Introduction

Over half of heat energy is lost during the energy conversion process; the recovery of waste heat will be beneficial to environmental protection and economic development1,15 and nano inclusions16,17.

GeTe is one of the most promising lead-free compounds working in the medium temperature range. Due to the intrinsically high carrier concentration (nH ≈ 1021 cm−3) and the weak interaction between acoustic and optical phonons, pure GeTe shows low S and high κL18. In earlier studies, the manipulation strategies of carrier transport can be mainly classified into two categories. One is the reduction of nH through Bi19,20, Sb21,22, etc. substitution for Ge. The other is the band structure modification by the use of dopants such as Zn23, Cd24, Pb25, Cr26, In27, Ga28 etc. Specifically, the former can indeed improve S by reducing nH, but inevitably deteriorates σ to some degrees. Although the latter helps to enhance S by increasing carrier effective mass (m*), the carrier mobility (μ) suffers from degradation due to the trade-off between m* and μ. Consequently, the deteriorated σ and increased S only lead to slight changes in PF. On the other hand, although the atomic mass and ionic radius of the dopants are different from the host atoms, giving rise to the mass/strain fluctuations, and hence lower κL, these scattering centers only aim to scatter high-frequency phonons, showing limited effects on the reduction in κL at low temperatures. Therefore, the large reduction in κL usually requires complex compositions with the total content of foreign atoms over 10%, which also strongly scatter carriers and deteriorate σ and PF29. As a result, the traditional do** methods usually yield modest ZT values. Therefore, a new strategy needs to be developed to decouple the nH and S, and introduce other phonon scattering centers, with the aim of improving PF and decreasing κL in the GeTe system.

According to the Mott equation30:

$$S=\frac{{\pi }^{2}}{3}\frac{{k}_{B}}{q}({k}_{B}T)\left[\frac{1}{n(E)}\frac{dn(E)}{dE}+\frac{1}{\mu (E)}\frac{d\mu (E)}{dE}\right]$$
(1)

where kB is the Boltzmann constant and q is the carrier charge, the TE performance can be optimized by introducing proper scattering sources. Notably, the interfaces can be rendered as a type of planar defect with its length scale in the order of nanometers to micrometers31.The additional heterogeneous interfaces can be easily introduced into the matrix materials by addition of nanoparticles.These appropriate heterogeneous interfaces hardly change the band structure of the matrix and m*, but augment the scattering factor and hence S. On the other hand, they can act as new scattering centers for phonons, resulting in obvious reduction in κL. Successful paradigms of enhancing TE performance were achieved in SiC/(Bi,Sb)2Te39, B4C/Cu2Se32, Nb/Mg3(Sb,Bi)24 and Co/Ba0.3In0.3Co4Sb1233 systems, which show huge potential in decoupling the adversely inter-dependent nH, S and κ in bulk materials.

According to our previous work, the boron inclusions play a significant role in minimizing κb + κL in (Bi,Sb)2Te3 system16. Herein, the boron particles are incorporated into GeTe matrix materials with the aim of enhancing both the carrier and phonon scattering, because of their potential in modulating the interfacial barriers as well as microstructures, as shown in Fig. 1a. The interfacial barrier blocks part of holes, increasing the scattering factor and S, while the big difference in thermal expansion coefficient between boron and GeTe lead to the large strain fluctuations near the interfaces, inducing the formation of dislocations. As a result, the adversely dependent nH and S are efficiently decoupled, leading to the enhanced PF with maximum values of 25.4 μWcm−1K−2 at 300 K and 47.7 μWcm−1 K−2 at 573 K, respectively. Furthermore, κL is suppressed because the mid-frequency phonons are scattered by the strain-induced high-density dislocations. Due to the synergistic optimization of carrier and phonon transport, the boron-added samples obtain an extremely high ZT value of 2.45 in R-GeTe compared to the samples prepared by the traditional do** methods (Fig. 1b). The maximum figure of merit (Zmax = 4.0 × 10−3 K−1) of synthesized GeTe-based material is the record-high value in GeTe-based TE materials, and competitive among the TE materials for medium temperature applications, which is more intuitive to evaluate the transport properties without temperature factor (Fig. 1c, Supplementary Fig. 1). Further, a segmented single-leg TE device with a high conversion efficiency of 13.7% under a temperature gradient of 455.9 K was successfully fabricated based on the boron-dispersed GeTe composites. Our work sheds light on the interfacial engineering strategy to enhance the TE properties.

Fig. 1: Synergistic control of the carrier and phonon transports via interfacial strategy.
figure 1

a The schematic image showing the positive effect on both carrier and phonons in boron/GeTe composites compared to the sample without boron53. b The comparison of the PF and the corresponding value of 1/κL at the peak ZT data point with different dopants: Bi do**19,20, Sb do**21,54, Cu do**23, (Cd, Bi) co-do**19, (Sb, Cr) co-do**54, (Mg, Sb) co-do**57, (Bi, Mn) co-do**58, (Cr, Bi) co-do**26, (Bi, Sc) co-do**59, (Sn, Sb) co-do**60, (Pb, Bi) co-do**25, (Pb, Bi2Te3) alloying61, (Zn, Sb, Cd) co-do**62, (Bi, Pb, Mn) co-do**63. c The comparison of Z values with different materials working in medium temperature: PbTe64, PbSe65, PbS66, SnTe67, SnSe68, BiCuSeO69, CoSb370, Cu2Se71, SiGe72.

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Results

Electrical transport

The temperature-dependent σ and S for Bi-doped GeTe samples are displayed in Supplementary Fig. 2. Bi is used to manipulate the carrier concentration here, reducing the σ and improving S. Figure 2a, b and Supplementary Fig. 3a illustrate the temperature-dependent σ and S for Bi0.05Ge0.94Te-y wt. % B samples (y = 0.00, 0.05, 0.10, 0.20, 0.40, namely B0/BGT, B5/BGT, B10/BGT, B20/BGT, B40/BGT). The σ decreases with the increasing temperature. Meanwhile, the positive S values show an opposite variation trend compared to σ, and indicate a typical p-type conducting mechanism (Fig. 2b and Supplementary Fig. 3). It is noteworthy that the σ shows a downward trend with increasing boron content. Notably, the S increases from 83.14 μVK−1 to 97.3 μVK−1 at 300 K as the boron content increases from 0 to 0.40 wt.%; the B0/BGT and B40/BGT samples reach maximum S values of 226.5 μVK−1 and 259.8 μVK−1 at 613 K, respectively (Fig. 2b).

Fig. 2: The electrical transport properties.
figure 2

a Temperature dependence of electrical conductivity for Bi0.05Ge0.94Te-y wt. % B (y = 0.00, 0.05, 0.10, 0.20, 0.40) samples. b Seebeck coefficient of Bi0.05Ge0.94Te-y wt. % B samples (T = 300 K and T = 613 K). c The effects of boron contents on carrier concentration and carrier mobility at 300 K. d The relationship between S and Hall carrier concentration for Bi0.05Ge0.94Te-y wt. % B samples at 300 K. The solid points represent for the Bi-doped GeTe samples. e Temperature dependence of power factor for B/BGT samples (B0/BGT and B10/BGT samples) and the comparison of power factor (for R-GeTe), and f average PF with the values in literatures20,29,42,23,58,59,74,75 and Pb-doped TE materials25,42,76,77.

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Phase and microstructure characterization

In order to clarify the regulatory mechanisms determining the electrical and phonon transport properties, the phase and microstructures of the as-prepared samples were investigated. The powder X-ray diffraction (PXRD) was used to investigate the crystal structure of B/BGT samples, as shown in Supplementary Fig. 9. The prominent peaks for all the samples correspond well to the rhombohedral GeTe in R3m space group, and the peaks of boron is undetectable here because of the low additive content. The lattice parameters were calculated by XRD Rietveld refinement, shown in Supplementary Fig. 10. The lattice parameter a and interaxial angle α are insensitive to boron addition (Supplementary Table 2). The in-situ high-temperature XRD is shown in Supplementary Fig. 11. To investigate the elemental distribution in the matrix, the electron probe micro-analysis (EPMA) and back-scattered electron imaging (BEI) were carried out (Supplementary Figs. 12–13). It is found that the trace of boron inclusions can be detected in the boron-added samples, along with the generally observed Ge precipitates. Furthermore, the field-emission scanning electron microscopy (FESEM) images of the fracture morphology are shown in Supplementary Fig. 14. It is also evident that the grain size decreases as the boron content increases, as a result of the Zener pinning effect34. This finding is consistent with the electron backscatter diffraction (EBSD) analysis (Supplementary Fig. 15).

The detailed structural information about the boron inclusions and matrix materials were further examined by scanning transmission electron microscopy (STEM) as shown in Supplementary Fig. 16. Energy-dispersive X-ray spectroscopy (EDS) map** confirms the presence of boron inclusion and the uniform distribution of Bi, Ge and Te in the matrix. Impressively, the boron inclusions in the size of several tens to hundreds of nanometers are present accompanied by high-density dislocations (Fig. 4b, c and Supplementary Figs. 17–19) compared to the sample without boron addition (Fig. 4a). As shown in Supplementary Fig. 18, the selected area electron diffraction (SAED) pattern of boron inclusions viewed in the [010] zone axis shows that the corresponding space group is indexed as R-3m (space group no. 166)35.

Fig. 4: Microstructure evolution led by boron addition.
figure 4

The low magnification transmission electron microscopy (TEM) for a the sample without boron addition and b the sample with boron addition. c The enlarged area (area 1) in b. d The HRTEM image showing the interface between the boron inclusion and GeTe matrix. The corresponding e, f IFFT images g FFT image showing the area 2 in d indicating the dislocations in GeTe matrix. Strain map** along h xx direction and i xy direction confirmed by geometric phase analysis (GPA).

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The interfacial contact between boron inclusions and GeTe matrix and the dislocations was further investigated by high-resolution TEM (HRTEM). As shown in Fig. 4d, the incoherent interface between boron and matrix is manifested. The HRTEM image (Supplementary Fig. 18b), and the fast Fourier transformation (FFT) images (Supplementary Fig. 18d–e) also indicate that there is no orientation relationship between the matrix and inclusions. Supplementary Fig. 20 shows another typical incoherent interface, the FFT image of which reflects the diffraction spots assigned to GeTe matrix in the [001] zone axis (marked in yellow) and the boron inclusions in [010] zone axis (marked in red). Furthermore, the inverse fast Fourier transformation (IFFT) was used to identify the dislocation structure and distorted lattice in Fig. 4e–f and Supplementary Figs. 18–19, indicating high-density dislocations at the interface. Supplementary Fig. 21 even shows deformation twinning structures at the interfaces, in addition to dislocations. It is also noted that the high-density dislocations were mainly distributed at the heterogeneous interfaces, the density of which shows an obvious reduction away from the boron inclusions (Supplementary Fig. 22).

Here, the presence of high-density dislocations around the inclusions can be ascribed to the difference in thermal expansion coefficients (TEC) between boron (around 1–5 × 10−6 K−1 (in a axis) and 4–8 × 10−6 K−1 (in c axis) in 300–873 K)36 and GeTe (5.60 × 10−5 K−1 in 296–648 K and 5.78 × 10−5 K−1 in 648–948 K (volume TEC))37. By the Eshelby’s inclusion model38,39, the misfit strain ε can be calculated by the following formula:

$$\varepsilon=({\alpha }_{M}-{\alpha }_{I})\cdot \varDelta T$$
(2)

where αM and αI is the TEC of matrix and inclusions, respectively, and ΔT is the temperature drop. Supplementary Fig. 23 shows the difference of TEC, and the strain here is calculated to be 2.5 %. The strain generated during the sintering process drive the evolution from vacancies to dislocations in Bi0.05Ge0.94Te (with 6 at. % Ge deficiency in theory)40,24). Both the s orbital energy of the dopants and the interaxial angle are key to inducing the band convergency42. According to the previous results23, the s orbital energy of Bi does not obviously contribute to the band convergency. Considering the changes in crystal structure induced by Bi (Supplementary Table 2), the valance band convergency is promoted, supported by our DFT calculation results. After Bi do**, the energy separation between the valence band maxima at the L and Σ points decreases from 174 meV to 74 meV. As a result, Bi do** improves the m* and S. As for boron addition, there are negligible effects on lattice parameters (especially the interaxial angle, Supplementary Table 2), and boron atoms hardly enters the matrix lattice. Therefore, the interface should be responsible for the phenomenon in Fig. 2d. Figure 1a shows the interfacial band diagram of the boron and GeTe, showing the work functions of two materials (GeTe: ~5.09 eV43, boron: ~4.45 eV44). The interface contact between the matrix and the boron inclusion is exactly a p-p homojunction. As the work function of GeTe is higher than that of boron, the electrons tend to transfer from boron to GeTe, resulting in an internal electric field pointing from boron to GeTe. Consequently, a depletion layer is revealed at the interface45. This depletion layer can perform as an interfacial potential barrier to block part of holes and modulate the carrier scattering factors.

$$S=[8{\pi }^{2}{{k}}_{{{{{{\rm{B}}}}}}}^{2}/(3{e}{{h}}^{2})]{{m}}^{\ast }{T}{[\pi /(3{n})]}^{2/3}(r+3/2)$$
(3)

is used to further figure out the carrier scattering factor, where e is the electron charge, h is the Planck constant and n is the carrier concentration46. The carrier scattering in the Bi-doped sample (the B0/BGT sample) is usually dominated by the acoustic phonons. Thus, r is fixed to be −0.5, and the m* can be determined to be 1.72m0 based on the SPB model. As for the boron-added samples, the r can be estimated given a fixed m*, and the r can be figured out, shown in Supplementary Table 3.

But the interfacial potential barrier also leads to a slight decrease in the mobility of B/BGT samples, especially in the sample with higher boron content. From the aspect of Mott equation, the increased S should be assigned to changes in carrier energy dependent mobility. From the microscopic point of view, S can be defined as the heat or more simply the entropy per carrier47. These inclusions generate abundant interfaces, which helps to enhance the carrier scattering, leading to larger entropy and hence increased S. It is found that the similar phenomenon is also observed in the boron-added samples sintered at 723 K (Supplementary Fig. 25).

Furthermore, the reduction in κL (Fig. 3b) can be attributed to the enhanced phonon scattering, deducted from the presence of strain-induced dislocations and boron inclusions (Fig. 4). The rise in κL might be attributed to the nonuniform distribution of excessive boron particles and their thermally conductive nature. In order to figure out the main reason for reduced κL, the Bi0.05Ge0.96Te and Bi0.05Ge0.96Te-0.1 wt. % B samples (less Ge deficiency samples) were fabricated. Supplementary Fig. 26 shows the cation-excessive sample have slight variations in κL value after boron addition, while the boron-added samples with more Ge deficiencies show remarkable reduction in the κL value, which can be assigned to the high-density dislocations at the interfaces. The regions enriched with high-density dislocations show higher Ge deficiencies (Supplementary Figs. 26–27), manifesting the role of Ge content in inducing dislocations. Furthermore, the boron-added sample with the same composition sintered at 723 K shows negligible variations in κL as shown in Supplementary Fig. 28. It is found that there are few dislocations in the matrix or near the boron inclusion in Supplementary Fig. 29. Through the comparison of the samples with the same boron content sintered at different temperatures (Fig. 3 and Supplementary Figs. 28–29), it can be deducted that the primary contribution to the reduction in κL is the formation of dislocations. Because the two samples have the same amount of boron inclusions, the formation of dislocations should be mainly attributed to the sintering temperature. On one hand, the higher sintering temperatures may promote the evolution of vacancies. On the other hand, the higher sintering temperatures may induce higher strains due to the higher temperature drop. Consequently, a minimum κL of 0.43 Wm−1K−1 is achieved in the B10/BGT sample, approaching the theoretical minimum κL of GeTe following the Clarke model48,49.

To further clarify the contributions from inclusions and high-density dislocations, the κL was fitted by the Debye–Callaway model (shown in “Supplementary Materials” section). Here, κL can be calculated from the following equation50:

$${\kappa }_{{{{{{\rm{L}}}}}}}=\frac{{k}_{{{{{{\rm{B}}}}}}}}{2{\pi }^{2}{\nu }_{{{{{{\rm{s}}}}}}}}{\left(\frac{{k}_{{{{{{\rm{B}}}}}}}T}{\hslash }\right)}^{3}{\int }_{\!\!\!\!0}^{{\theta }_{D}/T}{\tau }_{{{{{{\rm{tot}}}}}}}\frac{{z}^{4}{e}^{z}}{{({e}^{z}-1)}^{2}}dz$$
(4)

The integrand item, in conjunction with the coefficient of Eq. 4, is the spectral lattice thermal conductivity (κs), namely:

$${\kappa }_{s}=\frac{{k}_{B}}{2{\pi }^{2}{\nu }_{s}}{\left(\frac{{k}_{B}T}{\hslash }\right)}^{3}{\tau }_{tot}\frac{{z}^{4}{e}^{z}}{{({e}^{z}-1)}^{2}}$$
(5)

where kB is the Boltzmann constant, νs is the average sound speed, \(\hslash\) is the reduced Plank constant, θD is the Debye temperature, z = ℏω/kBT (ω represents the phonon frequency) is the reduced phonon frequency and τtot is the total relaxation time.

The phonon scattering mechanisms of the Umklapp process (U), grain boundaries (B), point defects (PD), dislocations (D), and precipitates (P) were taken into account based on the microstructure characterization (Supplementary Fig. 30). The pinning effect here leads to a decrease in grain size, which restricts the propagation of low-frequency phonons, whilst the point defects are the predominant factor for high-frequency phonons. Furthermore, κL is suppressed because the mid-frequency phonons are scattered by strain-induced high-density dislocations. According to the calculation results, the dislocations play a major role in scattering the mid-frequency phonons compared to the inclusions, which is consistent with our observations.

Fabrication and evaluation of TE device

A segmented single-leg thermoelectric device was designed by integrating (Bi,Sb)2Te3 with GeTe in view of their excellent TE performance within different temperature range (Fig. 3 and Supplementary Fig. 31). The output power density and conversion efficiency of the segmented single-leg device were simulated as a function of the current and the height ratio via the finite element method43. The total height of the single-leg was set as 9 mm, where the height ratio of (Bi,Sb)2Te3 to GeTe was defined as x/(1−x). According to our calculation results (Fig. 5a), the maximum TE conversion efficiency is 17.7% when x = 0.30 and I = 6.4 A. To achieve a higher TE conversion efficiency, the value of x = 0.30 was selected for the device fabrication.

Fig. 5: The stimulation and measurement results of the single-leg thermoelectric device.
figure 5

a Contour map of efficiency (η) of GeTe/(Bi,Sb)2Te3 segmented TE leg when Th = 723 K and Tc = 300 K. b, c The tested conversion efficiency and output power, respectively. The inset image in c showing the schematic diagram of the segmented TE leg. d The comparison of the conversion efficiency with the results in literatures17,43,51,52.

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Finally, a segmented single-leg TE device with a height ratio of 3:7 was fabricated, as illustrated in Supplementary Fig. 32. Ti and Ni were employed as the metallized layers linking to GeTe and (Bi,Sb)2Te3, respectively. The copper electrode is then connected with the device via soldering. As shown in Fig. 5b, the highest conversion efficiency (ηmax) of 13.7% is yielded (ΔT = 455.9 K). When ΔT = 455.9 K and I = 3.79 A, the maximum output power exceeds 0.18 W (Fig. 5c), and the corresponding V–I relationship and heat flow are shown in Supplementary Fig. 33. Figure 5d indicates the comparison of conversion efficiency in this work with previous studies17,43,51,52. However, the measured values still deviate from the calculated results, indicating that further optimization of the metallization layer and fabrication process is needed.

In summary, this work demonstrates the synergistic optimization of electrical and phonon transport properties via interfacial engineering strategy in the boron/GeTe composites, improving the TE performance of the R-GeTe. Boron/GeTe heterogeneous interfaces prove effective in scattering carriers, increasing the carrier entropy, and hence enhancing r and S. As the σ does not suffer from degradation, PF of the B/BGT samples are significantly improved. In particular, due to the improvement of PF in R-GeTe, the B10/BGT sample exhibit a high average PF, which is critical for the improvement in output power density of the TE module. Additionally, the incoherent interfaces between the matrix and the inclusions enhance the phonon scattering. The great difference in TEC between boron inclusions and GeTe leads to the large strain around the interfaces, inducing the evolution of dislocations, which play a major role in scattering mid-frequency phonons. The κL is reduced to 0.43 Wm−1K−1 at 613 K in the B10/BGT sample. Consequently, a maximum ZT value of 2.45 is achieved. An average ZT value of 1.1 is also obtained in the B10/BGT sample within the temperature range of 300–613 K. Moreover, the as-prepared GeTe-(Bi,Sb)2Te3 segmented single-leg TE device shows a high energy conversion efficiency of 13.7%.

Methods

Sample fabrication

Raw materials, germanium (granules, 2–5 mm, 99.999%, ZhongNuo Advanced Material (Bei**g) Technology Co., Ltd), tellurium (powder, 99.999%, ZhongNuo Advanced Material (Bei**g) Technology Co., Ltd), and bismuth (powder, 99.99%, Aladdin) were weighed in the glove box and loaded into tungsten carbide jars according to the stoichiometric ratios of BixGe0.99-xTe (x = 0, 0.01, 0.03, 0.05). First, the mixture (Bi, Ge and Te) was reacted via mechanical alloying (MA) in a planetary ball mill at 450 rpm for 10 h, with argon ( > 99.5%) as the protective gas. Next, the powders (Bi0.05Ge0.94Te) were mixed with amorphous boron (powder, 99%, Aladdin) via MA in a planetary ball mill at 300 rpm for 2 h to fabricate a series of boron-added samples (Bi0.05Ge0.94Te-y wt. % B samples, in which y = 0.00, 0.05, 0.10, 0.20, 0.40). The total mass of powders for one jar is 10 g, in which the addition amount of boron powder is 0 g, 0.005 g, 0.01 g, 0.02 g and 0.04 g for Bi0.05Ge0.94Te-y wt. % B samples where y = 0.00, 0.05, 0.10, 0.20, 0.40, respectively. Then, the obtained powders (about 7 g) were densified by spark plasma sintering (SPS 211Lx, Fuji Electronic, Japan) at 873 K for 5 min under a pressure of 60 MPa.

Characterization

We used X-ray diffraction (D8 ADVANCE, Bruker, Germany, Cu Kα, λ = 1.5418 Å) to identify the phase purity of samples. The field-emission scanning electron microscopy (Zeiss Merlin, Germany), and transmission electron microscopy (2100 F, JEOL, Japan) were used to investigate the grain morphology and microstructure. We used electronic probe microscopic analysis (JXA-8230, JEOL, Japan) to study the elemental distribution of samples.

Transport properties measurement

The obtained boron-added GeTe samples were cut into bars with dimensions of ~2.5 × 2.5 × 9 mm3, used for the measurements of the Seebeck coefficient and electrical conductivity via the measuring system (Ulvac Riko ZEM-3, Japan) under a helium atmosphere from room temperature to 723 K. The obtained samples were cut into disks with dimensions of φ ~ 6 mm and thickness of ~1 mm. The disks were coated with a thin layer of graphite for thermal diffusion coefficient (D) measurements using the laser flash method (LFA457, Netzsch, Germany). The thermal conductivity was calculated according to \(\kappa=D{C}_{p}\rho\), where Cp is the specific heat, and the density (ρ) was measured by Archimedes’ method. The Cp value was deduced via the Dulong-Petit limit, which was used for calculating the thermal conductivity. In Supplementary Fig. 8, the Cp value was measured by differential scanning calorimetry (STA 449 F3 Jupiter, Netzsch, Germany) with a heating rate of 5 K/min. We used the Wiedemann-Franz law \({\kappa }_{e}=\sigma {LT}\) to calculate the electrical thermal conductivity, where the Lorenz factor (L) was estimated according to the formula \(L=1.5+\exp (-\left|S\right|/116)\). The samples we used for the measurement of the electrical and thermal transport properties were perpendicular to the axial SPS pressure. The obtained samples were cut into pieces with dimensions of 10 × 10 × 0.5 mm3, used for Hall coefficient (RH) measurements (ResiTest 8340DC, Japan). We calculated the Hall carrier concentration (nH) and mobility (μH) according to the formula \({n}_{H}=1/(e{R}_{H})\) and \({\mu }_{H}=\sigma {R}_{H}\), respectively. We used the ultrasonic pulse-echo technique (5072PR, Olympus, Japan) to measure the sound velocity (v).

The fabrication and characterization of thermoelectric device

The thermoelectric single-leg module was assembled in a glove box and sintered by SPS. Ti and Ni is employed as the metallized layer at the side of GeTe and (Bi,Sb)2Te3, respectively. The copper electrode is connected via soldering. We calculated the energy conversion efficiency (η) of the segmented single-leg device according to the equation \(\eta=P/(P+Q)\times 100\%\), where the output power (P) and heat flow per unit time (Q) were measured by the commercial Thermoelectric Conversion Efficiency Evaluation System for Small Modules (Mini-PEM, Advance Riko, Japan). Due to the small size of the device and high testing temperature, the Q was revised according to the analysis system provided by the company. We used the COMSOL Multiphysics software to simulate and optimize the theoretical conversion efficiency of the single-leg device.