First-principles calculations and high thermoelectric performance of La–Nb doped SrTiO₃ ceramics

Abstract

SrTiO₃ is a promising thermoelectric material for high temperature application of waste heat electrical generation. However, its dimensionless figure of merit (zT) is restricted by its high thermal conductivity, which results from the simple perovskite structure and light elements of SrTiO₃. In this paper, we successfully obtained complex structured bulk SrTiO₃ with a TiO₂ second phase and a porous structure by tuning the doping ratios of the heavy elements La and Nb, resulting in a low thermal conductivity of 1.97 W m⁻¹ K⁻¹ and a high zT value of 0.31 at 1050 K. The first-principles calculation was utilized to calculate the formation energy, effective mass and electron band structure of La–Nb co-doped SrTiO₃, and the effects of the parameters on the thermoelectric properties were also discussed. We found that the doping ratio of La to Nb changed the electron band structure and controlled the formation of the TiO₂ second phase, which affected the electrical transport and thermal transport properties, respectively. The formation of the in situ TiO₂ second phase was related to the high formation energy derived from the high Nb concentration. These results offer an approach for the design of other thermoelectric materials with low thermal conductivity and a high power factor.

---

1. Introduction

In recent years, clean and efficient usage of energy sources has attracted increasing public attention. It is urgent to develop renewable energy resources to compensate for environmental pollution resulting from conventional fossil fuels and increasing energy demands, especially industrial waste heat.¹ Thermoelectric materials have been regarded as a potential energy conversion material, which can be used to directly convert waste heat into electrical energy. In addition, such thermoelectric energy conversion has the advantages of being nontoxic, environmentally friendly, low cost, without the introduction of moving parts, and so on. The energy conversion efficiency of a thermoelectric material is primarily evaluated by the dimensionless figure of merit zT = σS²T/κ_total, where σ, S, κ_total, and T represent the electrical conductivity, Seebeck coefficient, thermal conductivity and absolute temperature, respectively. A high zT can be obtained using a large σ and S as well as a small κ_total. However, these interdependent parameters need independent control.

Previous researchers have made efforts to improve the zT value by several ways. One successful strategy is to reduce the lattice thermal conductivity by structural modification and defect engineering, such as the introduction of nanostructures,² complex structures,³ point defects,⁴ dislocations,⁵ pores,⁶ and grain boundaries. Another route to improve the zT value is the enhancement of the power factor PF = S²σ, which can usually be realized by doping, band engineering and use of a heterojunction.^7–9 By using the above approaches, significant improvement in the zT values of many thermoelectric materials^10–15 has been achieved. Among classical oxides, SrTiO₃ is a potential thermoelectric material for high temperature applications due to its high Seebeck coefficient and good stability. However, its applications are limited by its low efficiency resulting from its high thermal conductivity. Table 1 summarizes the reported properties of several doped SrTiO₃ thermoelectric materials in previous studies, showing that almost all relatively large zTs were obtained in La or Nb single-doped SrTiO₃ materials, which are usually prepared by hot pressing, spark plasma sintering (SPS) or solid state reaction. The improvement of zT in SrTiO₃, however, is not significant due to its relatively high thermal conductivity. Although the introduction of structural modifications such as nanostructures,¹⁶ point defects¹⁷ and second phases¹⁸ into SrTiO₃ can decrease the thermal conductivity to some extent, it is hard to significantly decrease the thermal conductivity of SrTiO₃ using a single approach, where the simple perovskite structure and light elements of SrTiO₃ are the main reasons for the high thermal conductivity. Differing from the single-doping approach, the combination of heavy La and Nb co-doping, a second phase and pores can significantly change the microstructures and compositions of SrTiO₃ simultaneously, which is expected to decrease its thermal conductivity.

Table 1 Thermoelectric properties of doped SrTiO₃ materials obtained by different preparation methods

Composition	Processing conditions	zT	κ total (W m^−1 K^−1)
Sr2Ti1.6Nb0.4O7, Sr2.85Gd0.15Ti2O7, Sr2.85Sm0.15Ti2O7, Sr2.85La0.15Ti2O7 (ref. 19)	Hot pressing, Ar flow, 1723 K, 2 h	0.14, 0.24, 0.22, 0.15, 1000K	2.3
Sr0.94Y0.06TiO3 (ref. 20)	Hot pressing, Ar, 1627 K, 1 h, 31.2 MPa	0.14, 659 K	4.3
Sr0.9Y0.1TiO3 (ref. 21)	Hot pressing, Ar, 1673 K, 2 h, 25 MPa	0.14, 870K	5.3
Sr2.7Ga0.3Ti1.9Nb0.1O7 (ref. 22)	Hot pressing, Ar flow, 1673–1748 K, 1 h, 34 MPa	0.15, 1000 K	2.2
Sr0.8La0.08Dy0.12TiO3 (ref. 23)	Ar/5% H2, 1733 K, 4 h	0.36, 1076 K	2.3
Sr0.92La0.08TiO3 (ref. 24)	SPS, vacuum, 1573 K, 5 min, 34 MPa	0.37, 1045 K	2.2
SrTi0.8Nb0.2O3 epitaxial film^25	Pulsed laser deposition, 973 K	0.37, 1000 K	—
Sr0.1La0.6TiO3−δ (ref. 26)	N2/5% H2, 1773 K, 6 h, cold isostatic pressing at 200 MPa	0.4, 973 K	2.4

---

It is known that the first-principles calculation has been extensively used to calculate the formation energy, effective mass and electron band structure.²⁷ The formation energy can be used to characterize the stability of a compound. And then, the stability of a compound, the effective mass and electron structure are useful to determine the electron transport properties of thermoelectric materials. To the best of our knowledge, however, there has been no report so far focusing on first-principles calculations of the formation energy, effective mass and electron band structure of La and Nb co-doped SrTiO₃ materials.

In this paper, we first calculate the formation energy, effective mass and electron band structure of La–Nb doped SrTiO₃ using the first principles approach and then discuss the effects of the parameters on the thermoelectric properties. Based on the results of the calculation, we design desired n-type bulk SrTiO₃ with a reduced lattice thermal conductivity of 1.97 W m⁻¹ K⁻¹ by introducing La and Nb dopants, a second phase and pores, resulting in a high zT value of 0.31 at 1050 K.

2. Experimental procedure

2.1 Model and calculation method

The ideal SrTiO₃ has a cubic perovskite structure with a space group of Pm3̄m. The ground state atomic and electronic structures of La and Nb co-doped SrTiO₃ were calculated by first-principles density functional theory using CASTEP.²⁸ These calculations are based on density functional theory (DFT) with the generalized-gradient approximation (GGA) and the plane-wave pseudo potentials as implemented in CASTEP.²⁹ The exchange–correlation energy can be described by the Perdew–Burke–Ernzerhof (PBE) exchange–correlation function. The valence atomic configurations are 4s²4p⁶5s² for Sr, 2s²2p⁴ for O, 3s²3p⁶3d²4s² for Ti, 4s²4p⁶4d⁴5s¹ for Nb, and 5s²5p⁶5d¹6s² for La, respectively. The plane-wave cutoff energy is 340 eV, and the Monkhorst–Pack k-mesh is 3 × 3 × 3. The calculation precision was converged to be 1.0 × 10⁻⁵ eV per atom. All atoms are allowed to relax until the force on each atom is below 0.3 eV nm⁻¹, the internal stress is below 0.05 GPa, and the displacement of each atom is below 0.0001 nm simultaneously.

The total energy and formation energy of all samples were calculated using the following equation:^30,31

E_F = E_{SrTiO3:La2m–Nb2n} − E_SrTiO3 − μE_La2O3 − νE_Nb2O5 + 2μE_SrO + 2νE_TiO2 (1)

where E_{SrTiO3:La2m–Nb2n} and E_SrTiO3 are the total energies of La–Nb co-doped and un-doped SrTiO₃, respectively. E_La2O3, E_Nb2O5, E_SrO, E_TiO2 are the ground state energies of the La₂O₃, Nb₂O₅, SrO and TiO₂, respectively; μ and ν are the number of La₂O₃ and Nb₂O₅ molecules in the reactants, respectively.

2.2 Materials preparation

The Sr_1−xLa_xTi_1−yNb_yO₃ (0.03 ≤ x ≤ 0.1 and 0.03 ≤ y ≤ 0.2) powders were fabricated via a hydrothermal method. Table 1 lists the raw materials and their purity used in the experiments. First, Sr(NO₃)₂ (purity: 99.5%) and La(NO₃)₃·6H₂O (purity: 99%) were dissolved in deionized water. Then, Ti[OCH(CH₃)₂]₄ (purity: 98%) and NbCl₅ (purity: 99%) were dissolved in ethylene glycol to form uniform solutions and NaOH (purity: 96%) was dissolved in deionized water. Eventually, three solutions were mixed and slowly stirred with an electromagnetic agitator in a beaker, ensuring that the pH value of the mixed solution was adjusted to 13. After 5 minutes, the solution was decanted into a Teflon autoclave and reacted at 180 °C for 24 h. After the autoclave was cooled down to room temperature, the obtained precipitate was washed several times with deionized water and glacial acetic acid before being dried at 80 °C. The obtained solid blocks were pulverized into powders by using an agate mortar and pestle.

The obtained powders were sintered using a hot pressing sintering furnace (ZT-60-20Y, Chenhua, China). The preceding powders were filled in a cylindrical graphite die and pressed into a disk of 18 mm in diameter under a uniaxial pressure of 20 MPa using a graphite punch, followed by hot pressing sintering at 1573 K for 2 hours in a vacuum. Graphite foil (with a thickness of 0.15 mm) was placed into graphite mold gaskets before filling with the powders so that the disk can be easily taken out. All samples were polished down each side to ensure complete removal of the graphite foil. The prepared samples are Sr_0.97La_0.03Ti_0.97Nb_0.03O₃, Sr_0.95La_0.05Ti_0.95Nb_0.05O₃, Sr_0.93La_0.07Ti_0.93Nb_0.07O₃, Sr_0.9La_0.1Ti_0.9Nb_0.1O₃, Sr_0.95La_0.05Ti_0.9Nb_0.1O₃, Sr_0.9La_0.1Ti_0.95Nb_0.05O₃, and Sr_0.9La_0.1Ti_0.8Nb_0.2O₃, which are hereinafter referred to as La3Nb3, La5Nb5, La7Nb7, La10Nb10, La5Nb10, La10Nb5, and La10Nb20, respectively. The densities (ρ) of the sintered samples are higher than 93% of the theoretical density value except for the La10Nb20 sample with a density of 82%, as determined by the Archimedes method, which is 8% lower than the others.

2.3 Sample characterization

The phase composition was identified by X-ray diffraction (XRD, D/MAX 2500 PC, Rigaku) with Cu Kα doublet radiation. Rietveld refinements of the XRD patterns for the doped SrTiO₃ bulk were carried out using General Structure Analysis System (GSAS) software.³² The refinements were executed with the ICSD 27045 (cubic crystal structure with the space group Pm3̄m) as a reference for the structural model. The microstructures in the SrTiO₃ bulk were characterized by field-emission scanning electron microscopy (SEM, JSM7000F, JEOL), with the SrTiO₃ powders being characterized by transmission electron microscopy (TEM, JEM2010, JEOL Ltd.). The chemical composition of the bulk samples was acquired using an energy dispersive spectrometer (EDS). X-ray photoelectron spectroscopy (XPS, ESCALAB 250Xi, Thermo Fisher Scientific) was used to analyze the surface elemental compositions and valence states of the elements. The thermal diffusivity coefficient (D) was determined using a laser flash apparatus (LFA 427, Netzsch, Germany). The specific heat capacity (C_p) was measured using a differential scanning calorimeter (DSC 200 F3, Netzsch, Germany) under a flow of argon. The thermal conductivity was calculated by using the equation κ = DρC_p. The Seebeck coefficient and electrical conductivity were measured simultaneously using a Seebeck coefficient and electric resistance measuring system (LRS-3, Linseis, Germany). The test temperature range was between 300 and 1050 K, and the sealed sample chamber was filled with helium gas. The carrier concentration (n) and Hall mobility (μ_H) were measured using a Hall measurement system from 300 to 800 K. As for the La10Nb20 sample, the extremely high carrier concentrations lead to a Hall voltage too small to be measured accurately, so we do not show values of n and μ_H in this paper.

3. Results and discussion

3.1 Geometry optimization results

The lattice parameters, total energy, formation energy, electron effective mass and carrier concentrations for Sr_1−xLa_xTi_1−yNb_yO₃ calculated from first principles are presented in Table 2.

Table 2 Lattice parameter, total energy, formation energy, electron effective mass and carrier concentration of SrTiO₃ with varying doping concentration calculated from first principles

Sample	a/Å	E/eV	E F/eV	m*/m0	n/10^21 cm^−3
SrTiO3	3.946	−3758.94	—	4.49	—
SrTi0.9Nb0.1O3	3.959	−3753.69	−2.34	6.13	1.60
Sr0.9La0.1TiO3	3.950	−3761.33	−5.48	4.28	1.62
Sr0.95La0.05Ti0.95Nb0.05O3	3.955	−3757.66	7.17	7.40	1.61
Sr0.95La0.05Ti0.9Nb0.1O3	3.961	−3755.03	7.09	5.42	2.41
Sr0.9La0.1Ti0.95Nb0.05O3	3.957	−3758.99	−6.23	6.32	2.42
Sr0.9La0.1Ti0.9Nb0.1O3	3.963	−3756.35	−6.76	5.20	3.21
Sr0.9La0.1Ti0.8Nb0.2O3	3.973	−3751.05	21.34	4.91	4.77

---

The calculated lattice parameter for pure SrTiO₃ is a = 3.946 Å, in good agreement with the experimental value of a = 3.905 Å.³³ Although the ionic radius of La³⁺ (1.36 Å) is smaller than that of Sr²⁺ (1.44 Å) and Nb⁵⁺ (0.64 Å), it is larger than that of Ti⁴⁺ (0.605 Å);³⁴ the lattice parameters for all La–Nb-doped SrTiO₃ samples are larger than that for the pure sample, which may be related to the increasing ionic repulsive force arising from the excess positive charge of La³⁺ and Nb⁵⁺. The effect of Nb on the increase in lattice parameter is larger than that of La because the ionic radius of Nb⁵⁺ is larger than that of Ti⁴⁺, which further results in a large formation energy. The doping ratio of La to Nb affects the formation energy. Except for the formation energies of Sr_0.9La_0.1Ti_0.8Nb_0.2O₃, Sr_0.95La_0.05Ti_0.95Nb_0.05O₃ and Sr_0.95La_0.05Ti_0.9Nb_0.1O₃, the formation energies of the other samples are smaller than that of SrTi_0.9Nb_0.1O₃, indicating that these samples are more easily obtained by experiment, which is also confirmed by the fact that the SrTi_0.9Nb_0.1O₃ has been previously successfully synthesized by several experimental methods.^35,36

The critical carrier concentration in the degenerate SrTiO₃ semiconductor is n_c = 7.95 × 10¹⁰ cm⁻³, which can be calculated by the following equation:³⁷

a_Hn_c^1/3 = 0.26 (2)

where a_H and n_c are the Bohr radius and critical concentration for the degenerate semiconductor, respectively. All carrier concentrations (n) in the present study are > 10²¹ cm⁻³ (Table 2), which is far larger than the critical value of n_c = 7.95 × 10¹⁰ cm⁻³, suggesting that all the samples in the present study are a degenerate semiconductor. This is also confirmed by energy band structure analysis, as shown in Fig. 1. The Fermi level of pure SrTiO₃ lies on the top of the valance band, while the Fermi level of La and Nb co-doped SrTiO₃ shifts into the conduction band when n_c ≥7.95 × 10¹⁰ cm⁻³, following which the sample changes into a degenerate semiconductor. The degree of the shift in the Fermi level depends on the ratio of La to Nb, indicating that the La and Nb dopants play different roles in the electron transport properties.

Fig. 1 Energy band structure for (a) SrTiO₃, (b) Sr_0.95La_0.05Ti_0.95Nb_0.05O₃, (c) Sr_0.9La_0.1Ti_0.9Nb_0.1O₃ and (d) Sr_0.9La_0.1Ti_0.8Nb_0.2O₃.

The conduction band minimum (CBM) shows a flat band, which may be induced by the large electron effective mass. The electron effective mass m* can be calculated by the following equation:³⁸

where h is the Planck constant, κ is the wave vector, and the energy E(κ) can be estimated from the second-order derivatives in the G direction of the curves at the CBM. The electron effective mass also depends on the ratio of the dopants.

Fig. 2 shows the total density of states (DOS) and contribution of each component of the unit cell for pure and doped SrTiO₃, respectively. The valance band maximum (VBM) of either pure or doped SrTiO₃ is composed of O 2p states, with its CBM mainly composed of Ti 3d states, in good agreement with a previous report.³⁹ On the other hand, the Nb 4d and La 5d of doped SrTiO₃ show some contributions to the conduction band, with the contribution of the former being larger than that of the latter. This result indicates that the electrical transport properties can be optimized by the ratio of La to Nb.

Fig. 2 Total density of states (DOS) and contribution of each component of the unit cell for (a) SrTiO₃, (b) Sr_0.95La_0.05Ti_0.95Nb_0.05O₃, (c) Sr_0.9La_0.1Ti_0.9Nb_0.1O₃ and (d) Sr_0.9La_0.1Ti_0.8Nb_0.2O₃.

3.2 Characterization of SrTiO₃ powder and bulk samples

Fig. 3(a) shows the XRD patterns of hydrothermally synthesized SrTiO₃ powders and pure SrTiO₃ from the Powder Patterns Database (PDF# 84-0444). All the powder diffraction peaks of the La and Nb co-doped powders conformed to the cubic perovskite SrTiO₃ structure with the space group Pm3̄m and no impurity phase was observed within the detection limit of XRD. However, after hot pressing, a TiO₂ impurity phase appears for all doped SrTiO₃ bulks, as shown in Fig. 3(b). A shift to lower angles is also observed for all the SrTiO₃ and TiO₂ peaks. The relative amount of TiO₂ can be estimated using the following equation:⁴⁰where I_STO and I_TO are the intensities of the strongest XRD peak for SrTiO₃ and TiO₂; K_STO and K_TO are the reference intensities for SrTiO₃ and TiO₂, respectively. As shown in Table 3, the content of the TiO₂ second phase is related to the doping concentration, which can be explained from the formation energy. The La10Nb20 sample contains the maximum amount of the TiO₂ second phase due to its large formation energy, as shown in Table 2.

Fig. 3 (a) XRD patterns for powders and (b) XRD patterns for bulk samples. (c) Doping concentration dependence of the lattice parameter of SrTiO₃ bulk samples; the red circle shows the data obtained from Rietveld refinement using GSAS software, and the blue triangle and green square show the data calculated from the ion ratio using eqn (6) based on the assumption of the formation of equal amounts of Ti³⁺ with total doped elements and analytic content of Ti³⁺ from XPS, respectively.

Table 3 The effective mass m*/m at room temperature, density, ratio of Ti³⁺/Ti⁴⁺ and relative content of TiO₂ calculated from the XRD data measured for bulk samples

Sample	m*/m0	ρ (g cm^−3)	[Ti^3+]/[Ti^4+]	TiO2 content
La3Nb3	4.7258	4.85	0.067	—
La5Nb5	5.5203	5.00	0.120	—
La7Nb7	6.2033	5.03	0.193	3.81%
La5Nb10	6.0434	4.78	0.179	—
La10Nb5	5.8432	5.03	0.163	—
La10Nb10	5.3524	5.05	0.276	1.86%
La10Nb20	5.4982	4.50	0.351	7.76%

---

Fig. 3(c) shows the lattice parameters of the La and Nb co-doped SrTiO₃ samples derived from the Rietveld refinement (red circle), which increase proportionally with doping concentration (z, z = x + y). This variation tendency is in agreement with the result obtained from the first principles calculation (Table 2). This increase in the lattice parameter can be attributed to the interaction of two primary factors. First, the larger-sized Nb⁵⁺ ions (0.64 Å) substitute for the smaller Ti⁴⁺ ion (0.605 Å), and the smaller-sized La³⁺ ions (1.36 Å) substitute for the larger Sr²⁺ (1.44 Å) ions in the perovskite structure. Second, to compensate the excess electrons introduced by La and Nb co-donor doping, a partial conversion of the smaller Ti⁴⁺ ions to larger Ti³⁺ ions (0.67 Å) occurs.³⁴ The coexistence of a mixed valence state couple of Ti⁴⁺/Ti³⁺ can be confirmed by the Ti 2p XPS spectra in Fig. 4. All the binding energies were corrected using the C 1s peak (binding energy = 284.8 eV) as a reference and a Shirley background was used in the peak fitting. The fitting results show two broad peaks, which can be fitted using the two valence states Ti⁴⁺ and Ti³⁺. Table 3 lists the Ti³⁺ content calculated from the relative peak area ratio of Ti⁴⁺ and Ti³⁺, which depended on the doping concentration. The Ti³⁺ content in our samples presents an increasing tendency with the increasing total doping concentration. To validate the correctness of the above conjecture, an empirical equation is used to estimate the lattice parameters of cubic SrTiO₃ perovskites as follows:⁴¹

where a and a₀ are the lattice parameters of the doped and pure SrTiO₃, x_i is the mole fraction of the cation i substituting for the host cation; ΔR_i and ΔZ_i are the difference in the ionic radius and in the charge between the substituting cation i and the host cation, respectively. For our samples, the equation becomes

a = a₀ + 0.063x_Ti³⁺ − 0.076x_La³⁺ + 0.037x_Nb⁵⁺ (6)

Fig. 4 The XPS spectra of Ti 2p of samples with varying doping concentration. (a) La3Nb3, (b) La5Nb5, (c) La7Nb7, (d) La5Nb10, (e) La10Nb10 and (f) La10Nb20.

The theoretically calculated value (blue triangle in Fig. 3(c)) is based on the assumption of the formation of equal amounts of Ti³⁺ with total doped elements and ignoring the effect of oxygen vacancies. The analytically calculated value (green square in Fig. 3(c)) based on the analytic content of Ti³⁺ from XPS is extremely close to the experimental value (red circle), as shown in Fig. 3(c). This suggests that the above conjecture is correct. The calculated value is a little bit larger than the experimental value because a part of Ti³⁺ coming from TiO₂ is not subtracted during the calculation.

Fig. 5(a) shows a low magnification TEM image for the La10Nb20 powder. The individual grains show an irregular laminate shape with a size of 25 nm. The high-resolution TEM lattice fringe image shows the lattice fringes to be 0.27 nm, which corresponds to the typical (110) facets of cubic perovskite SrTiO₃ in Fig. 5(b). The inset in Fig. 5(b) shows the fast Fourier transformation (FFT) image of the square region in Fig. 5(b) along the [110] axis. The SEM images of La–Nb co-doped SrTiO₃ bulk samples are shown in Fig. 6. After sintering, the SrTiO₃ crystals present irregular polyhedral morphologies with an average grain size of 2–10 μm. It is clear that nano-crystallites grow during the sintering process.

Fig. 5 TEM images of the La10Nb20 powder sample. (a) Low magnification TEM image and (b) HRTEM image; the inset shows the FFT image of the red square region.

Fig. 6 SEM images of the La–Nb doped SrTiO₃ bulk samples. (a) La3Nb3, (b) La5Nb5, (c) La7Nb7, (d) La5Nb10, (e) La10Nb10 and (f) La10Nb20.

The grain size of the bulk sample increases with increasing doping concentration. Fig. 7 shows the TEM-EDS mapping and SAED pattern of the La10Nb20 sample. The precipitated TiO₂ is observed clearly from the TEM-EDS mapping image (Fig. 7(a)), which is consistent with the XRD results discussed above. The electron diffraction patterns verify that the grain marked with the red circle is the perovskite SrTiO₃ (Fig. 7(b)) and that the grain marked with the black square is rutile TiO₂ (Fig. 7(c)). Moreover, a typical structure of small TiO₂ grains surrounded by SrTiO₃ grains is observed using a combination of TEM-EDS analysis and electron diffraction patterns (Fig. 8). Pores are formed near the interfaces between TiO₂ and SrTiO₃ grains, indicating that the precipitation of TiO₂ promotes the formation of the pores.

Fig. 7 Microstructure of the La10Nb20 bulk sample: (a) HAADF-STEM image and elemental mapping for Sr, Ti, O, Nb and La; SAED patterns for the (b) red circle and (c) black square in (a).

Fig. 8 TEM image, TEM-EDS line-scan analyses, TEM-EDS mapping and electron diffraction pattern for the (a) La10Nb10 and (b) La10Nb20 bulk samples.

3.3 Thermoelectric properties of SrTiO₃ bulk samples

As shown in Fig. 9(a), the Seebeck coefficients (S) of all the samples are negative, indicating that electrons are the predominant charge carriers. With increasing temperature, the absolute values of the Seebeck coefficient (|S|) increase monotonously from 300 to 1000 K. Moreover, when the doping concentration ≤ 20 mol%, with increasing doping level, the |S| decreases, which is consistent with the result obtained for the Nb-doped SrTiO₃ epitaxial film,²⁵ as shown in Fig. 9(b). This can be attributed to the impurity ionization of donor impurities La³⁺ and Nb⁵⁺, leading to an increment in the electron concentration. However, the La10Nb10 and La10Nb20 samples show similar S, which may be related to the large amount of the second phase in La10Nb20, resulting in a decrease of its carrier concentration. The electron concentration obtained from Hall measurements (Fig. 9(c)) exceeds 10²⁰ cm⁻³ and does not significantly depend on the temperature in all the samples, showing a typical trait of degenerate semiconductors. On the other hand, the carrier concentration almost tends to increase with increasing doping level of La and Nb. The measured carrier concentrations are smaller than that obtained from the corresponding first-principles calculation, which may be closely related to the presence of second phases and Ti³⁺ and Nb⁴⁺ ions. At such high electron concentrations (≥10²⁰ cm⁻³), all the samples become an n-type degenerate semiconductor, as discussed in Section 3.1, with a Seebeck coefficient that can be demonstrated by the following equation:³where k_B,e, h, m* and n are the Boltzmann constant, electron charge, Planck constant, effective mass, and carrier concentration, respectively. The value of |S| decreases with increasing carrier concentrations. Although |S| in the present study is lower than that reported by Ohta et al.,⁴² it is larger than that of other oxide thermoelectric materials, such as Na₂CoO₄,⁴³ due to its relatively large electron effective mass m*/m₀ (m₀ is the free electron mass).⁴⁴m*/m₀ for all the samples is estimated from the experimental n and S values, as displayed in Table 3. The experimentally estimated m*/m₀ also varies with the doping ratio of La and Nb. The effective mass also satisfies the following equation:

m* = eτ/μ_H (8)

where e, τ, and μ_H are the electron charge, relaxation time and Hall mobility, respectively. Thus, the relaxation time is also affected by the dopant ratio of La and Nb.

Fig. 9 (a) Temperature dependence of Seebeck coefficient for double-doped SrTiO₃ samples. (b) Seebeck coefficient and electrical conductivity as a function of La and Nb concentrations at a temperature of 1000 K. (c) Temperature dependence of electrical conductivity, (d) carrier concentration, (e) Hall mobility and (f) power factor.

Fig. 9(d) reveals that the electrical conductivity (σ) of the samples increases with increasing the temperature up to 450 K, indicating a semiconductor property. At high temperatures above 450 K, the electrical conductivity decreases with increasing temperature and indicates a metallic behavior. As shown in the inset of Fig. 9(d), the electrical conductivity of all the samples decreases with a slope of T^−1.5 at a high temperature above 750 K, indicating that phonon scattering is the dominant mechanism. Similar variation trends for the electrical conductivity have also been reported for bulk Nd-doped SrTiO₃ and rare earth doped SrTiO₃.^45,46 To better understand the variation mechanism, we introduce the electrical conductivity formula σ = neμ_H, where n is the carrier concentration, e is the electron charge and μ_H is the carrier mobility. As shown in Fig. 9(e), μ_H gradually increases with increasing temperature at low temperature (T < 450 K) to allow the slope to be close to T^1.5, indicating that it is dominated by an impurity scattering mechanism. As the temperature increases above 450 K, μ_H decreases with a slope of T^−1.5, which shows a scattering mechanism dominated by acoustic phonons, e.g., the conduction electrons are scattered by phonons.⁴⁷ These variation trends are similar to those observed for the electrical conductivities, suggesting that the temperature dependence of the electrical conductivity is dominated by the carrier mobility. The electrical conductivity increases with increasing doping concentration (Fig. 9(b)), expect for the La10Nb20 sample. The electrical conductivity of the La10Nb20 sample is smaller than that of La10Nb10 at low temperature, owing to its high porosity and large amount of second phases, while the electrical conductivity of the La10Nb20 is close to that of La10Nb10 when the temperatures exceed 600 K, which is because the scattering mechanism is dominated by acoustic phonons at high temperature. Consequently, the large electrical conductivity, together with the large Seebeck coefficient, results in a large power factor at high temperature.

Fig. 9(f) shows the power factor PF (=S²σ) of all the samples as a function of temperature. The PFs for all the samples show a similar variation tendency to σ, which shows an initial increase, followed by a gradual decrease with increasing temperature. At temperatures above 600 K, the PF increases with increasing doping concentration before reaching the peak value for La10Nb10 and then starts to fall for the La10Nb20 sample. It is noted that the PF exhibits peak values above 1 mW m⁻¹ K⁻² in the temperature range of 450 to 650 K for several samples, with the La10Nb10 sample showing a maximum power factor as high as PF ∼ 1.32 mW m⁻¹ K⁻² at 600 K.

The temperature dependence of the thermal diffusivity and total thermal conductivity (κ_total) is shown in Fig. 10(a) and (b). The total thermal conductivity decreases proportionally with T⁻¹ with increasing temperature in the whole measurement temperature range, indicating a dominant phonon scattering due to the Umklapp process.⁴⁸ According to the theoretical formula for the total thermal conductivity, κ_total is composed of the lattice thermal conductivity (κ_L) and electric thermal conductivity (κ_e), κ_total = κ_L + κ_e. The value of κ_e is obtained from the Wiedemann–Franz law as κ_e = LTσ, where L is the Lorentz factor (L = 2.44 × 10⁻⁸ V² K⁻², Fig. 10(c)). Therefore, the lattice thermal conductivity is determined by subtracting the electric thermal conductivity from the total thermal conductivity. As shown in Fig. 10(c), κ_L is similar to κ_total, indicating that κ_L plays a major role in the total thermal conductivity. The La10Nb20 sample shows the lowest value of κ_L ∼ 3.7 W m⁻¹ K⁻¹ at 300 K, which decreases to a minimum value of 2.67 W m⁻¹ K⁻¹ at 1050 K. There is no significant difference among the other samples, indicating that the impurity atoms are not the main reason for the low total thermal conductivity of the La10Nb20 sample. Contributions from the secondary phase TiO₂ and high porosity are beneficial to reduce the lattice thermal conductivity. This is because the increased phonon scattering can reduce the phonon mean free path and, thus, lead to a further decrease in the lattice thermal conductivity, as observed in previous studies.^15,36,49 Furthermore, plenty of inhomogeneous mesoscale (∼0.1–1.0 μm) pores, due to the lower density (Table 3) of the La10Nb20 sample, 82.8%, compared with the other samples, effectively enhance the scattering of phonons with long mean free paths, resulting in a decrease in the lattice thermal conductivity.^50–52

Fig. 10 Temperature dependence of the (a) thermal diffusivity, (b) total thermal conductivity and heat capacity (inset), (c) electrical thermal conductivity and (d) lattice thermal conductivity for Nb–La doped SrTiO₃.

Fig. 11 shows the zT value for La–Nb doped SrTiO₃ bulk samples with varying doping concentrations. When the doping contents of Nb and La are equal, the zTs for the samples increase with increasing temperature and stabilize above a high temperature of 800 K. If the zT value can be further improved, this excellent high-temperature stability is particularly suitable for the application of thermoelectric devices at high temperature. The zT value of the samples with La : Nb ≠1 presents an increasing tendency with increasing temperature, with the La10Nb20 sample showing a maximum zT value of 0.31 at approximately 1050 K due to its lower thermal conductivity together with large PF. The maximum zT obtained is one of the highest values reported for the electron-doped SrTiO₃ prepared by hot pressing.

Fig. 11 Temperature dependence of zT for SrTiO₃ samples with different Nb and La doping concentrations.

4. Conclusion

In conclusion, first-principles calculations and measurements of the thermoelectric properties of La–Nb co-doped SrTiO₃ were carried out in this study, which show that the doping ratio of La to Nb affects the formation energy, effective mass and electron band structure of La–Nb doped SrTiO₃, leading to an improvement in the thermoelectric properties. The heavily Nb-doped sample shows a large formation energy; the larger formation energy promotes the precipitation of the second phase and increases the porosities of the samples, which can significantly reduce the thermal conductivity. By controlling the doping ratio, a lower lattice thermal conductivity of 1.97 W m⁻¹ K⁻¹ and a maximum zT value of 0.31 are achieved at 1050 K in La–Nb co-doped SrTiO₃ bulk materials. The low thermal conductivity is related to the introduction of La and Nb dopants, a second phase and porosity. The obtained maximum zT is one of the highest values reported for electron-doped SrTiO₃ prepared by hot pressing. The SrTiO₃ bulk samples doped with La and Nb elements (a molar ratio of 1 : 1) show a relatively stable zT value in a broad range of high temperatures, which is promising for high-temperature thermoelectric applications.

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

This project was supported by the National Natural Science Foundation of China under the No. 61751404, 51702168, 51774065, 51525401, 51772056, 61366008 and 61664007; the State Key Laboratory of New Ceramic and Fine Processing (Tsinghua University) under the No. KF201608; the Opening Project of State Key Laboratory of High Performance Ceramics and Superfine Microstructure under the NO. SKL201705SIC; the Guangxi Key Laboratory of Information Materials, Guilin University of Electronic Technology, under the No. 151004-K; the Natural Science Foundation of Inner Mongolia under the No. 2016BS0507; the Guangxi Natural Science Foundation of China under Grant No. 2015GXNSFFA139002 and the Science and Technology Major Project of Inner Mongolia Autonomous Region (2018-810). J. W. thanks Yanzhong Pei and Hongxia Liu from Tongji University for valuable discussion and support provided for the Hall effect measurements. J. W. thanks Xue Jiang from Dalian University of Technology for valuable discussion on the calculations of formation energy.

References

1. H. Lu, L. Price and Q. Zhang, Appl. Energy, 2016, 161, 497–511.
2. M. S. Dresselhaus, G. Chen, M. Y. Tang, R. G. Yang, H. Lee, D. Z. Wang, Z. F. Ren, J. P. Fleurial and P. Gogna, Adv. Mater., 2007, 19, 1043–1053.
3. G. J. Snyder and E. S. Toberer, Nat. Mater., 2008, 7, 105.
4. Y. Pei, L. Zheng, W. Li, S. Lin, Z. Chen, Y. Wang, X. Xu, H. Yu, Y. Chen and B. Ge, Adv. Electron. Mater., 2016, 2, 1600019.
5. Z. Chen, Z. Jian, W. Li, Y. Chang, B. Ge, R. Hanus, J. Yang, Y. Chen, M. Huang, G. J. Snyder and Y. Pei, Adv. Mater., 2017, 29, 1606768.
6. K. Zhao, H. Duan, N. Raghavendra, P. Qiu, Y. Zeng, W. Zhang, J. Yang, X. Shi and L. Chen, Adv. Mater., 2017, 29, 1701148.
7. L.-D. Zhao, G. Tan, S. Hao, J. He, Y. Pei, H. Chi, H. Wang, S. Gong, H. Xu, V. P. Dravid, C. Uher, G. J. Snyder, C. Wolverton and M. G. Kanatzidis, Science, 2016, 351, 141–144.
8. G. Tan, L. D. Zhao and M. G. Kanatzidis, Chem. Rev., 2016, 116, 12123–12149.
9. H. Ohta, T. Mizuno, S. Zheng, T. Kato, Y. Ikuhara, K. Abe, H. Kumomi, K. Nomura and H. Hosono, Adv. Mater., 2012, 24, 740–744.
10. B. Poudel, Q. Hao, Y. Ma, Y. C. Lan, A. Minnich, B. Yu, X. A. Yan, D. Z. Wang, A. Muto, D. Vashaee, X. Y. Chen, J. M. Liu, M. S. Dresselhaus, G. Chen and Z. F. Ren, Science, 2008, 320, 634–638.
11. K. Biswas, J. Q. He, I. D. Blum, C. I. Wu, T. P. Hogan, D. N. Seidman, V. P. Dravid and M. G. Kanatzidis, Nature, 2012, 489, 414–418.
12. H. Ohta, S. Kim, Y. Mune, T. Mizoguchi, K. Nomura, S. Ohta, T. Nomura, Y. Nakanishi, Y. Ikuhara, M. Hirano, H. Hosono and K. Koumoto, Nat. Mater., 2007, 6, 129–134.
13. S. A. Yamini, D. R. G. Mitchell, Z. M. Gibbs, R. Santos, V. Patterson, S. Li, Y. Z. Pei, S. X. Dou and G. J. Snyder, Adv. Energy Mater., 2015, 5, 1501047.
14. H. Zhao, J. Sui, Z. Tang, Y. Lan, Q. Jie, D. Kraemer, K. McEnaney, A. Guloy, G. Chen and Z. Ren, Nano Energy, 2014, 7, 97–103.
15. L. D. Zhao, S. H. Lo, J. He, H. Li, K. Biswas, J. Androulakis, C. I. Wu, T. P. Hogan, D. Y. Chung, V. P. Dravid and M. G. Kanatzidis, J. Am. Chem. Soc., 2011, 133, 20476–20487.
16. K. Park, J. S. Son, S. I. Woo, K. Shin, M.-W. Oh, S.-D. Park and T. Hyeon, J. Mater. Chem. A, 2014, 2, 4217–4224.
17. A. V. Kovalevsky, M. H. Aguirre, S. Populoh, S. G. Patrício, N. M. Ferreira, S. M. Mikhalev, D. P. Fagg, A. Weidenkaff and J. R. Frade, J. Mater. Chem. A, 2017, 5, 3909–3922.
18. N. Wang, L. Han, H. He, Y. Ba and K. Koumoto, J. Alloys Compd., 2010, 497, 308–311.
19. Y. Wang, K. H. Lee, H. Ohta and K. Koumoto, J. Appl. Phys., 2009, 105, 103701.
20. H. Takenouchi, T. Imai, H. Mae, M. Fujimoto, T. Kineri, T. Iida, N. Hamada, T. Watanabe and K. Nishio, MRS Proceedings, 2007, 1044, 1044-U06-11.
21. M. Ito and T. Matsuda, J. Alloys Compd., 2009, 477, 473–477.
22. K. H. Lee, S. W. Kim, H. Ohta and K. Koumoto, J. Appl. Phys., 2007, 101, 083707.
23. H. C. Wang, C. L. Wang, W. B. Su, J. Liu, Y. Sun, H. Peng and L. M. Mei, J. Am. Ceram. Soc., 2011, 94, 838–842.
24. A. Kikuchi, N. Okinaka and T. Akiyama, Scr. Mater., 2010, 63, 407–410.
25. S. Ohta, T. Nomura, H. Ohta, M. Hirano, H. Hosono and K. Koumoto, Appl. Phys. Lett., 2005, 87, 092108.
26. Z. Lu, H. Zhang, W. Lei, D. C. Sinclair and I. M. Reaney, Chem. Mater., 2016, 28, 925–935.
27. Q. Hou, J. Li, C. W. Zhao, C. Ying and Y. Zhang, Phys. B Condens. Matter, 2011, 406, 1956–1960.
28. M. D. Segall, J. D. L. Philip, M. J. Probert, C. J. Pickard, P. J. Hasnip, S. J. Clark and M. C. Payne, J. Phys.: Condens. Matter, 2002, 14, 2717.
29. J. Clark Stewart, D. Segall Matthew, J. Pickard Chris, J. Hasnip Phil, I. J. Probert Matt, K. Refson and C. Payne Mike, Z. Kristallogr. - Cryst. Mater., 2005, 567.
30. H. Shiiba, N. Zettsu, M. Nakayama, S. Oishi and K. Teshima, J. Phys. Chem. C, 2015, 119, 9117–9124.
31. H. Y. Xiao and W. J. Weber, J. Phys. Chem. B, 2011, 115, 6524–6533.
32. A. C. Larson and R. B. v. Dreele, National Laboratory Report, LAUR 86-748, 2004.
33. T. Tomio, H. Miki, H. Tabata, T. Kawai and S. Kawai, J. Appl. Phys., 1994, 76, 5886–5890.
34. R. D. Shannon, Acta Crystallogr., Sect. A: Cryst. Phys., Diffr., Theor. Gen. Crystallogr., 1976, 32, 751–767.
35. S. Ohta, T. Nomura, H. Ohta, M. Hirano, H. Hosono and K. Koumoto, Appl. Phys. Lett., 2005, 87, 092108.
36. N. Wang, H. Chen, H. He, W. Norimatsu, M. Kusunoki and K. Koumoto, Sci. Rep., 2013, 3, 3449.
37. P. P. Edwards and M. J. Sienko, Phys. Rev. B: Solid State, 1978, 17, 2575–2581.
38. I. Vurgaftman, J. R. Meyer and L. R. Ram-Mohan, J. Appl. Phys., 2001, 89, 5815–5875.
39. T. Okuda, K. Nakanishi, S. Miyasaka and Y. Tokura, Phys. Rev. B: Condens. Matter Mater. Phys., 2001, 63, 113104.
40. F. H. Chung, J. Appl. Crystallogr., 1974, 7, 519–525.
41. D. Neagu and J. T. S. Irvine, Chem. Mater., 2010, 22, 5042–5053.
42. S. Ohta, H. Ohta and K. Koumoto, J. Ceram. Soc. Jpn., 2006, 114, 102–105.
43. K. Fujita, T. Mochida and K. Nakamura, Jpn. J. Appl. Phys., 2001, 40, 4644.
44. S. Ohta, T. Nomura, H. Ohta and K. Koumoto, J. Appl. Phys., 2005, 97, 034106.
45. J. Liu, C. L. Wang, W. B. Su, H. C. Wang, J. C. Li, J. L. Zhang and L. M. Mei, J. Alloys Compd., 2010, 492, L54–L56.
46. H. Muta, K. Kurosaki and S. Yamanaka, J. Alloys Compd., 2003, 350, 292–295.
47. J. Shen, X. Zhang, S. Lin, J. Li, Z. Chen, W. Li and Y. Pei, J. Mater. Chem. A, 2016, 4, 15464–15470.
48. W. Li, S. Lin, X. Zhang, Z. Chen, X. Xu and Y. Pei, Chem. Mater., 2016, 28, 6227–6232.
49. Y.-L. Pei, J. He, J.-F. Li, F. Li, Q. Liu, W. Pan, C. Barreteau, D. Berardan, N. Dragoe and L.-D. Zhao, NPG Asia Mater., 2013, 5, e47.
50. R. H. Tarkhanyan and D. G. Niarchos, Int. J. Therm. Sci., 2013, 67, 107–112.
51. D. Mei, Y. Li, Z. Yao, H. Wang, T. Zhu and S. Chen, J. Alloys Compd., 2014, 609, 201–205.
52. R. H. Tarkhanyan and D. G. Niarchos, J. Electron. Mater., 2014, 43, 3808–3811.

---