Substantial thermoelectric enhancement achieved by manipulating the band structure and dislocations in Ag and La co-doped SnTe

Eco-friendly SnTe based thermoelectric materials are intensively studied recently as candidates to replace PbTe; yet the thermoelectric performance of SnTe is suppressed by its intrinsically high carrier concentration and high thermal conductivity. In this work, we confirm that the Ag and La co-doping can be applied to simultaneously enhance the power factor and reduce the thermal conductivity, contributing to a final promotion of figure of merit. On one hand, the carrier concentration and band offset between valence bands are concurrently reduced, promoting the power factor to a highest value of ∼2436 µW·m−1·K−2 at 873 K. On the other hand, lots of dislocations (∼3.16×107 mm−2) associated with impurity precipitates are generated, resulting in the decline of thermal conductivity to a minimum value of 1.87 W·m−1·K−1 at 873 K. As a result, a substantial thermoelectric performance enhancement up to zT ≈ 1.0 at 873 K is obtained for the sample Sn0.94Ag0.09La0.05Te, which is twice that of the pristine SnTe (zT ≈ 0.49 at 873 K). This strategy of synergistic manipulation of electronic band and microstructures via introducing rare earth elements could be applied to other systems to improve thermoelectric performance.


Introduction 
Clean, reliable, and sustainable energy utilization technologies become more and more important [1]. and lattice thermal conductivity (κ l ) [7][8][9][10]. Therefore, in order to obtain a high zT, it is necessary to optimize the power factor (PF = S 2 σ) and simultaneously reduce κ.
However, S, σ, and κ e , which are closely affected by the carrier concentration (n), have a strong coupling relationship with each other, making it difficult to individually optimize a certain parameter without damaging the others [11][12][13][14]. Due to the opposite promotion effect of n on S and σ, the strategy of optimizing TE performance by improving the power factor has become extremely significant, including the introduction of resonance levels [15,16], energy filtering [17], band convergence [18], increasing the band gap [19], etc. In addition, in order to reduce κ l , many researches focus on introducing point defects [20][21][22], dislocations [23], nano-precipitation [24,25], and grain boundaries [26] to act as the centers of phonon scattering, thereby effectively preventing phonon transport [27].
Recently, with the development of Pb-free TE materials, SnTe TE materials, which have a band structure similar to PbTe, have intensively attracted attention. Unfortunately, the high carrier concentration (~10 21 cm −3 ) caused by excessive Sn vacancies in SnTe greatly increases κ e and reduces S, which seriously affects the TE performance, bringing about a zT value of only about 0.6 at 873 K. Meanwhile, the excessive energy splitting (E v ) between light and heavy valence bands is also a reason for its poor TE performance. In response to these problems, various electronic band structure modulation and phonon scattering optimization approaches have been employed recently to enhance the TE performance of SnTe systems. Generally, Sn self-compensation can be used to partially control the carrier concentration [28,29]. At the same time, some foreign atomic doping is claimed to effectively converge the light and heavy valence bands, such as Ag [18,23], Mn [30], Cu [31], and Mg [19]. In particular, the co-doping of Ag associated with other elements was reported to effectively tune the electronic band structures for higher TE performance. For example, Banik et al. [15] declared that Ag doping reduces the energy splitting between the light and heavy valence bands while In doping introduces resonance levels inside the valence bands, leading to an improved Seebeck coefficient, and an improved thermoelectric figure of merit, zT ≈ 1, in SnAg 0.025 In 0.025 Te 1.05 at 856 K. Recently, Mn doping is employed to further converge the valence bands on the basis of Ag doping. As a consequence, E v decreases to 0.1 eV in Sn 0.83 Ag 0.03 Mn 0.17 Te compared to the value of 0.35 eV in pristine SnTe, and a high power factor of 24.8 W·m -1 ·K -2 at 816 K is attained [32]. On the other hand, ultralow lattice thermal conductivity could be realized by incorporating various microstructures, including dislocations [33,34], precipitates [35], mesoscale grain boundaries [36,37], and point defects [38]. For instance, the all-scale structure defects containing the atomic-scale In doping point defects, the nanoscale Sb precipitates, and the mesoscale grain boundaries substantially impede the phonon transport so that a minimum value of ~0.44 W·m -1 ·K -1 is realized in (Sn 1.06 Te) 0.95 (InSb) 0.05 at 823 K, leading to a maximum zT value of ~0.84 [39]. Zheng et al. [18] showed that Cu 2 Te acts as the source of interstitial defects to reduce the lattice thermal conductivity to the amorphous limit, achieving a high zT value (1.4 at 900 K). Motivated by these works, we pay attention to the collaboration with rare earth elements, which are rarely focused on SnTe systems, on the basis of Ag doping.
Herein, we obtained a series of Sn 1+δ Te (δ = 0−0.05), Sn 1.03−x Ag x Te (x = 0.01−0.09), and Sn 0.94 Ag 0.09 La y Te (y = 0.01−0.07) samples by combining a melting reaction and spark plasma sintering (SPS). The co-doping of Ag and La simultaneously optimizes the transport of carrier and phonon, increasing S while suppressing κ over the whole temperature range. The theoretical simulation calculation confirms that the Ag and La co-doping weaken the band offset of valence bands and broaden the band gap like a relay race. It is for this reason that the Seebeck coefficient has a jump over the entire temperature range, and no bipolar effect is observed in the Ag and La co-doped SnTe, whose carrier concentration is decreased and carrier mobility is increased. In addition, a large number of dislocations associated with impurity precipitates are formed to act as phonon scattering centers, due to the excessive content of foreign dopants that exceed their solubility limit in the host material. As a result, the Seebeck coefficient of the sample Sn 0.94 Ag 0.09 La 0.05 Te reaches 161 μV·K -1 , and the thermal conductivity drops to 1.87 W·m -1 ·K -1 , which doubles the zT value on the basis of the pristine SnTe (zT ≈ 0.49) to ~1.0 at 873 K. The improvement of TE performance in this work is comparable to the current research on SnTe based TE materials.

Experimental methods
For the preparation of high quality samples, ~9 g Sn 1+δ Te (δ = 0−0.05), Sn 1.03−x Ag x Te (x = 0.01−0.09), and Sn 0.94 Ag 0.09 La y Te (y = 0.01−0.07) cylinders with diameter of ~12.7 mm were synthesized by combining a melting reaction and spark plasma sintering (SPS). In detail, Sn (99.9%, Aladdin), Te (99.9%, Aladdin), Ag (99.9%, Aladdin), and La (99.9%, Aladdin) were weighted with stoichiometric composition and flame-sealed in quartz tubes under a vacuum pressure (< 1 Pa). The tubes were slowly heated to 1273 K in 12 h using a programmable furnace, then held for 6 h, and rapidly quenched by ice water. The obtained bulk materials were crushed and milled by hand with an agate mortar, and then transferred into graphite molds lined with carbon papers. Under vacuum condition (< 10 Pa), the samples were quickly transformed into cylinders with relatively high density ( 97%) by SPS under an axial press of 50 MPa at 823 K for 5 min.
The powders obtained by grinding the SPS sintered bulk materials were analyzed by using an X-ray diffraction measurement (XRD, D8 Advance, Bruker) with Cu Kα1 radiation (λ = 1.54 Å) at 40 kV and 40 mA. The microstructures of the as-synthesized samples were characterized by a transmission electron microscopy (TEM, FEI Talos F200X). An electron probe microanalyzer (EPMA, JEOL JXA-8230) was performed to determine the composition distribution. The measurements of electrical conductivity (σ) and Seebeck coefficient (S) were performed on a commercial CTA-3 instrument (Beijing Cryoall Science and Technology Co., Ltd., China) in the range of 300-873 K under a low helium atmosphere. The Hall coefficient (R H ) was measured by the van der Pauw technique (8404, Lakeshore, USA) under a reversible magnetic field of 1.5 T at room temperature. The carrier concentration (n) was estimated through the expression n = 1/(eR H ), where e is the elementary charge. The Hall carrier mobility (μ) was calculated from the expression μ = σR H . The thermal conductivity (κ) was determined by the expression κ = DC p , where D was the thermal diffusivity, C p was the specific heat indexed to the data from Ref. [40], and  was the density. The thermal diffusivity (D) was directly measured using the laser flash diffusivity method (Netzsch LFA-467 HT, Germany) at 300-873 K under an argon flow. The density of the samples was measured using the Archimedes method.
The electronic structures of pristine SnTe, Ag doped, Ag and La co-doped SnTe were simulated using the density functional theory (DFT) in the Vienna Ab initio Simulation Package (VASP) [41]. The projectoraugmented-wave (PAW) [40] and generalized gradient approximation (GGA) to exchange-correlation term with the Perdew, Burke, and Ernzerhof (PBE) were used in the computations [43]. The cut-off energy of plane-wave set was 400 eV. The theoretical models of pristine SnTe, Ag, La, double Ag, Ag and La co-doped SnTe were composed of a 3×3×3 super-cell with 54 atoms. Correspondingly, a Γ-centered 4×4×4 k-mesh was used in the Brillouin zone. Spin-orbit coupling was included in the band structure calculations but not added in the structure relaxation process.

Results and discussion
To suppress the excess inherent Sn vacancies, we adopted the approach of Sn self-compensation at first, which indeed effectively enhances the figure of merit zT (the detailed data is not shown here). In line with the previous reports [27,28], the sample with 3 mol% Sn self-compensation (Sn 1.03 Te) represents optimized thermoelectric performance in our experiments. On this basis, Ag doping was applied to manipulate the energy separation (E v ) between the light and heavy valence bands according to the literatures [15,32]. Among our synthesized Ag doped samples, Sn 0.94 Ag 0.09 Te had the best thermoelectric performance. Therefore, we carried out La doping in Sn 0.94 Ag 0.09 Te, namely Sn 0.94 Ag 0.09 La y Te (y = 0−0.07). Figure 1 gives the room-temperature XRD patterns of the pristine SnTe and the samples Sn 0.94 Ag 0.09 La y Te (y = 0−0.07). The main diffraction peaks as shown in Fig. 1(a) could be well matched with the cubic rock-salt phase of SnTe. In addition, weak peaks at ~29.7° and ~31.1°, which could be indexed to Ag 2 Te, can be observed in Sn 0.94 Ag 0.09 Te and Sn 0.94 Ag 0.09 La 0.01 Te ( Fig. 1(b)). However, the peak at ~31.1° disappears, and new peaks at ~29.8° and ~30.7° which may be ascribed to lanthanum telluride (La 4 Te 7 and LaTe 3 ) appear after the La doping. Besides, the peak at ~29.8° strengthens with increasing La content. This phenomenon suggests that the La doping inhibits the formation of Ag 2 Te phase and lanthanum tellurides precipitates generate if the La doping exceeds its low solubility limit ( 1 mol%). This is further demonstrated by EPMA of the polished surface, as typically shown in Fig. 2 for Sn 0.94 Ag 0.09 La 0.05 Te. The element mapping discloses that Ag rich (Fig. 2(d)) and La rich (Fig. 2(e))  regions exist in the SnTe matrix (Figs. 2(b) and 2(c)). The point elemental scanning shows that the Ag rich regions are Ag-Sn alloys (e.g., point 1 in Fig. 2(f) exhibits that the Ag/Sn atomic ratio is 2.72:1) rather than Ag 2 Te, though they were not detected by the XRD characterization, possibly due to its relatively low detection sensitivity. Suitable nanoscale impurity precipitates which induce lots of interfaces in matrix are expected to reduce the lattice thermal conductivity through blocking the transport of phonons [39]. Figure 3 represents the electronic transport properties as a function of measurement temperature. As displayed in Fig. 3(a), the electrical conductivity () of all samples decreases with increasing temperature, indicating that they act as electronic transport behavior of degenerate semiconductors and the bipolar diffusion effect can be ignored. With the help of Sn self-compensation and Ag doping, the electrical conductivity drops over the whole temperature range. Furthermore, the decline of electrical conductivity is relayed by the La doping, especially at low temperatures. For example, the electrical conductivity at 323 K is decreased from 6.9510 5 S·m -1 (the pristine SnTe) to 5.4110 5 S·m -1 (Sn 0.94 Ag 0.09 Te) by the Sn self-compensation and Ag doping, and further reduced to 3.4710 5 S·m -1 (Sn 0.94 Ag 0.09 La 0.05 Te) through the La doping. At 873 K, the electrical conductivity is depressed from 1.6210 5 to 0.8310 5 S·m -1 with the co-action of Sn self-compensation, Ag and La co-doping. It is well known that Sn self-compensation could suppress the hole concentration, leading to the decline of electrical conductivity [28,29]. To disclose the physical mechanism of electrical variation caused by the La doping, we obtained the carrier concentration (n) and mobility () depending on the content of La doping by the Hall effect measurement at room temperature. From Fig. 3(b), we can conclude that the carrier concentration gradually decreases with the rise of La content while the carrier mobility increases at www.springer.com/journal/40145 first and then reverses at 3 mol% La doping. Exactly, the carrier concentration is moderately reduced from 2.6810 20 cm -3 for Sn 0.94 Ag 0.09 Te to 1.8110 20 cm -3 for Sn 0.94 Ag 0.09 La 0.05 Te. The substitution of La 3+ on the cationic lattice sites (Sn 2+ ), which could serve as a donor type dopant in SnTe matrix, may be responsible for the reduction of carrier concentration. However, complete participation of 1 mol% La atoms into cationic lattice sites should theoretically produce a reduction of 3.210 20 cm -3 on carrier concentration, which suggests that only a small part of atomic La could enter into the cationic lattice sites ( 1 mol%). This is in accordance with the above XRD results, which exposes that lanthanum telluride precipitates formed even introduced only 1 mol% La. Meanwhile, the carrier mobility is increased from 136 to 208 cm 2 ·V -1 ·s -1 through a slight La doping (1 mol%), possibly due to the fact that a portion of Sn vacancies may be filled up by La atoms. In fact, the promotion of carrier mobility by filling up the cationic vacancies is also reported in Cu 2 Te-alloyed PbTe [44]. Nevertheless, the low solubility limit of La in the SnTe lattice ( 1 mol%) prohibits the further enhancement of carrier mobility and even the excessive La doping decreases the carrier mobility. It is reasonable to consider that the interfaces between lanthanum telluride precipitates and SnTe matrix induced by excessive La doping may play electron scattering centers, so that the carrier mobility is reduced to 170 cm 2 ·V -1 ·s -1 for the sample Sn 0.94 Ag 0.09 La 0.07 Te. In a word, the downward change of carrier concentration overcomes the improvement of carrier mobility, resulting in the reduction of electrical conductivity as evaluated by the formula  = ne. Figure 3(c) shows that the Seebeck coefficient of all samples is positive value, indicating that the majority carriers are holes. Besides, it increases with rising the measurement temperature, which could be ascribed to the gradual participation of heavy valence bands for electron transport at elevated temperatures. Furthermore, the integrated effect of Sn self-compensation, Ag and La co-doping indeed increases the Seebeck coefficient over the whole temperature range. For instance, the Seebeck coefficient at room temperature is 12 μV·K -1 for the pristine SnTe, which increases to 48 μV·K -1 for the sample Sn 0.94 Ag 0.09 Te, and further to 59 μV·K -1 for the sample Sn 0.94 Ag 0.09 La 0.05 Te. A maximum value of 161 μV·K -1 was obtained for the sample Sn 0.94 Ag 0.09 La 0.05 Te at 873 K. It is expected that the convergence of light bands and heavy bands as schematically shown in Fig. 3(d) should increase the Seebeck coefficient, according to the relationship [45]: where k B , h, N V , and * b m are the Boltzmann constant, the Plank constant, the valley degeneracy, and the effective mass of each valley, respectively. To clarify the origin of the boosted Seebeck coefficient, the Pisarenko plot calculated on the basis of a two-valence-band model is used as a reference line [46], where similar reported data is also cited for a comparison [32,47]. As shown in Fig. 3(e), the Seebeck coefficient of the samples Sn 0.94 Ag 0.09 Te and Sn 0.94 Ag 0.09 La y Te obviously stays above the Pisarenko line. Theoretical electronic band calculation is applied to prove that the band alignment induced by the Ag and La co-doping is the main reason holding out the Seebeck coefficient enhancement. Figure 4 shows the band structures of Sn 27 Te 27 , Sn 25 Ag 2 Te 27 , Sn 26 La 1 Te 27 , and Sn 25 Ag 1 La 1 Te 27 calculated by the first-principles simulation, where the effect of spin-orbit coupling (SOC) is taken into consideration since Te is a heavy element and its 5p orbital could contribute much to the valence band. The direct band gap (E g ) of Sn 27 Te 27 super-cell standing for the pristine SnTe is 0.1 eV at L point ( Fig. 4(a)), which is in line with the previous calculation (0.11 eV [15]). In contrast with the pristine SnTe, the Ag doping ( Fig. 4(b), Sn 25 Ag 2 Te 27 ), La doping (Fig. 4(c), Sn 26 La 1 Te 27 ), and Ag and La co-doping (Fig. 4(d), Sn 25 Ag 1 La 1 Te 27 ) effectively broaden the band gap to 0.11, 0.13, and 0.27 eV, respectively. The narrow band gap in SnTe may cause the bipolar diffusion effect if the carrier concentration is reduced, which could be reflected by a possible drop of Seebeck coefficient at high temperature, while the increased band gap should eliminate this problem. The disappearance of inflection point for the Seebeck coefficient in our experiments qualitatively supports the theoretical calculation. Moreover, the introduction of Ag and La synergistically decreases the band offset E v . Particularly, the Ag and La co-doping strongly weakens the band separation from 0.25 eV for Sn 27 Te 27 to 0.08 eV for Sn 25 Ag 1 La 1 Te 27 , and that is why we collected the superior Seebeck coefficient in the samples Sn 0.94 Ag 0.09 La y Te.
Thanks to the greatly improved Seebeck coefficient, the power factor (Fig. 3(f)) is elevated over the entire temperature range, and a highest value of ~2436 W·m -1 ·K -2 at 873 K is obtained for the sample Sn 0.94 Ag 0.09 La 0.01 Te. This is comparable to the best results reported in AgInTe 2 -alloyed SnTe, HgTe-alloyed Sn 0.98 Bi 0.02 Te, and In, Cd co-doped SnTe [15,16,48].  www.springer.com/journal/40145 figure, we could claim that the Ag and La co-doping worked together to depress the total thermal conductivity over the whole temperature range. At 323 K, the total thermal conductivity is remarkably reduced from 9.12 W·m -1 ·K -1 for the pristine SnTe to 4.19 W·m -1 ·K -1 for the sample Sn 0.94 Ag 0.09 La 0.05 Te. As a result, a minimum value of 1.87 W·m -1 ·K -1 (Sn 0.94 Ag 0.09 La 0.05 Te) is obtained at 873 K. The separated analysis of carrier and phonon contribution parts could provide a clear identification for the reduction of thermal conductivity. The carrier thermal conductivity ( e ) is estimated by using the equation  e = LT with the most used L of 1.510 -8 W··K -2 , and the lattice thermal conductivity is obtained from  l =  - e . As shown in Fig. 5(b), the carrier thermal conductivity is effectively decreased with the help of Ag and La co-doping as expected since the electrical conductivity is diminished. Correspondingly, the lattice thermal conductivity as a function of temperature is plotted in Fig. 5(c), which decreases continuously with increasing temperature. In surprise, the Ag and La co-doping greatly blocks the phonon transport at low temperature. For instance, the lattice thermal conductivity is decreased over one time, from 5.73 W·m -1 ·K -1 for the pristine SnTe to 2.53 W·m -1 ·K -1 for the sample Sn 0.94 Ag 0.09 La 0.05 Te. On the other hand, the corresponding variation of lattice thermal conductivity at high temperature is nearly indistinguishable, though a minimum value of 0.77 W·m -1 ·K -1 close to the theoretical minimum thermal conductivity (κ min ≈ 0.4 W·m -1 ·K -1 ) of SnTe is obtained for the sample Sn 0.94 Ag 0.09 La 0.05 Te at 873 K [49].
To understand the reduced lattice thermal conductivity attained in the sample Sn 0.94 Ag 0.09 La 0.05 Te, its microstructural information is characterized by TEM (Fig. 6). Figure 6(a) reveals that there exists lots of dislocations (marked by the red arrows). Besides, impurity precipitates and grain boundaries are other important microstructures, as identified by the purple dotted rhombus and yellow straight line, respectively. As shown in Fig. 6(b), the crystal plane spacing of ~6.67 Å for the impurity precipitate could be indexed to the (004) plane of LaTe 3 , while the matrix is the SnTe phase because of the well match between the crystal plane spacing of ~3.14 Å and (200) plane of SnTe. In addition, the observation of interface between impurity precipitates and matrix unveils that the mismatch of (220) crystal planes between LaTe 3 and SnTe is ~4.65° (the inset in Fig. 6(b)). This semi-coherent heterogeneous grain boundary may strongly prohibit the phonon transport while provide weak influence for the transport of carriers [50]. The IFFT pattern as given in Fig. 6(c) demonstrates that there exist lots of dislocations (marked by the dotted circles) at the semi-coherent heterogeneous grain boundary. In fact, the grain boundary could also be better described as a collection of dislocations rather than perfectly scattering interfaces for phonons [51]. Collectively, N d is evaluated to be ~3.1610 7 mm -2 through contrast intensity ( Fig. 6(d)), which is comparable to the level of melt-centrifuged (Bi,Sb) 2 Te 3 [52]. Mion et al. [53] showed that dislocation density above 10 5 mm -2 has a significant effect on the lattice thermal conductivity and thus we believe that the dislocation density in the sample Sn 0.94 Ag 0.09 La 0.05 Te is of an appropriate order of magnitude to lower the lattice thermal conductivity. Note that further increasing in La content could result in formation of excessive impurity aggregations with large size and high thermal conductivity (e.g., Ag-Sn alloys), which may be responsible for the elevation of  l on the sample Sn 0.94 Ag 0.09 La 0.07 Te.
The simultaneous optimization of carrier and phonon transport promotes the figure of merit zT. As given in Fig. 5(d), the Ag and La co-doping enhances the zT value over the whole temperature range. Finally, a maximum value of ~1.0 is achieved for the sample Sn 0.94 Ag 0.09 La 0.05 Te at 873 K, about one time enhancement in comparison with that of the pristine SnTe (~0.49). This promotion rivals most of the previous works for the SnTe based TE materials [2,38].

Conclusions
In summary, the co-doping of Ag and La optimizes the band structure (valence band convergence and widening band gap) to enhance the Seebeck coefficient together with introducing an appropriate density of dislocations as phonon scattering centers. As a consequence, our results show that the SnTe system co-doped with Ag and La achieves a satisfactory power factor (~2436 W·m -1 ·K -2 at 873 K), and its thermal conductivity is significantly reduced to 1.87 W·m -1 ·K -1 at 873 K. Ultimately, the thermoelectric performance of the sample Sn 0.94 Ag 0.09 La 0.05 Te (zT ≈ 1.0) is twice that of the pristine SnTe (zT ≈ 0.49) at 873 K. This work proves that dense dislocations of appropriate magnitude and electronic band engineering can be simultaneously generated by introducing rare earth element La to effectively improve the thermoelectric properties of SnTe, which has a certain guiding effect on the research of thermoelectric materials with similar crystal structure.