Superior performance and high service stability for GeTe-based thermoelectric compounds

ABSTRACT GeTe-based compounds have been intensively studied recently due to their superior thermoelectric performance, but their real applications are still limited so far due to the drastic volume variation that occurs during the rhombohedral–cubic phase transition, which may break the material or the material/electrode interface during service. Here, superior performance and high service stability for GeTe-based thermoelectric compounds are achieved by co-doping Mg and Sb into GeTe. The linear coefficient of thermal expansion before phase transition is greatly improved to match that after phase transition, yielding smooth volume variation around the phase transition temperature. Likewise, co-doping (Mg, Sb) in GeTe successfully tunes the carrier concentration to the optimal range and effectively suppresses the lattice thermal conductivity. A peak zT of 1.84 at 800 K and an average zT of 1.2 in 300–800 K have been achieved in Ge0.85Mg0.05Sb0.1Te. Finally, a Ni/Ti/Ge0.85Mg0.05Sb0.1Te thermoelectric uni-leg is fabricated and tested, showing quite good service stability even after 450 thermal cycles between 473 K and 800 K. This study will accelerate the application of GeTe-based compounds for power generation in the mid-temperature range.


INTRODUCTION
The International Energy Agency's Global Energy & CO 2 Report (2017) showed that global energy demand grew by 2.1% in 2017, more than twice as much as the increase in 2016. Meanwhile, global energy-related CO 2 emission grew by 1.4% in 2017, a resumption of growth after three years of stabilized global emissions [1]. Such huge energy demands and severe CO 2 emissions impose a pressing need to use energy more efficiently.
As a sustainable and eco-friendly energy conversion technology, thermoelectric (TE) technology has drawn increasing attention from both academic and industrial communities [2]. It can be potentially used to convert the waste heat from vehicle exhausts or plants directly into useful electricity, providing an alternative way to more efficiently utilize fossil energy [3]. Large-scale application of TE technol-ogy requires highly efficient and reliable TE devices [4,5]. The efficiency of a TE device is related to the material's TE figure of merit zT = S 2 σ T/(κ e + κ L ), where S is the Seebeck coefficient, σ is the electrical conductivity, κ L is the lattice thermal conductivity, κ e is the carrier thermal conductivity, and T is the absolute temperature. Thus, developing TE materials with high zT and good service stability is the foremost task in thermoelectrics.
Over the past two decades, the TE community has witnessed unprecedented success in improving the zT of classical TE materials and in the discovery of many types of novel TE materials [6][7][8][9][10][11][12][13][14][15][16]. As a rapidly growing class of TE materials, GeTebased compounds are very special and were to give high TE performance as early as the 1960s, but only recently has more attention been paid to them [17][18][19]. GeTe is a p-type narrow band-gap The inset shows a schematic map of the thermal cycling test. The hot side temperature is cycled from 473 K to 800 K. The cold side temperature is fixed at 300 K. The data are collected when the hot side temperature of the uni-leg is 800 K.
semiconductor crystallizing with a rhombohedral structure (R3m) at room temperature (Fig. 1a). Around 700 K, the rhombohedral R3m structure undergoes a ferroelectric structure transition and converts to the high-temperature cubic Fm3 m structure (Fig. 1a) [20]. Due to the presence of severe intrinsic Ge vacancy inside the lattice, GeTe has a very high carrier concentration in the order of 10 21 cm −3 at room temperature yielding very low S (∼ 30 μV K −1 ) and high κ e (∼ 5 W m −1 K −1 ) [21][22][23]. Thus, most of the studies for GeTe focus on reducing the over-high carrier concentration and pushing it to the optimal range. Along this route, many high-performance p-type GeTe-based compounds, such as Ge 0. 9 [31], and Zn 4 Sb 3 [32], which have maximum zT values around unity (Fig. 1b). Despite the superior zT values, the real application for GeTe-based compounds is greatly limited by the drastic volume variation occurring during the rhombohedral-cubic phase transition. As shown in Fig. 1c, an obvious discontinuity in the temperature dependence of the relative length variation (dL/L 0 ) is observed for GeTe around 700 K. The measured linear coefficient of thermal expansion (CTE) before the phase transition is only 11.2 × 10 −6 K −1 , while it increases to as high as 23.4 × 10 −6 K −1 after the phase transition. Moreover, abnormal negative CTE appears during the phase transition range. Similar characteristics have also been observed in many element-doped GeTe compounds, such as Sb-doped GeTe, (Bi, Sb) co-doped GeTe, and (Mn, Sb) co-doped GeTe (Fig. 1c). The drastic volume variation caused by such huge CTE mismatches makes it easy to break GeTe-based materials when they experience frequent thermal cycles due to large thermal stress. This is the possible reason why GeTebased devices are currently absent although they possess excellent TE performance.
In this study, Mg and Sb are co-doped in GeTe to successfully tune the carrier concentration to the optimal range and effectively suppress the lattice thermal conductivity, leading to a maximum zT of 1.84 at 800 K and an average zT of 1.2 at 300-800 K in Ge 0.85 Mg 0.05 Sb 0.1 Te (Fig. 1b). Furthermore, the CTE of the low-temperature phase is obviously enhanced to match the high-temperature phase ( Fig. 1c) for good service stability, which is well demonstrated in a Ni/Ti/Ge 0.85 Mg 0.05 Sb 0.1 Te TE uni-leg that has quite stable power output even after 450 thermal cycles between 473 K and 800 K (Fig. 1d).

RESULTS AND DISCUSSION
Volume expansion with increasing temperature is determined by the increased kinetic energy of composed atoms [33]. The crystal structure of the GeTe low-temperature rhombohedral phase can be viewed as a slightly distorted rock-salt lattice along the (111) direction [34], which has a pseudo-cubic lattice parameter a c and a pseudo-cubic angle α. Both a c and α can be related to the lattice constants (a and c) of the hexagonal unit cell in GeTe via the relations a = 2a c sin (α/2) and c = a c (3+6cosα) 1/1 [35]. The distortion degree is reflected by the deviation of the pseudo-cubic angle α from 90 • (Fig. 1a). In GeTe, α is about 88.28 • at 300 K, while it is 90 • above the phase transition temperature. Such small deviation in α is believed to be one of the origins of the CTE mismatch between the low-and hightemperature phases. If the α of the rhombohedral phase is close to 90 • , the CTE of the low-and hightemperature phases should be quite similar and thus is suitable to be used to fabricate stable TE devices.
Here we choose Mg and Sb co-dopants to tune the lattice parameters and TE properties of GeTe-based compounds. Figure 2a shows the room-temperature powder X-ray diffraction (PXRD) patterns for Ge 0.95-x Mg 0.05 Sb x Te (x = 0, 0.05, 0.075, and 0.1). The main diffraction peaks for Ge 0.95 Mg 0.05 Te can be well identified as belonging to the rhombohedral structure (R3m). A very tiny amount of Ge precipitates is observed, which is observed commonly in GeTe-based compounds [28,36,37]. The energy dispersive spectroscopy (EDS) elemental mapping for Ge 0.95 Mg 0.05 Te shows that there is no obvious Mg-rich phase ( Supplementary Fig. S1), confirming that all Mg atoms enter the lattice of GeTe. The actual chemical composition of Ge 0.95 Mg 0.05 Te characterized by electron probe microanalysis is listed in Table 1; this is almost the same as the nominal compositions. With increasing Sb-doping content, the double peaks [(024) and (220)] in 2θ around 41-45 • gradually approach each other. When the Sb-doping content x = 0.1, the double peaks almost merge together, suggesting that the pseudo-cubic angle α should be close to 90 • . Likewise, the EDS elemental mapping proves that there is no obvious Sb-rich or Mg-rich phase in the Ge 0.85 Mg 0.05 Sb 0.1 Te matrix ( Supplementary Fig. S2). The electron backscatter diffraction (EBSD) characterization performed on the sintered bulk Ge 0.85 Mg 0.05 Sb 0.1 Te sample shows that the grain size has a quite wide distribution in the range of 1-50 μm (Fig. 2b). Figure 2c shows the selected area electron diffraction (SAED) patterns along the zone axis of <11 0> performed on Ge 0.85 Mg 0.05 Sb 0.1 Te, which can be well identified as the rhombohedral structure. Rietveld refinement based on room-temperature Xray data is performed to obtain the pseudo-cubic lattice parameter (a c ) and pseudo-cubic angle (α). The details can be found in Supplementary Fig.  S3. As shown in Fig. 2d, doping Mg into GeTe scarcely alters a c and α, which is reasonable considering the similar ionic radii between Mg 2+ (0.72Å) and Ge 2+ (0.73Å). In contrast, with increasing Sbdoping content, both the a c and α gradually increase. For Ge 0.85 Mg 0.05 Sb 0.1 Te, α is already enlarged to 89.18 • . Supplementary Fig. S4 shows the heat-flow curves for Ge 0.95-x Mg 0.05 Sb x Te (x = 0, 0.05, 0.075, and 0.1) measured by differential scanning calorimetry (DSC). All samples have an endothermic peak around 500-700 K, indicating that the rhombohedral phase converts to the cubic phase in this temperature range.
Because the pseudo-cubic angles α in the (Mg, Sb) co-doped samples are close to 90 • , the CTE for the rhombohedral phase is also expected to be close to that for the high-temperature cubic phase. This is confirmed by the measured relative length variation dL/L 0 and CTE for the (Mg, Sb) co-doped materials (Fig. 1c, Fig. S5 and Table 2). With increasing Sb-doping content, the CTE before the phase transition gradually increases from 11.2 × 10 −6 K −1 for GeTe to 19.2 × 10 −6 K −1 for Ge 0.85 Mg 0.05 Sb 0.1 Te. The latter value is quite close to that after the phase transition (23.4 × 10 −6 K −1 ). In particular, the abnormal volume contraction during the phase transition range almost disappears for Ge 0.85 Mg 0.05 Sb 0.1 Te. As shown in Fig. 1c  changes quite smoothly in the phase transition temperature range, which is beneficial for achieving high stability during service. Since solely doping Mg or Sb into GeTe cannot eliminate such negative CTE (Fig. 1c), the disappearing abnormal volume contraction is believed to be due to the coupling effect of the Mg and Sb dopants. Figure 3 shows the measured TE properties for Ge 0.95-x Mg 0.05 Sb x Te (x = 0, 0.05, 0.075, and 0.1). The data for GeTe are included for comparison. All samples possess positive S throughout the entire measured temperature range, indicating that holes are the dominated carriers. Doping Mg into GeTe only slightly changes the S but significantly lowers the σ . At 300 K, the σ for Ge 0.95 Mg 0.05 Te is 4.4 × 10 5 S m −1 , about 40% of that for GeTe. However, like GeTe, Ge 0.95 Mg 0.05 Te still shows a typical highly degenerate semiconducting transport behavior with σ decreasing with increasing temperature. Compared with the Mg-doping, the Sb-doping in Ge 0.95 Mg 0.05 Te affects the electrical transport substantially (see Fig. 3a and b). With increasing Sbdoping content from x = 0 to x = 0.1, the σ is gradually decreased. The σ for Ge 0.85 Mg 0.05 Sb 0.1 Te is only 3.7 × 10 4 S m −1 at 300 K, about one order of magnitude lower than that for Ge 0.95 Mg 0.05 Te. Likewise, the S gradually increases with increasing Sbdoping content in the entire temperature range. The

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Xing et al. Table 2. Room-temperature physical properties of Ge 0.95-x Mg 0.05 Sb x Te (x = 0, 0.05, 0.075, and 0.1). The data for GeTe are also included.  Supplementary Fig. S6, the power factor PF (= S 2 σ ) for the (Mg, Sb) co-doped GeTe samples above 600 K is lower than that for GeTe. Figure 3d shows the total thermal conductivity (κ) for Ge 0.95-x Mg 0.05 Sb x Te (x = 0, 0.05, 0.075, and 0.1). All samples possess quite low κ values as compared with GeTe. The κ for Ge 0.85 Mg 0.05 Sb 0.1 Te is only about 1.2 W m −1 K −1 at 300 K, about oneeighth of that for GeTe and one-sixth of that for Ge 0.95 Mg 0.05 Te. Such greatly lowered κ is a result of two factors. One factor is the reduced carrier contribution in the thermal transport. Supplementary  Fig. S7 shows the calculated carrier thermal conductivity κ e for Ge 0.95-x Mg 0.05 Sb x Te (x = 0, 0.05, 0.075, and 0.1) based on the Wiedemann-Franz law (κ e = L 0 Tσ , where the Lorenz number L 0 is estimated based on the single parabolic band model with the value shown in Supplementary Fig. S8). Clearly, the (Mg, Sb) co-doping in GeTe greatly suppresses κ e by lowering σ . In addition, due to the atomic size and mass mismatch among Ge, Mg, and Sb, doping Mg and Sb at Ge sites also introduces additional mass and strain field fluctuations to strongly scatter heat-carrying phonons to lower the lattice thermal conductivity κ L . Figure 3d (Fig. 3f), which is among the top values reported in this temperature range [26,27,[38][39][40][41][42].
The reduced carrier concentration is one of the main reasons for the enhanced zT values in the present (Mg, Sb) co-doped GeTe. Figure 4a shows the measured Hall carrier concentration (n) for these samples at room temperature. Due to the presence of severe Ge vacancies inside the lattice, the n for the undoped GeTe is as high as 7.5 × 10 20 cm −3 , which significantly deviates from the optimal value (around 2 × 10 20 cm −3 ) for good electrical transport [43]. Although the valence state of Mg is +2 that is identical to that of the host atom Ge, doping Mg into GeTe further increases the n to 1.3 × 10 21 cm −3 . Similar phenomenon has been also observed in Mn-doped GeTe, in which Mn also adopts a +2 valence state [26]. The increased n should be attributed to the increased lattice defects such as Ge vacancies inside the lattice. On the other hand, differing from Mg and Mn, Sb behaves as an electron donor in GeTe. As shown in Fig. 4a, the n gradually decreases with increasing Sbdoping content. When the Sb-doping content x = 0.1, n is reduced to as low as 2.2 × 10 20 cm −3 at 300 K, about one-sixth of that for Ge 0.95 Mg 0.05 Te. For comparison, the n data for the Sb single-doped GeTe samples are also included in Fig. 4a [40,44]. Interestingly, with the same Sb-doping content, the Ge 0.95-x Mg 0.05 Sb x Te sample possesses almost the same n as that of Ge 1-x Sb x Te, indicating that Mg does not yield extra carriers when it coexists with Sb in GeTe. However, Fig. 4a shows that Mg obviously lowers the carrier mobility (μ). With the same Sb-doping content, the Ge 0.95-x Mg 0.05 Sb x Te sample possesses lower μ than that for the Ge 1-x Sb x Te samples. The reduced μ is responsible for the much-lowered electrical conductivity in the Mgincluding GeTe samples (Fig. 3a).
The relationship between n and μ for Ge 0.95-x Mg 0.05 Sb x Te can be more clearly illustrated in Fig. 4b. The μ values for the Ge 0.95-x Mg 0.05 Sb x Te samples obey a similar variation trend to those for the Ge 1-x Sb x Te samples [40,44]. Nevertheless, in a similar n range, the μ values for the Ge 0.95-x Mg 0.05 Sb x Te samples are much lower than those for the Ge 1-x Sb x Te samples, which should be due to the additional defect scattering introduced by Mg dopants at the Ge sites. Figure 4c plots S versus n for Ge 0.95-x Mg 0.05 Sb x Te. S increases with decreasing n. By using a single parabolic band model and assuming that scattering is dominated by acoustic phonons, the theoretical Pisarenko curves with different density-of-state effective masses (m * ) are also plotted in Fig. 4c. Obviously, the increased S with decreasing n is attributed to the heavier m * . For the

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Xing et al.  being consistent with the measured lower μ in these samples ( Fig. 4a and b). For comparison, the S and n data for the Ge 1-x Sb x Te samples are also included in Fig. 4c [40,44]. Clearly, in the same n range, the S values for the Ge 0.95-x Mg 0.05 Sb x Te samples are larger than those for the Ge 1-x Sb x Te samples. In order to better understand the effect of Mg in GeTe, the electronic band structures and density-of-state (DOS) near the Fermi levels for both pure GeTe and Mg-doped GeTe rhombohedral supercells (3 × 3 × 3) are calculated. As shown in Fig. 4d and Supplementary Fig. S9, doping Mg significantly modifies the band structures of both the rhombohedral phase and cubic phase, yielding steeper DOS near the valence band edge, especially in the range from −0.1 to −0.3 eV. The steeper DOS leads to the higher m * , which is responsible for the larger S and lower μ values for the Ge 0.95-x Mg 0.05 Sb x Te than those for the Ge 1-x Sb x Te in a similar n range ( Fig. 4b and d).
Generally, the weighted mobility μ W = μ(m * /m e ) 3/2 is a very effective performance indicator for the electrical transport in TE materials [45]. As shown in the inset of Fig. 4e, the μ W for Ge 0.95-x Mg 0.05 Sb x Te at 300 K gradually increases with decreasing n due to the enhanced m * . Correspondingly, the PF values for Ge 0.95-x Mg 0.05 Sb x Te exhibit similar n-dependence. As shown in Fig. 4e, Ge 0.85 Mg 0.05 Sb 0.1 Te has a maximum PF of 14.2 μW cm −1 K −2 at 300 K, which is about three times that of Ge 0.95 Mg 0.05 Te. For comparison, Fig. 4e also plots the PF and n data for Ge 1-x Sb x Te [40,44]. Despite the lower μ (Fig. 4b), the (Mg, Sb) co-doped GeTe samples possess similar PF values to those Sb single-doped Ge 1-x Sb x Te in a similar n range due to their higher m * . However, it should be noted that the Ge 0.95-x Mg 0.05 Sb x Te samples possess much lower κ L than the Ge 1-x Sb x Te samples with the same Sb-doping content, which can be well demonstrated by Fig. 4f. The additional mass and strain field fluctuations introduced by the Mg dopants at Ge sites are responsible for this phenomenon. Finally, the well-maintained high PF and significantly lowered κ L in Ge 0.95-x Mg 0.05 Sb x Te result in a higher zT than those for Ge 1-x Sb x Te ( Supplementary Fig. S10).
The Ge 0.95-x Mg 0.05 Sb x Te in this study provides a good possibility to fabricate stable and efficient TE modules applied in the mid-temperature range. Here, a GeTe-based TE uni-leg is obtained by onestep sintering of the Ge 0.85 Mg 0.05 Sb 0.1 Te powder, Ti powder, and Ni powder directly. The dimensions of the Ni/Ti/Ge 0.85 Mg 0.05 Sb 0.1 Te uni-leg are 4 × 6 × 8 mm. Excellent bonding without any cracks is observed in the Ti/Ge 0.85 Mg 0.05 Sb 0.1 Te interface area and Ni/Ti interface area (Fig. 5a). Furthermore, backscatter electron imaging mapping shows that there is no obvious diffusion layer formed near the interface areas (Fig. 5a). The electrical contact resistivity (R c ) of the Ti/Ge 0.85 Mg 0.05 Sb 0.1 Te interface in the uni-leg is measured on a homemade instrument [46]. As shown in Fig. 5b, a leap is observed from the Ge 0.85 Mg 0.05 Sb 0.1 Te side to the Ti side. The calculated R c based on this leap is 134 μ cm 2 , which is much larger than those observed in other TE modules, such as 20 μ cm 2 for a CoSb 3 /Ti interface [47]. However, the electrical contact resistance caused by the R c only contributes about 5% of the total resistance of the Ni/Ti/Ge 0.85 Mg 0.05 Sb 0.1 Te uni-leg; thus it is still an acceptable value.
The performance of the Ni/Ti/ Ge 0.85 Mg 0.05 Sb 0.1 Te TE uni-leg is measured using a home-built testing system. The current, output voltage, power output, and internal resistance are measured under different operating temperatures. Figure 5c shows the I-V curves, which exhibit a good linear relationship. The maximum power output (P max ) is 135 mW with the hot side temperature (T hot ) of the uni-leg being 800 K and the temperature difference ( T) across the uni-leg being 500 K. If the electrical contact resistivity R c of the Ti/Ge 0.85 Mg 0.05 Sb 0.1 Te interface can be further reduced, higher P max is expected.
A thermal cycling test is performed on the Ni/Ti/Ge 0.85 Mg 0.05 Sb 0.1 Te TE uni-leg to confirm its service stability. The hot side temperature is cycled between 473 K and 800 K, while the cold side temperature is fixed at 300 K. The output voltage, internal resistance, and power output of the unileg are collected when the hot side temperature is raised to 800 K. Normally, if any cracks have formed inside the material or at the interface area, the resistance will greatly increase, which would lead to a significant deterioration of the power output [48]. As shown in Fig. 5d and Fig. 1d, the internal resistance, output voltage, and power output are quite stable after even 450 cycles, suggesting that the Ge 0.85 Mg 0.05 Sb 0.1 Te material and its interface are well maintained during the thermal cycling test. This can be further confirmed by the scanning electron microscopy (SEM) characterization performed on the Ni/Ti/Ge 0.85 Mg 0.05 Sb 0.1 Te TE uni-leg after the thermal cycling test (Supplementary Fig. S11), which shows no cracks inside the material or near the interface area. The suppressed volume variation during the rhombohedral-cubic phase transition due to the improved CTE match between the rhombohedral and cubic phases (Fig. 1c) is believed to be responsible for the high service stability of the present Ni/Ti/Ge 0.85 Mg 0.05 Sb 0.1 Te TE uni-leg.

CONCLUSIONS
In summary, this study demonstrates that co-doping Mg and Sb into GeTe can obtain stable and efficient mid-temperature TE materials. A maximum zT of 1.84 at 800 K and a high average zT of 1.2 at 300-800 K have been achieved by simultaneously reducing lattice thermal conductivity and optimizing

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Xing et al. carrier concentration. More importantly, the suppressed volume variation during the phase transition due to the improved CTE match between the rhombohedral and cubic phases ensures that the TE uni-leg made by Ge 0.85 Mg 0.05 Sb 0.1 Te possesses quite high service stability even after 450 thermal cycles. This work should promote the real application of GeTe-based materials for TE power generation in the mid-temperature range.

Materials synthesis
High-quality polycrystalline samples were synthesized by melting of stoichiometric ratios of pure elemental Ge (shots, 99.999%), Te (shots, 99.999%), Sb (shots, 99.999%), and Mg (shots, 99.9%) in evacuated and sealed silica tubes. The mixtures were slowly heated up to 1373 K over 11 h and soaked at this temperature for 12 h, then quenched in ice water, followed by annealing at 873 K for five days. Next, the obtained ingots were hand-ground into fine powders in an agate mortar. Spark plasma sintering (SPS, Dr Sinter: SPS-2040) was carried out to obtain dense bulk samples under a uniaxial pressure of 60 MPa at 823 K for 10 min in graphite dies. The densities of the pellets were > 98% of the theoretical values, which are listed in Table 2.

Material characterization
Powder X-ray diffraction (D8 Advance, Bruker) was performed to analyze the phase purity of samples using Cu Kα radiation (λ = 1.5406Å) at ambient temperature. The lattice parameters were refined with a least-squares refinement method utilizing the WinCSD program package. The microstructures were observed by scanning electron microscopy (SEM, ZEISS Supra 55) and the chemical compo-sitions were characterized using energy dispersive spectrometry (EDS). A field emission transmission electron microscope (TEM, JEM-2100F) was employed to identify the crystal structure of the prepared samples. The electrical conductivity and Seebeck coefficient were measured on bulk samples with approximate dimensions of 2 × 2 × 8 mm, using commercial equipment (ZEM-3, ULVAC) under He atmosphere from 300 to 800 K. The thermal conductivity was calculated by κ = D × C p × ρ, where the heat capacity (C p ) was estimated using the Dulong-Petit law, the thermal diffusivity (D) was measured by the laser flash system (LFA457, Netzsch) under argon atmosphere and the density (ρ) was obtained using the Archimedes method. Hall coefficients (R H ), electrical conductivity and thermal conductivity from 5 K to 300 K were measured by a physical property measurement system (PPMS, Quantum Design). The maximum magnetic field reached 5 T in both positive and negative directions. The carrier concentration p and the carrier mobility (μ) were calculated according to the relation p = 1/eR H and μ = σ R H , respectively. Differential scanning calorimetric measurements (Netzsch DSC 404F3) were employed with a heating rate of 20 K/min to determine the phase transition characters of samples. The relative length variation (dL/L 0 ) with increasing temperature was measured by thermal expansion equipment (Netzsch, DIL 402 C). The linear coefficient of thermal expansion (CTE) was obtained by dividing the dL/L 0 in the assigned temperature range by the temperature difference ( T).

Uni-leg TE fabrication and testing
The p-type Ge 0.85 Mg 0.05 Sb 0.1 Te TE uni-leg with a thin Ti film as barrier layer and a thin Ni film as electrode was fabricated by sintering Ge 0.85 Mg 0.05 Sb 0.1 Te, Ti powder, and Ni powder directly using the hot-pressing technique. The sintering temperature, press, and time are 873 K, 60 MPa, and two hours, respectively. The obtained bulk was cut into bars with designed geometry using wire cutting. The Ni/Ti/Ge 0.85 Mg 0.05 Sb 0.1 Te interface was characterized by field emission scanning electron microscopy (FESEM, Magellan-400). The room-temperature electrical contact resistivity of the Ni/Ti/Ge 0.85 Mg 0.05 Sb 0.1 Te interface was measured by a home-made four-probe platform with the measurement details shown in Ref. [46]. The geometry of the measured sample is 4 × 6 × 8 mm 3 . The performance of the Ni/Ti/Ge 0.85 Mg 0.05 Sb 0.1 Te uni-leg is elevated by a home-made instrument. A schematic drawing is shown in Supplementary   Fig. S12. The current, output voltage, internal resistance, and power output were recorded at the temperature ramping process when the hot side temperature of the uni-leg reached 473 K, 573 K, 673 K, 773 K and 800 K. Circulating water with a fixed temperature of 300 K was used to cool the cold side. The maximum power output was obtained when the external electrical load was equal to the uni-leg's internal resistance. A thermal cycling test was performed by using a home-built testing system. The hot side temperature was repeatedly heated to 800 K at a rate of 50 K/min and held at this temperature for 5 min. Then the temperature was cooled to 473 K in 15 min. The output voltage, internal resistance, and power output of Ni/Ti/Ge 0.85 Mg 0.05 Sb 0.1 Te were collected when the hot side temperature was cycled to 800 K.

Calculation of the band structure
The first-principles calculations for the band structures were performed by employing the Vienna Ab Initio Simulation Package (VASP), implemented with the generalized gradient approximation functional and the projector-augmented wave (PAW) method. A 3 × 3 × 3 supercell of the GeTe formula unit was constructed for both the GeTe and Mg-doped GeTe with a cut-off energy of 400 eV for the plane-wave and an energy convergence criterion of 10 −3 eV per unit cell. The configuration with the lowest energy, optimized lattice parameters and atom positions is used for the defect-containing supercell.

SUPPLEMENTARY DATA
Supplementary data are available at NSR online.