High thermoelectric performance in rhombohedral GeSe ingots achieved by Pb alloying

Abstract

GeSe, as a medium-temperature thermoelectric (TE) material, exhibits great potential for power generation. Improving symmetry is a pivotal strategy for enhancing the TE properties of GeSe-based materials. Herein, we incorporated 10 mol% AgBiTe₂ as a solid solution into the GeSe matrix to enhance its structural symmetry. Then, we demonstrate a coordinated Pb-alloying strategy that drastically reduced lattice thermal conductivity (κ_lat) without compromising the electrical properties of GeSe-based materials, achieving an advance in thermoelectric performance and conversion efficiency. The Seebeck coefficient is significantly enhanced by the optimized carrier density and enlarged density of states effective mass, thus preserving electrical properties. The lattice conductivity is driven to the near-theoretical minimum through a concerted effect of chemical bonding softening and intensive point-defect phonon scattering. A minimum κ_lat of 0.44 W m⁻¹ K⁻¹ at 473 K is acquired. These concerted mechanisms culminate in a record ZT of 1.35 at 723 K in the (Ge_0.99Pb_0.01Se)_0.9(AgBiTe₂)_0.1 composition. Besides, a single-leg device of Pb-alloyed GeSe realizes a conversion efficiency of 5.5% at a ΔT of 300 K, underscoring its practical potential. This work not only demonstrates a feasible route toward high-performance GeSe thermoelectrics but also provides a generalizable materials-design paradigm applicable to a broad range of low-symmetry chalcogenides.

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1. Introduction

The conversion of waste heat into electricity via thermoelectric (TE) devices provides an elite route for sustainable energy harvesting. The conversion efficiency (η) is correlated with the value of ZT = (S²σT)/κ, where σ is the electrical conductivity, S represents the Seebeck coefficient, T denotes the absolute temperature and κ denotes the thermal conductivity.¹ The conversion efficiency not only favours excellent ZT but also prioritises the average ZT across the entire working temperature range (ZT_ave).² Cutting-edge TE materials necessitate a low κ and a superior power factor (PF =S²σ).³ An excellent PF requires high carrier mobility, optimal carrier density and a suitable band structure. And the κ comprises electronic (κ_ele) and lattice (κ_lat) contributions. The lattice component, which originates from phonon propagation, is the primary target for manipulation in TE materials.⁴ Numerous strategies are dedicated to achieving fast carriers and blocked phonons in TE systems. The manipulation of band shape,^5,6 lattice plainification^7,8 and deformation potential^9,10 ensures electrical transport properties, while hierarchical scattering architecture,¹¹ anharmonicity^12,13 and low-symmetry crystal structures¹⁴ are conducive to intensifying phonon scattering. Typically, additives in TE materials do not have a singular effect but trigger multiple effects on coupled TE properties due to the interdependence of thermoelectric parameters.

Among numerous TE materials, GeSe, a group IV–VI monochalcogenide, is noted for its theoretically predicted high ZT.¹⁵ However, pristine GeSe exhibits an intrinsically low carrier density (n_H ∼ 10¹⁶ cm⁻³), severely limiting its TE performance and resulting in a low ZT.¹⁶ Despite the exploration of various dopants for carrier concentration adjustment, the effectiveness has remained limited due to the low-symmetry orthorhombic phase (Pnma) of intrinsic GeSe. Recent breakthroughs have demonstrated that enhancing the crystal symmetry of GeSe to rhombohedral (R3m) or cubic (Fm3̄m) phases can simultaneously ameliorate carrier and phonon transport.^17,18 This symmetry enhancement can be triggered by entropy-driven alloying with compounds like In₂Te₃,¹⁹ AgSbSe₂,^17,20,21 AgBiTe₂,^22,23 or CdTe.²⁴ Within this paradigm, the introduction of lead (Pb) has emerged as a particularly potent strategy, which not only aids in stabilizing these high-symmetry phases but also actively participates in creating defect structures.^25,26

In this work, we elucidate the role of Pb in promoting the thermoelectric performance of (GeSe)_0.9(AgBiTe₂)_0.1 ingots. A prominent ZT of 1.35 at 723 K and an outstanding η of 5.5% with a ΔT of 300 K are realized in Pb-alloyed (GeSe)_0.9(AgBiTe₂)_0.1. A significant increase in S was achieved, which derives from the synergistic effect of an increased DOS effective mass (m*) and a decreased n_H induced by Pb alloying. Meanwhile, the incorporation of Pb drastically reduces κ_lat through a combination of weakened chemical bonds and intensive point-defect scattering, while simultaneously preserving the electrical properties. An ultralow κ_lat of 0.44 W m⁻¹ K⁻¹ at 473 K is attained in (Ge_0.96Pb_0.04Se)_0.9(AgBiTe₂)_0.1 near the amorphous limit of GeSe. Ultimately, the reduced lattice thermal conductivity combined with retained electrical properties culminates in markedly elevated thermoelectric performance, leading to a distinguish ZT_ave of 0.95 across 303 K to 723 K. Our work offers a new paradigm for the rational design of high-performance TEs, which can be extended to other low-symmetry chalcogenide systems.

2. Experimental section

Ge shot, Se bulk, Ag shot, Bi bulk, Te bar and Pb bar were weighted according to (Ge_1–xPb_xSe)_0.9(AgBiTe₂)_0.1 (x = 0–0.06) compositions. Then, GeSe ingots were synthesized via a temperature gradient method. Phase identification was conducted by powder XRD (LANScientific, China). The obtained crystals were processed into bars and square pieces. The S and σ were determined on a Cryoall CTA instrument, while thermal diffusivity was assessed employing a Netzsch LFA457 instrument. The n_H and µ_H were tested employing a Lake Shore 8400 Series system at 303 K. The single-leg module was assembled from (Ge_0.99Pb_0.01Se)_0.9(AgBiTe₂)_0.1 with dimensions of 2.787 mm × 2.878 mm × 9.4 mm. Ni as a barrier layer was electroplated using a commercial nickel-plating solution. A Cu electrode was attached with conductive silver paste. The output power and η of the devices were tested employing a TE conversion efficiency system. The experimental details are elaborated in the SI.

3. Results and discussion

The GeSe ingots exhibit excellent crystal quality, as shown in Fig. S1(a), and their densities are listed in Tab. S1. The powder X-ray diffraction (PXRD) results of (Ge_1–xPb_xSe)_0.9(AgBiTe₂)_0.1 (x = 0–0.06) are depicted in Fig. 1(a). Although the GeSe matrix contains up to 10% AgBiTe₂, the diffraction peaks of Pb-alloyed (GeSe)_0.9(AgBiTe₂)_0.1 demonstrate a pure phase, corresponding to a rhombohedral structure with space group R3m, which coincides with previous studies.²² The solubility of Pb in the (GeSe)_0.9(AgBiTe₂)_0.1 matrix exceeds 6%. The refined lattice parameters are depicted in Fig. 1(b) and they gradually increase as the Pb content rises. Owing to the difference in atomic radii between Ge and Pb, the enhanced lattice parameters indirectly prove that Pb effectively substitutes for Ge.

Fig. 1 Phase identification of (Ge_1–xPb_xSe)_0.9(AgBiTe₂)_0.1 (x = 0–0.06) includes (a) PXRD patterns and (b) lattice parameters.

The electrical properties of (Ge_1–xPb_xSe)_0.9(AgBiTe₂)_0.1 (x = 0–0.06) are illustrated in Fig. 2. The overall σ decreases with rising temperature and then fluctuates around 473–573 K, coinciding with a phase transformation.²³ Differential scanning calorimetry (DSC) measurements were performed, as illustrated in Fig. S2. The room-temperature σ sharply reduces from 437 S cm⁻¹ for (GeSe)_0.9(AgBiTe₂)_0.1 to 133 S cm⁻¹ for (Ge_0.94Pb_0.06Se)_0.9(AgBiTe₂)_0.1 by alloying Pb. And the overall Seebeck coefficient, presenting the opposite phenomenon, increases with rising Pb content, as depicted in Fig. 2(b). A significant (∼40%) improvement in the peak S at 473 K is achieved, increasing from 237 µV K⁻¹ K for (GeSe)_0.9(AgBiTe₂)_0.1 to 328 µV K⁻¹ for (Ge_0.94Pb_0.06Se)_0.9(AgBiTe₂)_0.1. The carrier density and mobility were measured to elucidate the variation between the S and electrical conductivity. The carrier density of the (GeSe)_0.9(AgBiTe₂)_0.1 ingot is 3.66 × 10²⁰ cm⁻³ at 303 K, which is higher than that of the reported (GeSe)_0.9(AgBiTe₂)_0.1 polycrystal.²³ The high carrier density contributes to the low carrier mobility in the (GeSe)_0.9(AgBiTe₂)_0.1 ingot. Besides, the carrier density reduces as the Pb content increases, as illustrated in Fig. 2(c). The hole density in germanium chalcogenides is correlated with the formation energy of the Ge vacancy (E_f (V_Ge)). The reduced carrier density arises from the enhanced E_f (V_Ge) induced by Pb alloying.^26–28 The carrier mobility experiences a slight decrease by incorporating Pb. Therefore, the decreased carrier mobility and density collectively result in a decline in electrical conductivity. The density of states (DOS) m* of (Ge_1–xPb_xSe)_0.9(AgBiTe₂)_0.1 (x = 0–0.06) is depicted in Fig. S1(b). The DOS effective mass is significantly enhanced from 0.65 m₀ for (GeSe)_0.9(AgBiTe₂)_0.1 to 1.05 m₀ for (Ge_0.94Pb_0.06Se)_0.9(AgBiTe₂)_0.1, primarily due to band convergence induced by Pb alloying.²⁶ The combination of diminished carrier density and the large DOS effective mass leads to superior Seebeck coefficients. Thus, a maximum power factor of 18 µW cm⁻¹ K⁻² at 673 K is achieved in (Ge_0.99Pb_0.01Se)_0.9(AgBiTe₂)_0.1, as presented in Fig. 2(d).

Fig. 2 The electrical properties of (Ge_1–xPb_xSe)_0.9(AgBiTe₂)_0.1 (x = 0–0.06): (a) σ, (b) S, (c) n_H and µ_H at 303 K, and (d) PF.

The thermal properties of (Ge_1–xPb_xSe)_0.9(AgBiTe₂)_0.1 (x = 0–0.06) are presented in Fig. 3. The total thermal conductivity (κ_tot) initially declines with rising temperature and then increases at 473 K, coinciding with the temperature of phase transformation, as depicted in Fig. 3(a). The ambient-temperature κ_tot decreases from 0.89 W m⁻¹ K⁻¹ to 0.63 W m⁻¹ K⁻¹ with increasing Pb content. A minimum κ_tot of 0.5 W m⁻¹ K⁻¹ is obtained at 473 K for (Ge_0.96Pb_0.04Se)_0.9(AgBiTe₂)_0.1. The κ_ele is estimated using κ_ele = LσT, where L denotes the Lorenz constant calculated from S employing a single parabolic band (SPB) model. (Fig. S1(c)) The electronic thermal conductivity significantly decreases as Pb content rises, stemming from the reduced carrier density and mobility. The κ_lat is derived by deducting the electronic component from the κ_tot, as presented in Fig. 3(b). The κ_lat at 303 K decreases from 0.66 W m⁻¹ K⁻¹ for (GeSe)_0.9(AgBiTe₂)_0.1 to 0.56 W m⁻¹ K⁻¹ for (Ge_0.94Pb_0.06Se)_0.9(AgBiTe₂)_0.1. The lowest κ_lat reaches 0.44 W m⁻¹ K⁻¹ for (Ge_0.96Pb_0.04Se)_0.9(AgBiTe₂)_0.1. The sound velocity is measured to investigate reduced κ_lat, as presented in Fig. 3(c). The sound velocities, including transverse (v_t) and longitudinal (v_l), decline with rising Pb content, demonstrating bond weakening after Pb alloying.^9,26 Besides, the large Pb atoms possess higher mass and larger radius than Ge atoms. Thus, the incorporation of Pb in the matrix generates mass and strain field fluctuations, as demonstrated by the scattering parameters of mass Г_M and strain Г_S, as illustrated in Fig. 3(d). The lattice softening and point defects collectively impede phonon transport, thus resulting in a decrease in κ_lat and approaching the limitation of κ_lat in GeSe-based materials.¹⁶

Fig. 3 The thermal properties of (Ge_1–xPb_xSe)_0.9(AgBiTe₂)_0.1 (x = 0–0.06): (a) κ_tot, (b) κ_lat, (c) sound velocity (v_l and v_t), and (d) distortion parameters Γ (Γ_M and Γ_S).

The thermoelectric performance is evaluated from the ratio of carrier mobility to κ_lat, as depicted in Fig. 4(a) to explicate the effects of Pb in GeSe-based materials. Pb alloying not only effectively intensifies phonon scattering via lattice softening and point defects but also preserves electrical transport properties, leading to a large µ_H/κ_lat in (Ge_0.99Pb_0.01Se)_0.9(AgBiTe₂)_0.1. Hence, remarkable thermoelectric performance is achieved by Pb alloying, as presented in Fig. 4(b). The peak ZT value is enhanced from 1.22 for (GeSe)_0.9(AgBiTe₂)_0.1 to 1.35 for (Ge_0.99Pb_0.01Se)_0.9(AgBiTe₂)_0.1. The peak average ZT (ZT_ave) across 303 K to 723 K could reach 0.95 for (Ge_0.98Pb_0.02Se)_0.9(AgBiTe₂)_0.1, as depicted in Fig. 4(d). The excellent TE performance in this work exhibits good thermal stability, which outperforms other GeSe systems, such as GeSe–AgBiSe₂, GeSe–AgSbTe₂, GeSe–AgSbSe₂, GeSe–Sb–Cd–Te, and GeSe–Bi–MnCdTe₂, as depicted in Fig. 4(c) and Fig. S3. The high ZT motivates us to further assemble a single-leg device for power generation. Ni and Cu are selected as the barrier layer material and electrode, respectively, and are connected using conductive silver paste. The voltage, efficiency and output power versus current are depicted in Fig. 5. And the heat flow is displayed in Fig. S1(d). The single-leg device fabricated from (Ge_0.99Pb_0.01Se)_0.9(AgBiTe₂)_0.1 acquires an eminent η of 5.5% with a ΔT of 300 K, which is higher than that of other GeSe-based materials at similar ΔT, as displayed in Fig. 5(d).^19,25,26

Fig. 4 The TE performance of (Ge_1–xPb_xSe)_0.9(AgBiTe₂)_0.1 (x = 0–0.06): (a) the ratio of µ_H/κ_lat, (b) ZT, (c) comparison of ZT with other GeSe systems, and (d) ZT_ave.

Fig. 5 The single-leg device performance of (Ge_0.99Pb_0.01Se)_0.9(AgBiTe₂)_0.1 with different ΔT: current-dependent (a) voltage, (b) η, and (c) output power. (d) Comparison of η with other GeSe-based materials,^19,25,26 with the inset showing the single-leg device connected to a Cu electrode during the test.

4. Conclusions

In summary, this work proposes a coordinated approach, employing AgBiTe₂ alloying to increase lattice symmetry and carrier density. And Pb is alloyed to concurrently modulate the electrical and thermal properties of GeSe, which ultimately leads to substantially improved thermoelectric performance and superior conversion efficiency. The S is promoted by enlarging the DOS m* and decreasing carrier density through Pb alloying, further preserving electrical properties. Meanwhile, Pb incorporation facilitates the attainment of an ultralow κ_lat through a combination of chemical bonding softening and intensive point defects. The minimal κ_lat is drastically reduced to 0.44 W m⁻¹ K⁻¹ at 473 K for (Ge_0.96Pb_0.04Se)_0.9(AgBiTe₂)_0.1, nearing the theoretical minimum. A distinguished ZT of 1.35 is acquired for (Ge_0.99Pb_0.01Se)_0.9(AgBiTe₂)_0.1 at 723 K. Furthermore, an outstanding conversion efficiency of 5.5% with a ΔT of 300 K is acquired in a single-leg device based on GeSe materials. This work opens a promising avenue for designing high-performance TE materials through coordinated property modulation, with potential extensions to other chalcogenide systems.

Conflicts of interest

There are no conflicts of interest to declare.

Data availability

The generated materials in this work are accessible from the corresponding author upon reasonable request.

Acknowledgements

The authors acknowledge support from the National Natural Science Foundation of China (52472184, 52402221, 52250090, 52002042, 51772012, and 51571007), the National Key Research and Development Program of China (2024YFA1210400), the Beijing Natural Science Foundation (JQ18004), the 111 Project (B17002), and the high performance computing (HPC) resources at Beihang University. L.-D. Z. acknowledges the support from the National Science Fund for Distinguished Young Scholars (51925101) and the Tencent Xplorer Prize.

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