Synergistic Zn/Cu Co-doping engineering for concurrent optimization of carrier transport and lattice thermal conductivity in p-type Mg₃Sb₂

INTRODUCTION

Thermoelectric materials can directly convert heat into electricity, and vice versa, under a temperature gradient. Owing to their solid-state nature, silent operation, and minimal maintenance requirements, they hold great promise for applications such as waste-heat recovery and distributed energy generation^[1-6]. Their performance is typically evaluated using the dimensionless figure of merit (ZT) = S²σT/κ, where S is the Seebeck coefficient, σ is the electrical conductivity, κ is the total thermal conductivity (κ = κ_ele + κ_latt; κ_ele is the electronic thermal conductivity, and κ_latt is the lattice thermal conductivity), and T is the absolute temperature^[7,8]. Achieving a high ZT requires the coordinated optimization of a high power factor (PF = S²σ) together with a low κ_latt^[9]. However, these parameters are intrinsically interdependent, making it particularly challenging to simultaneously enhance all thermoelectric properties^[10,11].

Among various thermoelectric systems, Zintl-phase compounds with the general formula AB₂Sb₂ (A = Mg, Yb, Ca, Ba; B = Mg, Zn, Cd, Ga, Al, etc.) have emerged as a research hotspot in recent years owing to their complex crystal structures and excellent chemical tunability^[12-14]. The Zintl-phase compound Mg₃Sb₂ is composed of earth-abundant and low-toxicity elements, exhibits intrinsically low κ, and maintains good thermal stability. These features make it a promising environmentally friendly thermoelectric material for medium-temperature applications (500-900 K)^[15-17]. Notably, n-type Mg₃Sb₂ has achieved a peak ZT exceeding 1.5, attributed to its high conduction-band degeneracy (N_v ≈ 6) and strong lattice anharmonicity^[12,18-23]. In contrast, p-type Mg₃Sb₂ suffers from low valence-band degeneracy (N_v ≈ 1) and a large valence-band effective mass^[12,13], which collectively restrict carrier transport, resulting in a peak ZT of less than 0.7 to date^[15,24-26]. For the construction of all-magnesium-based thermoelectric devices, the relatively poor performance of p-type components remains a critical bottleneck that limits their compatibility with high-performance n-type counterparts. Therefore, developing effective strategies such as band-structure engineering and defect modulation to enhance the thermoelectric performance of p-type Mg₃Sb₂ represents a key challenge in this field^[27].

A variety of strategies have been explored to overcome the performance bottleneck of p-type Mg₃Sb₂. Alkali-metal doping, such as Na^[15,28] or Li^[28,29], can effectively introduce holes, increase carrier concentration (n), and improve σ; however, it often leads to an increase in κ_latt, which offsets part of the performance gain. Ag doping^[30,31] can simultaneously increase mobility (μ) and n by reducing chemical bond polarity, although its ability to suppress κ remains limited. Electron-type dopants such as Zn^[24,32] can introduce mass fluctuation and local strain fields at Mg sites, thereby enhancing phonon scattering and significantly lowering κ_latt. Some studies also suggest that Zn may modify the valence-band structure and improve the PF^[33]. For example, Ren et al.^[33] demonstrated that Zn/Na co-doping can simultaneously suppress κ_latt and enhance μ, resulting in an increase in peak ZT from 0.6 to 0.8 and a 76% improvement in the engineering performance index ZT_eng. More complex co-doping strategies such as Zn/Ag^[30] or Zn/Yb^[12] have also yielded promising results: by introducing multiple point defects and enabling band modulation, these approaches enhance PF while reducing κ, achieving peak ZT values up to 0.84. After further Zn/Yb co-doping and carrier optimization, a peak ZT exceeding 1.1 has even been reported. Despite these advances, two major challenges remain: (i) bipolar conduction often emerges at high temperatures, causing substantial performance degradation; and (ii) the functional roles of dopants are difficult to decouple, making it challenging to simultaneously maintain high electrical performance and low κ across the full temperature range.

Building on the above insights, this study proposes a Zn/Cu co-doping strategy to achieve synergistic optimization of p-type Mg₃Sb₂-based materials, with both dopants substituting at the Mg sites. First, Zn is incorporated to introduce significant mass fluctuation and local lattice strain, which effectively scatters long-wavelength phonons and reduces the κ_latt. Meanwhile, Zn incorporation increases the density of states near the Fermi level (E_F), enabling modulation of the bandgap (E_g) and valence-band structure^[24]. Subsequently, Cu is introduced to further tailor the valence-band edge. Benefiting from the +1 valence state of the group-IB Cu element at elevated temperatures, Cu doping modifies the local chemical environment, optimizes hole concentration, and enhances the PF. By precisely controlling the doping sequence and site occupancy of Zn and Cu, this approach aims to achieve balanced thermoelectric transport properties across the entire operating temperature range, thereby advancing the practical application of this environmentally benign Zintl-phase material.

EXPERIMENTAL

RESULTS AND DISCUSSION

To verify the feasibility of Mg-site doping with Zn and Cu, first-principles calculations based on DFT were carried out. The supercell structures of Mg₁₆Zn₆Sb₁₆ and Mg₁₇Zn₆Cu₁Sb₁₆ are shown in Figure 1A and B, respectively. Both exhibit the typical cage-like framework of anti-La₂O₃-type layered Zintl-phase compounds (space group $$ P\bar{3}m1 $$)^[16]. In this structure, Mg primarily occupies the cationic sites, while Sb atoms form a stable anionic framework (The structures of additional supercells, Mg₂₄Bi₁₆ and Mg₂₃Cu₁Sb₁₆, are provided in Supplementary Figure 1A and B). In Mg₁₆Zn₆Sb₁₆, Zn substitutes part of the Mg atoms (highlighted in gray), introducing significant mass fluctuation within the lattice. This mass difference enhances phonon scattering and thereby reduces the κ_latt^[41]. In Mg₁₇Zn₆Cu₁Sb₁₆, Cu further occupies Mg sites (shown in blue), and its distinct atomic mass and chemical environment are expected to introduce additional point-defect scattering, further suppressing κ_latt^[42]. Figure 1C-F presents the calculated band structures of Mg₂₄Sb₁₆, Mg₁₆Zn₆Sb₁₆, Mg₂₃Cu₁Sb₁₆, and Mg₁₇Zn₆Cu₁Sb₁₆, respectively. As shown in Figure 1C, pristine Mg₂₄Sb₁₆ exhibits a clear indirect E_g with the valence-band maximum and conduction-band minimum located at different symmetry points^[27]. Its narrow E_g (0.21 eV) is favorable for achieving a large S at medium-high temperatures. Upon Zn doping [Figure 1D], both the conduction- and valence-band manifolds become more complex, and the conduction band sinks toward the valence band. The E_F shifts into the valence band, indicating a heavily doped p-type state. Multiple band-degeneracy features emerge near the M-K, Γ-A, and L-H directions, which denote high-symmetry k-paths in the Brillouin zone, and the flattened valence-band dispersion increases the carrier effective mass, contributing to an enhanced S^[43]. For Cu-doped Mg₂₃Cu₁Sb₁₆ [Figure 1E], band splitting occurs near the Γ point, and the conduction-band density increases slightly along Γ-A. The E_F also moves into the valence band, and the E_g narrows to 0.13 eV, demonstrating that Cu strongly perturbs the electronic structure and increases the hole concentration. The co-doped Mg₁₇Zn₆Cu₁Sb₁₆ system [Figure 1F] retains a band structure largely similar to that of Zn-only doping due to the dominant heavy Zn incorporation. At certain symmetry points, the conduction and valence bands overlap to form a metal-like contact. This overlap may be an artifact resulting from the tendency of this functional to underestimate the band gap in such narrow-gap systems. A similar band overlap was also observed in the work by Lei et al.^[12]. Experimental results confirm that the samples remain heavily doped semiconductors. Near the band contact regions, phonon scattering is enhanced, which further reduces κ_latt. Meanwhile, heavy co-doping leads to significant hole accumulation at the valence-band maximum, pinning E_F deeply within the valence band and thereby strengthening the p-type transport characteristics of the material^[13].

Figure 1. Crystal structures and electronic band structures of Mg₃Sb₂-based materials before and after doping. Supercell models of (A) Mg₁₆Zn₆Sb₁₆ and (B) Mg₁₇Zn₆Cu₁Sb₁₆; calculated electronic band structures of (C) Mg₂₄Sb₁₆, (D) Mg₁₆Zn₆Sb₁₆, (E) Mg₂₃Cu₁Sb₁₆, and (F) Mg₁₇Zn₆Cu₁Sb₁₆. E_g: denotes the bandgap.

The XRD patterns of the Mg_3.1-xZn_xSb₂ (x = 0, 0.4, 0.6, and 0.8) samples are shown in Figure 2A. Most diffraction peaks for all compositions match well with the standard PDF card of Mg₃Sb₂ (PDF#03-0375). A small peak at approximately 28.54° is observed only in the x = 0 sample, corresponding to trace Sb, which may originate from Mg volatilization during ball milling or sintering. The minor presence of the Sb phase may pin E_F near the p-type region, which is favorable for p-type behavior^[13,44]. Phase analysis was carried out using Jade 6.0 software (Materials Data, Inc., Livermore, USA). As the Zn content increases (x > 0.4), this impurity peak gradually disappears, indicating that Zn atoms successfully substitute the Mg site and stabilize the crystal structure. This observation is consistent with the findings of Ren et al.^[33]. Since Zn has a higher electronegativity (1.65) than Mg (1.31), the Zn-Sb bond exhibits stronger covalency compared to the Mg-Sb bond. The introduction of Zn can optimize the unsaturated bonding environment caused by Mg deficiency, thereby suppressing Mg volatilization. During the increase of x, the enlarged view of the XRD pattern [Figure 2B] reveals that the main diffraction peaks shift from 25.49° to 26.05°, accompanied by a decrease in the lattice parameters a and c [Figure 2C]. This peak shift can be attributed to the smaller ionic radius of Zn relative to Mg in this chemical environment, leading to lattice contraction and a reduced interplanar spacing (d) upon substitution. According to Bragg’s law (2d·sinθ = nλ), a decrease in d results in an increase in θ, causing the diffraction peaks to shift toward higher angles. Similar peak-shift behavior under heavy Zn doping has been reported by Huang et al.^[30], Ren et al.^[33], Xin et al.^[45], and Ahmadpour et al.^[46]. In addition, the introduction of microstrain and point defects during solid-solution formation leads to peak broadening^[47].

Figure 2. Phase characterization of Mg_3.1-xZn_xSb₂ (x = 0, 0.4, 0.6, and 0.8). (A) X-ray diffraction (XRD) patterns in the 2θ range of 20°-60°; (B) magnified XRD patterns from 21.19° to 27.69°; (C) evolution of lattice parameters a and c with Zn content. PDF: Powder diffraction file.

Figure 3A-D illustrates the morphological evolution of the Mg_3.1-xZn_xSb₂ (x = 0, 0.4, 0.6, and 0.8) samples. For x = 0 and x = 0.4, the sample surfaces appear relatively dense, with tightly bonded grains and only a few irregular pores. However, as the Zn content increases further (x = 0.6 and 0.8), the SEM images reveal a significant rise in both the number and size of pores in the heavily doped samples, accompanied by looser grain boundaries. This observation aligns with the measured decrease in ρ shown in [Supplementary Table 1]. We attribute this phenomenon primarily to the preparation process. For Mg-containing Zintl phases, prolonged high-energy ball milling typically leads to Mg volatilization. Additionally, as the Zn concentration increases, alloying effects may induce lattice distortions. During hot pressing, such distortions can disrupt mass transport and reduce effective diffusivity, thereby retarding interparticle neck growth. Furthermore, the extended hot-pressing duration, necessitated by the equipment’s slow heating and cooling rates (5~10 °C/min), exacerbates Mg loss, which further promotes pore formation. Such porosity can introduce additional carrier-scattering centers, which in turn influence both the σ and κ. Figure 3E-J shows the EDS elemental distribution maps for the x = 0.6 and x = 0.8 samples. The maps confirm that Mg, Sb, and Zn are uniformly distributed at the microscale, with no detectable phase segregation or elemental enrichment.

Figure 3. Microstructural characterization of Mg_3.1-xZn_xSb₂ (x = 0, 0.4, 0.6, and 0.8). (A-D) Scanning electron microscopy (SEM) images for x = 0, 0.4, 0.6, and 0.8; (E-G) Energy-dispersive X-ray spectrometer (EDS) elemental mapping for the x = 0.6 sample; (H-J) EDS elemental mapping for the x = 0.8 sample.

As shown in Figure 4A-I, heavy Zn doping at the Mg site significantly modifies the thermoelectric properties of Mg₃Sb₂-based materials. With increasing Zn content, the σ exhibits a pronounced upward trend across the entire temperature range up to 735 K [Figure 4A]. At low temperatures, limited thermal excitation results in fewer carriers and thus lower σ. As temperature increases, more holes are thermally activated into the valence band, leading to a substantial rise in n, consistent with the Hall measurements [Figure 4C]. However, heavy Zn doping shifts the E_F upward, driving the system toward metallic behavior. This causes the carrier energy distribution to concentrate near E_F, reducing the energy difference between the average carrier energy and E_F. Consequently, the thermoelectric voltage decreases, leading to a reduction in the S [Figure 4B]. This inverse relationship between n and S is consistent with classical thermoelectric transport theory^[10]. Notably, μ does not change monotonically after Zn doping but instead increases initially before decreasing [Figure 4C]. This behavior likely arises from the competing influences of point-defect scattering and grain-boundary scattering^[10]. Despite the reduction in S, the PF remains significantly higher than that of the undoped sample due to the substantial increase in σ [Figure 4D]. For example, at x = 0.6, the PF reaches 230 μW cm^-1 K^-2 at 735 K. Figure 4E shows the D. The undoped sample exhibits a higher D at room temperature, which gradually decreases with increasing temperature (from 0.64 to 0.40 mm² s^-1), consistent with the enhanced phonon-phonon (Umklapp) scattering at elevated temperatures^[48]. In contrast, the D of Zn-doped samples is significantly lower across the entire temperature range, and its temperature dependence becomes weaker. For the x = 0.6 and 0.8 samples, D decreases initially and then increases, indicating that mass fluctuation and local lattice distortion introduced by Zn substitution introduce strong phonon scattering, making defect scattering the dominant heat-transport mechanism^[49]. Figure 4F shows the κ. The undoped sample has the highest κ (0.92 W m^-1 K^-1) at room temperature, which decreases with temperature. Zn-doped samples display an overall reduction in κ, with the x = 0.8 sample reaching as low as 0.47 W m^-1 K^-1 at low temperatures. On the component level, κ decreases initially and then increases, a result of enhanced phonon-defect scattering dominating at low-to-mid temperatures and the subsequent strengthening of the electronic contribution at higher temperatures [Figure 4G and H]. According to the Wiedemann-Franz law (κ_ele = LσT)^[27,50] (L is defined as the Lorenz number), the κ_ele increases with heavy doping. Figure 4I summarizes the ZT evolution with Zn content. The ZT values of all doped samples increase continuously with temperature. For x = 0.6, ZT reaches 0.03 at 324 K and increases to 0.31 at 735 K, demonstrating that a favorable balance between electrical and thermal transport is achieved at this doping level. Although further increasing the Zn content (x = 0.8) enhances σ, the ZT does not continue to improve due to the combined effects of decreased S and the rise in κ_ele, which offsets the reduction in κ_latt.

Figure 4. Thermoelectric properties of Mg_3.1-xZn_xSb₂ (x = 0, 0.4, 0.6, and 0.8). Temperature-dependent (A) electrical conductivity (σ) and (B) Seebeck coefficient (S); x-dependent (C) carrier concentration (n) and mobility (μ) at room temperature; Temperature-dependent (D) power factor (PF); (E) thermal diffusivity (D); (F) total thermal conductivity (κ); (G) electronic thermal conductivity (κ_ele); (H) lattice thermal conductivity (κ_latt), and (I) dimensionless figure of merit (ZT).

The performance enhancement achieved through single-element doping in Mg_3.1Sb₂ is limited; therefore, Cu was introduced into the Mg_2.3Zn_0.8Sb₂ matrix to further improve the thermoelectric properties. Cu, as a group-IB dopant, is expected to introduce additional holes, increase the n, and further modulate the κ_latt through mass fluctuation. The composition x = 0.8 was selected as the base material because it exhibits a relatively high ZT_ave = 0.17 over the measured temperature range, providing a more representative evaluation of temperature-dependent transport behavior [Supplementary Figure 2]. Figure 5A presents the XRD patterns of Mg_2.3-yZn_0.8Cu_ySb₂ (y = 0, 0.075, 0.100, and 0.125). All diffraction peaks match well with the standard Mg₃Sb₂ pattern (PDF#03-0375), and no detectable secondary phases are observed, indicating that the main Mg₃Sb₂ crystal structure is preserved across all doping levels. Figure 5B presents the magnified local XRD patterns. As the Cu content increases, the primary diffraction peaks shift slightly toward higher angles (from 26.03° to 26.20°). This peak shift indicates that Cu successfully substitutes for Mg and leads to lattice distortion. Correspondingly, the lattice parameters a and c decrease [Figure 5C], confirming a slight lattice contraction, consistent with a reduced interplanar spacing (d) and an increase in the diffraction angle θ.

Figure 5. Phase characterization of Mg_2.3-yZn_0.8Cu_ySb₂ (y = 0, 0.075, 0.100, and 0.125). (A) XRD patterns in the 2θ range of 20°-60°; (B) magnified XRD patterns from 20.00° to 28.68°; (C) evolution of lattice parameters a and c with increasing Cu content. XRD: X-ray diffraction.

Figure 6A-C shows the SEM images of Mg_2.3-yZn_0.8Cu_ySb₂ (y = 0.075, 0.100, and 0.125). Numerous small cracks and pores are visible on the fracture surfaces of samples with different Cu contents, which is consistent with the density measurement results [Supplementary Table 2]. This morphology arises partly because the heavily Zn-doped matrix dominates the overall microstructure, making the samples exhibit a similar appearance, and partly due to Mg volatilization during ball milling and hot pressing, which reduces surface densification during alloy formation. Figure 6D-G presents the EDS elemental mapping of the y = 0.100 sample. The Mg, Sb, and Zn elements are uniformly distributed across the examined area. In contrast, the Cu signal is weak overall, with localized regions of enrichment, reflecting its low doping concentration. During high-temperature synthesis or sintering, Cu may migrate and segregate along grain boundaries, leading to local concentrations that exceed the nominal average. These Cu-rich regions can act as weak scattering centers, contributing to localized modulation of σ or κ.

Figure 6. Microstructure of Mg_2.3-yZn_0.8Cu_ySb₂ (y = 0.075, 0.100, and 0.125). (A-C) SEM images for y = 0.075, 0.100, and 0.125; (D-G) EDS elemental mapping for the y = 0.100 sample. SEM: Scanning electron microscopy; EDS: energy-dispersive X-ray spectrometer.

We further investigated the effects of Zn and Cu co-doping on the thermoelectric properties of the materials. Figure 7A-D shows the temperature-dependent σ, S, n, μ, and PF of Mg_2.3-yZn_0.8Cu_ySb₂ (y = 0, 0.075, 0.100, and 0.125). Overall, σ increases with temperature for all samples, and Cu-doped compositions exhibit significantly higher σ compared with the Cu-free sample. For example, at 735 K, the σ of the y = 0.100 sample reaches 1.98 × 10⁴ S m^-1, which is 2.68 times that of y = 0. This improvement is attributed to the band overlap caused by Zn and Cu co-doping; i.e., the top of the valence band approaches or contacts the bottom of the conduction band, such that at elevated temperatures (> 600 K), valence-band electrons are more easily thermally excited. The excitation leaves positively charged vacancies (holes) in the valence band, and the subsequent movement of electrons to fill these vacancies is equivalent to hole transport, thereby significantly increasing σ. However, S decreases markedly with Cu doping [Figure 7B]. This is because Zn and Cu co-doping pushes the E_F deeper into the valence band, reducing the energy difference between the average carrier energy and E_F. As a result, the heat-flow-driven energy distribution becomes narrower, leading to a lower S. Hall measurements at room temperature [Figure 7C] further confirm this trend: as y increases to 0.125, n increases while μ decreases. The rise in n arises from Cu substitution, which reduces the E_g, and E_g essentially disappears after co-doping, promoting more valence-band hole carriers. The reduction in μ is attributed to enhanced carrier-carrier scattering from higher n and increased interfacial scattering associated with partial Cu aggregation. Consistent with the Hall relation σ = neμ, n and μ vary inversely. Additionally, from the Mott relation (S $$ \propto $$ n^-2/3), an increase in n results in higher σ but lower S^[10]. Figure 7D shows that the PF improves significantly after Zn and Cu co-doping, rising from 220.37 μW cm^-1 K^-2 for y = 0 to 351.99 μW cm^-1 K^-2 for y = 0.100 at 735 K, primarily due to the large enhancement in σ. Figure 7E-H displays the temperature-dependent D, κ, κ_ele, and κ_latt after co-doping. Cu doping has a pronounced influence on D: across the measured temperature range, the Cu-doped samples exhibit higher D than the undoped sample. As y increases, D decreases initially (y = 0.075) and then increases (y = 0.100 and 0.125). This behavior likely arises from the initially low Cu content (where changes in D are minimal) and the subsequent increase in n at higher Cu levels. Because κ = DρC_p, κ follows a similar trend [Figure 7F], reaching approximately 0.61 W m^-1 K^-1 at 735 K. Figure 7G and H separate κ into its electronic (κ_ele) and lattice (κ_latt) components using the Wiedemann-Franz law (κ_ele = LσT, where L is the Lorentz number) and κ_latt = κ - κ_ele^[27,30]. The overall increase in κ with co-doping is mainly due to the rise in κ_ele, whereas κ_latt decreases slightly. The reduction in κ_latt can be attributed to the large mass differences among Mg (24.305), Zn (65.38), and Cu (63.546), which enhance point-defect phonon scattering. Finally, the co-doped sample with y = 0.100 achieves the highest ZT, as shown in Figure 7I. Benefiting from the optimized PF and controlled κ, the peak ZT of Mg_2.2Zn_0.8Cu_0.1Sb₂ reaches 0.42 at 735 K, representing a 147% improvement over the undoped sample.

Figure 7. Thermoelectric properties of Mg_2.3-yZn_0.8Cu_ySb₂ (y = 0, 0.075, 0.100, and 0.125). Temperature-dependent (A) σ and (B) S; y-dependent (C) n (red) and μ (blue) at room temperature; temperature-dependent (D) PF; (E) D; (F) κ; (G) κ_ele; (H) κ_latt, and (I) ZT. PF: Power factor; ZT: dimensionless figure of merit; D: thermal diffusivity; κ: total thermal conductivity; κ_ele: electronic thermal conductivity; κ_latt: lattice thermal conductivity.

CONCLUSIONS

p-Type Mg_3.1-xZn_xSb₂ (x = 0, 0.4, 0.6, and 0.8) and Mg_2.3-yZn_0.8Cu_ySb₂ (y = 0, 0.075, 0.100, and 0.125) samples were successfully synthesized by high-energy ball milling followed by hot pressing. First-principles calculations reveal that Zn and Cu co-doping at the Mg site effectively modulates the electronic band structure, driving the conduction band into direct contact with the valence band and shifting the E_F deep into the valence band. This restructuring increases the hole concentration and enhances the σ. In addition, the mass fluctuation introduced by Zn and Cu substitution generates local lattice distortion, strengthens phonon scattering, and reduces the κ_latt compared with the undoped material. As a result of the synergistic optimization of electrical and thermal transport, the Mg_2.2Zn_0.8Cu_0.1Sb₂ sample achieves a peak ZT of 0.42 at 735 K, representing a 147% improvement over the undoped sample. These findings demonstrate that Zn/Cu co-doping at the Mg site is an effective strategy for band-structure engineering in Mg₃Sb₂-based thermoelectrics. Furthermore, this approach provides a promising pathway for optimizing other Zintl-phase thermoelectric materials.