1. INTRODUCTION

Thermoelectric (TE) technology, which enables the direct and reversible conversion between waste heat and electrical energy, has attracted significant research interest as a sustainable energy harvesting solution ^{[1- 3]}. The efficiency of a TE material is evaluated by the dimensionless figure of merit, zT = (S²σ/κ_tot)T, where S, σ, T, and κ_tot are the Seebeck coefficient, electrical conductivity, absolute temperature, and total thermal conductivity, respectively. The term S²σ is defined as the power factor (PF), representing the electrical transport capability. Achieving high zT requires a strategic decoupling of these parameters, primarily by enhancing the power factor while simultaneously minimizing the lattice thermal conductivity (κ_latt) ^{[4, 5]}.

Recently, diamond-like I-III-VI₂ chalcopyrite compounds, such as CuInTe₂, have emerged as promising p-type TE materials for intermediate-temperature applications due to their intrinsically low κ_latt and high structural complexity ^{[6- 8]}. However, pristine CuInTe₂ typically suffers from a low intrinsic hole concentration (10¹⁷–10¹⁸ cm^-3), which is far below the optimal range for maximizing the power factor. To address this, various doping strategies have been explored. In particular, silver (Ag) substitution at the copper (Cu) site has been demonstrated as an effective approach to optimize carrier concentration ^{[9, 10]}. Previous reports have identified Cu_0.9Ag_0.1InTe₂ as a highly optimized baseline composition that achieves a carrier concentration in the 10¹⁹ cm^-3 range, providing a robust electrical foundation for further property tuning ^{[10, 11]}.

While carrier optimization is critical, further suppression of κ_latt is essential for achieving state-of-the-art TE performance. Alloying with isovalent or aliovalent compounds, such as CdTe or Sb-based chalcogenides, has been widely utilized to induce strong phonon scattering ^{[12- 14]}. For instance, recent studies have highlighted the effectiveness of doping and nanostructuring strategies, such as Sb-doping in SnSe₂ to enhance electrical conductivity ^[15] or Pd-decoration in Bi-Sb-Te systems to suppress bipolar thermal conductivity and enhance high-temperature performance ^[16]. In the case of CuInTe₂, CdTe alloying introduces significant mass and strain field fluctuations due to the substitution of cadmium (Cd) into the cation sublattice, leading to intensive point-defect scattering ^{[11, 17]}. Moreover, CdTe alloying promotes a structural transition from an ordered tetragonal phase to a disordered cubic phase, which further enhances phonon scattering via increased crystallographic disorder ^{[11, 14]}.

However, the temperature-dependent interplay between an optimized electrical baseline (Cu_0.9Ag_0.1InTe₂) and the structural disorder induced by CdTe alloying requires deeper investigation. Although CdTe alloying is exceptionally effective at reducing κ_latt, it also introduces substantial alloy scattering that may impede carrier mobility, particularly at elevated temperatures. In this study, we systematically investigate the thermoelectric transport properties of (Cu_0.9Ag_0.1InTe₂)_1-x(CdTe)_2x (x = 0, 0.05, 0.10, 0.15, 0.20) solid solutions. We focus on the synergistic enhancement of the power factor in the low-temperature regime and the consistent suppression of κ_latt across the entire measurement range. We also provide a detailed analysis of the high-temperature performance cross-over observed at 700 K, where the degradation of carrier mobility imposes a ceiling on the zT enhancement. This work provides critical insights into the optimization of diamond-like chalcogenides for specific temperature-targeted applications.

2. EXPERIMENTAL PROCEDURES

Polycrystalline samples of (Cu_0.9Ag_0.1InTe₂)_1-x(CdTe)_2x (x = 0, 0.05, 0.10, 0.15, and 0.20) were synthesized using a traditional solid-state reaction method. High-purity elemental starting materials—Cu (99.999%, chunk), Ag (99.99%, powder), In (99.999%, chunk), Cd (99.99%, chunk), and Te (99.999%, chunk)—were weighed according to the stoichiometric ratios. The mixtures were loaded into quartz tubes, which were then evacuated to a high vacuum (~10^-4 Torr) and flame-sealed. To ensure complete homogenization, the tubes were heated to 1323 K at a heating rate of 5 K/min, maintained at this temperature for 12 h, and subsequently quenched in water. The resulting ingots were annealed at 873 K for 72 h to achieve structural stability. The obtained products were pulverized into fine powders using an agate mortar and pestle. The powders were consolidated into high-density pellets using spark plasma sintering (SPS) at 823 K for 5 min under an axial pressure of 50 MPa in a vacuum.

The phase purity and crystal structure of the synthesized samples were characterized by X-ray diffraction (XRD, D/MAX-2500, Rigaku) with Cu Kα radiation (λ = 1.5406 Å). The XRD analyses were performed at the Center for Research Facilities, University of Seoul. The σ and S were measured simultaneously from 300 K to 700 K under a helium atmosphere using a commercial thermoelectric property measurement system (ZEM-3, ULVAC-RIKO). The Hall carrier concentration (n_H) and Hall mobility (μ_H) were determined at room temperature using a Hall effect measurement system (HMS-5300, Ecopia) based on the Van der Pauw configuration. The κ_tot was calculated using the equation κ_tot = α∙C_p∙ρ, where the thermal diffusivity (α) was measured using the laser flash method (LFA 467, Netzsch), the density (ρ) was obtained via the Archimedes method, and the specific heat capacity (C_p) was estimated using the Dulong–Petit law. The lattice thermal conductivity (κ_latt) was derived by subtracting the electronic contribution (κ_elec = L∙ σ ∙T) from κ_tot, where the Lorenz number (L) was calculated based on the single parabolic band (SPB) model.

The SPB model defines the relationship between the absolute value of the Seebeck coefficient (|S|) and the Hall carrier concentration (n_H) using Equations (1) and (2) ^[18].

Here, h, m_d ^*, e, k_B, η, and F_i are Planck’s constant, the density-of-states effective mass, the electron charge, Boltzmann’s constant, the reduced Fermi level, and Fermi integral of order i (refer to Equation (3)), respectively.

The non-degenerate mobility (μ₀), which is the basic parameter of the SPB model, is defined in Equation (4) ^[19].

Based on Equations (1) and (2), where S is solely dependent on η, η is inversely calculated from S. The value of μ₀ is predicted theoretically based on the experimental Hall mobility (μ_H) data and calculated η using Equation (4).

In accordance with Equations (1)–(3), where S depends solely on η, parameter n_H varies as a function of both η and m_d ^*. The value of S was theoretically predicted by altering η within the range of -1 to +15 with a fitted m_d ^*. Furthermore, the electrical conductivity (σ) and power factor were calculated based on σS² and the following equation: σ = n_Heμ_H. To evaluate the total thermal conductivity (κ_tot), the lattice thermal conductivity (κ_latt) was fixed to experimental value, and the Lorenz number (L) was calculated as a function of η according to equation (5) ^[20]:

Here, r was set to −1/2 for acoustic phonon scattering. Finally, the dimensionless figure of merit (zT) was obtained as a function of n_H by dividing the calculated power factor by κ_tot.

3. RESULTS AND DISCUSSION

The powder X-ray diffraction (XRD) patterns of the synthesized (Cu_0.9Ag_0.1InTe₂)_1-x(CdTe)_2x (x = 0, 0.10, 0.15, 0.20) samples are shown in Figure 1(a). For the x = 0 sample, all diffraction peaks are well-matched with the standard chalcopyrite tetragonal structure of CuInTe₂ (JCPDS #01-081-1937, space group I-42d). The absence of secondary phases or impurity peaks indicates that the 10% Ag substitution at the Cu site is successfully incorporated into the host lattice, consistent with previous reports on the solubility of Ag in diamond-like chalcogenides. As the CdTe alloying content (x) increases, the diffraction peaks systematically shift toward lower 2θ angles, serving as clear evidence for the formation of a solid solution. This shift is driven by the substitution of host cations (ionic radii of Cu⁺ ~0.77 Å and In³⁺ ~0.80 Å) with the larger Cd²⁺ ions (ionic radius ~0.97 Å), leading to a continuous expansion of the crystal lattice. The evolution of the lattice parameters (a and c) and the unit cell volume as a function of CdTe content is presented in Figure 1(b). Both the a-axis and c-axis lattice parameters exhibit a linear increase with increasing x, adhering to Vegard’s law. Specifically, the a-axis parameter increases from approximately 6.21 Å at x = 0 to 6.27 Å at x = 0.20, while the unit cell volume expands from ~479 ų to ~489 ų.

Fig. 1. (a) Powder X-ray diffraction (XRD) patterns of (Cu_0.9Ag_0.1InTe₂)_1-x(CdTe)_2x (x = 0, 0.10, 0.15, and 0.20) samples. All major diffraction peaks are indexed to the chalcopyrite CuInTe₂ phase. (b) Composition dependence of the lattice parameters (a-axis and c-axis) and unit cell volume of (Cu_0.9Ag_0.1InTe₂)_1-x(CdTe)_2x.

To investigate the underlying mechanisms of electrical transport, room-temperature Hall effect measurements were performed as a function of CdTe content (x). As shown in Figure 2(a), the Hall carrier concentration (n_H) for the baseline sample (x = 0) is approximately 3 × 10¹⁷ cm^-3. Upon CdTe alloying (x ≥ 0.1), n_H dramatically increases by two orders of magnitude, reaching a plateau at approximately 2-3 × 10¹⁹ cm^-3. This significant surge in hole concentration is attributed to the acceptor-like behavior induced by the Cd substitution, which effectively shifts the Fermi level deeper into the valence band. Specifically, within the CuInTe₂ lattice, the substitution of divalent Cd²⁺ ions into the trivalent In³⁺ sites creates an effective acceptor defect, denoted as Cd_In. Furthermore, the systematic incorporation of CdTe and the accompanying structural disorder are expected to alter the formation energy of intrinsic point defects, thereby facilitating the spontaneous generation of copper vacancies (V_Cu). The cooperative effect of these dominant acceptor defects (Cd_In and V_Cu) successfully provides additional hole carriers, driving the dramatic two-order-of-magnitude increase in hole concentration up to the optimal regime ~ 10¹⁹ cm^-3, as presented in Figure 2(a). In contrast, the Hall mobility (μ_H) exhibits a sharp decline from ~64 cm²V^-1s^-1 at x = 0 to below 20 cm²V^-1s^-1 for alloyed samples (x = 0.1–0.2), as illustrated in Figure 2(b). This reduction in mobility is a combined result of increased carrier-carrier scattering at high carrier densities and enhanced alloy scattering originating from the significant mass and strain field fluctuations in the multi-component cation sublattice. The density-of-state (DOS) effective mass (m_d ^*), estimated using the single parabolic band (SPB) model, shows a slight decrease from ~1.4 m₀ to ~1.2 m₀ for the alloyed samples (Figure 2(c)). This “band sharpening” effect suggests a subtle modification of the valence band structure, which may help maintain electrical transport capability despite the increased structural disorder. Furthermore, the weighted mobility (μw), calculated at 300 K (Figure 2(d)), reveals a significant decrease with increasing CdTe content.

Fig. 2. Room-temperature Hall transport parameters of (Cu_0.9Ag_0.1InTe₂)_1-x(CdTe)_2x as a function of CdTe alloying content x: (a) Hall carrier concentration, n_H, (b) Hall mobility, μ_H, (c) density-of-states effective mass, m_d ^*, and (d) weighted mobility, μ_W, at 300 K and 700 K.

The temperature dependence of the electrical transport properties is presented in Figure 3. As shown in Figure 3(a), the σ of x = 0 shows a typical semiconducting behavior, increasing exponentially with temperature. However, the alloyed samples exhibit much higher σ at low-to-intermediate temperatures due to the optimized n_H (Figure 2(a)), while showing a degenerate semiconducting behavior at higher temperatures. The S, shown in Figure 3(b), is positive for all compositions, indicating p-type conduction. The x = 0 sample exhibits very high S values (~580 μV/K at 300 K), which decrease sharply with temperature. For the alloyed samples, S is substantially lower at 300 K (~200 μV/K) due to the high carrier density, but it remains relatively stable across the measured temperature range. The resulting PF are shown in Figure 3(c). At low-to-intermediate temperatures (300–500 K), CdTe alloying leads to a significant enhancement in PF, with values reaching ~0.35 mWm^-1K^-2 at 300 K, which is more than three times higher than that of x = 0 sample. This enhancement is primarily driven by the massive increase in σ (Fig. 3(a)) that outweighs the reduction in S. However, at high temperatures (> 550 K), the PF of the alloyed samples becomes lower than that of the x = 0 sample, as the PF continues to rise through thermal activation while the alloyed samples are limited by mobility degradation. The experimental PF vs. n_H plot (Figure 3d) along with SPB model curves confirms that CdTe alloying successfully shifts the carrier density into the optimal regime (~3-5 × 10¹⁹ cm^-3). Nevertheless, the lower peak PF of the alloyed samples compared to the x = 0 sample quantitatively reflects the penalty in μw (Fig. 2(d)) caused by the intensified alloy scattering.

Fig. 3. Temperature-dependent electrical transport properties of (Cu_0.9Ag_0.1InTe₂)_1-x(CdTe)_2x: (a) electrical conductivity, σ, (b) Seebeck coefficient, S, and (c) power factor, PF. The inset in (c) shows the composition dependence of PF at 300 K and 700 K. (d) Experimental PF as a function of Hall carrier concentration, n_H, together with the SPB model. Here, ‘SPB’ represents the theoretical curves calculated based on the Single Parabolic Band model, while ‘EXP’ denotes the corresponding experimental data points.

The temperature-dependent thermal transport properties of (Cu_0.9Ag_0.1InTe₂)_1-x(CdTe)_2x are presented in Figure 4. As shown in Figure 4(a), the κ_tot decreases monotonically with increasing temperature for all compositions. The x = 0 sample exhibits the highest κ_tot over the entire temperature range, whereas the CdTe-alloyed samples show consistently reduced values. At 300 K, κ_tot decreases from about 2.6 W/mK for x = 0 to below 2.0 W/mK for x = 0.20, and this reduction is maintained up to 700 K. This behavior indicates that CdTe alloying is highly effective in suppressing heat transport in the Cu_0.9Ag_0.1InTe₂ matrix.

The κ_elec, calculated from the electrical transport data, is shown in Figure 4(b). For all samples, κ_elec remains much smaller than κ_tot, indicating that lattice vibration is the dominant contributor to thermal conduction. Although the alloyed samples exhibit slightly higher κ_elec than the x = 0 sample at low-to-intermediate temperatures due to their enhanced electrical conductivity, the absolute magnitude of κ_elec remains limited lower than 0.12 W/mK throughout the measured range. Therefore, the major effect of CdTe alloying is not to increase electronic heat transport but to reduce the lattice contribution effectively. The κ_latt, obtained by subtracting κ_elec from κ_tot, is shown in Figure 4(c). A pronounced decrease in κ_latt is observed with increasing CdTe content over the entire temperature range. The inset of Fig. 4(c) explicitly shows the decreases of κ_latt at 300 and 700 K. The x = 0.20 sample exhibits the lowest κ_latt throughout the whole temperature range, reaching approximately 0.6 W/mK at 700 K. This substantial suppression can be attributed to strong point-defect scattering caused by the simultaneous mass fluctuation and strain-field fluctuation introduced by Cd substitution in the Cu/Ag/In sublattice. To evaluate the potential microstructural effects on the thermoelectric transport properties, it is worth noting that all samples were synthesized under identical mechanical milling and SPS conditions. The rapid consolidation characteristic of the SPS process successfully suppressed unwanted grain growth, resulting in highly dense and uniform bulk samples across all compositions. Consequently, no significant differences in microstructural features, such as grain size distribution or relative density, were expected among the specimens. This uniformity ensures that the drastic reduction in κ_latt is predominantly driven by the atomic-scale point-defect scattering (mass and strain field fluctuations) induced by CdTe alloying, rather than macroscale microstructural variations.

Fig. 4. Temperature-dependent thermal transport properties of (Cu_0.9Ag_0.1InTe₂)_1-x(CdTe)_2x: (a) total thermal conductivity, κ_tot, (b) electronic thermal conductivity, κ_elec, and (c) lattice thermal conductivity, κ_latt. (d) κ_tot as a function of Hall carrier concentration, n_H, together with the SPB model. Here, 'SPB' represents the theoretical curves calculated based on the Single Parabolic Band model, while 'EXP' denotes the corresponding experimental data points.

Figure 4(d) shows the relationship between κ_tot and n_H. In contrast to the electrical transport properties, the reduction in thermal conductivity cannot be explained simply by the change in carrier concentration. Instead, the overall downward shift of κ_tot with increasing CdTe content indicates that the dominant mechanism is the suppression of lattice-mediated heat transport by alloy disorder. These results clearly show that CdTe alloying provides an effective route for reducing κ_latt in Cu_0.9Ag_0.1InTe₂, which is beneficial for improving thermoelectric performance, particularly in the low-temperature region.

Figure 5(a). shows the temperature dependence of the zT. In the low-temperature range, all CdTe-alloyed samples exhibit higher zT values than the x = 0 sample. This trend is particularly evident below ~500 K, where the increase in power factor observed in Figure 3(c), together with the reduced κ_tot and κ_latt in Figure 4, leads to a clear enhancement in thermoelectric performance. At 300 K, the alloyed samples already show noticeably higher zT than the x = 0 sample. These results demonstrate that CdTe alloying is highly beneficial for improving the near-room-temperature thermoelectric response of Cu_0.9Ag_0.1InTe₂. As shown in the inset of Figure 5(a), the zT value at 300 K increases with CdTe content, whereas the zT value at 700 K decreases systematically with increasing x. Figure 5(b) explicitly shows the improvement of zT at lower temperatures ≤ 500 K, by showing average zT between 300 and 500 K. The zT versus n_H relationship plotted in Figure 5(c) further supports this interpretation. The alloyed samples are shifted toward the n_H range that is favorable for maximizing thermoelectric performance at low-to-intermediate temperatures, which explains the enhanced low-temperature zT.

Fig. 5. (a) Temperature dependence of the dimensionless Fig. of merit, zT, for (Cu_0.9Ag_0.1InTe₂)_1-x(CdTe)_2x. The inset shows the composition dependence of zT at 300 K and 700 K. (b) average zT at low-to-intermediate temperature regime between 300 and 500 K. (c) Experimental zT as a function of Hall carrier concentration, n_H, together with the SPB model. (d) average zT of the measured temperature range.

However, the temperature dependence of zT also reveals a clear crossover behavior at higher temperatures. While the baseline sample continues to show a sharp increase in zT with increasing temperature, the alloyed samples exhibit a much more moderate increase and eventually lower zT values than the baseline at the highest measured temperatures. Figure 5(d) shows the average zT of the measured temperature range, which shows gradual degradation upon CdTe alloying This contrasting trend directly reflects the trade-off between thermal conductivity suppression and electrical transport degradation. Although κ_latt continues to decrease with CdTe alloying, the power factor of the alloyed samples becomes increasingly limited at elevated temperatures because the weighted mobility is significantly reduced by intensified alloy scattering and phonon scattering, as already shown in Figures 2 and 3. The present CdTe alloying strategy successfully improves both the power factor and thermal conductivity balance in the low-temperature regime, but does not sustain the same advantage at high temperature, where the mobility loss becomes dominant.

Taken together, these results demonstrate that CdTe alloying in Cu_0.9Ag_0.1InTe₂ is an effective approach for enhancing low-temperature thermoelectric performance through simultaneous carrier concentration optimization and suppression of lattice heat transport. At the same time, the high-temperature crossover behavior suggests that further improvement of zT at elevated temperatures will require an additional strategy capable of preserving carrier mobility while maintaining strong phonon scattering.

4. CONCLUSIONS

In summary, the thermoelectric transport properties of (Cu_0.9Ag_0.1InTe₂)_1-x(CdTe)_2x (x = 0, 0.05, 0.10, 0.15, and 0.20) solid solutions were systematically investigated to clarify the effect of CdTe alloying on the optimized Cu_0.9Ag_0.1InTe₂ baseline. X-ray diffraction analysis confirmed the formation of a solid solution accompanied by lattice expansion and structural evolution from the tetragonal chalcopyrite phase toward a more disordered high-symmetry cubic phase with increasing CdTe content. This structural modification played an important role in suppressing phonon transport. Room-temperature Hall measurements revealed that CdTe alloying induces effective carrier activation, significantly increasing the hole carrier concentration from the order of 10¹⁷ cm^-3 to 10¹⁹ cm^-3, while simultaneously decreasing carrier mobility because of intensified alloy scattering. As a result, the alloyed samples exhibited substantially enhanced electrical conductivity and power factor in the low-to-intermediate temperature region (300-500 K). In particular, the power factor at 300 K was improved by more than three times compared with the x = 0 composition. At higher temperatures, however, the benefit of carrier concentration optimization became less effective because the mobility degradation increasingly limited the electrical transport performance. In parallel, CdTe alloying effectively reduced the lattice thermal conductivity over the entire temperature range. The lowest lattice thermal conductivity was obtained for the highest alloyed composition, which is attributed to enhanced point-defect scattering caused by mass and strain-field fluctuations as well as increased structural disorder. Owing to the simultaneous enhancement in low-to-intermediate temperature electrical transport and suppression of lattice heat transport, the alloyed samples showed significantly improved zT values in the low-to-intermediate temperature range. Nevertheless, a clear crossover behavior was observed at high temperatures, where the x = 0 sample exhibited higher zT than the alloyed samples because the reduction in mobility outweighed the thermal conductivity benefit.