Synergistic band modulation and phonon suppression to improve PbBi₂S₄ thermoelectric performance

Abstract

PbBi₂S₄ has emerged as a promising thermoelectric material due to its distinctive layered structure and low thermal conductivity. However, its practical applications are hindered by suboptimal electrical transport properties, and engineering the complex electronic band structure derived from the layered lattice is crucial to addressing this challenge. This study presents a dual-approach optimization strategy involving Sb doping and Se alloying to synergistically improve the electrical and thermal properties of PbBi₂S₄. First, Sb as an aliovalent dopant regulates carrier density to optimize charge transport, while Sb incorporation induces conduction band flattening. Hence, Sb doping simultaneously enhances both the electrical conductivity (increasing carrier density) and Seebeck coefficient (band flattening), which manifests in a nearly doubled weighted mobility (μ_w) at room temperature, leading to substantial improvement in electrical performance (power factor). Then, Se alloying further suppresses the lattice thermal conductivity (κ_lat) to 0.27 W m⁻¹ K⁻¹ through enhanced phonon scattering, while maintaining optimized charge transport. The ratio of weighted mobility to lattice thermal conductivity (μ_w/κ_lat), a comprehensive indicator of thermoelectric performance, is significantly enhanced to ∼2.3 times at 300 K and ∼2.2 times at 773 K that of pure PbBi₂S₄. The charge and phonon transport mechanisms underlying the thermoelectric enhancement are well elucidated by the theoretical band structure calculations and microstructure characterization. Finally, a maximum ZT value of 0.78 is achieved in Pb_0.91Sb_0.09Bi₂S_3.95Se_0.05, representing ∼1.7 times improvement over the pristine PbBi₂S₄, making it one of the most competitive ternary S-based compounds.

---

1. Introduction

As a type of all-solid and environmentally friendly energy technology, thermoelectric materials can convert low-grade waste heat into useful electricity, playing a pivotal role in the field of power generation.^1–4 In general, the performance of thermoelectric materials can be assessed based on the dimensionless figure of merit (ZT), ZT = (S²σT)/(κ_ele + κ_lat), where S, σ, T, κ_ele and κ_lat denote the Seebeck coefficient, electrical conductivity, working temperature, electronic thermal conductivity and lattice thermal conductivity.^5–7 Obviously, the pursuit of a trade-off between excellent electrical transport properties and extremely low thermal conductivity will determine the upper limit of the thermoelectric ZT for materials.^8–10 However, achieving synergistic or independent optimization of electrical and thermal transport in a material is a key challenge.

For a long time, the thermoelectric field has been focused on finite binary material systems with highly symmetrical crystal structures, such as Bi₂Te₃,^11,12 PbQ (Q = Te, Se and S),^9,13,14 GeTe,^15,16etc. These materials exhibit excellent electrical transport properties due to high energy degeneracy or multi-valley structure features, but also endowing them with high thermal transport properties. On the other side, ternary compounds often possess low crystal symmetry and complex chemical bonding environments, which result in low lattice thermal conductivity, while also offering a variety of possibilities for the electronic band structure modification.^17,18 Therefore, the intrinsic low thermal conductivity provides an opportunity to focus on optimizing the electrical properties of materials. In recent years, ternary compounds have made significant advancements. For example, Kim et al. achieved a high ZT value of 1.2 in AgSbTe₂,¹⁹ and Jiang et al. even obtained an outstanding ZT value of 1.3 in Ag₉GaSe₆.²⁰ Ternary PbBi₂S₄ exhibits an intrinsic low thermal conductivity of ∼0.57 W m⁻¹ K⁻¹, attributed to its complex crystal structure and strong interlayer scattering. Coupled with a favorable carrier density of 5.7 × 10¹⁹ cm⁻³ and effective mass of 0.74 m_e, PbBi₂S₄ is considered a promising material for medium-temperature thermoelectric application.^21,22 To date, doping and band structure modification have provided additional opportunities to optimize electrical transport properties.^23–25 However, most current strategies primarily focus on enhancing either electrical conductivity or the Seebeck coefficient. Notably, the weighted mobility (μ_w) can be directly derived from σ and S measurements, which not only comprehensively evaluates the relationship between carrier density-dependent mobility and effective mass, but also serves as a crucial parameter for effectively guiding the optimization of electrical transport properties.^26,27 Increasingly, the characterization of μ_w becomes essential for measuring the thermoelectric performance of materials with low carrier mobility.

In this work, Sb not only serves as an ideal dopant to effectively regulate the carrier density, but also plays a positive role in band structure modulation. Specifically, Sb doping increases the carrier density of PbBi₂S₄, enhancing σ, while Sb-induced conduction band flattening increases the effective mass, mitigating the excessive deterioration of S. As shown in Fig. 1a, the μ_w of the Sb-doped sample is substantially increased by nearly 2 times, leading to a notable optimization of the power factor (PF). On this basis, Se alloying further enhances phonon scattering, resulting in a significant reduction in lattice thermal conductivity. The ratio of weighted mobility to lattice thermal conductivity (μ_w/κ_lat) increases by approximately 2.3 times at 300 K and 2.2 times at 773 K relative to pristine PbBi₂S₄, respectively, as shown in Fig. 1b. The remarkable elevation in μ_w/κ_lat values represents a highly favorable improvement trend, making a maximum trade-off between high electrical transport and low thermal conduction. Benefiting from these synergistic effects, the maximum PF (PF_max) and average PF (PF_ave) of Pb_0.91Sb_0.09Bi₂S_3.95Se_0.05 reach 4.5 μW cm⁻¹ K⁻² and 3.4 μW cm⁻¹ K⁻², respectively. Ultimately, the maximum ZT (ZT_max) and average ZT (ZT_ave) values of 0.78 and 0.41 are achieved in Pb_0.91Sb_0.09Bi₂S_3.95Se_0.05, respectively, which are both ∼1.7 times that of the pristine PbBi₂S₄ matrix, see Fig. 1c and d. These results collectively indicate that regulating the μ_w/κ_lat ratio is a promising approach for enhancing the ZT value.

Fig. 1 (a) PF as a function of electrical conductivity, the solid lines are derived from the single parabolic band (SPB) model with different weighted mobilities, (b) the ratio of weighted carrier mobility to lattice thermal conductivity (μ_w/κ_lat) at 300 K and 773 K, (c) ZT_max value as a function of PF_max, and (d) ZT_ave as a function of PF_ave.

2 Experimental section

2.1 Sample synthesis

High-purity raw materials of Pb, S, Bi, Sb and Se were weighed according to stoichiometric ratios for the compositions Pb_1−xSb_xBi₂S₄ (x = 0–0.1) and Pb_0.91Sb_0.09Bi₂S_4−ySe_y (y = 0–0.1). These mixtures were then loaded into silica tubes, which were flame-sealed under a residual pressure below ∼10⁻⁴ Torr. The samples were slowly heated to 1373 K over 20 h, held at that temperature for 12 h (soaking), and then cooled to room temperature. The obtained ingots were ground into powders and densified using a hot-pressing furnace (OTF-1700X-RHP4) at 773 K for 60 min under an axial compressive stress of 50 MPa, resulting in highly densified disk-shaped samples of Φ15 × 10 mm³.

2.2 Crystal structure characterization

Phase identification was performed through powder X-ray diffraction with Cu Kα (λ = 1.5418 Å) radiation in a reflection geometry operating at 40 kV and 40 mA. The lattice parameters were calculated and refined by using a software package, named “Materials Analysis using Diffraction (GSAS-II)”. X-ray photoelectron spectroscopy measurement was conducted on a Thermo Scientific ESCALAB Xi + spectrometer equipped with a monochromatic Al K_α X-ray source. Chemical compositions were detected by scanning electron microscopy (Hitachi SU6600 FESEM) and energy-dispersive X-ray spectroscopy (EDS Oxford).

2.3 Thermoelectric transport property measurements

Cryoall CTA was used to measure the electrical conductivity and the Seebeck coefficient simultaneously (sample size: 12 × 4 × 4 mm³). The laser flash diffusivity method (Cryoall CLA-1000) was used to measure the thermal diffusivity (D) (sample size: Φ6 mm with a thickness d of ∼1 mm). The thermal conductivity was calculated according to the formula κ_tot = ρDC_p, where ρ and C_p are the density of the sample and heat capacity, respectively. The Van der Pauw technique (Lake Shore 8400 Series, Model 8404, USA) was used to measure Hall coefficients (R_H) with a magnetic field of ∼0.9 T (sample size: 6 × 6 × 0.7 mm³). The carrier density (n_H) was calculated using n_H = 1/(eR_H), and carrier mobility (μ_H) was calculated using the relationship μ_H = σR_H. More experimental details can be found in the SI.

3 Results and discussion

PbBi₂S₄ possesses inherently low thermal conductivity, making enhanced electrical transport properties critical for optimizing its thermoelectric performance. Doping engineering is the most common and effective approach for optimizing electrical transport properties. The Sb element has long been considered a typical dopant, playing significant roles in regulating both carrier density and band structure.^28,29 For this purpose, we synthesize a series of Sb-doped samples Pb_1−xSb_xBi₂S₄ (x = 0–0.1). No second phase is detected, and all samples are well retained in the PbBi₂S₄ phase, as shown in Fig. S1a and S2. The Sb-doped samples exhibit a lattice contraction tendency in Fig. S1b and Table. S1. Fig. 2a illustrates the temperature-dependent σ of Sb-doped samples Pb_1−xSb_xBi₂S₄ (x = 0–0.1), showing a gradual increment with increasing Sb doping content compared to the pristine ternary PbBi₂S₄ compound. Among them, the highest σ reaches 219 S cm⁻¹ for Pb_0.93Sb_0.07Bi₂S₄ at 300 K, and 137 S cm⁻¹ for Pb_0.9Sb_0.1Bi₂S₄ at 773 K, which are approximately 1.8 times and 2.6 times that of the pristine PbBi₂S₄ sample, respectively. The substantial increase in σ can be ascribed to the replacement of Pb²⁺ by Sb³⁺, which provides supplementary electrons to the system, thereby leading to an augmentation in carrier density, as shown in Fig. 2b and Table. S2. In contrast, the increase of carrier density will also cause strong scattering between carriers, decreasing carrier mobility. The high-resolution X-ray photoelectron spectroscopy (XPS) spectra of PbBi₂S₄ are shown in Fig. S3, with no external impurities, and Pb, Bi, and S all exhibit a single valence state. The binding energies of Pb 4f and Bi 4f in Fig. S4 are shifted after Sb doping, mainly due to the Sb-induced charge redistribution and chemical bonding reconfiguration. Moreover, the signal of Sb 3d gradually enhances with increasing Sb doping content, and the peaks corresponding to Sb 3d_3/2 and 3d_5/2 are observed at binding energies of approximately 539.5 and 530.3 eV, respectively. These values are higher than those of metallic Sb, indicating that the Sb is in an ionic state (Sb³⁺).^30,31 Our previous work has demonstrated that the S of ternary PbBi₂S₄ at room temperature is ∼ −100 μV K⁻¹, which falls within the ideal carrier density range.^21,32 However, in Fig. 2c, the increase in carrier density after Sb doping further increases the S to −110 μV K⁻¹ at room temperature, rather than causing a reduction. The Pisarenko function well explains this phenomenon. As shown in Fig. 2d, Sb doping not only increases the carrier density but also effectively enhances the carrier effective mass (m*) of the matrix. The m* increases from 0.74 m_e in pristine PbBi₂S₄ to 1.27 m_e in Pb_0.91Sb_0.09Bi₂S₄, implying a modulation in the electronic band structure. Therefore, Sb dopants have two positive effects: the increase in carrier density improves the electrical conductivity, while the increase in effective mass enhances the Seebeck coefficient.

Fig. 2 Thermoelectric performance of Pb_1−xSb_xBi₂S₄ (x = 0–0.1): (a) electrical conductivity, (b) carrier density and carrier mobility as a function of Sb content, (c) Seebeck coefficient, (d) Pisarenko relationship, the inset shows effective mass (based on the SPB model), (e) weighted mobility, and (f) power factor.

To fully assess the temperature-dependent complex relationship between σ and S, the μ_w can describe an optimal state of the underlying electrical transport phenomena. As displayed in Fig. 2e, the μ_w of all samples is significantly optimized with Sb doping. The room-temperature μ_w in Pb_0.91Sb_0.09Bi₂S₄ reaches ∼29 cm² V⁻¹ s⁻¹, nearly twice that of the pure PbBi₂S₄ sample, which largely contributes to the improvement of PF. As shown in Fig. 2f, the PF of Pb_0.91Sb_0.09Bi₂S₄ increases from 1.2 μW cm⁻¹ K⁻² to 2.4 μW cm⁻¹ K⁻² at 300 K, while the PF_max increases from 2.8 μW cm⁻¹ K⁻² to 4.3 μW cm⁻¹ K⁻² at 773 K. In summary, Sb doping results in a notable enhancement in the overall electrical performance, as reflected in the average power factor (PF_ave). The PF_ave of the Pb_0.91Sb_0.09Bi₂S₄ sample is improved by ∼55% relative to the pure PbBi₂S₄, as illustrated in Fig. S5a. It should be noted that our previous work has demonstrated that lower out-of-plane thermal conductivity in PbBi₂S₄ leads to more favorable thermoelectric performance.²¹ Therefore, in this work, we focus on exploring the thermoelectric performance in this direction.

To further elucidate the source of the increased carrier effective mass, we calculate the band structures of PbBi₂S₄ without and with Sb doping. As shown in Fig. 3a, PbBi₂S₄ is an indirect band gap semiconductor with a complex band structure,^32,33 and the conduction band of Sb-doped PbBi₂S₄ is significantly different from pure PbBi₂S₄. The enlarged view clearly shows that the conduction band minimum (CBM) flattens after Sb doping, as displayed in Fig. 3b, thereby increasing single band effective mass. Therefore, the increased m* from 0.74 m_e in PbS₂Bi₄ to 1.27 m_e in the Pb_0.91Sb_0.09Bi₄ sample should be attributed to the increased single band effective mass. From the corresponding projected density of states (PDOS), it can be interpreted that Sb doping increases the orbital hybridization at the CBM. Specifically, in pure PbBi₂S₄, the electronic orbitals at the CBM are contributed from Bi_p, Pb_p and S_p states, as shown in Fig. 3c. The Sb-doped sample Pb_0.91Sb_0.09Bi₂S₄ exhibits stronger Sb_p-S_p and Pb_p-Sb_p orbital hybridization at the CBM compared to the pure PbBi₂S₄. And simultaneously, the Sb_p state contributes more obviously than the Pb_p state to the CBM, as shown in Fig. 3d, thereby resulting in significant band flattening. Generally, increasing the carrier density can significantly improve the σ, but the increased carrier density will in turn reduce the S. Thus, both σ and S need to be carefully balanced to optimize the PF. According to n_opt ∝ (m*T)^1.5, the optimal carrier density (n_opt) is proportional to the effective mass m*.^34,35 Sb doping simultaneously increases carrier density and enhances effective mass, achieving a positive regulation of both. The results clarify that Sb doping synergistically boosts both σ at higher optimal carrier density and S by band flattening (enhanced m*), thereby improving its electrical performance.

Fig. 3 Band structure of (a) pure PbBi₂S₄ and Sb-doped PbBi₂S₄ (Pb_0.91Sb_0.09Bi₂S₄), and (b) a locally enlarged view of the corresponding band structure. Projected density of states of (c) pure PbBi₂S₄ and (d) Sb-doped PbBi₂S₄ (Pb_0.91Sb_0.09Bi₂S₄).

Furthermore, Sb doping also significantly suppressed the thermal transport properties of the matrix. As shown in Fig. S5b, the total thermal conductivity (κ_tot) exhibits a downward trend, from 0.65 W m⁻¹ K⁻¹ in PbBi₂S₄ to 0.57 W m⁻¹ K⁻¹ in Pb_0.91Sb_0.09Bi₂S₄ at room temperature. Fig. S5c presents the temperature-dependent κ_lat in Pb_1−xSb_xBi₂S₄, and the κ_lat is significantly reduced upon Sb doping. The lowest κ_lat in the Pb_0.91Sb_0.09Bi₂S₄ sample is as low as 0.48 W m⁻¹ K⁻¹ at 300 K and 0.37 W m⁻¹ K⁻¹ at 773 K. The underlying mechanisms behind such exceptionally low lattice thermal conductivities will be investigated in detail later. In short, the simultaneous optimization of both electrical and thermal transport properties is achieved in Sb-doped samples. Ultimately, the ZT_max value reaches 0.62 in Pb_0.91Sb_0.09Bi₂S₄ at 773 K, which is 32% higher than that of the pristine PbBi₂S₄, as shown in Fig. S5d and Table. S3. Other relevant thermoelectric parameters are presented in Fig. S6.

Besides doping, forming a solid solution is also an effective method to minimize lattice thermal conductivity due to the enhanced alloying phonon scattering.^36,37 Therefore, we further alloy Se into the Pb_0.91Sb_0.09Bi₂S₄ matrix. Fig. S7 and S8 show that no impurity phases are found in all samples, which can be also confirmed from the subsequent microstructural analysis. The XRD Rietveld refinement results in Table. S4 show that the Se-alloyed samples exhibit a lattice expansion tendency. As shown in Fig. 4a, the κ_tot of Pb_0.91Sb_0.09Bi₂S_4−ySe_y samples decreases with increasing Se content; especially at 773 K, the κ_tot reduces from 0.53 W m⁻¹ K⁻¹ in Pb_0.91Sb_0.09Bi₂S₄ to 0.44 W m⁻¹ K⁻¹ in Pb_0.91Sb_0.09Bi₂S_3.95Se_0.05. It is worth noting that the κ_lat of all Se-alloyed samples is further significantly reduced across the entire temperature range, as shown in Fig. 4b. Among them, an extremely low κ_lat of 0.27 W m⁻¹ K⁻¹ is achieved in Pb_0.91Sb_0.09Bi₂S_3.95Se_0.05 at 773 K, which is 27% lower than that of the Pb_0.91Sb_0.09Bi₂S₄ sample and 34% lower than that of the pristine PbBi₂S₄. Analysis of the relationship between the phonon mean free path and Se content shows a downward trend in all Se-alloyed samples (Fig. S9a), indicating that phonon scattering is enhanced after Se alloying. The average sound velocity in Table. S5 also exhibits a downward trend. Hence, Se alloying exerts a more prominent suppressive effect on κ_lat, as depicted in Fig. S9b and S10. A more detailed clarification will be provided later from the microstructural perspective.

Fig. 4 Thermoelectric performance of Pb_0.91Sb_0.09Bi₂S_4−ySe_y (y = 0–0.1): (a) total thermal conductivity, (b) lattice thermal conductivity, (c) electrical conductivity, (d) Seebeck coefficient, (e) PF as a function of weighted mobility at 300 K and 773 K, and (f) the ratio of weighted carrier mobility to lattice thermal conductivity (μ_w/κ_lat).

The results show that Se alloying markedly reduces thermal conductivity in Pb_0.91Sb_0.09Bi₂S₄, while preserving its electrical transport properties. As shown in Fig. 4c, the σ in Se-alloyed samples does not change significantly, remaining comparable to that of the unalloyed state. Moreover, the S in Fig. 4d also remains constant within the entire temperature range. These results can be attributed to the fact that the carrier density remains unaffected in Pb_0.91Sb_0.09Bi₂S_4−ySe_y samples during the alloying process, as depicted in Fig. S11a and Table. S2. Although the alloying process will inevitably introduce defects, Se has a lower electronegativity than S,^38,39 which effectively weakens carrier scattering, thereby maintaining comparable electrical transport properties to those of the Pb_0.91Sb_0.09Bi₂S₄ sample, as depicted in Fig. S11b. Based on the relationship between μ_w and PF in Fig. 4e, it is observed that the PF in the Pb_0.91Sb_0.09Bi₂S_3.95Se_0.05 sample increases by 92% at 300 K and 96% at 773 K compared to the pristine matrix. As shown in Fig. S12, the Te element exhibits better electrical transport properties after replacing the S element due to its lower electronegativity, but Te alloying cannot effectively suppress the thermal conductivity of the matrix, as will be explained in detail later, which limits the improvement of the final ZT value. In contrast, Se-alloyed samples will exhibit more desirable thermoelectric performance due to remarkably optimized electrical and thermal transport properties, as evidenced by the obviously optimized μ_w/κ_lat value in Fig. 4f.

Scanning electron microscopy (SEM) can facilitate our comprehension of the mechanism by which Sb and Se reduce the thermal conductivity of PbBi₂S₄. The SEM image in Fig. 5a demonstrates a smooth surface of the Pb_0.91Sb_0.09Bi₂S₄ sample, and the corresponding energy dispersive spectroscopy (EDS) reflects that all elements are homogeneously distributed in the matrix, as depicted in Fig. 5b and c, without any precipitated phase. Consequently, in the Pb_1−xSb_xBi₂S₄ series, the mismatch in atomic and mass between Sb and Pb will significantly interfere with periodic lattice vibrations,^40,41 and this strong point defect scattering is the primary reason for the decreased κ_lat. Nevertheless, with continued Se incorporation into Pb_0.91Sb_0.09Bi₂S₄, distinct grain boundaries are observed on the smooth surface, as shown in Fig. 5d. The scale of the region surrounded by grain boundaries is 10–20 μm. Apparently, the Se alloying-induced grain boundaries will also serve as a new phonon scattering source. As shown in the magnified region in Fig. 5e and corresponding EDS analysis, the constituent elements are uniformly distributed within both the grain boundaries and the matrix, and no secondary phase exists in Fig. 5f and g, which is consistent with the XRD results. The above microstructure analysis reveals the absence of nano-precipitated phases and a well-ordered internal microstructure that promotes considerable electrical transport properties in the matrix, as also demonstrated by the results presented in Fig. 4. In contrast, the Te-alloyed Pb_0.91Sb_0.09Bi₂S_3.95Te_0.05 sample retains a smooth surface, and no discernible grain boundaries are observed across various magnifications, as shown in Fig. S13a–c. The corresponding EDS shows that all elements are homogeneously distributed in the matrix, and no secondary phase is found in Fig. S13d. Therefore, in Se-alloyed Pb_0.91Sb_0.09Bi₂S_4−ySe_y (y = 0–0.1) samples, the phonon scattering of pristine PbBi₂S₄ is further enhanced due to the atomic size and mass differences between Se and S. On the other hand, Se-induced grain boundaries markedly reduce the phonon mean free path, and further lower the κ_lat, as shown in Fig. S9. As a result, extremely low thermal transport properties are achieved in the Sb-doped and Se-alloyed samples, which is beneficial for improving the final thermoelectric performance.

Fig. 5 Microstructure observation of Pb_0.91Sb_0.09Bi₂S₄ and Pb_0.91Sb_0.09Bi₂S_3.95Se_0.05: (a) low magnification SEM morphological image of Pb_0.91Sb_0.09Bi₂S₄, (b) overlay EDS mapping, and (c) the corresponding respective EDS elemental mapping of S, Pb, Bi and Sb, (d) and (e) low magnification SEM morphological image of Pb_0.91Sb_0.09Bi₂S_3.95Se_0.05, (f) overlay EDS mapping, and (g) the corresponding respective EDS elemental mapping of S, Pb, Bi, Sb and Se.

The combination of significantly enhanced PF and suppressed κ_lat certainly achieves a remarkable thermoelectric performance optimization in Pb_0.91Sb_0.09Bi₂S_4−ySe_y (y = 0–0.1) samples. The effect of Sb and Se on the thermoelectric transport properties of PbBi₂S₄ can be further evaluated through the quality factor B. As shown in Fig. 6a, the B value is gradually enhanced over the entire temperature range after Sb doping and Se alloying. At 773 K, the maximum B value is improved more than 2 times. Correspondingly, the ZT_max increases from 0.47 in PbBi₂S₄ to 0.62 in Pb_0.91Sb_0.09Bi₂S₄, finally reaching 0.78 in Pb_0.91Sb_0.09Bi₂S_3.95Se_0.05 at 773 K, as shown in Fig. 6b and S14a. Overall, a high wide-temperature ZT (average ZT, ZT_ave) value of 0.41 is achieved in the Pb_0.91Sb_0.09Bi₂S_3.95Se_0.05 sample, as shown in Fig. S14b, approximately 1.7 and 1.2 times that of PbBi₂S₄ and Pb_0.91Sb_0.09Bi₂S₄, respectively. In general, excellent thermoelectric performance can be reflected by the ratio of weighted mobility to lattice thermal conductivity. Fig. 6c shows the μ_w/κ_lat values for the optimized S-based ternary compounds at 300 K and their peak ZT values at high temperatures, indicating a prominent thermoelectric superiority in PbBi₂S₄-based materials. In this work, the introduction of Sb induces band flattening, increasing the effective mass and μ_w. The subsequent introduction of Se further enhances the phonon scattering, reducing the κ_lat. The synergistic optimization of electrical and thermal transport demonstrates promising thermoelectric performance in PbBi₂S₄-based materials. Ultimately, the Pb_0.91Sb_0.09Bi₂S_3.95Se_0.05 sample stands out as one of the most outstanding ternary S-based compounds, as shown in Fig. 6d, highlighting its great potential for practical applications.

Fig. 6 Thermoelectric performance of Pb_0.91Sb_0.09Bi₂S_4−ySe_y (y = 0–0.1): (a) quality factor B and (b) ZT values. Comparison of (c) μ_w/κ_lat and (d) ZT values of the Pb_0.91Sb_0.09Bi₂S_3.95Se_0.05 compound with some other S-based ternary compounds, such as Cu₇Sn₃S_9.1Cl_0.9,⁴² Cu₂Sn_0.9In_0.1S₃,⁴³ Bi₂SeS₂-3%CuBr,⁴⁴ Co_0.92Ni_0.08SbS,⁴⁵ Cu_0.98Zn_0.02FeS₂,⁴⁶ Cu_1.576Zn_0.024Bi_4.6S₈,⁴⁷ AgBiS_1.92Se_0.08,⁴⁸ Cu₄Sn_7.5S₁₅Se,⁴⁹ Cu₃Sn_1.2S₄,⁵⁰ PbBi₂S_3.92Cl_0.08,⁵¹ and Pb_0.6Sn_0.4Bi₂S₄.³²

4. Conclusion

In summary, we have demonstrated the feasibility of dual optimization in weighted mobility and lattice thermal conductivity through Sb doping and Se alloying. First, by introducing the Sb dopant, we achieve an increase in the optimum carrier density (improving σ) related to effective mass, while Sb-induced band flattening precisely enhances the effective mass (enhancing S). This brings about a twofold increase in μ_w and PF at room temperature. Then, Se alloying further enhances the defect-induced phonon scattering while preserving the excellent electrical transport properties of Sb-doped PbBi₂S₄. The SEM results clarify that Se-induced grain boundaries also have a significant effect on lattice thermal conductivity. The lowest κ_lat reaches an extremely low value of 0.27 W m⁻¹ K⁻¹ in Pb_0.91Sb_0.09Bi₂S_3.95Se_0.05, and the μ_w/κ_lat values more than double across the entire working temperature range. Ultimately, a maximum ZT value of 0.78 and an average ZT value of 0.41 are achieved for Pb_0.91Sb_0.09Bi₂S_3.95Se_0.05, both of which are ∼1.7 times that of the pristine PbBi₂S₄ matrix. The results obtained for PbBi₂S₄ exhibit competitive performance compared to other ternary S-based compounds, demonstrating it as a promising medium-temperature thermoelectric candidate material.

Author contributions

Wei Liu: designed the experiments, prepared the samples, conducted the measurement of thermoelectric properties, and wrote the original manuscript; Zhanxiang Yin: measurement of thermal diffusivity of some samples; Peng Ai and Shuwei Tang: conducted theoretical calculations; Xinxiu Cheng: XRD data curation; Chaoguang Deng: measurement of the carrier density of some samples; Taohua Liang: supervised this program; Wenke He: project administration and revised this manuscript; Yu Xiao: conceptualization, formal analysis, project administration, supervision, writing – review & editing and funding acquisition.

Conflicts of interest

The authors declare no competing interests.

Data availability

The data supporting this article have been included as part of the SI. See DOI: https://doi.org/10.1039/d5ta05246g.

Acknowledgements

We acknowledge the financial support from the National Natural Science Foundation of China (grant no. 52172236 and no. 22205032), and the fund of Sichuan Provincial Natural Science Foundation (grant no. 2025ZNSFSC0385). This work was also supported by the “Bairen” Program from the University of Electronic Science and Technology of China.

References

1. J. Guo, Y.-K. Zhu, L. Chen, Z.-Y. Wang, Z.-H. Ge and J. Feng, J. Mater. Sci. Technol., 2022, 100, 51–58.
2. X. Tang, Z. Li, W. Liu, Q. Zhang and C. Uher, Interdiscip. Mater., 2022, 1, 88–115.
3. P. Acharyya, K. Pal, B. Zhang, T. Barbier, C. Prestipino, P. Boullay, B. Raveau, P. Lemoine, B. Malaman, X. Shen, M. Vaillant, A. Renaud, B. P. Uberuaga, C. Candolfi, X. Zhou and E. Guilmeau, J. Am. Chem. Soc., 2024, 146, 13477–13487.
4. Z. Yin, L. Xu and Y. Xiao, Chem. Commun., 2025, 61, 9157–9168.
5. S. Zheng, S. Xiao, K. Peng, Y. Pan, X. Yang, X. Lu, G. Han, B. Zhang, Z. Zhou, G. Wang and X. Zhou, Adv. Mater., 2023, 35, 2210380.
6. J. Feng, J. Li and R. Liu, Nano Energy, 2024, 126, 109651.
7. S. Wu, X. Wang, X. Mi, S. Zheng, K. Yang, Z. Zhou, H. Wang, G. Han, X. Lu, Y. Pan, G. Wang and X. Zhou, Adv. Energy Mater., 2024, 14, 2400184.
8. W. Liu, T. Hong, S. Dong, D. Wang, X. Gao, Y. Xiao and L.-D. Zhao, Mater. Today Energy, 2022, 26, 100983.
9. B. Jia, D. Wu, L. Xie, W. Wang, T. Yu, S. Li, Y. Wang, Y. Xu, B. Jiang, Z. Chen, Y. Weng and J. He, Science, 2024, 384, 81–86.
10. S.-T. Kim, J. M. Park, K.-I. Park, S.-E. Chun, H. S. Lee, P.-P. Choi and S. Yi, J. Mater. Sci. Technol., 2021, 94, 175–182.
11. B. Zhu, W. Wang, J. Cui and J. He, Small, 2021, 17, 2101328.
12. H. Choi, K. Jeong, J. Chae, H. Park, J. Baeck, T. H. Kim, J. Y. Song, J. Park, K.-H. Jeong and M.-H. Cho, Nano Energy, 2018, 47, 374–384.
13. W. Liu, L. Xu, Y. Xiao and L.-D. Zhao, Chem. Eng. J., 2023, 465, 142785.
14. L. Xu, Y. Xiao, S. Wang, B. Cui, D. Wu, X. Ding and L.-D. Zhao, Nat. Commun., 2022, 13, 6449.
15. X. Zhang, Z. Bu, S. Lin, Z. Chen, W. Li and Y. Pei, Joule, 2020, 4, 986–1003.
16. J. Li, X. Zhang, Z. Chen, S. Lin, W. Li, J. Shen, I. T. Witting, A. Faghaninia, Y. Chen, A. Jain, L. Chen, G. J. Snyder and Y. Pei, Joule, 2018, 2, 976–987.
17. S. Zhan, T. Hong, B. Qin, Y. Zhu, X. Feng, L. Su, H. Shi, H. Liang, Q. Zhang, X. Gao, Z. H. Ge, L. Zheng, D. Wang and L.-D. Zhao, Nat. Commun., 2022, 13, 5937.
18. Y. Zhu, B. Wei, J. Liu, N. Z. Koocher, Y. Li, L. Hu, W. He, G. Deng, W. Xu, X. Wang, J. M. Rondinelli, L.-D. Zhao, G. J. Snyder and J. Hong, Mater. Today Phys., 2021, 19, 100428.
19. K. Kim, S. Choo, J. Lee, H. Ju, S. h. Jung, S. Jo, S. H. Lee, S. Baek, J. Y. Kim and K. T. Kim, Adv. Sci., 2024, 11, 2402934.
20. B. Jiang, P. Qiu, H. Chen, Q. Zhang, K. Zhao, D. Ren, X. Shi and L. Chen, Chem. Commun., 2017, 53, 11658–11661.
21. W. Liu, B. Chen, L. Xu, D. Wang, C. Xiang, X. Ding and Y. Xiao, J. Mater. Sci. Technol., 2024, 198, 12–19.
22. M. Ohta, D. Y. Chung, M. Kunii and M. G. Kanatzidis, J. Mater. Chem. A, 2014, 2, 20048–20058.
23. B. Jiang, X. Liu, Q. Wang, J. Cui, B. Jia, Y. Zhu, J. Feng, Y. Qiu, M. Gu, Z. Ge and J. He, Energy Environ. Sci., 2020, 13, 579–591.
24. Y. Jiang, J. Dong, H. L. Zhuang, J. Yu, B. Su, H. Li, J. Pei, F. H. Sun, M. Zhou, H. Hu, J. W. Li, Z. Han, B. P. Zhang, T. Mori and J. F. Li, Nat. Commun., 2022, 13, 6087.
25. P. Chen, C. Yuan, H. Wu, Y. Yan, B. Zhang, X. Gong, J. Liu, D. Li, G. Ding, X. Zhou and G. Wang, J. Mater. Sci. Technol., 2025, 230, 120–128.
26. G. J. Snyder, A. H. Snyder, M. Wood, R. Gurunathan, B. H. Snyder and C. Niu, Adv. Mater., 2020, 32, 2001537.
27. Y. Huang, J. Lei, H. Chen, Z. Zhou, H. Dong, S. Yang, H. Gao, T.-R. Wei, K. Zhao and X. Shi, Acta Mater., 2023, 249, 118847.
28. X. Hu, Y. Zhang, Y. Jiang, C. Li, Q. Yang, X. Wang, J. Zhang, S. Li and K. Guo, Inorg. Chem. Front., 2024, 11, 3897–3905.
29. Z. Z. Luo, S. Cai, S. Hao, T. P. Bailey, H. Xie, T. J. Slade, Y. Liu, Y. Luo, Z. Chen, J. Xu, W. Luo, Y. Yu, C. Uher, C. Wolverton, V. P. Dravid, Z. Zou, Q. Yan and M. G. Kanatzidis, J. Am. Chem. Soc., 2022, 144, 7402–7413.
30. M. Yan, Z. Wei, Z. Gong, B. Johannessen, G. Ye, G. He, J. Liu, S. Zhao, C. Cui and H. Fei, Nat. Commun., 2023, 14, 368.
31. B. Wu, X. Zhao, M. Jia, D. Yang, Y. Liu, H. Song, D. Wang, A. Cabot and M. Li, Appl. Phys. Lett., 2024, 125, 223901.
32. W. Liu, T. Hong, X. Cheng, L. Xu, G. Yan, W. He and Y. Xiao, J. Materiomics, 2024, 11, 100938.
33. F. Cai, R. Dong, W. Sun, X. Lei, B. Yu, J. Chen, L. Yuan, C. Wang and Q. Zhang, Chem. Mater., 2021, 33, 6003–6011.
34. Y. Yu, C. Zhou, X. Zhang, L. Abdellaoui, C. Doberstein, B. Berkels, B. Ge, G. Qiao, C. Scheu, M. Wuttig, O. Cojocaru-Mirédin and S. Zhang, Nano Energy, 2022, 101, 107576.
35. Y. Xiao, W. Liu, Y. Zhang, D. Wang, H. Shi, S. Wang, Y. Jin, W. Qu, H. Wu, X. Ding, J. Sun and L.-D. Zhao, J. Mater. Chem. A, 2021, 9, 23011–23018.
36. W. Li, Y. Luo, T. Xu, Z. Ma, C. Li, Y. Wei, Y. Tao, Y. Qian, X. Li, Q. Jiang and J. Yang, Small, 2023, 19, 2301963.
37. J. Dong, F.-H. Sun, H. Tang, K. Hayashi, H. Li, P.-P. Shang, Y. Miyazaki and J.-F. Li, ACS Appl. Mater. Interfaces, 2019, 11, 28221–28227.
38. J. Zhang, L. Song, K. A. Borup, M. R. V. Jørgensen and B. B. Iversen, Adv. Energy Mater., 2018, 8, 1702776.
39. H. Shi, D. Wang, Y. Xiao and L.-D. Zhao, Aggregate, 2021, 2, e92.
40. X. Li, B. Ma, S. Liu, F. Zhang, Y. Li, X. Chao, Z. Yang, J. He and D. Wu, ACS Appl. Energy Mater., 2023, 6, 530–536.
41. G. Tan, C. C. Stoumpos, S. Wang, T. P. Bailey, L.-D. Zhao, C. Uher and M. G. Kanatzidis, Adv. Energy Mater., 2017, 7, 1700099.
42. T. Deng, T. Xing, M. K. Brod, Y. Sheng, P. Qiu, I. Veremchuk, Q. Song, T.-R. Wei, J. Yang, G. J. Snyder, Y. Grin, L. Chen and X. Shi, Energy Environ. Sci., 2020, 13, 3041–3053.
43. Q. Tan, W. Sun, Z. Li and J.-F. Li, J. Alloys Compd., 2016, 672, 558–563.
44. M. Ruan, F. Li, Y. Chen, Z. Zheng and P. Fan, J. Alloys Compd., 2020, 849, 156677.
45. Z. Liu, H. Geng, J. Shuai, Z. Wang, J. Mao, D. Wang, Q. Jie, W. Cai, J. Sui and Z. Ren, J. Mater. Chem. C, 2015, 3, 10442–10450.
46. H. Y. Xie, X. L. Su, G. Zheng, T. Zhu, K. Yin, Y. G. Yan, C. Uher, M. G. Kanatzidis and X. F. Tang, Adv. Energy Mater., 2017, 7, 1601299.
47. J. Y. Ahn, J.-Y. Hwang, B. K. Ryu, M.-W. Oh, K. H. Lee and S. W. Kim, CrystEngComm, 2016, 18, 1453–1461.
48. S. N. Guin and K. Biswas, Chem. Mater., 2013, 25, 3225–3231.
49. J. Cui, T. He, Z. Han, X. Liu and Z. Du, Sci. Rep., 2018, 8, 8202.
50. Y. Yang, P. Ying, J. Wang, X. Liu, Z. Du, Y. Chao and J. Cui, J. Mater. Chem. A, 2017, 5, 18808–18815.
51. K. Maji, B. Raveau, S. Fujii, T. Arai, S. Le Tonquesse, C. Prestipino, P. Acharyya, M. Yoshiya and E. Guilmeau, Chem. Mater., 2024, 36, 4631–4641.

---