Challenges in Improving Performance of Oxide Thermoelectrics Using Defect Engineering

Abstract

Oxide thermoelectric materials are considered promising for high-temperature thermoelectric applications in terms of low cost, temperature stability, reversible reaction, and so on. Oxide materials have been intensively studied to suppress the defects and electronic charge carriers for many electronic device applications, but the studies with a high concentration of defects are limited. It desires to improve thermoelectric performance by enhancing its charge transport and lowering its lattice thermal conductivity. For this purpose, here, we modified the stoichiometry of cation and anion vacancies in two different systems to regulate the carrier concentration and explored their thermoelectric properties. Both cation and anion vacancies act as a donor of charge carriers and act as phonon scattering centers, decoupling the electrical conductivity and thermal conductivity.

1. Introduction

The demand for alternate energy of fossil fuel becomes a challenging task for the researcher and scientist. A possible strategy for an alternate energy source is thermoelectric (TE) materials, whereby unwanted heat is changed to useful electrical energy with no harmful emissions compared to other traditional power plants [1, 2]. The performance of a TE materials can be evaluated by the figure of merit, zT = S²σT/κ, where σ represents the electrical conductivity, S is the Seebeck coefficient, T is the temperature, and κ is the thermal conductivity [3, 4]. The high zT can be obtained with high electrical conductivity, high Seebeck coefficient, and low thermal conductivity. However, the correlations between them are complex and cannot be treated independently [5, 6]. For instance, the increase in the carrier concentration, rises the electrical conductivity, drop the Seebeck coefficient, and rise the electronic thermal conductivity [7]. Therefore, the optimization of TE performance is a challenging task.

To date, many innovative TE materials like Bi₂Te₃, PbTe, CoSb₃ XNiSn, and SiGe have been commercially applied because of their high performance as compared to other TE materials [5, 8, 9, 10, 11, 12]. However, these materials have restricted applications due to their high price, instability in oxidizing atmospheres, and the most important toxicity [8, 13, 14, 15]. Therefore, many studies on alternative TE materials with low cost, high efficiency, and environmentally friendly characteristics have been explored [16, 17, 18]. In this relay, oxide materials have been considered as the best alternative, such as layered cobalt oxide (NaCo₂O₄), and strontium titanium oxide (SrTiO₃) due to their low price, thermal stability, and eco-friendly compatibility [19, 20]. For TE applications, n-type and p-type materials should be coupled. So it is important to develop high performance both n-type and p-type materials.

Layered structure p-type NaCo₂O₄ has been explored and is considered as one of the candidate materials for TE applications [16, 21]. This layered structure contains two layers CoO₂ and Na. The CoO₂ layers play the role of electron source which results in high electrical conductivity, while the layer of Na ions is sandwiched among nearby CoO₂ layers which decreases the thermal conductivity along the stacking direction [22, 23]. Various studies propose that such layered structured CoO₂ exhibits low thermal conductivity with metallic-like electrical conductivity, which is very attractive for TE applications [16, 24].

Similar to highly studied NaCoO₂ TE material, LiNbO₂ has a layered configuration in which the NbO₆ trigonal-prismatic layers and Li planes are stacked, as shown in the schematic Figure 1(a). This similarity proposes that LiNbO₂ could be a new promising TE material. LiNbO₂ is a sub-oxide of the main (LiNbO₃), and its Li-intercalated structure Li_1-xNbO₂ was first explored as a promising superconductor [25, 26, 27]. It has also been considered as a potential candidate material for numerous technological applications [28, 29, 30, 31]. The removal of Li atoms provide additional holes to the valence band, made up of Nb $d_Z^2$ states, which affects the oxidation of the Nb-atoms and raises the density of states (DOS) at the Fermi level (just like when holes are introduced into NaCoO₂). These Li-vacancies increase the carrier concentration, which will raise the electrical conductivity. Moreover, the intrinsic defects in Li_1-xNbO₂ would act as a scattering center for thermal conductivity. So, defected Li_1-xNbO₂ is estimated to be extremely favorable for TE applications because of higher electrical and lower thermal conductivities.

Figure 1.

Schematic illustration of (a) LiNbO₂ (b) SrTiO₃.

Stoichiometric SrTiO₃ has a cubic perovskite structure, where oxygen anions form an octahedron with one Ti⁴⁺ atom lying at the center as shown in the schematic Figure 1(b). SrTiO₃ have been studied widely and is considered as one of the favorite n-type TE materials due to its high absolute Seebeck coefficient [32, 33]. Virgin SrTiO₃ is considered to be an insulator and with a bandgap of 3.25 eV [34]. To boost the power factor (PF), only the electrical conductivity needs to be increased through appropriate doping on A-site and/or B-site [19, 35, 36, 37, 38, 39]. The role of the oxygen vacancy, which also acts as electron dopants, is very important for TE materials. Besides, creating oxygen vacancies offer a chance to decrease thermal conductivity through phonon scattering without remarkably affecting electrical conductivity [40, 41, 42]. The cationic nonstoichiometry and controlling oxygen partial pressure in SrTiO₃ can produce cation and oxygen vacancies, which play an important role in the TE performance. To understand the defect chemistry and its consequence on the TE performance, pure SrTiO₃ should be considered.

Considering the importance of defects in oxide materials as discussed above, it is important to study cation and anion defect engineering in oxide materials. Here in this chapter we have considered LiNbO₂ (p-type) and SrTiO₃ (n-type) with different vacancy concentrations and explore the experimental observations and correlate them with density functional theory (DFT). We elucidate that the defect engineering which may provide a new track for enhancing the TE performance.

2. Cation defect engineering

2.1 Experimental and computational approaches

2.1.1 Preparation of Li_1-xNbO₂ compounds

Nonstiochiometric Li_1-xNbO₂ (x = 0–0.6) compounds were prepared by conventional solid-state reaction using commercially available Li₂CO₃, NbO, and Nb₂O₅ with purity level more than 99.99%. First, Li_3-yNbO₄ was prepared by mixing Li₂CO₃ and Nb₂O₅ (y = 0, 0.015, 0.3, 0.6, 0.9, 1.2, and 1.8) at 1173 K in air for 50 hrs. Next, Li_1-xNbO₂ (x = 0–0.6) were prepared by mixing Li_3-yNbO₄ (y = 0, 0.015, 0.3, 0.6, 0.9, 1.2, and 1.8) for corresponding x = (0, 0.05, 0.1, 0.2, 0.4 and 0.6), and NbO in a ratio of 1: 2 for 24 hrs in ethanol. The dried slurries were crushed, sieved, and consulidated by spark plasma sintering (SPS) at 1323 K under 50 MPa for 15 min [43].

2.1.2 Theoretical calculations of Li_1-xNbO₂

The electronic structures of Li_1-xNbO₂ were explored using DFT with the local density approximations [44]. The lattice constants were calculated and all the atomic sites were relaxed till the forces were met to less than 0.01 eV/Å. For Li-vacancies computations various supercells (1x1x1, 1x1x2, 2x2x1, and 2x2x2) were considered. For the TE calculations, the BolzTraP package based on the Boltzmann transport theory and a constant relaxation time were applied [45, 46]. For band structures calculations QE code and the energy dispersion relation E(n,k) as a function of band index n and wave vector k were used.

2.1.3 Characterization of Li_1-xNbO₂

X-ray diffraction (XRD) analysis was performed by Rigaku D/MAX-2500/PC with Cu Kα emission. The pictographs of the samples were observed by using the scanning electron microscope (SEM, Verios 460 L, FEI). Rectangular specimens were cut for the measurements of the electrical properties using (ZEM-3, ULVAC-RIKO). Temperature-dependent charge transport properties were measured using HT-Hall, Toyo Corporation, ResiTest 8400. Circular discs were used for thermal diffusivity measurement (DLF-1300, TA instrument). All samples have ≥95% of the theoretical density.

2.2 Results and discussion

Figure 2(a) displays the XRD patterns of all samples. The main peaks of the compounds were indexed according to the LiNbO₂ hexagonal structure which can be regarded as alternatively arranged close-packed Li-layers inserted among the two O-Nb-O slabs along the c-axis [29]. In addition to the main peaks, all samples showed small impurity peaks of LiNbO₃ and NbO₂. LiNbO₃ peaks are expected due to moderate PO₂ level during the consolidation process, which changes the oxidation state from Nb³⁺ to Nb⁵⁺. The additional NbO₂ peaks can be described by the following defect reaction (1).

Figure 2.

(a) X-ray diffraction patterns and (b-g) microstructure for Li_1-xNbO₂ samples [43].

$$2NbO+L{i}_{3}Nb{O}_4\to 3\mathit{LiNb}{O}_2$$E1

At lower Li-vacancy concentrations, the Li atoms to combine with Nb³⁺ ([1/3Nb⁵⁺+2/3Nb²⁺]³⁺) make LiNbO₂. But, at high Li-vacancy concentrations, there are insufficient Li-atoms to react with Nb³⁺ ([1/3Nb⁵⁺+2/3Nb²⁺]³⁺) atoms to form LiNbO₂ which turn into the NbO₂ phase. Furthermore, at lower oxygen partial pressure the Nb⁵⁺ in the Li₃NbO₄ compound is thermally reduced to Nb⁴⁺ which is the consequence of the NbO₂ phase. Additionally, the Li-vacancies lead to an increase in the repulsive force among the two adjacent oxygen layers which increases the c-lattice of the unit cell. In the meantime, the a lattice decreases due to the shrinkage of Nb-O bonds in NbO₆ octahedra. The experimental lattice constant shown in the inset Figure 2(a) is close to reported work and with our DFT results [47, 48].

Figure 2(b)–(f) displays the fractured cross-section of Li_1-xNbO₂ samples. The dense of all the samples support the high relative densities larger than 95%. All grains are homogeneously distributed, no obvious segregations, and are randomly oriented. Moreover, the Li-vacancy concentrations have no significant effects on the size and shape of the grains.

Figure 3(a) shows the temperature-dependent electrical conductivities of Li_1-xNbO₂ samples. At first, the electrical conductivities of the samples increased with Li-vacancy concentrations, suggesting that more holes are created, as shown in the defect reaction [2]. The decreasing trends in the electrical conductivity measurements with temperature suggesting metallic behavior. However, for higher Li-vacancies concentrations, i.e., x ≥ 0.4, and at high temperatures the metallic conduction changed to semiconducting-like behavior. For high Li-vacancy concentrations, this transition point is moved to lower temperatures, suggesting that hole creation is inhibited by electrons formed by the replacement of Nb with Li atoms. Above this transition point, the electrical conductivity is governed by electrons which can be described by the defect reactions displayed in Eqs. (3)–(5).

Figure 3.

(a) Temperature dependence of electrical conductivity and (b) calculated electronic density of states of Li_1-xNbO₂ (x = 0, 0.2, 0.4, 0.6, and 0.6) [43].

$$L{i}_{2}O+N{b}_2{O}_3\to 2V_{Li}^{\prime }+2h^{{}^{.}}+2N{b}_{Nb}^X+4O_O^X$$E2

$$L{i}_{2}O+N{b}_2{O}_3\to V_{Li}^{\prime }+N{b}_{Nb}^{{}^{..}}+L{i}_{Li}^X+N{b}_{Nb}^X+4O_O^X$$E3

$$L{i}_{2}O+N{b}_2{O}_3\to N{b}_{Li}^{{}^{..}}+V_{Li}^{\prime }+e^{\prime }+N{b}_{Nb}^X+4O_O^X$$E4

$$L{i}_{2}O+N{b}_2{O}_3\to N{b}_{Li}^{{}^{..}}+2e^{\prime }+L{i}_{Li}^X+N{b}_{Nb}^X+4O_O^X$$E5

To deeply understand the above experimental results DFT calculations were also employed and the electronic structures were calculated. The calculated electronic structure suggests that virgin LiNbO₂ has a band-gap of 1.65 eV. It should be noted that DFT-LDA generally miscalculates the band-gap. But, the calculated band-gap in our work is consistent with the reported works [45]. Figure 3(b) summarizes the electronic DOS for various holes concentrations. It suggests that virgin LiNbO₂ is a semiconductor and suggesting a metallic behavior for holes incorporated samples. Besides, the DOS at the Fermi energy also increases, suggesting that the electrical conductivity of Li_1-xNbO₂ should increase with increasing holes concentrations.

Figure 4(a) shows the temperature-dependent Seebeck coefficients (S) for all samples. It can be seen that both the calculated and experimentally observed S are very close. The positive sign indicates that holes are the majority carrier which can be connected to the deviation from stoichiometry in the Li- sublattice [49]. The S values of x ≤ 0.1 samples increase with temperature, showing a degenerately doped semiconductor. Sample with x = 0.2 and at high temperatures the increasing trend in the S values is low suggesting that the hole generation is suppressed by an electron. Additional increase in the Li-vacancy concentrations (x > 0.2) and at high temperatures, the S values starts decreasing, and finally, a changeover is observed. This changeover from p-type to n-type could be due to cation disorder which is very similar to the σ-T as displayed in Figure 3(a). The behavior could be clearly understood by the defect reaction (2)– (5).

Figure 4.

Temperature dependence of (a) Seebeck coefficient, (b) carrier concentration, (c) carrier mobility, and (d) normalized mobility as a function of $T^{r-1}\left(r=\frac{1}{2}\mathit{and}-\frac{1}{2}\right),\mathit{of}L{i}_{1-x}Nb{O}_2$ [43].

Figure 4(b)–(d) shows the temperature-dependent Hall measurements for all Li_1-xNbO₂ samples. The obtained by the Hall measurements agreed with the electrical conductivity and Seebeck coefficient data. It can be seen clearly that the carrier concentration increases with the creations of Li-vacancies $\left(2V_{Li}^{\prime }\to 2h^{{}^{\text{.}}}\right)$. Samples with lower Li-vacancy concentrations (x ≤ 0.2) were not influenced by temperature, suggesting degenerately doped behavior. However, high Li-vacancy concentrations (x ≥ 0.4), and at high temperatures show a slight rise in the carrier concentration. This tendency is similar to the Seebeck coefficients as shown in Figure 4(a). In the case of a degenerately doped p-type semiconductor, the Fermi level lies below the valence band maxima (VBM) and the carrier concentration is temperature independent of up to the intrinsic-extrinsic transition temperature [50]. Therefore, it is expected that Li_1-xNbO₂ is a heavily doped semiconductor. Figure 4(c) shows the temperature dependence mobility of nonstoichiometric Li_1-xNbO₂ compound and the carrier mobility decreases with increasing temperature. Together with the Hall measurements and the defect reactions (2)– (5), it is expected that the tendency in electrical conductivity is directed by mobility in the region holes are dominant and by carrier concentration in the region where electrons are dominant (x ≥ 0.4 and at high temperature). All samples show negative temperature-dependence carrier mobility, resulting from the phonon scattering (μ ∝ T^r−1), where $r=-\frac{1}{2},\frac{1}{2},\mathrm{and}\frac{3}{2}$ signify acoustic, optical, and ionized impurity phonon scattering, respectively [51, 52, 53]. To know the scattering mechanism in Li_1-xNbO₂, mobilities were re-plotted as a function of T^r−1 and shown in Figure 4(d). The samples x ≤ 0.2 shown a linear correlation with T^−1/2, suggesting that mobility is dominantly encountered by optical phonon scattering. However, samples with x ≥ 0.4, as shown in Figure 4(d) inset, displayed a linear relationship with T^−3/2, suggesting that the mobility is encountered by acoustic phonon scattering. The transition mechanism is not clear, however, it could be due to the dominant defect change with Li-vacancies, corresponding to Equations (2) and (3), to Nb replacements for Li sites, corresponding to Eqs. (4) and (5).

Figure 5(a) represents the temperature-dependent total thermal conductivities (κ_tot) of Li_1-xNbO₂ samples. It can be seen that total thermal conductivity is decreased significantly with increasing Li-vacancies. The Wiedemann-Franz relationship was used to estimate the electronic and lattice thermal conductivity as shown in the inset of Figure 5(a) [54]. It is found that the main influence on the total thermal conductivity originates from lattice vibrations and decreased substantially with Li-vacancies. This suggests that Li-vacancies act as a scattering center for phonons. However, for higher vacancy concentrations (x ≥ 0.2), the thermal conductivity increases to some extent. This increase could be due to a change in the scattering mechanism from optical phonon to acoustic phonon by $N{b}_{Li}^{\cdot \cdot }$ contribution as described above. This mechanism is schematically illustrated in Figure 5(b)–(d). Therefore, it could be suggested that samples with low Li-vacancies concentrations may have localized double phonon (optical and acoustic phonons), which may play a role as a phonon scattering center, showing a substantial decrease of lattice thermal conductivity. However, with higher Li-vacancies concentrations, the lattice vibration is scattered by a single phonon type of acoustic phonon. Also, the increase in the thermal conductivity could be due to secondary phases [55] as detected in XRD (see Figure 2(a)).

Figure 5.

Temperature-dependent (a) total thermal conductivities for Li_1-xNbO₂ sample and (b-d) schematic illustration of phonon scattering [43].

The figure-of-merit (zT) for all Li_1-xNbO₂ samples is presented in Figure 6. A substantial improvement in zT is observed in the whole temperature range and reaches a maximum value of 0.125 at 970 K, which is around ~220% (3-times) higher compared to the virgin LiNbO₂ sample. The observed tendency suggests that zT could be higher at higher temperatures. The samples after high-temperature measurement were rechecked by XRD and found that all Li_1-xNbO₂ samples are highly stable as shown in the inset of Figure 6. This confirms that all samples are stable and can be utilized as a new promising material for high-temperature TE applications.

Figure 6.

Temperature dependence of the dimensionless figure of merit of Li_1-xNbO₂ samples [43].

3. Anion defect engineering

3.1 Experimental and computational methods

3.1.1 Preparation of SrTiO_3-δ

Pristine SrTiO₃ samples were synthesized by using conventional solid-state reaction techniques, using TiO₂ and SrCO₃ with a purity level higher than 99.9%. The stoichiometric powders were ball-milled for 24 hr. Next, the ball-milled powders were calcined at 1373 K for 3 hrs. The powders were then sieved and pressed into thicknesses of 3 mm. The pressed pellets were sintered at 1573 K for 30 hrs under the air atmosphere. To create an Anion defect in SrTiO₃ (Oxygen vacancies), the samples were annealed by allowing 1%H₂/Ar, 5%H₂/Ar, 10%H₂/Ar, and 20%H₂/Ar gases at 1573 K for 30 hrs, and the samples were designated with the prefix “1HAr, 5HAr, 10HAr, and 20HAr”, respectively.

3.1.2 Theoretical calculations of SrTiO_3-δ

To understand the anion defect engineering in SrTiO₃, DFT with the local density approximations were applied and correlated with experimental work [44, 56]. To properly pronounce the electronic band structures of pristine and O-vacancies in SrTiO₃, we also considered the LDA + U methodology by selecting the effective on-site Coulomb modification (U = 5.0 eV) is applied to d-orbital electrons in Ti-atom in agreement with the reported works [57, 58]. To compute the oxygen vacancy in SrTiO₃, a 2 × 2 × 2 supercell was considered and the BoltzTraP program was used for TE properties [45, 46].

3.1.3 Charascterization of SrTiO_3-δ

For SrTiO_3-δ characterizations, the same techniques were followed as described in section 2.1.3.

3.2 Results and discussion

Figure 7 shows the XRD pattern of the reduced SrTiO_3-δ samples. The XRD patterns of all reduced samples exhibit a single-phase perovskite cubic structure. The lattice constant of the reduced samples was refined through Rietveld refinements. The lattice constant increased with decreasing$P_{O_2}$levels. The variations in the lattice constant are similar to the reported values [36, 59]. The variations in the lattice constant indicate that during the annealing process, the oxygen in SrTiO₃ sublattice combine with H₂ which increases the O-vacancies among the cations, and thus the coulombic repulsion force of cations increases. This leads to a rise in the lattice constant as presented in Table 1.

Figure 7.

Refined XRD patterns of oxygen-deficient SrTiO_3-δ. ceramics annealed at 1573 K for 30 hrs in (a) 1%H2/Ar (1HAr), (b) 5%H2/Ar (5HAr), (c) 10%H2/Ar (10HAr), and (d) 20%H2/Ar (20HAr) atmospheres [60].

Sample	Lattice parameter (Å)	Carrier concentration; (×10^19 cm^−3)	Oxygen vacancies (×10^19 cm^−3)	Mobility; (cm^2V^−1 s^−1)	Estimated $P_{O_2}$; (atm)
[1HAr]	3.8991	0.106	0.0530	6.316	2.24 × 10^−11
[5HAr]	3.8999	0.198	0.099	5.373	7.78 × 10^−15
[10HAr]	3.9012	5.24	2.62	4.885	2.23 × 10^−23
[20HAr]	3.9047	10.660	5.33	3.694	3.17 × 10^−25

Table 1.

The carrier concentration, the lattice constant, oxygen vacancies, mobility, and estimated$P_{O_2}$of SrTiO_3−δ samples [60].

Figure 8 shows the microstructure of thermally etched SrTiO_3-δ samples in high vacuum conditions. It shows that all samples have similar microstructures, well densified, and support the measured densities>95%. There is no substantial variance in the size and shape of the grains.

Figure 8.

SrTiO_3-δ. ceramics annealed at 1573 K for 30 hrs in (a) 1%H2/Ar (1HAr), (b) 5%H2/Ar (5HAr), (c) 10%H2/Ar (10HAr), and (d) 20%H2/Ar (20HAr) atmospheres [60].

Figure 9 displays the high-resolution transmission electron microscopy (HRTEM) of oxygen-deficient SrTiO_3-δ samples. It is interesting to see that the sample reduced under different PO₂ levels shows different reduction levels. In the case of low oxygen-deficient samples, we could not see a clear defective area. However, for the high oxygen-deficient samples, we identify two different kinds of defected areas labeled by A1 and A2 in Figure 9(c,d). The area labeled by A1 denotes the local lattice defect which is due to high oxygen vacancy in the lattice and area A2 shows a different lattice structure from the matrix. It is expected that the area A2 is probably related to the Ruddlesden-Popper phases [SrO·(SrTiO₃)_n] [61], which could be the reason for the metallic conduction in highly reduced samples.

Figure 9.

High-resolution transmission electron microscopy for 1HAr (a, b) and 20HAr (c, d) SrTiO_3-δ [60].

Annealing under a reducing atmosphere at ambient temperature leads to different kinds of defects in materials. Oxygen vacancies could be one of the main defects in the SrTiO₃ due to the low formation-energy compared to other atoms in the lattice. Below Eq. (6) shows in the Kröger-Vink notation [62].

$$O_O^x\leftrightarrow \frac{1}{2}{O}_2+V_O^{\cdot \cdot }+2e^{\prime }$$E6

where $V_O^{\cdot \cdot }$ denotes the doubly ionized oxygen vacancy and $O_O^x$ denotes the neutral oxygen that exists on its lattice position. The quasi-free electrons generated by oxygen vacancies was determined using the Hall measurements and then using the free electrons, the oxygen partial pressure PO₂ was estimated using Eq.(7) (See Table 1) [63].

$$P_{O_2}={\left(\frac{M{2}^{\frac{1}{3}}{K}_0^{\frac{1}{3}}exp\left(\frac{-\Delta h_{Re}}{3k_{B}T}\right)}{n_e}\right)}^6$$E7

where ∆h_Re represents the enthalpy for reduction, M is the number of oxygen atoms in unit volume (cm⁻³), k_B is the Boltzmann’s constant, K₀ is a constant including an entropy term, n_e is nominal carrier concentration, and T is the annealing temperature.

The observed carrier concentrations in our samples are in the range of 10¹⁸ to 10²⁰/cm³, which is a typical range for Mott transition, i.e., insulator–metal transition. This transition can be calculated from the Mott criterion, n_e^1/3a₀ ~ 0.25, where a₀ is the Bohr radius related to the carrier and n_e which represents the electronic carrier concentration [64]. In the case of 1HAr and 5HAr samples, the calculated Mott transition is on the boundary of Mott transitions, and 10HAr and 20HAr samples are metallic-like, which supports the temperature-dependency of electrical conductivity.

The temperature-dependent electrical conductivity and Seebeck coefficient of reduced SrTiO_3-δ samples are represented in Figure 10(a) and (b). As abovementioned that each O-vacancy produces two electrons through charge neutrality conditions, $n_{\mathrm{e}}\approx 2\left[V_O^{••}\right]$, and henceforth the carrier concentrations would increase, causing an enhance in the electrical conductivity [63]. Moreover, as shown in Figure 10(a) that the electrical conductivities for low reduced samples i.e., 1HAr and 5HAr-annealed are low (0.5 to 2 S/cm, correspondingly) in the entire temperature with semiconducting-like. However, in the case of highly reduced samples (increasing O-vacancies (δ) as shown in Table 1) i.e., 10HAr and 20HAr samples, the electrical conductivities are relatively higher (41 and 63 S/cm, correspondingly). This increase of electrical conductivity evidently suggests electron doping due to oxygen vacancy, which is analogous to donor-doped SrTiO₃ [65]. This would fill the n-type conduction band (CB), which evident by the negative sign of the Seebeck coefficient as shown in Figure 10b. Additionally, the increase in n-type charge carrier from 1HAr to 20HAr is consistent with the electrical conductivity and Seebeck coefficient data.

Figure 10.

(a) Temperature-dependent electrical conductivity and (b) Seebeck coefficient of O-deficient SrTiO_3-δ, (c) band structure, and (d) total and projected density of states of SrTiO_3-δ [60].

DFT calculations were also used to understand the effect of O-vacancies in SrTiO₃. The electronic band structures of virgin and O-deficient SrTiO₃ samples were calculated using DFT + U, and the results are presented in Figure 10(c). Our DFT + U calculated electronic band-gap results suggest that of virgin SrTiO₃ at Г-point is 2.31 eV (1.93 eV), which is close reported work [34, 66]. However, in the case of oxygen-deficient SrTiO₃, the electronic band-gap is reduced to 2.18 eV at Г-point. The band structure calculations show a band below the conduction band, and an electron pocket which can be seen at the Г- point. Such an electronic pocket suggests electrons in the conduction band, which is largely formed by the Ti-d electrons. This electron pocket not only decreases the bandgap but also raises the carrier concentrations that can additionally improve the electrical conductivity of SrTiO_3-δ. The projected density of states in Figure 10(d) shows that the electron pockets are primarily contributed by the Ti-d and Sr-p electrons nearby the oxygen vacancy. We also found that at a large O-vacancy concentration, an insulator–metal transition occurs. In addition to this, the charge transfer study also suggests that O-vacancies change the conduction mechanism from nondegenerate to degenerate. We also calculated the room temperature DOS effective mass $\left(m_d^{\ast }\right)$ using nondegenerate and degenerate models Eqs. (8) and (9).

$$S=-\frac{k_B}{e}\left[ln\left(N_c/n_e\right)+A\right]$$E8

$$S=\frac{8\pi k_B^2}{3e{h}^2}{\left(\frac{\pi }{3n}\right)}^{\frac{2}{3}}{m}_d^{\ast }T$$E9

where k_B represents the Boltzmann constant, h is the Planck constant, n is the carrier concentration, $Nc\left(\mathrm{T}\right)=2\cdot {\left[\left(2\pi k_{B}T{m}^{\ast }\right)/h^2\right]}^{3/2}$ is the effective density of states in the conduction band, A is the scattering factor, usually ranges between 0 and 4. By fitting Eq. (8) as shown in Figure 11a with A = 1, 2, and 3, it can be seen that the effective mass for low O-vacancies samples suggests a nondegenerate semiconductor. However, the Pisarenko relation fitting Eq. 9 suggests that high O-vacancies samples have degenerate semiconducting like behavior. Furthermore, the DOS effective mass rises with increasing O-vacancies as shown in Figure 11b. This increase from 0.43 m° to 4.4 m° could be a reason for Hall mobilities reduction as shown in Table 1.

Figure 11.

(a) Seebeck coefficients as a function of carrier concentration: The solid lines represent the estimated Seebeck coefficients using a degenerate semiconducting model and dashed lines for a nondegenerate semiconducting model. (b) DOS effective mass $m_d^{\ast }$resulting from Seebeck coefficient and carrier concentration [60].

Figure 12(a) represents the temperature-dependent thermal conductivity of SrTiO_3-δ samples. This decreasing tendency suggests that O-vacancies act as phonon scattering centers despite their electrical conductivity increased as shown in Figure 10(a). Using Wiedemann-Franz law relation with Lorentz number of (2.45 × 10⁻⁸ V²K⁻²), the influence of electronic (κ_e) and phononic (κ_L) to total thermal conductivity was calculated and observed that the lattice thermal conductivity is dominant as presented in Figure 12(b). The lattice thermal conductivity was also plotted as a function of T⁻¹ as shown in inset Figure 12(b). The linear connection proposes that the lattice thermal conductivity is affected dominantly by Umklapp scattering [67]. Also, one should note that the similar grain sizes as shown in Figure 8, suggests that the reduction in thermal conductivity is mainly due to oxygen vacancy rather than grain boundary scattering.

Figure 12.

Temperature-dependent (a) total thermal conductivity, (b) lattice thermal conductivity, (c) power factor, (d) DFT calculated powder factor for various carriers concentrations, (e) temperature-dependent ratio of the electrical to thermal properties (σ/κ), and (d) ZT values of various oxygen-deficient SrTiO₃ samples [60].

Figure 12(c) illustrates the temperature-dependent PF for various oxygen-deficient SrTiO₃ samples. The substantial enhancement in the PF is due to the combination of moderate Seebeck coefficient values and high electrical conductivity. The PF obtained in this work is comparable to the PF obtained in doped-SrTiO₃ [65]. The DFT calculated PF for various carrier concentrations (10¹⁸–10²²/cm³) suggests that the highly reduced SrTiO₃ samples would have higher PF as shown in Figure 12(d) [68]. Additionally, one of the most remarkable features of this study is the decoupling among electrical and thermal conductivity of SrTiO_3-δ through solely oxygen vacancy as shown in Figure 12(e). This opposite behavior led to a significant increase in the ratio of electrical to thermal conductivity (σ/κ), which is a key motive for TE materials. The complete outcome of oxygen vacancies in the TE materials can be represented by the temperature dependence of the ZT as shown in Figure 12(f). It can be observed that the introduction of oxygen vacancy substantially increases the ZT value of 4.7 × 10⁻² for [20HAr] reduced samples at 670 K. Therefore, we suggest that carefully adjusting the oxygen vacancy could be an effective strategy for oxide TE materials.

Table 2 shows that the efforts in the layer-structured cobaltites and SrTiO₃ based materials. It shows that significant improvements have been achieved in oxide TE materials, which could be of great interest for power generation applications at high operating temperatures. As compared with other oxides, the materials investigated in this study show relatively low figure of merit (zT), which is because the investigated Li_1-xNbO₂ and SrTiO_3-δ are pure, undoped materials to understand the mechanism for cation and anion defects effects.

Materials	Type	Maximum zT value	Working temperature (K)	References
Cd-doped Ca3Co4O9	p	0.35	1000	[69]
NaxCoO2	p	0.31	800	[70]
NaxCoO2/Ag/Au	p	0.4–0.5	1000	[71]
Li1-xNbO2	p	0.125	970	This work
Nb-doped SrTiO3	n	0.165	900	[72]
La-doped SrTiO3single crystal	n	0.27	1073	[73]
Pr-doped SrTiO3	n	0.35	773	[74]
SrTiO3-δ	n	4.7 × 10^−2	670	This work

Table 2.

The dimensionless figure of merit zT of p-type and n-type oxide thermoelectric materials for comparison.

3.3 Conclusion

In conclusion, this work demonstrated that cation and anion vacancies can successfully control the thermoelectric performance of oxide-based thermoelectric materials. These findings suggest that both cation defect and anion defect can be engineered by reducing atmospheres and the defects in oxide thermoelectric materials simultaneously act as a source of charge carriers and phonon scattering centers. This decoupled behavior between electrical conductivity and thermal conductivity can lead to a substantial increase in the thermoelectric performance of oxide materials. The concept applied in this work is generally important and has the possibility of impacting the thermoelectric performance of oxide thermoelectrics and other functional oxide materials.

Acknowledgments

The experimental work was conducted by using the facilities in the Korea Institute of Ceramic Engineering and Technology (KICET). The authors, Jamil Ur Rahman and Soonil Lee are grateful to all colleagues for help and support in the same research group at KICET.

Conflicts of interest

There are no conflicts of interest to declare.