Structural Modularization of Cu2Te Leading to High Thermoelectric Performance near the Mott–Ioffe–Regel Limit

To date, thermoelectric materials research stays focused on optimizing the material's band edge details and disfavors low mobility. Here, the paradigm is shifted from the band edge to the mobility edge, exploring high thermoelectricity near the border of band conduction and hopping. Through coalloying iodine and sulfur, the plain crystal structure is modularized of liquid‐like thermoelectric material Cu2Te with mosaic nanograins and the highly size mismatched S/Te sublattice that chemically quenches the Cu sublattice and drives the electronic states from itinerant to localized. A state‐of‐the‐art figure of merit of 1.4 is obtained at 850 K for Cu2(S0.4I0.1Te0.5); and remarkably, it is achieved near the Mott–Ioffe–Regel limit unlike mainstream thermoelectric materials that are band conductors. Broadly, pairing structural modularization with the high performance near the Mott–Ioffe–Regel limit paves an important new path towards the rational design of high‐performance thermoelectric materials.


Introduction
Thermoelectric (TE) material-based energy conversion technology has attracted increasing global attention in virtue of the technical merits such as no moving parts, no greenhouse www.advmat.de www.advancedsciencenews.com of hybrid crystals as they contain specific structural-functional modules such as the sublattices respectively undertaking charge conduction and phonon scattering.
The structural hybridity or modularity does not need to be native, extrinsic defects act as endowed structural-functional modules. For example, static point defects and mobile ions, [9,10] nanoscale lattice strains, and microscale grain boundaries jointly suppress the lattice thermal conductivity. [11,12] Meanwhile, the doping induced resonant electronic states, [13] the energy filtering effect at grain boundary, [14] and the doping regulated carrier concentration optimization and band convergence enhance the electronic transport properties via optimizing the material's electron band structure, especially the details of band edge. [15,16] In the context of band conduction, the minimal carrier mobility is achieved when the carrier mean free path approaches the average atomic distance, i.e., the Mott-Ioffe-Regel (MIR) limit. [17] To date, the state-of-the-art TE materials are band conductors with decent carrier mobilities on the order of 10 cm 2 V −1 s −1 and above. On the other hand, hopping conductors in which the mobility edge governs the electronic transport are thought to make poor thermoelectrics because of low carrier mobilities.
An important question follows directly, can we utilize doping to structurally modularize an otherwise plain crystal structure? Further, as structural modularization degrades the carrier mobility, a key ingredient of the TE quality factor, [18] would such structurally modularized low-mobility materials be able to yield state-of-the-art TE performance? The answers are potentially paradigm shifting.
Here we present a case study in copper telluride (Cu 2−x Te), a liquid-like TE material known for its complex atomic orderdisorder of Cu ions in a number of structural polymorphs. [19][20][21][22] The nearly degenerate crystal structures make Cu 2−x Te a good material template to implement structural modularization and study the pertinent effects on the TE properties. The electric field instability [2] of Cu 2−x Te is a least concern among copper chalcogenides as Cu 2 Te has an ionic conductivity much lower than Cu 2 S and Cu 2 Se; [23] more generally, long-range ionic migration can be restricted by keeping the voltage drop across the material below the threshold [24] and via doping or nanostructuring. [25] We do not observe any macroscopic material instability or Cu precipitation in the present study. Compared to other TE materials, doped copper tellurides have fairly high carrier concentrations in the range of 2-4 × 10 21 cm −3 , and the room temperature carrier mobilities are in the range of 15-30 cm 2 V −1 s −1 , [19][20][21][22] well above the carrier mobility at the MIR limit (μ MIR ) that delimits band conduction and hopping conduction. [17] Through co-alloying with iodine and sulfur, we structurallyfunctionally modularize Cu 2−x Te with (i) the atomic-scale aliovalent I dopants on the Te sites that act as effective donors to reduce the hole concentration and scatter the heat-carrying phonons at elevated temperatures; (ii) the highly size mismatched yet crystalline S/Te sublattice that chemically quenches the Cu sublattice and also drives the electronic states from itinerant to localized with increasing S content; and (iii) the mosaic nanograins that joint force with other types of defects to suppress the thermal conductivity. A greatly enhanced Seebeck coefficient (260 μV K −1 at 850 K) and a record-high figure of merit (1.4 at 850 K) in Cu 2 Te 0.5 I 0.1 S 0.4 (cf. Figure 1a) are attained near the MIR limit, a paradigm shift from the state-of-theart TE materials that are well-established band conductors (cf. Figure 1b).

Results and Discussion
Figure 2a displays the room-temperature powder X-ray diffraction patterns (PXRD) of Cu 2 Te 1−x I x (x = 0.0, 0.05, and 0.1) and Cu 2 Te 0.9−y I 0.1 S y (y = 0.1, 0.2, 0.3, 0.4, and 0.5) samples. The crystal structure of pristine Cu 2 Te tends to be structurally polymorphic, in accordance with literatures. [20,21] Upon doping I on the Te site (denoted by the x ratio), the X-ray diffraction (XRD) peaks are readily indexed to the Cu 2 Te-like hexagonal structure (space group P6/mmm). The maximum solubility of I in Cu 2 Te is found to be around 10% (cf. Figure S1  I x , Cu 2 Te 0.9−y I 0.1 S y , and Cu 2 Te 1−y S y series. The grey symbols denote the literature data of doped, composited and nanostructured Cu 2 Te-based materials. [21,22,26,27] The dashed line is guide to the eyes. The four different functional modules are illustrated in the inset. b) Maximal z values as a function of the room temperature carrier mobility for a number of representative TE materials. [9,12,28,29] The green region denotes the range of carrier mobility at Mott-Ioffe-Regel (MIR) limit (μ MIR , Table S1, Supporting Information); the vertical dashed line at around 1.2 cm 2 V −1 s −1 denotes the μ MIR for Cu 2 Te 0.9−y I 0.1 S y . High z values are achieved near the MIR limit in the present work. The carrier mobility for Cu 2 Te 0.4 I 0.1 S 0.5 is too low to be reliably measured, and the corresponding z value is not the highest among the samples studied, so the red dashed line bends downward at the lower side of the carrier mobility.
www.advmat.de www.advancedsciencenews.com Information), below which I enters the Te site and serves as a substitutional point defect and also an effective donor. The lattice parameters remain unchanged upon I doping as the atomic size of I is close to that of Te (cf. Figure 2b). In the presence of I, further alloying S on the Te site (denoted by the y ratio), the (001) peak at 2θ = 12° gradually diminishes with increasing y value and finally disappears at y > 0.2, indicating the structural transition from the Cu 2 Te-like hexagonal structure (P6/mmm) to Cu 2 S-like hexagonal structure (P6 3 /mmc). The linearly decreasing lattice parameter with increasing S ratio confirms the substitution of S on the Te sites.
The solubility of S in Cu 2 Te is much larger than that of I in Cu 2 Te even though the atomic radius of I (1.40 Å) is closer to Te (1.40 Å) than that of S (1.00 Å). Notably, hump features are clearly detected in the XRD patterns of the samples with high S content (x > 0.2), pointing toward the presence of amorphous component in the relevant samples (cf. Figure 2a). Such observation is well consistent with our previous study that the Cu sublattice is chemically quenched into an amorphous state by the anionic S/Te sublattice with large atomic size mismatch. [5,8] The atom probe tomography (APT) analysis in Figure 2c confirms the homogeneity of all elements down to tens-ofnanometers scale. Furthermore, the imaging contrast variations of the atomically resolved high angle annular dark field (HAADF) image (cf. Figure S2, Supporting Information) indicate the uniform distribution of Te, I, and S in the anionic framework. Cu ions are hard to discern due to the disordered nature. All these results unequivocally corroborate that I and S randomly substitute Te and exist as point defects.
Other than the aforementioned atomic scale defects and size mismatched S/Te sublattice, the I/S codoped samples contain nanoscale mosaic microstructures and amorphous component on the Cu sublattice. Figures 3b shows the selected-area electron diffraction (SAED) pattern of the red circle area in Figure 3a along the [0001] zone axis. Closer scrutiny reveals that the diffraction patterns are not sharp dots but short arclike Bragg streaks, a signature of diffuse diffraction and reminiscent of the SAED pattern of mosaic nanograins with lowangle grain boundaries reported by He et al. in Cu 2 Te 1−y S y samples. [26,30] This is further corroborated by the bright-field and dark-field images in Figure 3c  . a) Room temperature powder X-ray diffraction patterns for Cu 2 Te 1−x I x and Cu 2 Te 0.9−y I 0.1 S y . Weak diffraction peaks belonging to cubic phase are observed in Cu 2 Te 0.9−y I 0.1 S y . b) Room temperature lattice parameters (a and c) as a function of I content (x) and S content (y). The lattice parameters are markedly decreased with increasing S content due to the much smaller atomic radius of S than that of Te. The dashed lines are guide to the eyes. The crystal structures of hexagonal Cu 2 Te (P6/mmm) and hexagonal Cu 2 S structure (P6 3 /mmc) are illustrated in the insets. c) Elemental mapping obtained by 3D atom probe tomography (APT) analysis for Cu 2 Te 0. 5   www.advmat.de www.advancedsciencenews.com contrast in bright-field and dark-field images. The size of each grain is only several to tens of nanometers, which plays a key role in scattering mid-to-long wavelength heat-carrying phonons. Besides, the diffraction rings in Figure 3b indicate the presence of amorphous component, i.e., glass-like Cu sublattice in Cu 2 Te 0.9−y I 0.1 S y , in accordance with our XRD results. Figure 3g,h shows the high-resolution transmission electron microscopy (TEM) image and fast Fourier transformation (FFT) diffractogram for Cu 2 Te 0.6 I 0.1 S 0.3 sample. The FFT diffractograms of mosaic nanograins are almost the same except for variations in the brightness of diffraction spots, suggesting a slight misorientation among these nanograins. The shape of mosaic nanograins is irregular and its size is comparable to or smaller than the sample thickness, leading to the overlapping of grain boundaries in the vertical direction. Therefore, it is hard to discern the edge-on interface between nanograins. Note that the mosaic nanograin is not a precipitate or a second phase; it has the same composition as the whole sample (Figure 3i).
The interplay between the I dopants and S dopants has an interesting effect on the carrier concentration. Doping iodine into Cu 2 Te, the hole concentration (p) is decreased from (2-3) × 10 21 to 1.3 × 10 21 cm −3 for Cu 2 Te 0.9 I 0.1 (cf. Figure 4a; Figure S3a, Supporting Information) as iodine acts as a donor. With further alloying S in the I-doped Cu 2 Te 0.9−y I 0.1 S y , the hole concentrations are barely changed. This is somewhat a surprise as the early study showed that the p was gradually reduced with increasing S alloying content when S is solely alloyed in Cu 2 Te 1−y S y (cf. Figure 4a). [8,31] To probe the interplay between iodine doping and sulfur doping, we performed defect formation energy (E v ) calculations to find out what occurs upon S alloying with or without I doping. A 2 × 2 × 2 Cu 2 Te supercell containing 48 atoms (i.e., Cu 32 Te 16 ) was used to simulate the alloyed system (cf. Figure 4b). The Cu vacancy (V Cu ) formation energy (E v ) for Cu 32 Te 16 (i.e., Cu 2 Te) is around 0.08 eV (cf. Figure 4c). Substituting Te by S, the E v of V Cu is increased to 0.18-0.29 eV, and thus the formation of V Cu is substantially suppressed. Using extrinsic point defects to regulate the formation energy and thus the concentration of native point defects is a routine to tune the electrical properties of narrow bandgap semiconductors by isoelectronic doping. [15,32] The change of E v of V Cu explains the observed reduction of p in S alloyed Cu 2 Te 1−y S y . Substituting Te by I, the E v values for V Cu1 , V Cu2 , and V Cu4 are substantially enhanced but the E v for the Cu bonded to I, namely, V Cu3 , is reduced to negative. It is hard to conclude on the trend of the total Cu vacancy concentration upon iodine doping. Nonetheless, the overall carrier concentration should be somewhat reduced as iodine dopants serve as donors. Co-alloying Cu 2 Te with both S and I, the variations of E v of V Cu are found to be similar to those of sole I-doping (cf. Figure 4c). With regard to the net carrier concentration variation, S alloying seems to play a minor role on the formation of V Cu in the presence of I. As a result, the carrier concentration is expected to be barely changed in Cu 2 Te 0.9−y I 0.1 S y with increasing S content, agreeing with what we experimentally observed (cf. Figure 4a). Figure 4d shows the room temperature carrier mobility (μ) of Cu 2 Te 1−x I x , Cu 2 Te 0.9−y I 0.1 S y , and Cu 2 Te 1−y S y as a function of I/S content. Upon doping I, the μ of Cu 2 Te is largely suppressed due to the enhanced ionized-impurity scattering.
When alloying S in Cu 2 Te 0.9 I 0.1 while fixing the I ratio at 0.1, the μ is further reduced by nearly one order of magnitude. The minimum μ at room temperature of the y = 0.4 sample is only 0.8 cm 2 V −1 s −1 , which is lower than the carrier mobility at MIR limit (μ MIR = 1.2 cm 2 V −1 s −1 ). [17] It seems the phase transition from P6/mmm to P63/mmc structure has negligible influence on the general trend of carrier mobility because the disorder is implanted in both structures. Note that a relatively large carrier mobility (12 cm 2 V −1 s −1 ) far above μ MIR is observed in our previously reported (Cu 1−x Ag x ) 2 (Te 1−y S y ) materials, [5] which suggests that the carriers are still in the band conduction. Though we were unable to measure the carrier mobility above room temperature due to general technical restrictions and the already ultralow mobility values, the mobility values of the high S-ratio samples are expected to be near, if not lower than, the MIR limit at temperatures where these samples attain their maximum zT values. By contrast, the state-of-the-art TE materials are featured by well-established band conduction with the carrier mobilities on the order of 10 2 cm 2 V −1 s −1 and above. The μ of y ≤ 0.3 samples exhibit weak temperature dependence, in contrast, the μ of y = 0.4 sample exhibits a slight yet clear positive slope with increasing temperature from 25 to 300 K (cf. Figure S3b, Supporting Information). Since the I content stays the same in the samples studied, ionized impurity scattering alone cannot be the cause of the positive slope of μ versus T for the y = 0.4 sample. The high magnitude on the order of 10 21 cm −3 and the weak temperature dependence of the carrier concentration ( Figure S3a, Supporting Information) exclude the Mott localization and band gap opening as the main cause of the S-content driven resistivity and Seebeck coefficient behavior changeovers shown in Figure 4a Hence, the phonon-assisted hopping mechanism is a plausible scenario, and the reduction of μ is mainly ascribed to the S-alloying induced disorder and Anderson localization. [8,33] When the periodicity of the lattice is destroyed, the electron wave function is no longer extended in the whole lattice, but localized around confining area and decays exponentially in space. As a result, the electronic conduction is dominated by hopping conduction when the Fermi level is in localized state, while it is dominated by band conduction when the Fermi level is in extended state. [34] With increasing S content, the degree of disorder is increased, the electron transport behavior is thus driven from itinerant conduction to hopping conduction, leading to a large reduction of μ. On the other hand, the electronic conduction of a material governed by a mobility edge is expected to have strong TE response, i.e., large Seebeck coefficient, on the insulating side of the mobility edge. [35] Indeed, the room temperature Seebeck coefficients of the S-alloyed samples studied herein are in the range of 40-120 μV K −1 (cf. Figure 4e) at high carrier concentrations on the order of 10 21 cm −3 (cf. Figure 4a), which is hard to explain by band conduction and points towards hopping conduction.
The Seebeck coefficient α is significantly enhanced upon I doping and/or S alloying. Specifically, a maximum α of 119 μV K −1 at room temperature is obtained for Cu 2 Te 0.4 I 0.1 S 0.5 , which is four times larger than that of Cu 2 Te and three times higher than that of S-free Cu 2 Te 0.9 I 0.1 (cf. Figure 4e). Figure 4f shows the Seebeck coefficient as a function of carrier concentration at room temperature for Cu 2 Te 1−x I x , Cu 2 Te 0.9−y I 0.1 S y , and www.advmat.de www.advancedsciencenews.com Cu 2 Te 1 − y S y . Though the electronic conduction in the samples studied is complex, which may be no longer band conduction at high S content, the Pisarenko plot gives some insights into the microscopic conduction mechanism. Specifically, the data of I-doped samples lie around the Pisarenko plot with effective mass of 2.1 m e , suggesting that I doping shifts the Fermi level without obviously altering the band structure. In contrast, the S-alloyed samples clearly show much larger Seebeck coefficient than the calculated Pisarenko plot. For Cu 2 Te 1−y S y , the Seebeck coefficient α are improved by nearly three times while the carrier concentration is reduced to half the value of Cu 2 Te. For the Cu 2 Te 0.9−y I 0.1 S y samples, the Seebeck coefficients α are also significantly increased after alloying S although the carrier concentrations are barely changed. This is quite unusual since such large enhancement of α at comparable p has only been reported in several cases such as the existence of resonant states, [13,36] band convergence/ overlapping, [37] or electron critical scattering. [38] We attribute the enhanced α to the disorderinduced electronic localization, [34,39] which qualitatively alters the nature of the wavefunction and changes the conduction mechanism from band conduction to hopping. For amorphous materials or complex crystalline systems with large disorder, the Seebeck coefficient is intimately related to the enthalpy barrier of carrier hopping between neighbor localized states. [34,40] Adv. Mater. 2022, 34, 2108573   Figure 4. a) Carrier concentration (p) as a function of I content (x) or S content (y) for Cu 2 Te 1−x I x , Cu 2 Te 0.9−y I 0.1 S y , and Cu 2 Te 1−y S y at 300 K. b) The crystal structure used for DFT calculations of copper vacancy formation energy. c) Calculated copper vacancy formation energy in Cu 32 Te 16 , Cu 32 Te 15 S, Cu 32 Te 15 I, and Cu 32 Te 14 IS. d) Carrier mobility (μ) as a function of I content (x) or S content (y) for Cu 2 Te 1−x I x , Cu 2 Te 0.9−y I 0.1 S y , and Cu 2 Te 1−y S y at 300 K. The inset shows a schematic of the localized electronic states and extended electronic states. The red dashed line denotes the carrier mobility at MIR limit (μ MIR ). [17] e) Seebeck coefficient (α) as a function of I content (x) or S content (y) for Cu 2 Te 1−x I x , Cu 2 Te 0.9−y I 0.1 S y , and Cu 2 Te 1−y S y at 300 K. f) Seebeck coefficient (α) as a function of carrier concentration (p) at 300 K. The carrier concentration of Cu 2 Te 0.4 I 0.1 S 0.5 is hard to measure because of localized electronic states. Here the p of Cu 2 Te 0.4 I 0.1 S 0.5 (grey sphere) is assumed to be the same as that of Cu 2 Te 0.5 I 0.1 S 0.4 . The dashed line is the calculated Pisarenko plot based on a single parabolic band (SPB) model. [15] The reported α versus p experimental data of Cu 2 Te 1−y S y and Cu 2 Te 0.5+x S 0.5−x are included for comparison. [8,26] www.advmat.de www.advancedsciencenews.com With increasing S content, the disorder strength is gradually increased, resulting in larger enthalpy barriers and thus higher Seebeck coefficients.
The TE properties of Cu 2 Te 1−x I x and Cu 2 Te 0.9−y I 0.1 S y as a function of temperature are plotted in Figure 5. Both electrical resistivity (ρ) and Seebeck coefficient (α) are significantly increased with an increasing amount of I and S content. The ρ for pristine Cu 2 Te is on the order of 10 −6 Ω m, which is enhanced by nearly two orders of magnitude, reaching (1-3) × 10 −4 Ω m in Cu 2 Te 0.4 I 0.1 S 0.5 . With increasing values of ρ, the temperature coefficient of resistivity (TCR) gradually turns from positive in Cu 2 Te to negative in Cu 2 Te 0.4 I 0.1 S 0.5 (Figure 5a; Figure S3c, Supporting Information). The change of sign of TCR is reminiscent of the Mooij correlation, [41] which is typically related with the incipient Anderson localization in highly disordered metals. [42] Furthermore, the low temperature electrical resistivities of Cu 2 Te 0.5 I 0.1 S 0.4 and Cu 2 Te 0.4 I 0.1 S 0.5 follow the relation lnρ versus T −1/4 ( Figure S4, Supporting Information), [34] which is also a signature of variable-range hopping conduction for disordered systems. The maximum α for pristine Cu 2 Te is only 74 μV K −1 , which is improved to 102 μV K −1 for Cu 2 Te 0.9 I 0.1 , and further enhanced to 260 μV K −1 for Cu 2 Te 0.4 I 0.1 S 0.5 (Figure 5a). The positive sign of Seebeck coefficients and the positive sign of Hall coefficients indicate that holes are the majority charge carrier. The power factor (PF) is slightly improved when the S alloying content y is lower than 0.3; however, with further increasing y, the PF is gradually decreased. Specifically, a maximum PF of 8.7 μW cm −1 K −2 is obtained for Cu 2 Te 0.6 I 0.1 S 0.3 at 850 K. The electrical properties of Cu 2 Te 0.9 − y I 0.1 S y are practically repeatable after 4 progressive heating-cooling cycles ( Figure S5, Supporting Information), attesting to good thermal stability at high temperatures. Figure 5d displays the total thermal conductivity (κ) as a function of temperature for Cu 2 Te 1−x I x and Cu 2 Te 0.9−y I 0.1 S y . Most samples exhibit complex temperature dependencies of κ from 300 to 850 K due to the existence of multiple structural transformations. [19,20] Notably, κ is significantly reduced with increasing I and S content, which largely stems from the decreased electronic contribution to thermal transport. The  The open and filled symbols refer to the data of I-doping Cu 2 Te 1−x I x and S-alloying Cu 2 Te 0.9 − y I 0.1 S y samples, respectively. The data of Cu 2 S are included for comparison. [29] f) Comparison of zT values for several reported Cu 2 Te-based TE materials. [15,21,22,26,27] www.advmat.de www.advancedsciencenews.com Adv. Mater. 2022, 34, 2108573 is only one ninth of that of Cu 2 Te. The lattice thermal conductivity (κ L ) for Cu 2 Te 1−x−y I x S y is lower than 0.5 W m −1 K −1 over the entire temperature range studied (cf. Figure S6, Supporting Information), approaching the amorphous limit. The low κ L is attributed to the strong phonon scattering by the as formed hierarchical structural modularity and/or the emerging quasiparticles such as propagons, diffusons, and locons instead of the phonons in the strict sense. [43] Benefiting from the improved PF and reduced κ, the TE figures of merit zT are greatly enhanced over the entire temperature range studied (cf. Figure 5e). Specifically, a record-high zT of ≈1.4 at 850 K is achieved in Cu 2 Te 0.5 I 0.1 S 0.4 , an improvement of ≈370% over that of the pristine Cu 2 Te (zT = 0.29). We have prepared four batches of Cu 2 Te 0.5 I 0.1 S 0.4 samples, which show good reproducibility (cf. Figure S7, Supporting Information). The high zT value obtained in this work is not only much higher than the literature data of Cu 2 Te-based TE materials (cf. Figure 5f) but also attained near the MIR limit in contrast to most other state-of-the-art TE materials that are band conductors (cf. Figure 1b).

Conclusion
In summary, we devise an effective method to integrate the structural-functional modules in the liquid-like TE material Cu 2 Te. The aliovalent I dopants in the Te-sites not only stabilize hexagonal structure at room temperature but also act as donors to substantially reduce the hole concentration otherwise too high. Meanwhile, the introduction of isovalent S dopants induces sublattice-level distortions and Anderson localization, which enables a great enhancement of Seebeck coefficient and an ultralow lattice thermal conductivity. Near the MIR limit where the carrier mobility is exceptionally low, a state-of-the-art zT of 1.4 is achieved at 850 K in Cu 2 Te 0.5 I 0.1 S 0.4 , in contrast to the state-of-the-art TE thermoelectric materials that are wellestablished band conductors. The doping induced hierarchical structural modularity and the discovery of high zT values near the MIR limit in copper tellurides thus present a case of paradigm shift from the band edge to the mobility edge in TE materials research.

Experimental Section
Synthesis: Polycrystalline Cu 2 Te 1−x−y I x S y samples were synthesized by a melting-annealing method followed by spark plasma sintering. Highpurity raw materials of Cu (Sigma Aldrich, 99.999%), Te (Sigma Aldrich, 99.999%), CuI (Sigma Aldrich, 99.9%), and S (Sigma Aldrich, 99.999%) were weighed according to the nominal compositions of Cu 2 Te 1−x I x (x = 0.05, 0.1, 0.12, and 0.15) and Cu 2 Te 0.9−y I 0.1 S y (y = 0.1, 0.2, 0.3, 0.4, and 0.5) and then put inside a pyrolytic boron nitride crucible that sealed in evacuated quartz tubes. The loaded tubes were flame-sealed and then heated to 1403 K in 12 h, soaked at this temperature for 12 h, cooled to 923 K in 50 h, annealed at 923 K for 4 d, and subsequently cooled to room temperature by turning off the furnace power. After removing the copper precipitate on the surface, the obtained ingots were hand-ground into fine powders and then densified using a spark plasma sintering (Sumitomo SPS-2040) apparatus at 773-823 K under a pressure of 60-65 MPa. Boron nitride was sprayed on the carbon foils and the inner walls of the graphite die to prevent currents from going through the samples causing undesired ionic migration. Finally, highly dense (>97% of theoretical density) disk-shaped pellets were obtained ( Figure S8a, Supporting Information).
Characterization: Room-temperature powder XRD characterization was performed using Rigaku Rint 2000 diffractometer equipped with a Cu-K α source. Rietveld refinement was performed to calculate the lattice parameters using FULLPROF software. The sample compositions were estimated using energy dispersive X-ray analysis (EDS, Horiba 250) that equipped in field emission scanning electron microscopy (FESEM, Magellan-400). Atom-probe tomography (APT) analysis was performed in a Cameca Instruments (LEAP 5000 XR) by applying a DC voltage of 2-4 kV and laser pulse energy of 3 pJ. 20 million ions were collected by the APT with a 50 K measurement temperature and a detection rate of 1%. The needled-sharped samples for the APT analysis were prepared using the standard lift-out procedure by a focused ion beam lift-off methodology (Helios, Nanolab 600). Aberration-corrected scanning transmission electron microscopy (STEM) investigation was conducted on a probe-corrected Hitachi HF5000 operating at 200 kV. The electrical conductivity (σ) and Seebeck coefficient (α) were simultaneously measured by the ULVAC ZEM-3 apparatus. The thermal diffusivity (D) was measured via the laser flash technique with a Netzsch LFA-457 and the results are shown in Figure S8b in the Supporting Information. The specific heat (C p ) was estimated by using the Dulong-Petit law. The pellet density (d) was measured by the Archimedes method. The total thermal conductivity (κ) was calculated from the equation κ = d × C p × D. The Hall coefficient (R H ) was measured using PPMS-9 with magnetic field swept from −3 to 3 T. The Hall carrier concentration (p) and mobility (μ) were calculated by p = 1/eR H and μ = σR H , respectively.
Defect Formation Energy Calculations: The calculations were performed within the framework of density functional theory (DFT) with projector-augmented wave (PAW) method, as implemented in the Vienna Ab Initio Simulation Package (VASP). [44] The cutoff energy of the plane wave was set at 500 eV. The energy convergence criterion was chosen to be 1 × 10 −5 eV per unit cell. A 2 × 2 × 2 Cu 2 Te supercell containing 48 atoms was used in all DFT calculations. The Brillouin zone integration was sampled using Monkhorst-Pack grids [45] with a 9 × 9 × 9 k-point mesh. The E v of a Cu vacancy (V Cu ) is calculated according to the equation where E tot and tot, Cu E V are the cohesive energies of the supercell before and after the introduction of a Cu vacancy, respectively; E Cu is the cohesive energy of copper with fcc crystal structure.

Supporting Information
Supporting Information is available from the Wiley Online Library or from the author.