Compromise and synergy in thermoelectric GeTe–CuSbS₂ alloys†

Zi-Wei Feng‡ ^a, Meng Li‡ ^b, Yongqi Chen ^b, Siqi Liu ^b, De-Zhuang Wang ^a, Liang-Cao Yin ^a, Hao Wu ^a, Wei-Di Liu ^b, Xiao-Lei Shi ^b, Yifeng Wang ^c, Zhi-Gang Chen *^b and Qingfeng Liu *^a
aState Key Laboratory of Materials-Oriented Chemical Engineering, College of Chemical Engineering, Nanjing Tech University, Nanjing 211816, China. E-mail: qfliu@njtech.edu.cn
^bSchool of Chemistry and Physics, ARC Research Hub in Zero-emission Power Generation for Carbon Neutrality, and Centre for Materials Science, Queensland University of Technology, Brisbane, Queensland 4000, Australia. E-mail: zhigang.chen@qut.edu.au
^cCollege of Materials Science and Engineering, Nanjing Tech University, Nanjing 211816, China

First published on 20th June 2025

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Introduction

Thermoelectric technology, being capable of converting waste heat into electric energy, offers a sustainable solution for mitigating the global energy crisis and climate-related issues.^1–3 The conversion efficiency of a thermoelectric device is primarily governed by the dimensionless figure-of-merit (ZT) of thermoelectric materials, defined as ZT = S²σT/κ, where S, σ, T, and κ are the Seebeck coefficient, electrical conductivity, temperature in kelvin, and thermal conductivity, respectively.^4,5 Note the κ usually comprises the electronic (κ_e) and lattice vibration (κ_l) contributions. Due to the interdependence of these parameters, achieving a ZT value higher than 2.5 is still challenging. Recent research has focused extensively on decoupling the S and σ that are otherwise inversely dependent on the carrier concentration (n).⁶ Enhancing power factor (PF = S²σ) can therefore be realized via versatile band engineering, including band convergence,^7,8 resonant states,^9,10 and valley nestification.¹¹ An alternative approach is decreasing the independent κ_l by impeding phonon propagation. Specifically, hierarchical lattice defects are formed to scatter phonons in wide frequencies, such as point defects,^12,13 dislocations,¹⁴ stacking faults,^15,16 and nanoprecipitates.^17,18

Group IV–VI semiconductors such as PbTe,^19–21 PbSe,^22,23 and SnSe^24–26 are recognized as intrinsic thermoelectric systems due to their optimal bandgap (E_g) and the stereochemical expression of lone pairs,²⁷ which facilitate a high PF while maintaining a low κ_l. Notably, PbTe has played a pivotal role in shaping modern thermoelectric theory, as many conceptual breakthroughs in the field are derived from the studies on this system.^28,29 However, the fear of toxicity and the environmental impact of lead-based compounds has spurred growing interest in alternative thermoelectric systems, particularly GeTe, for mid-temperature applications.³⁰ As has been well documented, pristine GeTe undergoes a reversible ferroelectric transition from the rhombohedral phase (R-GeTe) with an E_g of 0.56 eV to the cubic phase (C-GeTe) with a reduced E_g of 0.37 eV at approximately 650 K.³¹ This structural metastability leads to easy formation of germanium vacancies as native acceptors, which results in a hole concentration of ∼10²¹ cm⁻³ beyond the desirable range of 1–3 × 10²⁰ cm⁻³.^32,33 As a result, the ZT of the Ge-deficient GeTe is perversely below unity.

Alloying GeTe with I–V–VI₂ compounds (I = Li, Na, Cu, Ag; V = Sb, Bi; VI = S, Se, Te; see Fig. 1a) is an effective strategy to simultaneously optimize n towards a high PF and decrease the κ_l, ultimately enhancing the quality factor (B) and thus the ZT.^34,35 For instance, Jin et al. obtained a remarkable ZT of 2.6 at 673 K in GeTe–CuSbSe₂ alloys, thanks to the precise control of n near 10²⁰ cm⁻³ and a substantial reduction in κ_l, facilitated by stream-like Cu_mSe_n minority phases and intercalated copper atoms.³⁶ Likewise, Duan et al. reported a ZT of 2.35 at 773 K in GeTe–NaSbTe₂ alloys through suppressing germanium vacancies and band alignment.³⁷ It is worth mentioning that while I–V–VI₂ tellurides and selenides have been widely used in this system, I–V–VI₂ sulfides are underutilized, presumably due to the concerns of degraded carrier mobility (μ) by sulfur that has very different ionic radii and electronegativity compared to tellurium. However, sulfur offers distinct advantages in suppressing the vacancies at cation sites and scattering phonons due to its much higher chemical potential and lower atomic mass than tellurium. In this regard, the alloying effects of I–V–VI₂ sulfides may have been previously underestimated.

In this study, we investigate the crystallography, microstructures, and thermoelectric properties of GeTe alloyed with I–V–VI₂ sulfides based on synthesized GeTe–CuSbS₂ alloys with different alloying ratios. Advanced synchrotron techniques are employed to probe oxidation states and local-to-average structural details with high precision. Scanning and transmission electron microscopy (SEM/TEM) analyses are used to determine the phase composition and lattice defects, offering critical insights into structural evolution with increasing alloying ratio. To explain the influence of the pertinent alloying effects on thermoelectric properties, we integrate Hall measurements, analytical modeling, and density-functional theory (DFT) calculations in our study. As shown in Fig. 1a and b, the peak ZT of 1.72 is achieved in GeTe–4% CuSbS₂ at 773 K. Such a modest value compared with other GeTe–IVVI₂ alloys is mainly due to the inferior carrier mobility,^{14,35,36,38–40} which can be further increased by populating the density-of-states (DOS) near the band edge and/or promoting phase homogeneity. This work represents an insightful understanding of the compromise and synergy in thermoelectric GeTe–CuSbS₂ alloys, providing guidance for the design of high-performance thermoelectric alloys.

Results and discussion

Sample preparation and characterization

To start with, we synthesize GeTe–xCuSbS₂ (x = 0, 2, 4, 6, 8, 10, 12, 20, 30%) samples using a melt-quenching method. The phase purity and average crystal structures are examined by X-ray diffraction (XRD). As shown in Fig. 2a, all samples are generally in a homogeneous phase. The x = 0 sample (pristine GeTe) can be indexed as the R-GeTe structure (ICSD #56041) with a space group of R3m, which has few impurities with a diffraction peak at 27°, originating from the intrinsic germanium vacancies. The noticeable double diffraction peaks at 41–45° are mainly due to the slight break of symmetry from the cubic to rhombohedral phase, mainly reflecting on the effect of Sb alloying. With increasing x, the two peaks tend to get closer due to a gradual increase in symmetry. Upon x = 12%, the two peaks are totally merged, indicating the attainment of the C-GeTe structure (ICSD #638014) with a space group of Fmm. Such crystal structural evolution is due to two reasons. First, copper and sulfur suppress germanium vacancies by enhancing the point defect formation energy.⁴¹ The enhanced occupancy at cation sites in turn weakens the ferroelectric distortion force.⁴² Second, copper and antimony quench the expression of Ge_4s² lone pairs, leading to symmetric local bonding coordination.⁴³ Cu₂S impurities are detected from x = 12%, implying a surpassed copper solubility at this alloying ratio.

In addition, X-ray photoelectron spectroscopy (XPS) is performed on x = 4% and 20% samples to analyze oxidization states and elemental quantities. According to the quick surveys in Fig. S1,† all the constituent elements are in consistent compositions with the initial recipe for synthesis, indicating their uniform distribution. Fine scans of Cu_2p spectra displayed in Fig. 2b can be well fitted with Cu_2p_3/2 and Cu_2p_1/2 characteristic peaks, with their binding energies, respectively, at 932.3 and 952.1 eV, meaning that only Cu⁺ ions are heterovalent dopants acting as acceptors in the matrix and indeed forming a Cu₂S impurity phase. Moreover, the S_2p spectra can be well fitted with S_2p_3/2 and S_2p_1/2 characteristic peaks, with their binding energies, respectively, at 161.7 and 162.7 eV, indicating the existence of S²⁻ ions as homovalent dopants and Cu₂S impurities.

Since XPS may be influenced by chemical and electrostatic shifts and is subject to surface only, we then conduct synchrotron X-ray absorption spectroscopy (XAS) measurements. X-ray absorption near-edge structure (XANES) spectra of the Cu_K and Ge_K edges of x = 4% and 20% samples as well as references are recorded and normalized, see Fig. 2c. Specifically, the standard edge energies of Cu⁰, Cu⁺ and Cu²⁺ are calibrated based on pure copper foil, Cu₂S, and CuSO₄, respectively. The Cu_K edge energies of both x = 4% and 20% samples slightly exceed Cu⁺ towards Cu²⁺ (8.988 keV), indicating the existence of Cu²⁺ ions that may be located in either interstitials or an electron donating environment. Similarly, the standard edge energies of Ge⁰ and Ge²⁺ are calibrated based on pure germanium foil and GeSe. Pristine GeTe exhibits a Ge_K edge energy below Ge²⁺ (11.106 keV), indicating the existence of germanium impurities. In contrast, the Ge_K edge energies of x = 4% and 20% samples are almost identical to Ge²⁺, mainly due to the suppression of germanium vacancies by copper and sulfur. An advantage of XAS measurements is the ability to reveal local structures in the extended X-ray absorption fine structure (EXAFS) spectra. To present data in real space (R) (Fig. 2d) Fourier transformation is performed based on eqn (1):⁴⁴

	(1)

It is seen that the Cu_K radical spectra prove the existence of Cu₂S impurities in x = 4% and 20% samples. Note that, in the x = 4% sample. there is an apparent peak at 2.8 Å that corresponds to the chemical bonds between copper dopants and neighboring tellurium ions. Moreover, the Ge_K radical spectra show split main peaks at 2.2 and 2.9 Å in pristine GeTe, corresponding to the short and long Ge–Te bonds, respectively. By alloying 4% CuSbS₂, the two peaks get closer, consistent with XRD results. Further alloying 20% CuSbS₂ leads to a chaotic radical structure, indicating the existence of multiple phases.

In addition to spectroscopy investigations, electron microscopy analyses are used to characterize microstructures and crystal lattices. We first perform scanning electron microscopy (SEM) analyses using second electron (SE), back-scattered electron (BSE), and energy dispersive spectrometry (EDS) detectors. Fig. 3a and b show the BSE images taken on the polished surface of x = 4% and 20% samples, respectively, superposed with EDS elemental mapping. As can be seen, while the x = 4% sample is in a homogeneous phase without apparent agglomeration of elements, the x = 20% sample clearly shows three contrasts in its BSE image, implying the existence of three phases with different average atomic masses. EDS elemental quantitative analyses clarify that the three phases are the GeTe-rich matrix, germanium precipitates, and Cu₂S precipitates.

We then perform transmission electron microscopy (TEM) analyses using bright field (BF), high-angle annular dark-field imaging (HAADF), and EDS detectors. Fig. 3c shows a HAADF image taken from GeTe–4% CuSbS₂ lamellar specimen, showing periodic contrasts arising from alternative crystallographic orientations of the adjacent domains. Such fractal twinning structures, also known as the herringbone structures,⁴⁵ are indexed in the selected area electron diffraction (SAED) patterns in Fig. 3d. As can be seen, the twined diffraction points can be observed in both [110] and [100] zone axes. Since the resolution of SEM-EDS is subject to the interaction volume of the electron beam that is usually micrometers, we also perform TEM-EDS analyses to seek for nanoprecipitates, and the results are presented in Fig. 3e. It is evident that the germanium and sulfur agglomerations refer to germanium and Cu₂S nanoprecipitates, respectively, and their shape and distribution are consistent with those exhibiting different contrasts with the matrix in HAADF image. High-resolution TEM (HRTEM) images are further taken to understand their atomic structures. Fig. 3f and g show the HRTEM images of the matrix in its [110] and [100] zone axes, respectively, which is roughly in a R-GeTe structure except for the larger interaxial angle approaching 60°, further verifying the increase in symmetry due to alloying CuSbS₂. The d-spaces of 11, 1, 002, and 022 lattice planes are measured as 3.393, 3.464, 2.833, and 2.929 Å, respectively. Fig. 3h shows the HRTEM image of Cu₂S nanoprecipitates in the [221] zone axis, which are in a tetragonal phase with a space group of P4₃2₁2 to minimize the lattice mismatch with matrix. The d-spaces of 02 and 01 lattice planes are measured as 3.085 Å.

Electrical properties and electronic transport

To understand the roles of alloying effects in modulating electrical properties, we measure the temperature-dependent σ and S of all samples. As is seen in Fig. 4a, σ shows a dampening temperature dependence with an increase of the overall value by incrementing x from 0 to 10%, indicating the degenerated semiconductor nature of these samples.^46,47 However, when x = 12%, 20%, and 30%, the σ is inconsistent with the CuSbS₂ alloying ratio. To obtain insight into the reason behind, the logarithmic plots are shown in Fig. 4b. A clear T^−3/2 temperature dependency is seen when x = 0–10%, implying that acoustic phonons dominate the carrier scattering in these samples. However, for x ≥ 12%, while the T^−3/2 temperature dependency in the R-GeTe temperature range implies a perverse acoustic phonon carrier scattering mechanism, the switch to a T^3/2 temperature dependency in the C-GeTe temperature range suggests the existence of an ionized impurity or a mixed carrier scattering mechanism.⁴⁸ In addition to σ, Fig. 4c displays temperature-dependent S measured on the same samples. The positive sign of S indicates p-type conductance.⁴⁹ Similar to σ, the overall S first increases with the increment of x from 0 to 10%, then decreases with higher x, attaining a maximum value of 259 μV K⁻¹ at 723 K. It is also noticed that the highest PF reaches 46.3 μW cm⁻¹ K⁻² in GeTe–4% CuSbS₂ at 723 K, reflecting on the compromise between σ and S. A further increase in x drastically dampens PF.

To explain the change of PF with varying x, we calculate the weighted mobility based on⁵⁰

	(2)

where h, e, m_e, and k_B are the Planck constant, elementary charge, electron mass, and the Boltzmann constant, respectively. Note that eqn (2) is a simplified analytic formalism based on the exact Drude–Sommerfeld free electron model, where the term k_B/e = 86.3 μV K⁻¹ refers to the natural limit of thermopower in metals.⁵¹ Basically, μ_w, defined as a product of μ and DOS, represents a quantitative measurement of how good the electronic transport is for thermoelectric applications by characterizing the PF term in ZT. As plotted in Fig. 4d, the first increasing then decreasing trend of calculated μ_wversus x is consistent with the change of PF. The deterioration of μ_w can be attributed to two factors: (a) the apparently different electronegativity between sulfur (2.58) and tellurium (2.10) distorts the Coulomb field; (b) highly dense Cu₂S nanoprecipitates scatter charge carriers.

We then measured the n and μ at room temperature based on the Hall effect, reflecting on the microscopic picture of charge transport. Fig. 4e and f compare the n and μ of GeTe–CuSbS₂ alloys compared to GeTe alloyed with I–V–VI₂ telluride or selenide reported elsewhere.^35,36 Due to the much higher chemical potential of sulfur over tellurium, alloying I–V–VI₂ sulfides renders an effective suppression of germanium vacancies to reduce n from 4.3 × 10²⁰ to 1.1 × 10¹⁹ cm⁻³ when x = 30%. Meanwhile, the μ is reduced from 105.5 to 7.5 cm² V⁻¹ s⁻¹. The much lower μ_w of heavily alloyed GeTe is mainly due to the degradation of μ overwhelming the population of DOS.

Fig. 4g presents the DFT calculations of the electron's ground states. The electronic band structures are calculated along the high-symmetry k-path. To eliminate the influence of band folding induced by the traditional supercell method, band unfolding is performed to calculate the effective band structures in the first Brillouin zone.⁵² As can be seen, the hybridization between Ge_4p and Te_5p orbitals dominate valence band maxima, while the anti-bonding states arising from the Ge_4s and Te_5s orbitals are responsible for conduction band minima. The introduction of Cu_4s and S_3s and 3p electrons mainly contribute to the deeper states in valence bands. Due to the lack of the central symmetry point, an apparent Rashba splitting can be observed at the L point in R-GeTe–CuSbS₂ alloys, which disappears in the C-GeTe phase due to symmetrization that vanishes ferroelectric polarization.⁵³ Moreover, there is an evident shrinkage of bandgap (E_g) from 0.49 to 0.31 eV in the rhombohedral phase and from 0.12 to 0.09 eV in the cubic phase, leading to a large effective mass (m*) and high PF.

Thermal properties and phononic transport

Fig. 5a shows temperature-dependent κ based on thermal diffusivity (D, measured using a laser flash analyzer), density (ρ, measured by the Archimedes method), and specific heat capacity (C_p) estimated based on the Dulong–Petit law. Clearly, with the increase of x from 0 to 20%, κ exhibits an overall dampening temperature dependence. Whereas for x = 30%, an abnormal temperature dependence is seen, presumably due to the existence of multiple impurity phases. By subtracting κ_e from κ and neglecting the bipolar thermal conductivity, given all samples are heavily acceptor-doped semiconductors, Fig. 5b calculates the κ_l of pristine GeTe and GeTe–4% CuSbS₂. The Wiedemann–Franz law is used to estimate the value of κ_e, with the Lorenz number determined based on eqn (3) under the single parabolic band and acoustic phonon scattering assumptions:⁵⁴

	(3)

It should be noted that the κ_l of GeTe–4% CuSbS₂ reaches its minimum value of 0.30 W m⁻¹ K⁻¹ at 623 K, which is below the Cahill limit and the Clarke limit, right above the diffusion limit.

In the preceding discussion, we demonstrate that highly dense lattice defects exist in GeTe–CuSbS₂ alloys. In this context, the Debye–Callaway model⁵⁵ is further used to interpret the ultralow κ_l. Such a phenomenological model is built on the constant relaxation time approximation, given by

	(4)

In eqn (4), ħ is the reduced Planck constant, Θ_D is the Debye temperature, and x = ħω/k_BT is the reduced phonon energy dependent on the angular phonon frequency (ω). The well-fitted results indicate that in pristine GeTe as well as GeTe–CuSbS₂ alloys, the relaxation rate in resistive processes plays a dominant role in determining the total relaxation rate (τ) of phonons. To distinguish the contribution of different types of lattice defects, Fig. 5c plots spectral lattice thermal conductivity (κ_s) calculated based on eqn (5):⁵⁶

	(5)

Explicitly, we consider the normal and Umklapp scattering (U), grain boundaries (B), point defects (PD, mainly the Cu, Sb, and S substitution at the host sites), twinning boundaries (stacking faults, which can be seen as stacking faults, SF), nanoprecipitates (NP, mainly Ge and Cu₂S inclusions), and resonant scattering of the Einstein oscillators (RS, with the Einstein frequency determined as the lowest optical phonon mode).⁵⁷ Since the integral of κ_s is defined as κ_l, the region between two adjacent curves equals the decreased κ_l by the corresponding type of scattering mechanisms. As can be seen, the processes of U, SF/NP/RS, and B scatter high-, mid-, and low-frequency phonons, respectively, combining a hierarchical phonon scattering approach to effectively decrease κ_l.

DFT calculations are performed to further understand how the U and RS contribute to phonon scattering processes. Fig. 5d compares the calculated phonon group velocity (v_g) on the basis of ω. The pristine GeTe exhibits a maximum ω of 5.4 THz and the highest v_g of 3.7 km s⁻¹, where all phonons transport in a continuous and propagative approach. After alloying 12% CuSbS₂, the highest v_g decreases to 3.5 km s⁻¹, and the phonons span in a much broader range of up to 8.8 THz to transport in a propagative approach plus a discontinuous wave-like diffusive approach. Such a dual-channel approach⁶¹ is basically responsible for a low v_g and thus low κ_l. We also examine the lattice vibrations corresponding to the lowest optical mode at the Γ point, indicating that the slow and wave-like phononic transport is mainly due to the strong lattice anharmonicity, which should be attributed to the large atomic mass fluctuations by alloying CuSbS₂.⁶² To learn the origin of these anharmonic features, we calculate the crystal orbital Hamilton population (COHP) and its integration of the characteristic cation–anion bonds by partitioning the band's electronic energies into pairwise atomic or orbital interactions.⁶³ As shown in Fig. 5e, the Cu–Te bonds are of more populated anti-bonding states than Ge–Te bonds below the Fermi level (E_F), indicating the softening of the bonding strength and optical modes that can be correlated to the Einstein oscillators in the ground states.

Conclusion

In this study, we systematically investigate the thermoelectric properties of GeTe–CuSbS₂ alloys from multiple perspectives. Structurally, CuSbS₂ alloying increases the symmetry and suppresses the germanium vacancy formation, while the low solubility of copper in this system also leads to Cu₂S impurities. Electrically, Cu⁺ ions act as acceptor dopants, optimizing both the n and DOS, but this effect is offset by S²⁻ ions which degrade the μ and μ_w. Thermally, while the κ_l is significantly reduced, the presence of dual-channel phononic transport suggests further optimization potential. These combined effects yield a moderate ZT of 1.72 at 773 K in GeTe–4% CuSbS₂. Future efforts in GeTe–IVVI₂ alloy design should focus on strategically balancing these interactions to achieve higher ZT values.

Data availability

The data supporting this article have been included in the ESI.†

Author contributions

Zi-Wei Feng: data curation, formal analysis, investigation, methodology, validation, visualization, writing – original draft. Meng Li: conceptualization, data curation, formal analysis, resources, supervision, validation, visualization, writing – original draft. Yongqi Chen: data curation, software. Siqi Liu: data curation. De-Zhuang Wang: methodology, formal analysis. Liang-Cao Yin: methodology, formal analysis. Hao Wu: formal analysis. Ming-Hang Hu: methodology. Shu-Qing Li: formal analysis. Wei-Di Liu: formal analysis, supervision. Xiao-Lei Shi: methodology, formal analysis, supervision. Yifeng Wang: resources. Zhi-Gang Chen: conceptualization, formal analysis, funding acquisition, project administration, supervision, validation, visualization, writing – review & editing. Qingfeng Liu: conceptualization, data curation, formal analysis, funding acquisition, investigation, project administration, resources, supervision, validation, writing – review & editing.

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

Q. F. L. thanks the financial support from the National Natural Science Foundation of China (no. 52272040), the State Key Laboratory of Materials-Oriented Chemical Engineering Program (SKL-MCE-23A04), the Priority Academic Program Development of Jiangsu Higher Education Institutions, and the Jiangsu Specially Appointed Professor Program. Z.-G. C. thanks the financial support from the Australian Research Council and the QUT Capacity Building Professor Program. M. L. thanks the financial support from the Australian Research Council and the AINSE Ltd. Early Career Researcher Grant (ECRG). The DFT calculations were conducted on the National Computational Infrastructure via the National Computational Merit Allocation Scheme (NCMAS 2025). The XAS measurements were performed at the MEX-1 beamline at the Australian Synchrotron, part of the ANSTO.

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Footnotes

† Electronic supplementary information (ESI) available: Experimental details. See DOI: https://doi.org/10.1039/d5ta03477a

‡ These authors contributed equally to this work.

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