Dual Interstitials Doping to Advance PbSe Thermoelectric at Wide Temperatures

doi:10.21203/rs.3.rs-3603206/v1

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Dual Interstitials Doping to Advance PbSe Thermoelectric at Wide Temperatures

https://doi.org/10.21203/rs.3.rs-3603206/v1

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Interstitial doping has been widely verified in optimizing thermoelectric performance due to its carrier and phonon decoupling effect. To maximize the role of interstitial, this work develops a novel strategy of Pb and Cu dual interstitials doping in n-type Pb_1.02Se-0.2%Cu, and a considerably improved average ZT value of 1.01 at 300–773 K can be achieved, which obviously outperforms previous single interstitial doped PbSe systems. Its superior thermoelectric performance mainly originates from optimally tuned carrier and phonon transport properties caused by synergy of Pb and Cu dual interstitials. Firstly, Pb and Cu dual interstitials in n-type Pb_1.02Se-0.2%Cu can fully optimize temperature-dependent carrier density in the whole temperature range, from 1.27×10¹⁹ cm^− 3 at 300 K to 3.90×10¹⁹ cm^− 3 at 773 K, thus contributing to maximal power factor of 32.83 µW cm^− 1 K^− 2 and average power factor of 24.18 µW cm^− 1 K^− 2. Furthermore, Pb and Cu dual interstitials doping can cause hierarchical defects, including interstitials, vacancies, dislocations and precipitates, thus to largely lower the lattice thermal conductivity. As a result of the optimized electrical and thermal transport properties, the thermoelectric performance in n-type Pb_1.02Se-0.2%Cu is largely enhanced at wide temperatures.

Physical sciences/Materials science/Materials for energy and catalysis/Thermoelectrics

Physical sciences/Energy science and technology/Thermoelectric devices and materials

Dual interstitials doping

carrier density

PbSe

thermoelectric materials

Thermoelectric technology enables direct conversion between heat and electricity based on the Seebeck effect and Peltier effect, which can be applied in waste heat utilization and thermoelectric refrigeration, respectively.^1–3 The energy conversion efficiency of thermoelectric technology is mainly determined by thermoelectric materials and it is characterized by the dimensionless figure of merit (ZT), ZT = S²σT/(κ_ele + κ_lat), where S, σ, T, κ_ele and κ_lat denote Seebeck coefficient, electrical conductivity, absolute temperature in kelvin, electronic thermal conductivity and lattice thermal conductivity, respectively. Due to the strong coupling relations between electrical and thermal transport properties, the ZT value is usually optimized by increasing power factor PF = S²σ or reducing κ_lat.^4–6 Many effective strategies have been developed to enhance the thermoelectric performance, including band structure manipulation to increase PF value,^7–12 and defect engineering to reduce κ_lat.^13–18 Nevertheless, it is challengeable to pursue high ZT value through decoupling carrier and phonon transport properties.

It is reported that the strategy of interstitial doping in thermoelectric material can synergistically optimize electrical and thermal transport properties, and even decouple the carrier and phonon transport due to large difference in mean free paths.^{19, 20} In PbQ (Q = Te, Se and S) compounds, Zn,^{21, 22} Ni,^{22, 23} Cu^23–26 and Ag²⁷ atoms can form interstitials in matrix lattice. These sub-nanoscale interstitials could intensify the phonon scattering to decrease lattice thermal conductivity due to the comparable size with phonon mean free path, while simultaneously maintaining carrier transport because of much larger carrier mean free path. Additionally, interstitials play multiple roles to optimize thermoelectric performance and have been also proved in other material systems. Interstitial doping, such as Yb,^{28, 29} In,^{30, 31} Ce,³² Ti,³³ Ta³⁴ and Br,³⁵ can fill the icosahedron voids in skutterudite to form rattling atoms, thus blocking phonon transport and suppressing lattice thermal conductivity. Ni or Cu interstitials in Half-Heusler can regulate carrier density and simultaneously produce point defect to scatter phonon transport.^36–38 Besides, Cu interstitial doping in Half-Heusler can induce wetting layers between grains and form coherent grain boundaries to optimize carrier transport properties.³⁸ In Bi₂Q₃ (Q = Te, Se and S) compounds, Cu and Ag interstitial atoms can enter into layer gap and accelerate the electron transport across the layers, thus enhancing the electrical transport properties.^39–43 Similar carrier transport phenomenon has also been found in layered SnSe₂ compound with Cu or Ag interstitial doping.^44–46 These remarkable roles of interstitials in thermoelectric materials discussed above are realized through single interstitial doping. To maximize the roles of interstitial doping on balancing phonon and carrier transport, the strategies of dual interstitials doping or multiple interstitials doping are worth being further explored in thermoelectric materials.

This work takes PbSe compound as an example to demonstrate the feasibility of dual interstitials doping in thermoelectric material. Pb and Cu atoms are selected as dual interstitials dopant to firstly compensate the intrinsic Pb vacancies and subsequently produce massive interstitials in stoichiometric PbSe compound, which can dynamically optimize the temperature-dependent carrier density. The synergy of Pb and Cu interstitials doping in n-type Pb_1.02Se-0.2%Cu can tune the carrier density to optimal range, from 1.27×10¹⁹ cm^− 3 at 300 K to 3.90×10¹⁹ cm^− 3 at 773 K. The dynamically optimized carrier density in n-type Pb_1.02Se-0.2%Cu with dual interstitials doping leads to high average power factor of 24.18 µW cm^− 1 K^− 2 at wide temperatures (300–773 K), which is obviously larger than that in Pb or Cu single interstitial doped sample. Furthermore, the theoretical calculation and microstructure observation unclose hierarchical defects in Pb_1.02Se-0.2%Cu, including sub-nanoscale Pb and Cu interstitials, Se vacancies, dislocations and some nanoscale Pb precipitates, and these electron-dominated defects can preserve high electron transport but impede phonon propagation. As a result, the ZT_ave value enhances from 0.46 in Pb_1.02Se and 0.91 in PbSe-0.2%Cu to 1.01 in Pb_1.02Se-0.2%Cu at 300–773 K, which is obviously higher than other single interstitial doped PbSe systems.

Advanced thermoelectric performance in Pb _1.02 Se-0.2%Cu. The strategy of dual interstitials doping is introduced into n-type PbSe thermoelectric material by selecting Pb and Cu, which can firstly fill intrinsic Pb vacancies in stoichiometric PbSe and then induce massive interstitials to optimize electrical transport properties. Notably, Pb and Cu dual interstitials doping in n-type Pb_1.02Se-0.2%Cu contributes to superior thermoelectric performance compared with other n-type PbSe samples optimized by single interstitial doping (Fig. 1). A maximum room-temperature PF value of 32.83 µW cm^− 1 K^− 2 can be obtained in n-type Pb_1.02Se-0.2%Cu, which exceeds other n-type PbSe samples with single interstitial doping, including 21.85 µW cm^− 1 K^− 2 in PbSe-4%Pb,⁴⁷ 26.69 µW cm^− 1 K^− 2 in PbSe_0.996,⁴⁸ 23.72 µW cm^− 1 K^− 2 in PbCu_0.00125Se,²⁵ 19.91 µW cm^− 1 K^− 2 in PbZn_0.0125Se,²¹ and 17.11 µW cm^− 1 K^− 2 in PbNi_0.01Se²³ (Fig. 1a). In this work, the room-temperature PF value increases from 25.18 µW cm^− 1 K^− 2 in Pb_1.02Se and 28.14 µW cm^− 1 K^− 2 in PbSe-0.2%Cu to 32.83 µW cm^− 1 K^− 2 in Pb_1.02Se-0.2%Cu. Such high room-temperature PF value in Pb_1.02Se-0.2%Cu stems from its suitable carrier density tuned by Pb and Cu dual interstitials doping, which finally contributes to an enhanced room-temperature ZT value of 0.54 in (Fig. 1b).

Both the electrical conductivity (σ) and Seebeck coefficient (S) are closely related to carrier density. Therefore, the optimized carrier density in Pb_1.02Se-0.2%Cu with Pb and Cu dual interstitials doping can tune these two thermoelectric parameters (σ and S) into an optimal range, thus resulting in large PF (PF = S²σ) value (Fig. 1c). Moreover, the well optimized electrical conductivity and Seebeck coefficient in Pb_1.02Se-0.2%Cu not only enhance near-room-temperature PF (PF_RT) value but also obviously boost the average PF (PF_ave) value and average ZT (ZT_ave) value to 24.18 µW cm^− 1 K^− 2 and 1.01 at 300–773 K (Fig. 1d). Compared with other n-type PbSe with single interstitial doping, Pb_1.02Se-0.2%Cu present much higher value in both PF_ave value and ZT_ave value at wide temperatures, indicating large advantages of dual interstitials doping strategy.

Electrical Transport Properties. This work firstly prepared n-type PbSe samples with single Pb interstitial doping, Pb_1 + xSe (x = 0.005–0.03), and then introduced Cu interstitial doping into optimum Pb_1.02Se component to work as dual interstitials dopant. The powder X-ray diffraction (PXRD) patterns of Pb_1 + xSe (x = 0.005–0.03) and Pb_1.02Se-y%Cu (y = 0.0–1.0) are shown (Supplementary Fig. 1). Thermoelectric performance in Pb_1 + xSe (x = 0.005–0.03) and Pb_1.02Se-y%Cu (y = 0.0–1.0) are presented (Supplementary Fig. 2–6 and Supplementary Table 1), and the optimal content are picked out to make a comparison. Although extra Pb phase can be observed in Pb interstitial doped PbSe matrix, the expanded lattice parameter and increased carrier density (Supplementary Fig. 7) can prove that part Pb and Cu atoms indeed successfully enter into interstitial sites in PbSe lattice, which can favorably tune the electron transport properties in n-type PbSe thermoelectric materials.

Temperature-dependent electrical transport properties in n-type Pb_1.02Se, PbSe-0.2%Cu and Pb_1.02Se-0.2%Cu samples are compared (Fig. 2). Pb_1.02Se-0.2%Cu shows medium electrical conductivity at low temperature range (300–600 K) and then exceed the values in Pb_1.02Se and PbSe-0.2%Cu at high temperature (600–773 K), which obviously shows dynamically tuned electrical transport properties (Fig. 2a). And the temperature-dependent Seebeck coefficient (Fig. 2b) shows same tendency with electrical conductivity. To unveil these special electrical transport properties in Pb and Cu interstitials doped PbSe samples, temperature-dependent carrier density and carrier mobility are measured. Both Pb_1.02Se and PbSe-0.2%Cu samples with single interstitial doping present dynamic carrier density optimization that the carrier density continuously increases with rising temperature (Fig. 2c). This dynamic optimization in carrier density arises from the growing solubility of Cu or Pb interstitial in PbSe matrix when temperature rises, and Cu or Pb interstitial will release extra free electron into matrix to amplify the carrier density.^{25, 26, 49} It is shown that Pb_1.02Se owns smaller carrier density than that in PbSe-0.2%Cu in the whole temperature range, indicating a lower interstitial solubility of Pb in PbSe matrix. When Pb and Cu as dual interstitials doping in Pb_1.02Se-0.2%Cu, its temperature-dependent carrier density can be fully optimized in a large range, from 1.27×10¹⁹ cm^− 3 at 300 K to 3.90×10¹⁹ cm^− 3 at 773 K, due to the combined effects of Pb and Cu interstitials. The temperature-dependent carrier mobility (Fig. 2d) show all the interstitial doped PbSe can preserve high carrier mobility, thus leading to excellent electrical transport properties.

The PF value in Pb_1.02Se, PbSe-0.2%Cu and Pb_1.02Se-0.2%Cu samples were picked for further analysis (Fig. 2e). It is seen that Pb_1.02Se-0.2%Cu with dual interstitial doping has an obviously higher PF value compared with Pb_1.02Se and PbSe-0.2%Cu with single interstitial doping. To further unclose the relation between carrier density and PF value, theoretical calculations are presented based on single Kane band (SKB) model and the electrical transport coefficients can be written as follows:

Hall carrier density

is Fermi level. In PbSe thermoelectric material, the variable constants band degeneracy N_V=4, longitudinal effective mass ≈ 0.7 m_e, transverse effective mass ≈ 0.4 m_e,⁵⁰ average longitudinal elastic modulus C_l≈9.1×10¹⁰ Pa,⁵¹ band gap E_g≈0.29 eV and deformation potential coefficient E_def≈25 eV.⁵² The calculation results (Fig. 2f) show that the theoretical maximum power factor in n-type PbSe requires an optimal dynamic optimization in carrier density in the whole temperature range. Owning to the fully optimized temperature-dependent carrier density in Pb and Cu dual interstitials doped Pb_1.02Se-0.2%Cu, its experimental PF value can well match the theoretical value, thus leading to high PF_ave value at wide temperatures.

Theoretical Charge Density. Theoretical charge density and electron local density are employed to investigate the bonding environment that has close relations with electrical transport properties. From the defect formation calculation results (Supplementary Fig. 8), Cu interstitial (Cu_i), Pb interstitial (Pb_i) and Se vacancy (V_Se) have low formation energy in Pb_1.02Se-0.2%Cu sample at Pb-rich condition. Thus, the density functional theory (DFT) calculation is implemented with these defects in this work to analyses effect of Pb and Cu dual interstitials doping on carrier transport properties in Pb_1.02Se-0.2%Cu.

The 2D iso-surface representation of charge density within (10 − 1) plane in undoped PbSe and Pb_1.02Se-0.2%Cu are calculated (Fig. 3a, b). The charge density analysis shows the transfer of electrons among Pb, Se, and Cu atoms, in which the red and blue color means the large accumulation and depleted region of charge, respectively. Both Pb interstitial and Cu interstitial can produce overlapping electron clouds with matrix to form broad charge channel (Fig. 3b), which significantly facilitates the charge transfer and could benefit high carrier transport properties. Moreover, larger range of overlapping electron clouds induced by Cu interstitial than that in Pb interstitials can be clearly observed in the 3D iso-surface charge density (Fig. 3c), which results in superior electrical conductivity in PbSe-0.2%Cu than that in Pb_1.02Se. Se vacancy (Fig. 3e) cause deficiency of charge density but it can theoretically provide two free electrons into PbSe matrix. Therefore, all these Cu_i, Pb_i and V_Se are intrinsic electron-dominated defects, and they could play favorable roles in electron transport in n-type Pb_1.02Se-0.2%Cu. Additionally, the electron localization function (ELF) provides yard stick for the degree of electron localization.⁵³ The ELF map of Pb interstitial, Cu interstitial and Se vacancy are given (Supplementary Fig. 9), and the value is definition between 0 and 1. When ELF = 1, it indicates that electron is perfect localization, while ELF = 0.5 suggests homogeneous electron gas.^54–58 The ELF value of 0.2 around Cu interstitial is very low, which signifies that the electrons around Cu interstitial is easy to delocalize. Pb interstitial has an ELF value above 0.5 with high electron localization, but the electrons around Pb interstitial can be also partly delocalized to participate carrier transport. As a result, both theoretical charge density and electron localization function confirm Pb and Cu dual interstitials can benefit high carrier transport properties in n-type Pb_1.02Se-0.2%Cu.

Microstructure Observations. The microstructures in Pb and Cu dual interstitials doped Pb_1.02Se-0.2%Cu are observed by Cs-corrector transmission electron microscopy and also compared with undoped PbSe samples. The annular bright field (ABF)-STEM morphological image in Pb_1.02Se-0.2%Cu (Fig. 4a) reveal the presence of some ellipsoidal nanoprecipitates and dislocation lines. In order to identify the composition, the EDS analysis is conducted and the results are depicted (Fig. 4b1-b4). Figure 4b1 is a magnified image of the nanoprecipitate captured in. It can be observed that the Pb element is enriched in the precipitate area, and the precipitate size is approximately several hundred nanometers. Figure 4c displays an enlarged ABF-STEM image of the other regions shown in Fig. 4a, and numerous dislocations can be evidently observed. While stoichiometric PbSe sample has scare dislocation lines but a large number of Pb vacancies (Supplementary Fig. 10). Thus, it can be concluded that the Pb interstitial doping can effectively fill the Pb vacancies and the dislocations in Pb_1.02Se-0.2%Cu mainly arise from Pb and Cu dual interstitials doping.

The high angle annular dark field (HAADF)-STEM image at the atomic level (Fig. 4d) show that some interstitial atoms present in the middle part of the image. Additionally, Fig. 4e displays an enlarged depiction of Fig. 4d with observed direction along the [110] axis. As the contrast of the HAADF image is proportional to the atomic number, it enables a clear distinction between brighter Pb (atomic number 82) and darker Se (atomic number 34) atoms. The presence of Pb interstitial atoms is confirmed by the line profile along the red line in the inset of Fig. 4e, because clear interstitial atoms have the same intensity as Pb atoms. A typical atomic image of the dislocation region is displayed (Fig. 4f), while an inverse fast Fourier transform (IFFT) image (Fig. 4i) provides a clearer depiction of the dislocation lines. The HAADF-STEM image of the interstitial Cu atoms region are demonstrated (Fig. 4g, h and Supplementary Fig. 11). The presence of interstitial atoms in the marked lattice site (labeled with a white box) is indicated (Fig. 4h). Due to the principle of Z-contrast, the atomic number of Cu being 29, its contrast is expected to be close to that of Se atoms, but much darker than the Pb atoms. Additionally, the smaller atomic size of Cu enables it to be clearly distinguished from the interstitial Pb atoms observed (Fig. 4e). Consequently, it can be determined that the interstitial atoms indicated by the red arrows (Fig. 4h) represent Cu interstitial in PbSe matrix. Thus, the introduction of additional Pb and Cu results in a large number of Pb nanoprecipitates, dislocations, and interstitial Pb and Cu atoms in the Pb_1.02Se-0.2%Cu sample. And these hierarchical defects can block the phonon transport thus largely decrease the lattice thermal conductivity.

Thermal Transport Properties and ZT values. The temperature-dependent total thermal conductivity in Pb_1.02Se, PbSe-0.2%Cu and Pb_1.02Se-0.2%Cu, in which Pb_1.02Se and Pb_1.02Se-0.2%Cu have parallel lower values (Fig. 5a). The low total thermal conductivity of Pb_1.02Se originate from the low electronic thermal conductivity (Supplementary Fig. 12d), but relatively low total thermal conductivity of Pb_1.02Se-0.2%Cu stem from the inferior lattice thermal conductivity is provided (Fig. 5b). The lattice thermal conductivity can be obtained by subtracting the electronic thermal conductivity from total thermal conductivity, κ_lat = κ_tot-κ_ele, in which κ_ele = LσT based on the Wiedemann-Franz law, and the Lorenz number L is calculated by experimental Seebeck coefficient according to Single Parabolic Band (SPB) model (Supplementary Fig. 12c). The comparatively lower lattice thermal conductivity in PbSe-0.2%Cu than that in Pb_1.02Se indicates that Cu interstitials can more easily enter interstitial sites than Pb interstitials, which is consistent with the results of defects formation energies calculation (Supplementary Fig. 8).²³ The further reduced lattice thermal conductivity in Pb_1.02Se-0.2%Cu compared with PbSe-0.2%Cu at high temperature could arise from the dynamic effect of Pb and Cu dual interstitials doping to promote phonon scattering.

To compare results of single Pb interstitial doping, single Cu interstitial doping and dual interstitials doping at 300–773 K, the temperature-dependent ratio of weighted carrier mobility to lattice thermal conductivity (µ_W/κ_lat) are calculated out (Fig. 5c). Obviously, the µ_W/κ_lat value of Pb_1.02Se-0.2%Cu surpass that of Pb_1.02Se and PbSe-0.2%Cu at 300–773 K, which demonstrate Pb and Cu dual interstitials doping in PbSe is a valid method to simultaneously boost electrical and thermal transport properties at wide temperatures. More detailed thermoelectric transport properties in Pb_1.02Se, PbSe-0.2%Cu and Pb_1.02Se-0.2%Cu can be found in Supplementary Fig. 12. Finally, the temperature-dependent ZT values are further enhanced in Pb_1.02Se-0.2%Cu than that in single Pb or Cu interstitial doped PbSe samples, and the ZT_RT value enhances from 0.40 in Pb_1.02Se and 0.37 in PbSe-0.2%Cu to 0.54 in Pb_1.02Se-0.2%Cu at 300 K (Fig. 5d). Such distinct enhancement of ZT value at 300–773 K are mainly benefit from the increased PF value. Compared with other single interstitial doped PbSe, such as PbSe_0.996,⁴⁸ PbCu_0.00125Se,²⁵ PbSe-4%Pb,⁴⁷ PbZn_0.0125Se,²¹ and PbNi_0.01Se,²³ Pb_1.02Se-0.2%Cu presents an optimal temperature-dependent PF values (Fig. 5e), which contribute a largely enhanced ZT value at 300–773 K (Fig. 5f). The PF_ave value of 24.18 µW cm^− 1 K^− 2 and ZT_ave value of 1.01 at 300–773 K can be achieved in Pb_1.02Se-0.2%Cu (Supplementary Fig. 13). The superior thermoelectric properties in Pb_1.02Se-0.2%Cu demonstrate a viable strategy of dual interstitials doping to advance lead chalcogenide thermoelectric materials at wide temperatures.

In summary, the strategy of dual interstitials doping has been implemented to synergistically optimize carrier and phonon transport properties in n-type Pb_1.02Se-0.2%Cu at wide temperatures, and its thermoelectric properties are distinctly superior than other n-type PbSe samples with single interstitial doping. Dual Pb and Cu interstitials doping in Pb_1.02Se-0.2%Cu can produce Pb interstitial, Cu interstitial, Se vacancy, dislocation and Pb-rich precipitate, and all these defects in matrix are electron-dominated regions, which can facilitate the carrier transport in n-type Pb_1.02Se-0.2%Cu. Furthermore, the temperature-dependent solubility of Pb and Cu interstitials in PbSe can dynamically tune the carrier density at a wide range, thus contributing to high average power factor. These hierarchical defects induced by Pb and Cu interstitials doping in Pb_1.02Se-0.2%Cu not only benefit high carrier transport properties, but also impede the phonon propagation to largely reduce the lattice thermal conductivity. This work proves the feasibility of dual interstitials in effectively decoupling carrier and phonon transport, and more strategies of dual or multiple interstitials doping are worthy being explored as universal methods to be extended to other thermoelectric materials.

Synthesis. High purity raw materials, Pb bulk (99.999%), Se particles (99.999%), Te bulk (99.999%) and Cu wires (99.99%) with stoichiometric composition were weighted and flame-sealed in silica tubes at a residual pressure below ~ 10^− 4 Torr, slowly heated to 1323 K in 12 h and kept at this temperature for 6 h followed by furnace cooling to room temperature. The obtained ingots were ground into powders and densified by hot-pressing furnace (OTF-1700X-RHP4) at 773 K for 35 mins in a Ф 15 mm cylindrical die under an axial compressive stress of 50 MPa in vacuum, resulting in highly densified disk-shaped samples. Finally, the disk-shaped samples were annealed at 773 K for 6 h.

Structural characterization

The phase identification was characterized 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 the software package which named “Materials Analysis using Diffraction (MAUD)”. The scanning transmission electron microscopy (STEM) analysis was performed using a Cs-corrector JEM-ARM200F NEOARM with a cold FEG at 200 kV. The thin samples for transmission electron microscopy were prepared by the following methods, including cutting, grinding, polishing and Ar-ion milling on a liquid nitrogen cooling stage.

Density functional theory (DFT) calculations

The charge density and electron local density (ELF) are calculated by using the Vienna ab initio simulation package (VASP).^{59, 60} The projector-augmented wave (PAW) potentials method⁶¹ was utilized with Perdew-Burke-Ernzerhof (PBE) functional revised for solids to describe the exchange-correlation functional.⁶² A cutoff energy of 400 eV was selected for the calculations. The unit cell was fully optimized until the force on each atom was less than 10^− 6 eV Å⁻¹. A k-point of 11 × 11 × 11 was used and the total energy convergence criterion was set to 10^− 8 eV. To accurately simulate experimental local electron density, we constructed a preliminary 3 × 3 × 3 supercell, which accommodated 216 atoms. This supercell was used to calculate the pure PbSe and PbSe with different types of defects, considering Cu interstitial doping, Pb interstitial doping, and Se vacancy.

Thermoelectric transport properties measurements

The obtained highly-densified hot-pressing (HP) processed disk-shaped samples were cut into bars with dimensions around ~ 11.5 mm×4 mm×4 mm to measure electrical conductivity (σ) and Seebeck coefficient (S) in 300–773 K by using a CTA-3 (Cryoall, China) equipment under a low-pressure helium atmosphere. The HP disk-shaped samples were cut and polished into a square with sizes of ~ 8 mm×8 mm and ~ 1.5 mm thickness for thermal diffusivity (D) measurements. The samples were coated with a thin graphite layer to minimize errors from the emissivity method in CLA-1000 (Cryoall, China) instrument. The sample density (ρ) was determined using the dimensions and mass of the samples. The specific heat capacity (C_p) was calculated by the Debye model. The thermal diffusivity data was analyzed using a Cowan model with pulse correction.

Data availability

The authors declare that the data supporting the findings of this study are available on reasonable request.

Acknowledgements

The authors acknowledge the financial support from National Natural Science Foundation of China, Grant No. 52172236 and the fund of the state Key Laboratory of Solidification Processing in NPU, Grant No. SKLSP202314. Z. Gao acknowledges the support of the National Natural Science Foundation of China (No.12104356, No.52250191), the Opening Project of Shanghai Key Laboratory of Special Artificial Microstructure Materials and Technology (Ammt2022B-1), and the Fundamental Research Funds for the Central Universities. Y. Xiao would like to acknowledge the support of “Bairen” Program from University of Electronic Science and Technology of China, and the help from Prof. Z. Luo and Dr. Z. Chen of Fuzhou university for the carrier density analysis.

Author contributions

Y. X. and L. X. designed the experiment, synthesized the samples, carried out the transport property measurements and wrote the manuscript. Y. W., Y. W. and Z. G. performed the DFT calculations. X. D. and Y. X. discussed the results and revised this manuscript.

Competing interests

The authors declare no competing interests.

Additional information

Supplementary information: The online version contains supplementary material available at XXX.

Correspondence and requests for materials should be addressed to Yu Xiao.

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The strategy of dual interstitials doping can synergistically optimize carrier and phonon transport properties in thermoelectric materials at wide temperatures. The dynamically optimized carrier density in Pb_1.02Se-0.2%Cu with Pb and Cu dual interstitials doping leads to high average power factor, which contribute a superior ZT value at 300-773 K compared with other single interstitial doped n-type PbSe compounds.

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Dual Interstitials Doping to Advance PbSe Thermoelectric at Wide Temperatures

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