₃ + 4% TiB₂ sample at 300 K. According to Fig. 10(b), the heightened electrical transport properties through modulation doping boost the quality factor (B) of these samples in the tested temperature range. Therefore, the sample with 4% TiB₂ obtained a ZT_max value of ∼0.23 at 923 K (Fig. 10(c)), and TiB₂ improved the thermoelectric performance of the STO-based materials over the complete tested temperature range. The optimal performance of the Nb-doped, La–Nb co-doped and modulation-doped samples, with ZT_ave values of ∼0.003, ∼0.013, and ∼0.15 at 473–923 K, respectively (Fig. 10(d)), showed the significant benefits of the synergetic improvement of n and μ.

Fig. 10 Thermal transport properties of Sr_0.875La_0.125Ti_0.85Nb_0.15O₃ + z% TiB₂ (z = 0–5): (a) σ; (b) quality factor B; (c) ZT; and (d) average ZT of SrTi_0.85Nb_0.15O₃, Sr_0.875La_0.125Ti_0.85Nb_0.15O₃ and Sr_0.875La_0.125Ti_0.85Nb_0.15O₃ + 4% TiB₂.

We compared the thermoelectric performance of the materials in this work with that of other reported work on STO systems, including SrTi_0.8Nb_0.2O₃,³¹ Sr_0.93Bi_0.07TiO₃,⁴² (La_0.12Sr_0.88)_0.95TiO_3−δ,⁴³ Sr_0.87Dy_0.07Nd_0.06TiO₃⁴⁴ and Sr_0.92La_0.08TiO₃,⁴⁵ as shown in Fig. 11. Due to the significantly heightened σ and PF values over the whole tested temperature range, the ZT_max of our work showed strong competitiveness among the STO systems, indicating that STO has the potential to become an excellent thermoelectric material.

Fig. 11 Thermoelectric properties from this work and from other SrTiO₃-based materials: (a) σ; (b) PF; (c) κ_tot; (d) ZT.^31,42–45

3. Conclusion

In this study, the thermoelectric properties of SrTiO₃ were gradually enhanced by synergistically improving electrical transport by increasing n and retaining high μ via E_F regulation and modulation doping through co-doping and compositing. Firstly, we introduced Nb doping to adjust the E_F of the pristine STO material to enter the conduction band, transforming it from an insulator to a semiconductor. Secondly, the La–Nb co-doped samples showed obvious semiconductor behavior even at 300 K due to the enhanced n. Thirdly, TiB₂ compositing simultaneously improved the n with high μ in SrTiO₃ through modulation doping. Therefore, a promising new kind of n-type STO-based polycrystal was obtained through co-doping and compositing, and the ZT_max value of Sr_0.875La_0.125Ti_0.85Nb_0.15O₃ + 4% TiB₂ reached ∼0.23 at 923 K, with a ZT_ave ∼0.15 at 473–923 K. Despite the advancements mentioned above, there is still potential for future research progress, such as reducing thermal conductivity through enhanced phonon scattering.

Conflicts of interest

There are no conflicts of interest to declare.

Acknowledgements

This work was supported by the National Key Research and Development Program of China (2018YFA0702100 and 2018YFB0703600), National Natural Science Foundation of China (52002042), the National Science Fund for Distinguished Young Scholars (51925101), China Postdoctoral Science Foundation (2021M690280), Natural Science Foundation of Chongqing, China, cstc2019jcyj-msxmX0554, National Postdoctoral Program for Innovative Talents (BX20200028), and the high performance computing (HPC) resources at Beihang University.

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Footnote

† Electronic supplementary information (ESI) available. See DOI: 10.1039/d2tc00719c

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