Introduction

Thermoelectric (TE) technology has significant potential for alleviating the global energy and environmental crisis, as it can directly convert waste heat into useful electrical energy in an environmentally friendly manner1,2,3,4. However, the primary obstacles to the practical application of TE materials and devices are their low TE conversion efficiency and high cost5,6. A high TE conversion efficiency requires reliable interface materials between TE materials and electrodes to prevent chemical reactions and diffusion, as well as high performance of the TE materials, which can be defined by the figure of merit zT = S2σT/κtot, where S, T, σ, and κtot are the Seebeck coefficient, absolute temperature in Kelvin, electrical conductivity, and total thermal conductivity [the sum of electronic (κele) and lattice (κlat) parts], respectively. Over the past few decades, significant efforts have been made to increase the zT value of materials, primarily by optimizing the carrier concentration (nH)7,8, modulating the electronic structure1,9, improving the power factor (PF = S2σ), and designing unique crystal defects10 to increase phonon scattering to reduce κlat. However, most of these strategies for optimizing charge carrier and phonon transport have been aimed almost exclusively at independently enhancing electrical performance and reducing thermal transport11, often with adverse effects on each other. Therefore, the bottleneck in improving the zT of materials lies in exploring a single, effective strategy that simultaneously optimizes both S2σ and κlat.

As a long-established TE material, PbTe has been used for power generation at intermediate temperatures (500–900 K) for a long time12,13,14,15,16,17,18. However, due to the scarcity of Te in the Earth’s crust (only 0.001 ppm), the high material costs and insufficient sustainability have limited its widespread application. Due to the abundance of Se19, PbSe is a promising alternative to PbTe. PbSe has an electronic structure similar to that of PbTe1,20, where the heavy Σ and light L valence bands have a small energy separation that degenerates with increasing temperature. This results in the zT value of p-type PbSe being significantly greater than that of n-type PbSe, which has only a single conduction band for transport. In fact, with continued research on p-type PbSe in recent years, its zT value at 900 K has approached ~2.021,22,23. However, identifying practical strategies to improve n-type PbSe TE materials for matching is imperative for realizing high-performance TE devices (TEDs). To optimize the TE performance of n-type PbSe, although Cu doping has been shown to effectively optimize nH over a wide temperature range8,24,25, its doping mechanism has not been fully elucidated. Additionally, despite recent improvements in the performance of n-type PbSe polycrystals, the reliance on doping with multiple elements and high Te content, such as Pb0.95Sb0.033Se0.6Te0.426 and Pb0.89Sb0.012Sn0.1Se0.5Te0.25S0.2527, complicates the preparation process and increases the cost.

In addition to optimizing the material performance, another challenge in current research on n-type PbSe is the design of compatible interface materials and further device integration. In TE modules, p-type and n-type materials (legs) are electrically connected in series and thermally connected in parallel through metal electrodes (such as Cu, Ag, Ni, and their derivatives)5,28. However, in practical applications, TE materials cannot be directly soldered to these electrode materials because they tend to diffuse into each other, reducing the TE performance, especially at high temperatures. For example, Ni and GeTe can form metal tellurides at interfaces, leading to decreased TE performance and cracking of the GeTe/Ni junction28. Therefore, designing and identifying suitable TE interface materials (TEiMs) is crucial for developing efficient TE modules. Unfortunately, there are currently no systematic studies on the rational design and performance characterization of PbSe TEiMs. Consequently, there is an urgent need to develop high-performance n-type PbSe and compatible TEiMs to construct efficient and reliable PbSe-based TEDs.

Here, we propose a rational design strategy based on Cu-doped lattice defect engineering to fill the above research gap. This involves utilizing a high level of Cu doping to achieve interstitial Cu (Cui) defects while simultaneously inducing the formation of a large number of uniformly distributed nanoscale semicoherent precipitates. This approach effectively regulates nH and transport properties, significantly enhancing S and S2σ (Fig. 1a). Moreover, the κlat is reduced by synergistically enhancing the scattering of phonons with different wavelengths, ultimately achieving ultrahigh TE performance for n-type PbSe, which is highly competitive with reported values (Fig. 1b)7,9,27,29,30,31. In addition, regarding the design of device interfaces, we conducted a detailed characterization of ten candidate TEiMs and demonstrated that Co can serve as a reliable diffusion barrier for high-performance PbSe. The Ag/Co/PbSe interface design successfully prevented chemical reactions and diffusion, with negligible additional resistance (Fig. 1c). This contributed to a high conversion efficiency (η) of ~13.1% under a temperature difference (ΔT) of 460 K in segmented TED (Fig. 1d), which is significantly superior to the η of previously reported PbSe-based TEDs23,27,32,33,34,35,36.

Fig. 1: Introduction of advancing n-type PbSe-based thermoelectrics through the elaborate manipulation of compositions and screening of stable thermoelectric interface materials (TEiMs).
figure 1

a Power factor (S2σ) as a function of y and temperature (T) for Pb0.98Cuy+0.04Se. b T-dependent figure of merit (zT) for n-type Pb0.98Cu0.043Se in comparison with other state-of-the-art n-type PbSe7,9,27,29,30,31. Error bars of 15% are applied. c Room-temperature electrical contact resistivity (ρc) for the Co/PbSe junction based on the four-probe technique (inset in c). d Conversion efficiencies (η) for our Pb0.98Cu0.043Se-based segmented module and the literature results23,27,32,33,34,35,36. The inset shows a photo of our Pb0.98Cu0.043Se-based segmented module.

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Results and discussion

Design principle and structure characterization of the materials

We first calculated the defect formation energies (Edef) of potential Cu-related defects in the PbSe system based on density functional theory. These defects include Cui, substitution-interstitial Cu pairs (Pb31Cu2Se32), and Cu/Pb substitution (CuPb) to understand the possible doping mechanisms of Cu37,38,39,40. The calculation results indicate that Pb31Cu2Se32 has the lowest Edef (Supplementary Fig. 1 and Supplementary Table 1), suggesting that intentionally introducing cation vacancies in PbSe can promote the formation of more Cui to some extent, thereby increasing nH. Therefore, to obtain low-cost, high-performance n-type PbSe TE materials, we designed the Pb1−xCu2x+ySe system [Pb1−xCu2x+ySe → xCu2Se + yCui + (1−x)PbSe] based on the Edef results and the following four aspects. First, the Cu+ ions occupying the interstitial site (Cui) in PbSe are ideal electron donors8 for ensuring n-type conductivity (Fig. 2a). Second, considering the low solubility of Cu in PbSe8, the addition of excess Cu induces complex crystal defects, such as the highly anharmonic liquid-like Cu2Se41 and other solute-rich defects8, which significantly suppress κlat. Third, we aim to reveal the microstructural evolution of the dopant content and the potential crystallographic relationship between the nanostructures and the PbSe matrix and explore how these factors affect the TE properties. Finally, controlling Cu doping simplifies the material preparation process and reduces costs.

Fig. 2: Crystal structures obtained via synchrotron radiation measurements.
figure 2

a Schematic diagram of the interstitial Cu (Cui) in the PbSe lattice. b The Cu K-edge X-ray absorption near-edge structure (XANES) spectra of the Pb0.98Cu0.043Se (y = 0.003) sample and a Cu foil. The insets in (b) are the corresponding difference curves. c Radial distributions surrounding Cu and their corresponding real-part components (solid lines and open circles are the fitted and experimental values) for Pb0.98Cu0.043Se. d Variable-temperature synchrotron radiation X-ray diffraction (SXRD) pattern of Pb0.98Cu0.043Se (first measurement).

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The powder X-ray diffraction (XRD) patterns of Pb1−xCu2x+ySe indicate that the prepared samples can be entirely classified as having a NaCl structure. With increasing x and y values, the lattice parameter remains nearly unchanged but expands slightly in Pb1−xCu2x+0.002Se (x = 0, 0.01, 0.02, 0.03, and 0.04) (Supplementary Fig. 2) and Pb0.98Cu0.04+ySe (y = 0.001, 0.002, 0.003, 0.004, and 0.005) (Supplementary Fig. 3). The former is primarily attributed to the formation of semicoherent Cu2Se nanostructures, while the latter involves more Cu entering the interstitial lattice of PbSe. To determine the local structure of the Cu-doped samples, we performed X-ray absorption fine structure (XAFS) spectroscopy to identify the local coordination environment for the absorbing atomic center42. Figure 2b shows the normalized X-ray absorption near-edge structure (XANES) spectra of the Cu K-edge. For the Pb0.98Cu0.043Se (y = 0.003) sample, the position of the Cu absorption edge shifts noticeably to a higher energy than that of Cu foil, indicating an increase in the oxidation state of Cu. We fitted the least squares extended XAFS (EXAFS) curves for the first coordination shell of Cu using the Cu–Se backscattering pathway43. The results show a high degree of consistency between the experimental data and theoretical curves, indicating that most of the Cu atoms form a Cu2Se phase (Fig. 2c and Supplementary Table 2). The Se K-edge XANES spectra of the representative samples are presented in Supplementary Fig. 4. It is evident that the Se absorption edge for all samples shifts towards the high-energy side relative to the Se foil (Supplementary Fig. 4b). Notably, the Se K-edge absorption energy in the Cu-doped samples is in line with that of the pristine PbSe, revealing that Se retains a valence state of –2. Based on these results, Cu is in the +1 valence state in the Cu-doped samples. Compared with that of pristine PbSe, the distance between Se and the first-shell atom was shorter in the PbCu0.002Se (x = 0) and Pb0.98Cu0.042Se (x = 0.02) samples (Supplementary Fig. 5 and Supplementary Table 3). This decrease is attributed to the formation of Cui and Cu2Se precipitates, which bring the Cu atoms in the first coordination shell of Se closer to Pb, thereby shortening the Se–Pb distance. The Debye–Waller factor (B) increases from 0.017 to 0.021 Å2 with increasing x content (Supplementary Table 3). This matches the refinement results of XRD (Supplementary Fig. 6), indicating enhanced atomic disorder. Additionally, we performed high-precision synchrotron radiation X-ray diffraction (SXRD) measurements on the Pb0.98Cu0.043Se (y = 0.003) sample over a temperature range from 303 to 823 K. No additional characteristic diffraction peaks were observed across the temperature range, and the main peak shifted to a lower angle than expected due to temperature-induced lattice expansion (Fig. 2d). Furthermore, the results of the repeatability tests have substantiated its excellent stability (Supplementary Fig. 7).

Atomic-scale evolution of nanodefects with increasing Cu dopant content

To directly observe the microstructural evolution in the PbSe matrix caused by different Cu doping levels, we conducted atomic-resolution scanning transmission electron microscopy (STEM) characterization. For the PbCu0.002Se (x = 0) sample, the introduction of trace amounts of Cu created a dense dislocation network within the matrix (Supplementary Fig. 8a-d). It has been demonstrated that introducing dislocations in lead chalcogenides can effectively scatter mid-wavelength phonons and reduce κlat18,24. With a slight increase in the Cu doping content, several nanoscale Cui nanoclusters are exposed within the matrix8,44,45, which is consistent with the low Edef of Cui in PbSe. These nanoclusters are metastable regions within PbSe that form Guinier–Preston (GP) zones46 and serve as nucleation precursors for the formation of larger and more stable Cu2Se precipitates. Thus, with a further increase in the Cu doping content, a large number of uniformly distributed Cu-rich precipitates are embedded within the matrix (Supplementary Fig. 9). Considering that the sample synthesis was carried out under prolonged annealing (for five days), we suppose that the large Cu2Se precipitates grow by consuming the metastable Cui nanoclusters through the Ostwald ripening mechanism47.

The low-magnification high-angle annular dark-field (HAADF) and annular bright-field STEM images of the Pb0.98Cu0.042Se (x = 0.02) sample show denser dislocation clusters (Supplementary Fig. 8e, f) and abundant nanoscale Cu2Se plate-like precipitates (Fig. 3a and Supplementary Fig. 8e–h), respectively. Despite its simple chemical formula, Cu2Se has a rather complex atomic arrangement, especially in the room-temperature α-phase48,49,50,51. Specifically, within the lattice, Se anions and Cu cations form a rigid cubic sublattice and a liquid-like sublattice (Fig. 3b, c), respectively. Moreover, accurately observing the connection structure between complex precipitates and the TE matrix at the atomic scale has been a significant challenge. This has led to almost all precipitated phases being merely phonon scattering sources, while their impact on carrier transport has been overlooked. Therefore, determining the orientation relationship (OR) between Cu2Se nanoprecipitates and the PbSe matrix is crucial for understanding the mechanism behind abnormal TE enhancement. Figure 3d and e clearly show atomic-resolution HAADF-STEM images of the sharp interfaces of the Cu2Se/PbSe nanocomposites along different zone axes. Based on the crystallographic analysis, the ORs are [101]PbSe ∥ \([10{\mbox{-}}1]_{{{\mathrm{Cu}}}_{2}{{\mathrm{Se}}}}\) and [110]PbSe ∥ \([0{\mbox{-}}10]_{{{\mathrm{Cu}}}_{2}{{\mathrm{Se}}}}\) (Supplementary Figs. 10 and 11). Due to the slight lattice mismatch between these parallel planes (less than 5%, Supplementary Table 4), semicoherent interfaces are constructed between the Cu2Se nanoprecipitates and the PbSe matrix, which supports the nearly constant lattice parameters of the Pb1−xCu2x+0.002Se samples with increasing x content (Supplementary Fig. 2). The representative extra half-atomic plane in the Pb0.98Cu0.042Se (x = 0.02) matrix is marked by a Burger vector (red arrow) of 1/2[101] (Fig. 3f). The corresponding geometric phase analysis (GPA) reveals a significant linear strain field near the dislocation core (inset in Fig. 3f), which enhances phonon scattering. Figure 3g shows an atomic schematic diagram corresponding to Fig. 3d. The unique semicoherent phase enhances the electrical transport properties while further scattering phonons. Interestingly, compared with that in the Pb0.98Cu0.042Se (x = 0.02) sample, the number of precipitates in the Pb0.96Cu0.082Se (x = 0.04) sample increases, as expected. However, the number of dislocations unexpectedly decreased, and the dislocations were pinned around the semicoherent Cu2Se nanoprecipitates (Supplementary Fig. 8i), leading to anomalous changes in both nH and κlat.

Fig. 3: Atomic micro/nanostructural characterization of Pb0.98Cu0.042Se (x = 0.02).
figure 3

a Low-magnification scanning transmission electron microscopy (STEM) image displaying dense Cu-rich nanoprecipitates (denoted by the green arrows). b, c Atomic-resolution STEM images and corresponding atomic model clearly indicating the structure of Cu2Se along the [10-1] and [0-10] zone axes, respectively. The inset in (c) is the corresponding fast Fourier transform (FFT) image. d, e High-resolution high-angle annular dark-field (HADDF) STEM images of the semicoherent interfaces at the phase boundary between the Cu2Se nanoprecipitate and PbSe matrix viewed along different zone axes. The phase interfaces and dislocations are marked by dashed lines and yellow symbols respectively. f High-resolution HADDF-STEM image of a typical dislocation. The yellow arrows give a complete Burgers loop of a dislocation, and the estimated Burgers vector (red arrow) is BD = 1/2[101]. The dislocation is marked by white symbols. The inset image shows the geometric phase analysis (GPA) strain analysis of the entire area in (f). g Illustration of the semicoherent Cu2Se nanoprecipitates and influence on phonon and electron transport.

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Ultrahigh thermoelectric performance

The temperature-dependent carrier transport characteristics are significantly influenced by the Cu doping content. The results from Hall measurements for Pb1−xCu2x+0.002Se are shown in Fig. 4a, b. For the sample with x = 0, the nH remains nearly constant below 520 K but increases sharply with increasing temperature, attributed to the dynamic doping effect8. For samples with x = 0.01~0.04, the nH increases significantly. This trend supports the calculated Edef of Cu, suggesting that introducing Pb vacancies facilitates the generation of more Cui. Furthermore, the unusual decrease in nH of Pb1−xCu2x+0.002Se (x = 0.01~0.04) between 400 and 520 K is attributed to the transformation of α-phase Cu2Se into cubic β-phase Cu2Se45,48, as confirmed by differential scanning calorimetry (Supplementary Fig. 12). The substantial increase in the hole concentration in the Cu2Se material, triggered by the phase transition near 400 K, further confirms the corresponding decrease in the electron concentration6,48,49,50. The dynamic Cu doping behavior of PbSe is attributed to the high mobility of Cu ions within the rigid cubic lattice formed by Se anions in Cu2Se precipitates, which move to interstitial positions in PbSe45. This behavior is further validated by the semicoherent interface observed between the Cu2Se precipitates and the PbSe matrix. The tightly connected interface minimizes the lattice mismatch at the phase boundary, creating a favorable pathway for the rapid migration of Cu ions into the lattice gaps of PbSe at high temperatures, as indicated by the red arrow in Fig. 3g. The rapid movement of Cu ions in Cu2Se also occurs above 500 K41,52, aligning with the temperature at which self-optimization of nH is observed (Fig. 4a). Specifically, the dynamic behavior of Cu originates from the phenomenon that temperature drives the Cu ions of the semicoherent Cu2Se precipitates in the matrix to enter the lattice gap of PbSe.

Fig. 4: Thermoelectric properties of Pb1−xCu2x+0.002Se and Pb0.98Cuy+0.04Se.
figure 4

Temperature-dependent a carrier concentration (nH) and b mobility (μH) for Pb1−xCu2x+0.002Se. The black arrow serves as a guide to show the trend of μH. c The variation in the nH of the absolute S (|S|) at different temperatures. me is the free electron mass. The reported experimental data for n-type PbCu0.005Se8 and Br-doped PbSe7 are represented by solid circles. d Schematic diagram of the energy barrier between the Cu2Se precipitates and the PbSe matrix. The potential barrier at the conduction band (CB) can selectively block low-energy electrons. EF and VB are the Fermi energy and the valence band, respectively. e Calculated scattering parameter (rx) and interface potential barrier (EB) for Pb1−xCu2x+0.002Se. Error bars of 5% are applied. f nH as a function of μH for Pb1−xCu2x+0.002Se, along with literature data for representative n-type PbSe systems7,8,9,29,30,35. g Temperature-dependent lattice thermal conductivity (κlat) of PbSe, Pb1−xCu2x+0.002Se and the reported Cu2Se48. h Average S2σ (S2σavg) from 303 to 823 K for y = 0.003 and 0.004 samples, compared with reported high-performance PbSe8,21,23,24,25,27,31,62,63,64. i Temperature-dependent figure-of-merit (zT) for Pb0.98Cuy+0.04Se.

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Figure 4b shows the temperature-dependent carrier mobility (μH) of the Pb1−xCu2x+0.002Se (x = 0~0.04) samples. The μH of PbCu0.002Se (x = 0) sample exhibits a consistent trend (μH ~ T–2.5) with that reported for the PbCuxSe system in the literature8, confirming that the dominant carrier scattering mechanism in these samples is primarily governed by acoustic phonons7,8,25,53,54. However, for samples with x > 0, the μH significantly deviates from the T-2.5 behavior. Both σ and S are displayed in Supplementary Fig. 13. The theoretical Pisarenko relationship55 is simulated based on acoustic phonon-dominated charge transport. The absolute S (|S|) data for PbCu0.002Se (x = 0), along with the reported values for PbCu0.005Se8 and Br-doped PbSe7, align well with the same theoretical curves (Fig. 4c). This consistency confirms that the addition of Cui does not alter the conduction band structure of PbSe8,24,25. The same carrier effective mass (m*) of the x = 0 sample and Br-doped PbSe7 at various temperatures (Supplementary Fig. 14) also provides strong support for this conclusion. Unexpectedly, the experimental |S| values for samples with x = 0.01~0.04 are significantly higher than the theoretical values. We calculated the effect of substitution-intrinsic Cu pairs on the density of states effective mass37,38,39 of n-type PbSe based on the minimum Edef of Cu (for more details, see the Supplementary Information). There was no significant change in m* near the Fermi level (Supplementary Fig. 15), indicating that the increase in |S| was attributed to the energy filtering effect rather than alterations in the electronic structure56. This conclusion is further supported by the anomalous variations observed in the temperature-dependent μH (Fig. 4b). The energy filtering effect arises from the band bending caused by the dense Cu2Se nanoprecipitates, which create a slowly varying potential that hinders the movement of low-energy carriers57 (Figs. 3g and 4d). Since the carrier scattering for the sample with x = 0 is dominated by acoustic phonons, the scattering factor r0 should be −0.5 at room temperature. The ratio of the scattering parameter rx + 1 for Pb1−xCu2x+0.002Se (x = 0.01~0.04) to r0 + 1 for x = 0 can be calculated58 using the formula \(S=[8{{{{\rm{\pi }}}}}^{2}{k}_{{{{\rm{B}}}}}^{2}/(3{h}^{2}e)]{m}^{*}T[{{{\rm{\pi }}}}/(3n)]^{3/2}({r}_{x}+1)\), where kB, h, and e represent the Boltzmann constant, Planck constant, and electron charge, respectively. Thus, the ratio (rx + 1)/(r0 + 1) can be written as58:

$$\frac{{r}_{x}+1}{{r}_{0}+1}=\frac{{S}_{x}}{{S}_{0}}\left({\frac{{n}_{x}}{{n}_{0}}}\right)^{2/3}$$
(1)

As shown in Fig. 4e, the scattering factor rx exhibits a positive correlation, confirming that the increase in S is due to the increase in rx caused by the formation of sufficient nanoprecipitates. The linear fitting of ln(σT 1/2) and 1/(kBT) for the Pb1−xCu2x+0.002Se (x = 0~0.04) samples (Supplementary Fig. 16) can effectively evaluate the interface potential barrier (EB)59. The EB in the matrix decreases with increasing x content (Fig. 4e), validating that the semicoherent Cu2Se material benefits carrier transport, which is consistent with the nearly equal μH for x = 0.01~0.04 samples (Supplementary Fig. 17a). The room-temperature μH of PbCu0.002Se sample in this work is higher than that of PbCu0.005Se sample reported in the literature8, as the carrier and defect scattering in our sample is less pronounced, as illustrated in Fig. 4f. In particular, compared to other reported n-type PbSe systems7,9,29,30,35, the Pb1−xCu2x+0.002Se samples exhibit distinct μH values for the same nH (Fig. 4f), further highlighting the advantage of the semicoherent interface. By introducing dense and uniformly distributed Cu2Se nanoprecipitates into the matrix, we achieved the combined effect of self-optimization of nH in the mid-temperature range and compensation for the intrinsically low |S| of PbSe. This significantly enhances the S2σ of Pb1−xCu2x+0.002Se (x = 0.01–0.04) across temperatures from 500 to 873 K (Supplementary Fig. 17b).

The thermal transport properties of Pb1−xCu2x+0.002Se are shown in Supplementary Fig. 18 and Fig. 4g. Compared with that of pristine PbSe, κlat is significantly suppressed for Pb1−xCu2x+0.002Se (Fig. 4g). When x ≤ 0.02, the reduction in κlat is due to the stronger phonon scattering caused by the increase in dislocation and nanoprecipitate density. Although the number of nanoprecipitates continues to rise with higher doping levels (x > 0.02), the dislocations with a size similar to the phonon mean free path60 is greatly reduced, which leads to a slight increase of κlat. Supplementary Fig. 19a indicates that the κlat of conventional element-doped PbSe, such as Cd9, Te26, Cr61, and Ga62, decreases along the power law of ~T−1. In contrast, the κlat of high-content Cu-doped PbSe exhibits a complex trend with increasing temperature8,25,44,63, as shown in Fig. 4g and Supplementary Fig. 19b. Research usually focuses only on reducing κlat8,25,44,63 and discussing its origin in the PbSe system while neglecting the abnormal changes in κlat near 400 K. The experimental κlat of CuSe48 is shown in Fig. 4g. Obviously, the κlat in Cu2Se suddenly increases from 0.25 to 0.58 W m−1 K−1 at ~400 K (other TE parameters in Supplementary Fig. 20). Hence, the κlat for Pb1−xCu2x+0.002Se (x = 0.01~0.04) slowly decreases and even plateaus from 400 to 550 K, which is the signal of the Cu2Se phase transition. In brief, when a large number of semicoherent Cu2Se nanoprecipitates enter the PbSe matrix, the electrical performance is distinctly enhanced, and the thermal transport is synergistically optimized, leading to an improvement in the TE performance of n-type PbSe (Supplementary Fig. 21).

Considering that the sample with x = 0.02 in Pb1−xCu2x+0.002Se (x = 0~0.04) has the lowest κlat and the highest zT of 1.63, the Pb0.98Cuy+0.04Se (y = 0.001~0.005) samples were further optimized to advance PbSe TE materials. As expected, the room-temperature nH increases with increasing y content (Supplementary Fig. 22a) since additional Cu occupies the interstitial position of the PbSe lattice to provide electrons. The electrical parameters (nH, μH, σ, S) are shown in Supplementary Fig. 22b–e. The addition of excess Cu does not distinctly alter the carrier scattering mechanism (Supplementary Fig. 22c), resulting in |S| still maintaining an enhancement superiority at the same nH (Supplementary Fig. 22f). Therefore, an outstanding S2σ is achieved by further optimizing nH compared with that of the Pb0.98Cu0.042Se (x = 0.02) sample (Fig. 1a). Notably, the ultrahigh average S2σ (S2σavg) for the y = 0.004 sample, measured from 303 to 823 K, reaches ~24.4 μW cm−1 K−2, surpassing most reported values for high-performance PbSe systems8,21,23,24,25,27,31,63,64,65 (Fig. 4h). The thermal parameters (κtot, κele, κlat) for Pb0.98Cuy+0.04Se (y = 0.001~0.005) are shown in Supplementary Fig. 23a-c. The κlat is significantly suppressed with increasing y content, reaching an ultralow value of ~0.25 W m−1 K−1 (Supplementary Fig. 23c), which is close to the theoretical limit of ~0.23 W m−1 K−1 66. Eventually, the peak zT value reaches ~1.9 (Fig. 4i and Supplementary Fig. 24d). This is almost the highest value among all the n-type PbSe-based TE materials and is comparable to that of n-type PbTe14 (Supplementary Fig. 23d).

Screening of TEiMs and manufacturing of high-performance modules

High-performance materials must fully utilize their potential at the device level, which largely depends on matching TEiMs, particularly at high temperatures. In this work, we employed a high-throughput screening strategy67 to expedite the identification of potential TEiMs for PbSe. Powders of ten candidate metals (Ti, Zr, V, Cr, Mn, Ni, Nb, Mo, Fe, and Co) were mixed with undoped PbSe powder and sintered according to the standard parameters for PbSe TE materials. Energy dispersive spectroscopy (EDS) scanning analysis and scanning electron microscopy (SEM) images of the representative interface microstructures between these metals and PbSe are shown in Supplementary Figs. 25–29. These metals can be categorized into three groups based on their reaction with PbSe. The first group includes Ti, Zr, V, and Cr, which exhibit minimal reactions with Se and form corresponding compounds, consistent with their binary phase diagrams (Supplementary Figs. 25 and 26). The second group consists of Mn, Ni, Nb, and Mo. Among them, Mn and Ni undergo significant selenization, likely due to their relatively low melting points (Supplementary Fig. 27). On the other hand, Nb and Mo form well-alloyed phases with Pb and PbSe, respectively (Supplementary Fig. 28). Due to the short duration of the sintering process, the metals in the first and second groups are unsuitable as TEiMs for PbSe. The third group included Fe and Co, which exhibited excellent chemical inertness after sintering and formed strong bonds with the PbSe matrix (Supplementary Fig. 29).

In addition to chemical inertness, a compatible TEiM must also form a low-energy-loss interface with TE materials, ensuring a lower electrical contact resistance (ρc) at the junction. To evaluate this phenomenon, we used a one-step hot pressing method to fabricate PbSe single legs with Co and Fe as TEiMs. The ρc of the Co/PbSe junction is ~10.9 μΩ cm2 (Fig. 1c), which is significantly lower than that of the Fe/PbSe junction (~20.2 μΩ cm2) (Supplementary Fig. 30). This indicates that Co serves as a more effective diffusion barrier material than Fe in this context. This is the first test and report of the ρc value in PbSe, which is also much lower than that of other TE materials, such as ~30 μΩ cm2 for the Sb/CdSb junction68 and ~210 μΩ cm2 for the Ni/Bi2Te2.7Se0.3 junction69. Additionally, we performed detailed interface characterization on the Ag/Co/PbSe leg. No significant diffusion or cracking was observed between the Ag electrode, the Co TEiM, or the PbSe material (Fig. 5a, b), validating the results from our high-throughput screening. Given that the hot side of TE generators operates at high temperatures for extended periods, the heat endurance at the most vulnerable junction of TEiM/TE material is a crucial factor for evaluating device stability. To assess this phenomenon, we conducted aging tests on the Ag/Co/PbSe assembly after annealing at 873 K for 48 h. The results showed that the contact interface retained excellent thermal stability and robust bonding (Supplementary Fig. 31). These characteristics make Co a promising TEiM for manufacturing high-efficiency and reliable TE modules.

Fig. 5: The interface microstructures and power generation performance of the segmented module.
figure 5

a Scanning electron microscopy (SEM) images and energy dispersive spectroscopy (EDS) mapping of the PbSe/Co/Ag leg. b EDS line scan of the Co/PbSe junction. c Optimized length ratios of n-type Bi2Te3/PbSe (rn) and p-type Bi2Te3/GeTe (rp) segments determined by numerical simulation when the hot-side temperature (Th) and the cool-side temperature (Tc) are 773 and 303 K, respectively. Current-dependent d output voltage (V) and output power (P). e Heat flow (Q) and conversion efficiency (η) as a function of current.

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To demonstrate the mid-temperature power generation performance of Pb1−xCu2x+ySe, we developed p-type materials with comparable TE performance (Supplementary Fig. 32) and constructed a seven-pair single-stage TE module composed of n-type Pb0.98Cu0.043Se with Co as the TEiM and p-type GeTe with Ni as the TEiM (details in the Supplementary Information). Supplementary Fig. 33 shows the output performance of this single-stage module (10 mm × 10 mm × 4 mm), achieving a maximum η (ηmax) of ~9.6% and a power density of ~20 kW m−2 at a hot-side temperature (Th) of 740 K. To increase the ηmax of the TE module, we conducted finite-element simulations to meticulously design and optimize the geometrical configuration of the module, which was segmented with p-type and n-type Bi2Te3-based materials (Fig. 5c and Supplementary Fig. 34). We then manufactured the corresponding seven-pair devices (10 mm × 10 mm × 6 mm, inset in Fig. 1d). The current (I)-dependent output voltage (V) and output power (P) of the segmented module at different Th values are shown in Fig. 5d. As Th increases from 450 to 760 K, the open-circuit voltage (Voc) increases from 0.35 to 1.33 V due to the improved |S| of the TE material. P initially increases with current, peaking when the external load resistance matches the module’s internal resistance. The measured ηmax reaches ~13.1% at a ΔT of 460 K (Fig. 5e), setting a record for PbSe-based TE modules27.

In conclusion, introducing Cu into Te-free n-type PbSe (i.e., Pb1−xCu2x+ySe) can result in an ultrahigh peak zT of ~1.9. This approach enables electron‒phonon decoupling, leading to an extraordinary average power factor exceeding 24 μW cm−1 K−2 and an ultralow lattice thermal conductivity of 0.25 W m−1 K−1. Notably, we identified an exceptional TE interface material by high-throughput screening. The robust Co/PbSe junction design effectively prevents chemical diffusion and reaction, achieving a low electrical contact resistivity of ~10.9 μΩ cm2 with excellent durability and stability. Consequently, we manufacture a segmented TE module and achieve a record-high efficiency of 13.1% at a temperature difference of 460 K. These findings are expected to advance the application of Te-free thermoelectrics.

Methods

Synthesis

High-purity initial materials Pb (99.999%), Se (99.999%), Cu (99.9999%) were weighted according to the stoichiometric composition of PbSe and Pb1-xCu2x+ySe. Subsequently, the raw materials were sealed in the evacuated quartz tubes (<10–3 Pa) and heated up to 1423 K in 6.5 h, held for 8 h, quenched to room temperature, and annealed at 923 K for 100 h. The PbSe and Pb1-xCu2x+ySe ingots were finely powdered in an agate mortar and then sintered by hot pressing at an axial pressure of 55 MPa and 873 K for 0.5 h to obtain high-density cylindrical samples with a diameter of ~12.7 mm (Supplementary Table 5). For the screening of TEiMs, the powder of ten candidate materials (Ti, Zr, V, Cr, Mn, Ni, Nb, Mo, Fe and Co) were co-mixed evenly with pristine PbSe powder in an agate mortar. According to the above Pb1-xCu2x+ySe sintering parameters, the mixed powders were sintered into a bulk. The weight of each candidate metal powder is about 0.2% of the PbSe.

Characterization

Room-temperature data for XRD were collected utilizing the lab X-ray diffractometer. Synchrotron radiation X-ray characterization was conducted on various advanced beamlines at Beijing Synchrotron Radiation Facility (BSRF) and Shanghai Synchrotron Radiation Facility (SSRF). In-situ variable temperature XRD experiments were performed for Pb0.98Cu0.043Se sample using an incident energy of 40 keV with nitrogen (N2) as a protective gas in the temperature range from room temperature to 823 K. The 2D XRD patterns were acquired in transmission mode with the PerkinElmer 1621 N flat-panel detector (pixel size 200 μm × 200 μm). The XRD data were calibrated with CeO2 leading to the determination of the sample-to-detector distance. The Cu K-edge and Se K-edge XANES and the EXAFS were conducted in fluorescence mode or transmission mode using a Si (111) double-crystal monochromator at ambient conditions. The photon energies were calibrated using the first inflection point of the K-edges from metallic Cu foil and elemental selenium, respectively. The topography of TE materials and junctions were investigated using field emission SEM equipped with EDS. Microstructure measurements were performed on the TEM (JEOL-F200) and Cs-corrected STEM (JEOL-NEOARM 200F). The geometrical configuration of the segmented TE module was optimized utilizing the finite element analysis software, where the temperature-dependent σ, S, and κtot of Bi2Te3, PbSe, and GeTe from the experiment were used as an input parameter for the program.

Thermoelectric property measurements

The Hall measurements was conducted utilizing the Van der Pauw method in a high purify He2. The S and \(\sigma\) of samples were measured simultaneously on a commercial CTA instrument (Cryoall, China). The thermal diffusivity (D) was collected using Netzsch LFA 467. The κtot was obtained from κtot = dDCp, where the heat capacity Cp in this work is theoretically evaluated by Debye model, which has been widely used in PbSe systems. The density d is measured by the Archimedes’ drainage method. The electronic thermal conductivity κele is calculated using the Wiedemann-Franz law: κele = σLT, where σ represents the experimental electrical conductivity of the samples. The Lorenz number L is determined based on the experimental Seebeck coefficient and the single Kane band (SKB) model. The lattice thermal conductivity κlat is estimated by subtracting κele from the total thermal conductivity κtot.

Segmented module fabrication

The n-type PbSe legs with Co and Ag on both sides were sintered by one-step hot pressing. The Bi2Te3 and GeTe materials were electroplated with Ni as TEiM. The Bi2Te3, PbSe and GeTe bulks were cut into dimensions of about 1.5 mm × 1.5 mm × 2 mm, 1.5 mm × 1.5 mm × 4 mm and 1.5 mm × 1.5 mm × 4 mm, respectively. After polishing, the high-temperature and low-temperature legs were directly sintered onto copper alumina ceramics using commercial nano-silver paste to assemble 7 pairs of segmented TE module. The copper-wires were welded to the low-temperature side copper electrode.