Lead-free and scalable GeTe-based thermoelectric module with an efficiency of 12%

Abstract

GeTe-based materials with superior thermoelectric properties promise great potential for waste heat recovery. However, the lack of appropriate diffusion barrier materials (DBMs) limits not only the energy conversion efficiency but also the service reliability of the thermoelectric devices. Here, we propose a design strategy based on phase equilibria diagrams from first-principles calculations and identify transition metal germanides (e.g., NiGe and FeGe₂) as the DBMs. Our validation experiment confirms the excellent chemical and mechanical stabilities of the interfaces between the germanides and GeTe. We also develop a process for scaling up the GeTe production. Combining with module geometry optimization, we fabricate an eight-pair module using mass-produced p-type Ge_0.89Cu_0.06Sb_0.08Te and n-type Yb_0.3Co₄Sb₁₂ and achieve a record-high efficiency of 12% among all reported single-stage thermoelectric modules. Our work thus paves the way for waste heat recovery based on completely lead-free thermoelectric technology.

High-efficiency GeTe thermoelectric module was realized by computation-guided design of diffusion barrier materials.

INTRODUCTION

Industrial production is one of the top-three energy consuming sectors worldwide and, meanwhile, produces massive waste heat (1). Thermoelectric (TE) generators, which can directly convert such waste heat into electricity through the Seebeck effect, provide a promising strategy to recover low-grade thermal energy (2, 3) and serve as an effective tool for CO₂ mitigation. The maximum energy conversion efficiency η_max of a TE device assembly (or module) can be expressed as (4)

$${\mathrm{\eta }}_{\max }=\frac{\text{Δ}T}{T_{\mathrm{h}}}\frac{\sqrt{1+ZT}-1}{\sqrt{1+ZT}+T_{\mathrm{c}}/T_{\mathrm{h}}}$$ (1)

where ΔT = T_h − T_c is the difference between the hot-side temperature (T_h) and cold-side temperature (T_c) of the TE module and $ZT=\frac{1}{\text{Δ}T}{\int }_{T_{\mathrm{c}}}^{T_{\mathrm{h}}}z(T)TdT$ is related to the temperature-dependent Seebeck coefficient (S), electrical conductivity (σ), and lattice and electronic thermal conductivities (κ_L and κ_e) of the TE materials through z = S²σ/(κ_L + κ_e). While boosting the zT value at a specific temperature is currently the main thrust of the research on TE materials, η_max is of greater importance when evaluating whether a material is competitive for practical applications.

The temperature range from 500 to 800 K (or the mid-temperature range) is usually considered the most relevant to waste heat recovery (5). Within this range, PbTe has long been perceived to be the best-performed TE material. However, the toxicity of Pb and the evaporation of Pb at high temperature have always been a general concern. To develop lead-free alternatives for PbTe, skutterudites (SKDs) have been intensively studied (6). Unfortunately, p-type SKDs still suffer from inferior performance to their n-type counterparts. In recent years, GeTe stands out for its excellent performance in the mid-temperature range (7–9). By optimizing carrier concentration (10, 11), band structure (12–15), and microstructure (16–18), p-type GeTe has achieved peak zT values above 2.0 and provides an attractive option for integrating with n-type SKDs to fabricate TE modules.

Compared with the extensive studies on material properties, there have been few reports on GeTe-based TE modules. GeTe single legs have demonstrated η_max up to 14% (19, 20), but such a structure is not practical for TE applications. The p-GeTe/n-Mg₃Sb₂ module yielded a η_max higher than 10%, but the T_h of ~600 K is not high enough to unleash the full potential of GeTe for mid-temperature applications (21). N-type SKDs were introduced so that the T_h can reach ~850 K, but the η_max of 7.8% is still much lower than its theoretical value (22). Recent work used high-entropy p-(Ge, Pb, Ag, Sb, Bi)Te and n-PbTe, where the single-stage module achieved a η_max of 10.5%. But this module still highly relies on Pb (23).

Given the zT of a TE material as a function of T, a TE module made of this material has a maximum efficiency η_max as estimated from Eq. 1 by finite element method (FEM) calculation (see Materials and Methods). Therefore, one can assess the performance of a TE module by defining the completion ratio (r_η) between the measured and theoretical values of η_max. To increase the theoretical η_max of a TE module, it is necessary to increase the ZT (i.e., the overall zT profile) and ΔT (preferably with the T_h higher than the temperature where the zT peaks). Practically, it is usually more challenging to improve r_η, i.e., having the measured η_max approaching the theoretical η_max. Both the T_h and r_η are strongly related to the quality of the TE module.

A major obstacle to realizing high-performance GeTe-based modules is the lack of an ideal diffusion barrier material (DBM), which affects not only the energy conversion efficiency through T_h and r_η but also the high-temperature service reliability of the TE modules (24, 25). However, experimental studies were seldom dedicated to the selection of the DBMs for GeTe-based modules. Although several materials [such as Mo (22), Ti (26), SnTe (21), and Al/Si (27)] have been used as the DBMs in GeTe-based TE modules, the achieved r_η as shown in Fig. 1A still cannot compete with the mature TE materials, such as half-Heusler (HH) (28–31), SKDs (32, 33), and Bi₂Te₃-based modules (34, 35). Thus, designing previously unidentified DBMs has become an urgent need for GeTe-based modules.

Fig. 1. Performance of state-of-the-art thermoelectric (TE) modules.

(A) Ratio between experimental and theoretical η_max (defined as completion ratio r_η) of TE modules plotted versus the average zT of p and n legs for different TE material systems, including HH (28–31), SKD (32, 33), Bi₂Te₃ (34, 35), Cu₂Se (56), Mg₃Sb₂ (57, 64, 65), PbTe (58), SnSe (66) and GeTe (21, 22)-based modules. The details of these TE modules from these references are listed in Table S1 in the supplementary material (SM). (B) Comparison of η_max of single-stage TE modules reported in the literature, including GeTe (21–23), SKD (33), PbTe (58), HH (29), Mg₃Sb₂ (57), and Cu₂Se-based (56) modules (HH and SKD stand for half-Heusler and skutterudite, respectively). All the theoretical η_max values in (A) are recalculated by finite element method (FEM) on the basis of the reported data in the corresponding literature without considering heat loss in the integration process (see Materials and Methods).

Here, by discovering chemically inert germanide DBMs, realizing a scalable GeTe synthesis process, and optimizing module geometry, we develop a full-fledged technique for fabricating high-performance mid-temperature lead-free TE modules ready for practical applications. As both the low T_h and low η_max can be partly attributed to the issues on the DBM, we first carry out screening of previously unidentified DBMs by combining first-principles calculation and experimental validation, which identify transition metal germanides (e.g., NiGe and FeGe₂) as the candidates. Next, we develop a process for the mass production of GeTe materials with well-reproducible TE performance. Then, assisted by FEM calculation based on a full-parameter model for module geometry optimization (36), we fabricate a TE module with eight pairs of p-type Ge_0.89Cu_0.06Sb_0.08Te and n-type Yb_0.3Co₄Sb₁₂ SKD, which achieves a record-high η_max of 12% under a temperature difference of 545 K. Figure 1B compares our current module with other high-performance single-stage modules reported in the literature. From Fig. 1A, it can also be seen that the r_η of our module is above 88%, approaching the most mature TE module based on the HH material. This work demonstrates that GeTe is highly promising for lead-free power generation applications in the mid-temperature range.

RESULTS AND DISCUSSION

Screening of diffusion barrier materials

The DBM layer connects the TE material and the electrode and, therefore, is required to be chemically inert, but mechanically adhesive, to both the TE and electrode materials. The DBMs should also have low thermal and electrical resistivities to minimize energy loss during operation. In addition, matching the coefficient of thermal expansion (CTE) with the TE material is also critical (37, 38). If the selection of DBMs is confined to elemental metals, then there is nearly no satisfactory choice for GeTe. Some commonly used metal elements such as Ti, Mn, Cu, Ag, and Cr are effective heavy dopants in GeTe (9, 15, 18, 39, 40), indicating that they are reactive with GeTe. Other chemically inert metal elements such as W and Mo have too high melting points to form direct bonding at the synthesis temperature of GeTe. In addition, to reduce the overall cost of the module, noble metal elements such as Au and Pt are excluded.

In this work, we started with Fe, Co, and Ni as the candidates because we found that these elements were difficult to be doped into GeTe. Taking a sandwich structure of GeTe/Ni/GeTe, we carried out a bonding experiment. We observed an interfacial reaction layer between Ni and GeTe, as shown in fig. S1. By elemental mapping and line scan under scanning electron microscopy (SEM), it was determined that the reaction layer consists of Ni and Ge, suggesting the formation of a germanide layer. After annealing at 773 K for 30 min, the sample exhibited cracks between the Ni and germanide layer (see fig. S1B), suggesting mismatched CTEs of the two materials. Similar results were also observed when Fe and Co were used in the middle layer of the sandwich structure (see figs. S2 and S3).

The results above, on the one hand, excluded the possibility of using elemental Fe, Co, or Ni as the DBM but, on the other hand, inspired us to consider using germanides as the DBM. The germanides could naturally be inert and adhesive to the GeTe layer. However, there exist a large number of possible germanides of Fe, Co, and Ni. To screen out the best candidate, we resort to the phase equilibria diagram (PED) obtained by first-principles calculations. We considered all possible related compounds in Materials Project (41) and in the Inorganic Crystal Structure Database (42) and calculated their formation energy to obtain the PED (see table S1 for the details of the considered compounds). Figure 2 (A to C) shows the PEDs for the Fe-Ge-Te, Co-Ge-Te, and Ni-Ge-Te systems. The first requirement for a compound to form a thermodynamically stable interface with GeTe is to have a direct line connecting this compound with GeTe on the PED. These lines are highlighted in red color in the figures. It can be seen that FeGe, NiGe, FeTe₂, CoTe₂, and NiTe₂ satisfy this requirement. However, the three tellurides usually have very high resistivity compared with the germanides (43–45) and therefore are not suited to be used as DBM.

Fig. 2. Design of diffusion barrier materials informed by phase equilibrium diagrams.

(A to C) Calculated phase equilibria diagrams (PEDs) at 0 K for the Fe-Ge-Te, Co-Ge-Te, and Ni-Ge-Te systems, respectively. Solid and empty circles represent stable and unstable phases at 0 K. (D to F) Calculated interfacial reaction energy (E_IR) between GeTe and potential diffusion barrier materials for the Fe-Ge-Te, Co-Ge-Te, and Ni-Ge-Te systems, respectively.

The PEDs in Fig. 2 (A to C) were obtained by density functional theory calculations at 0 K. For the purpose of DBM screening, it is ideal that the PEDs are calculated at the temperature for synthesizing GeTe. Unfortunately, these calculations are usually too expensive. The missing information from the 0-K PEDs is that the high-temperature stabilized phases might be overlooked. To remedy this issue, we also consider the metastable phases of germanides at 0 K for DBMs, which could be the stable high-temperature phases. These phases are marked by empty circles in Fig. 2 (A to C). We used the interfacial reaction energy (E_IR) as the criterion. The details for evaluating E_IR are given in the Supplementary Materials. As long as E_IR is positive for all possible reactions, the considered compound should be chemically inert to GeTe. Figure 2 (D to F) shows the results for the Fe, Co, and Ni systems (see table S3 for the values). In addition to FeGe and NiGe as found in Fig. 2 (A to C), FeGe₂ and NiGe₂ also appear to be the candidates.

On the basis of the screening results, we assessed two of the candidates, i.e., NiGe and FeGe₂, by the melting-annealing method, as from the Ni-Ge and Fe-Ge binary phase diagrams the two germanides can sustain the soldering temperature (~850 K) for fabricating the GeTe-based module (46, 47). The structure characterizations are given in fig. S4. The measured electrical and thermal conductivity of NiGe and FeGe₂ is one order of magnitude higher than that of GeTe (see fig. S5). Also, the CTEs of the two germanides are very close to that of the rhombohedral GeTe (see fig. S6). These properties satisfy the basic requirements for the DBM. We then prepared the sandwich-structured samples of NiGe and FeGe₂ to investigate the interfacial properties. As shown in figs. S7 and S8, the elemental line scans show no reaction layers near the interfaces between the germanides and GeTe.

Given the higher electrical and thermal conductivities of NiGe than FeGe₂ (fig. S5), we will focus on the GeTe/NiGe interface below. A high-resolution transmission electron microscope was used to further examine the GeTe/NiGe interface. As shown in Fig. 3 (A and B), the element distribution of Ni and Te exhibits a sharp interface, and the elemental line scan in Fig. 3C shows no interdiffusion beyond 2 nm. These results demonstrate that NiGe is chemically inert to GeTe, consistent with our first-principles calculations. The measured interfacial resistivity between the GeTe and NiGe layers is initially ~1 microhm·cm² and remains below 3 microhm·cm² after aging at 773 K for 10 days (Fig. 3D and fig. S9). Meanwhile, the interfacial microstructure exhibits no notable changes after the aging test (see fig. S7), demonstrating superior thermal and chemical stability. All the results above support that NiGe is an excellent DBM for GeTe-based modules. To understand the stability of the interface between GeTe and NiGe with no notable interdiffusions observed, we theoretically study the bonding features of this interface. Strong electron accumulation is observed in the middle areas between the atoms around the GeTe/NiGe interface (see fig. S10), suggesting the formation of covalent or metallic-like chemical bonds between these atoms. This bonding feature is also observed in the interface between metal and HH compounds (48) and can account for the firmly bonded interface observed in experiments. We further calculate the work of separation (W_sep) of this interface, which indicates the work required to separate the interface into two free surfaces and can be used to evaluate the bonding strength of the interface (49, 50). The W_sep of the typical interface, i.e., GeTe(001)/NiGe(011), is calculated to be 0.91 J/m², which is larger than that of the GeTe(001) and GeTe(111) surfaces (0.13 and 0.27 J/m², respectively). The much larger W_sep of the GeTe/NiGe interface than that of GeTe surfaces means that the bonding of the interface is even stronger than the interlayer interactions in GeTe, thus verifying the strength of the interface in the device.

Fig. 3. Validation of the predicted diffusion barrier materials.

(A) Energy-dispersive spectrometry (EDS) mapping and (C) elemental line scan results of Ni, Te, and Ge under transmission electron microscopy. (B) Atomic structure to show a sharp interface between GeTe and NiGe. (D) Interfacial contact resistivity of NiGe and FeGe₂ barrier layers after aging and compared to literature results, such as Mo (22), Ti (26), Al₆₆Si₃₄ (27), and SnTe (21). “Broken” in (D) means that the Fe layer peels off the GeTe matrix, and the GeTe/Fe interface is broken after the aging.

Thermoelectric performance of mass-produced GeTe materials

To scale up TE module fabrication, it is essential to realize the mass production of the GeTe materials that can achieve reproducible high TE performance. In this work, Ge_0.89Cu_0.06Sb_0.08Te (GeTe for short) and Yb_0.3Co₄Sb₁₂ (SKD for short) were chosen as p-type and n-type TE materials, respectively, for the fabrication of TE modules. Mass production of the SKD materials has been realized in our previous study (36, 51). As for the GeTe materials, although the peak zT values have exceeded 2.0, the preparation of the pellets for device fabrication repeatable with high zT values was still limited to lab scale of ~5 g (21), hindering the development of large GeTe-based modules with high efficiency. Here, we achieved the sintering of cylindrical pellet of ~54 g with uniform material properties as discussed below, which can once support for the integration of three to four modules.

The GeTe samples were cut from the sintered pellet, as illustrated in the inset of Fig. 4A. The x-ray diffraction (XRD) patterns (see fig. S11) show that the main phase of the samples is GeTe in the rhombohedral structure with a small amount of Ge precipitates. SEM and energy-dispersive spectrometry (EDS) analyses (see fig. S12) confirm that Ge, Cu, Sb, and Te are uniformly distributed in the samples. The observation of Ge secondary phases is consistent with the XRD results. The characterizations above confirmed good homogeneity of the large-size GeTe pellet.

Fig. 4. Thermoelectric performance of mass-produced GeTe materials.

Temperature-dependent (A) electrical conductivity, (B) Seebeck coefficient, (C) thermal conductivity, and (D) figure of merit for p-type Ge_0.89Cu_0.06Sb_0.08Te materials. The inset in (A) shows a schematic illustrating the sliced bars and sheets used for measurements of thermoelectric (TE) transport properties. Comparisons are made with lab-scale samples and the record values in the literature (60).

Temperature-dependent electrical and thermal transport properties of three groups of GeTe samples were measured and plotted in Fig. 4. By comparing the mass-produced and lab-scale samples, it can be seen that the TE properties of the GeTe samples are well reproducible (also see fig. S13). The zT values of ~1.7 at 750 K (Fig. 4D) achieved by our mass-produced samples are lower than the lab-scale samples and the record value in the literature (23), which may be attributed to slight oxidation introduced in the hot-pressing process. Nevertheless, the zT of 1.7 manifests that the mass-produced GeTe could yield superior TE performance, compared with p-type SKD for mid-temperature applications.

Geometry optimization of the GeTe/SKD module

A high-performance TE module requires that TE and related physical properties of p- and n-legs should be matched as much as possible. As the TE performance of n-type GeTe is evidently inferior to p-type GeTe (52, 53), we used n-type lead-free SKD to couple with p-type GeTe. Moreover, the CTE of SKD is comparable with the rhombohedral GeTe (54) so that reliable connection through electrodes between the two materials can be made.

Optimization of the module geometry is critical for maximizing performance. FEM-based numerical simulations (see Materials and Methods) were used here to design the optimal geometry of the GeTe/SKD module, as illustrated in Fig. 5A. The T_h and T_c were set to 873 and 293 K, respectively, and the total cross-section area, A_pn = A_p + A_n, was kept constant, where A_p and A_n represent the cross-section areas for a single p- and n-leg, respectively. All these parameters and the measured TE properties (fig. S14) were imported into the full-parameter multi-physical field model that we proposed to optimize the module geometry (36).

Fig. 5. Optimization of the geometry of GeTe/skutterudite (SKD) single-stage module.

(A) Schematic illustration of p-GeTe and n-SKD device and related structural parameters. Simulated (B) power density P_d and (C) maximum conversion efficiency η_max as a function of the ratio of the cross-sectional areas of the p- to n-legs (A_p/A_n) and the ratio of the height to the total cross-sectional area (H/A_pn) for the GeTe/SKD module. These calculation results are based on the boundary conditions specified by T_h = 873 K and T_c = 293 K.

Figure 5A shows a schematic of an eight-pair module. The dependence of open-circuit voltage (V_oc), internal resistance (R_in), power density (P_d), and η_max on the ratio of A_p/A_n and H/A_pn, where H represents the height of the legs, is shown in Fig. 5 (B and C) and fig. S15. As H/A_pn increases from 0.1 to 0.5 mm⁻¹, V_oc increases by ~25% due to the increased effective temperature difference ΔT (fig. S15A). Meanwhile, R_in becomes several times greater (fig. S15C) leading to a sharp decline of P_d. As H/A_pn increases, η_max increases first but becomes saturated when H/A_pn exceeds 0.35 mm⁻¹ because the interfacial contact resistivity with respect to that of the bulk is already low enough. At a given H/A_pn, with A_p/A_n increasing, both P_d and η_max increase first and then decrease. Our simulation suggests that η_max and P_d reach the maximum values when A_p/A_n is about 2.6 and 1.7, respectively.

Fabrication and evaluation of GeTe/SKD module

On the basis of the simulation results, an eight-pair p-GeTe/n-SKD single-stage TE module was fabricated with A_p/A_n = 2.6 and H/A_pn = 0.39 mm⁻¹. A photo of the module is shown in the inset of Fig. 6B. The output performance of the module was tested by a home-built system with T_c maintained at 300 K and T_h varied from 473 to 873 K.

Fig. 6. Characterization of the GeTe/skutterudite (SKD) single-stage module.

(A) Output voltage V and output power P, and (B) conversion efficiency η of the module as a function of the current I at different operating temperatures. Comparisons of the measured (C) open-circuit voltage V_oc and internal resistance R_in, and (D) maximum conversion efficiency η_max and maximum output power P_max with corresponding simulated values. Note that the simulations in (C) and (D) considered the heat loss in the integration process (see Materials and Methods).

Figure 6A plots the dependence of output voltage V and output power P versus the measured current I. As ΔT increases from 173 to 545 K, V_oc increases from 0.3 to 1.6 V, while the maximum value of P increases and reaches a peak value of 4.0 W at ΔT = 545 K, which corresponds to power density P_d = 1.0 W cm⁻². Figure 6C shows the measured V_oc and R_in of the module as a function of ΔT, which are compared with the simulated results. The measured and simulated V_oc show excellent consistency in the whole temperature range, suggesting the uniformity of TE materials and a negligible temperature difference loss caused by the contacts. The measured R_in increases before the phase transition temperature of GeTe and at higher temperature reaches a plateau. This behavior is also reflected by the temperature-dependent electrical conductivity curves of GeTe and SKD (fig. S14A).

The measured and simulated R_in curves also show good agreement. In previous studies, the measured R_in of p-GeTe/n-SKD modules is substantially larger than the simulated ones, resulting in relatively deteriorated output performance (22, 55). This result indicates that the NiGe DBM layer and the module fabrication process as developed in this work sufficiently benefit the improvement of TE performance of the GeTe-based modules.

Figure 6B shows the measured energy conversion efficiency η as a function of the current I. A similar current dependence to that of P can be seen. At ΔT = 545 K, η reaches the maximum value of 12.0%. Figure 5D shows the measured P_max and η_max of the module as a function of ΔT compared with simulation results. The measured P reasonably agrees with the simulation. As the temperature increases, gradual deviation occurs due to the increased R_in as shown in Fig. 6C.

For comparison, Fig. 1B summarizes the reported η_max versus ΔT for various TE modules. It can be seen that the present eight-pair p-GeTe/n-SKD single-stage module achieves η_max of 12% at ΔT = 545 K, which is the highest among all reported single-stage modules (21–23, 29, 56–59) and even close to the values of segmented modules in the same temperature range (29, 36, 58). Note that the peak zT of our mass-produced p-GeTe and n-SKD materials is 1.7 and 1.2, respectively, which are still lower than the record values from lab-scale synthesis methods, suggesting that there is still space to further improve η_max.

We have conducted a rational interface and structure design of GeTe-based TE modules toward scaling up this technology. A key contribution is a proposal of using transition metal germanides as the DBM. We characterized the interface between NiGe and GeTe and demonstrated superior chemical and mechanical stability in aging experiments. Meanwhile, we explored scale-up production of Ge_0.89Cu_0.06Sb_0.08Te of more than 50 g per pellet and well-reproducible zT_max of 1.7. Combining the mass-produced p-type GeTe and n-type and Yb_0.3Co₄Sb₁₂ SKD, we fabricated an eight-pair single-stage module and achieved the record-high efficiency of 12% at ΔT = 545 K, reaching 88% of the theoretical limit. The successful use of first-principles calculations for screening DBMs from binary compounds expanded the space of interface design for TE materials.

MATERIALS AND METHODS

Synthesis

High-quality polycrystalline samples of p-type Ge_0.89Cu_0.06Sb_0.08Te were prepared by a melting-annealing method as described in our previous work (60). High-purity raw materials of Ge (pieces, 99.999%), Te (pieces, 99.999%), Cu (shots, 99.999%), and Sb (shots, 99.999%) with stoichiometric composition were used to synthesize GeTe pellets. After annealing, the pellets were hand-grounded into fine powders and well-mixed for high homogeneity.

For the synthesis of transition metal germanides, e.g., NiGe, FeGe₂, CoGe, and CoGe₂, the raw materials of Ni (slug, 99.99%), Fe (granule, 99.98%), Co (powder, 99.99%), and Ge (pieces, 99.999%) were weighed stoichiometrically and sealed in the evacuated silica tubes. The mixtures were heated up to 1423 K, held for 20 hours, cooled down to room temperature, and then hand-grounded into fine powders.

Characterizations

To characterize the interfacial resistivity between the GeTe layer and DBM layers, sandwich-structured GeTe/DBM/GeTe samples were prepared by spark plasma sintering (SPS; Dr. Sinter: SPS-2040) under a uniaxial pressure of 50 MPa for 10 min at 813 K. Bars of 3 mm by 3 mm by 6 mm were cut from the sintered pellets for long-term aging at 773 K in a vacuum. The measurements of interfacial resistivity were conducted on a home-built four-probe platform (36).

The phase compositions and crystal structures were characterized by powder XRD (D8 Advance, Bruker; Cu Kα: λ = 1.5406 Å) at ambient conditions. The surface morphology and microstructures of the interfaces of the sandwich-structured samples were examined by field emission SEM (ZEISS Supra 55) equipped with EDS. Atomic structures of the GeTe/NiGe interface were investigated by scanning transmission electron microscopy (Hitachi HF5000). The detailed characterization methods for TE properties can be found in our previous work (60).

First-principles calculations

The first-principles calculations were carried out by the Vienna Ab initio Simulation Package program (61). The Perdew-Burke-Ernzerhof functional was used to optimize the crystal structures and calculate the total energies for all the considered elemental substances and compounds (62). The core-valence interaction was described by the projector-augmented wave potentials with a cutoff energy of 400 eV for the plane-wave basis set (63). The k-point meshes satisfy that the products of the lengths of lattice vectors and the numbers of k-points along all directions are about 40 Å. The atoms in the supercell were relaxed until the residual forces on all atoms were smaller than 0.01 eV. The formation energy of the compounds was calculated with respect to their elemental substances. To model the GeTe(001)/NiGe(011) interface, a supercell containing five GeTe(001) and six NiGe(011) atomic layers was constructed which naturally includes two equivalent interfaces. The lattice vector parallel to the interface was fixed as the commensurate value of those of GeTe(001) and NiGe(011) surfaces, while the vector vertical to the interface was allowed to be optimized and the atoms of the supercell were fully relaxed. The work of separation (W_sep) for the interface was then calculated on the basis of $W_{\mathrm{sep}}=(E_{\mathrm{total}}-E_{\mathrm{GeTe}}^{\mathrm{slab}}-E_{\mathrm{NiGe}}^{\mathrm{slab}})/2A$, where E_total is the total energy of the interfacial supercell, $E_{\mathrm{GeTe}}^{\mathrm{slab}}$ and $E_{\mathrm{NiGe}}^{\mathrm{slab}}$ are the energy of the surface slabs of GeTe(001) and NiGe(011), respectively, with the same strain imposed as in the interfacial supercell, and A is the cross-section area of the interface. The W_sep of the GeTe(001), GeTe(111), and NiGe(001) surfaces is essentially equivalent to their surface energy calculated as $\mathrm{\sigma }=(E_{\mathrm{x}}^{\mathrm{slab}}-N{E}_{\mathrm{x}}^{\mathrm{bulk}})/2A$, where $E_{\mathrm{x}}^{\mathrm{slab}}$ is the energy of the surface slab with all of the lattice vectors and atoms fully relaxed, $E_{\mathrm{x}}^{\mathrm{bulk}}$ is the total energy per atom of the bulk material, and N is the number of atoms in the slab.

Finite element method simulations

The FEM simulations of module efficiency were based on the ANSYS-Workbench program. In this study, GeTe and SKD were used as p-type and n-type legs, respectively. The temperature-dependent S, σ, and κ of GeTe and SKD were collected from the experiment as the input to the program. To make the simulations reflect the real status and give effective guidance, the measured σ and κ of the barrier layer were also considered in our simulation. In addition, the interfacial resistivities for the electrode interface in p- and n-legs were also input to our simulation. The interfacial heat transfer coefficients of hot and cold sources, as well as the thermal conductivity of the gap fillers, were obtained from our previous work (36). It is noted that the purpose of Fig. 1 is to compare the intrinsic properties of the materials by ignoring the effects due to device integration; the calculations of theoretical η_max were only based on the TE properties of various TE material systems without consideration of heat loss caused by the different integration process and different measurement systems.

Module fabrication and measurements

The p-type GeTe legs with NiGe on both sides were fabricated by a one-step sintering process. The NiGe powders and Ge_0.89Cu_0.06Sb_0.08Te powders were sequentially loaded into a graphite die of Φ30 mm and hot-pressed under 50 MPa for 45 min at 873 K. The thickness of each NiGe layer is ~100 μm. The obtained pellets of Φ 30 mm by 12.5 mm were cut into bars with 5.8 × 4 × 12.5 mm³ for TE module integration. The n-type SKD legs were prepared following our previous work (36). The dimensions of the n-type leg were 2.2 × 4 × 12.5 mm³.

The p-GeTe and n-SKD single-stage module was assembled by a soldering process in a vacuum. The p- and n-legs are bridged with Mo-Cu as the hot-side electrode and the direct-bonded copper alumina plate as the cold-side electrode, respectively. The solders used for the hot side and the cold side are Ag-Cu-Zn (soldering temperature, ~850 K) and Sn-based solders (soldering temperature, ~450 K), respectively. The glass fibers were used to fill the gaps between the p- and n-legs to diminish the heat loss caused by convection and radiation. The framework dimensions of the module made of eight pairs are 20 mm by 20 mm by 14.5 mm. The TE conversion efficiency of this module was measured by a home-built testing system when the hot side was heated from 298 to 873 K and the cold side was maintained at room temperature. The conversion efficiency was obtained by

$$\mathrm{\eta }=\frac{P}{P+Q_{\mathrm{c}}}\times 100\mathrm{\%}$$

where P is the output power of the module and Q_c is the heat flow measured by a flux probe at the cold end. The power density (P_d) was calculated by P_d = P/A, where A is the envelope area of the module.

Supplementary Materials

This PDF file includes:

Figs. S1 to S15

Tables S1 to S3

Evaluation of interfacial reaction energy