Self-doping enables flexible Ag₂Se bulk materials for room-temperature thermoelectric generators and coolers

Abstract

Achieving both deformability and high efficiency in thermoelectric materials (TEs) remains challenging, as most high-performance TEs are inherently brittle and rely on toxic tellurium. We demonstrate that off-stoichiometry in silver chalcogenides intrinsically tailors both transport and mechanical properties, enabling enhanced and bendable TEs without extrinsic doping. Adjusting the Ag–Se stoichiometry to yield Ag₂Se_1.04 (SeAg₂Se) and Ag_2.02Se (AgAg₂Se) reveals a strong correlation among defect chemistry, structural stability, and mechanical adaptability. Notably, SeAg₂Se sustains a compressive strain of up to 15% before fracture, underscoring its exceptional bendability. This ductile behavior originates from nanoscale Se inclusions that serve as internal stress relievers and phonon scatterers, leading to an ultralow lattice thermal conductivity of 0.3 W m⁻¹ K⁻¹ (480 K) and an enhanced zT of 0.7, indicative of a soft yet efficient thermoelectric material. The SeAg₂Se single-leg outperforms its AgAg₂Se counterpart, underscoring its potential as a tellurium-free thermoelectric generator (TEG). In addition, SeAg₂Se demonstrates excellent cooling capability, achieving a maximum temperature difference of 49.1 K, comparable to that of commercial Bi₂Te₃. Intrinsic stoichiometric control provides a sustainable design strategy, where self-doping bridges mechanical toughness and thermoelectric efficiency, paving the way for durable, tellurium-free energy devices.

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Introduction

Energy generation and environmental protection have long stood at the forefront of global challenges and will remain so, demanding sustained advances in fundamental science and decisive industrial commitment. Thermoelectric (TE) technology, which directly converts heat into electricity through solid-state transport processes,^1–3 has emerged as a promising pathway toward sustainable energy solutions. The performance of a TE material is quantified by the dimensionless figure of merit zT = S²σT/κ, where S is the Seebeck coefficient, σ is the electrical conductivity (or collectively expressed as the power factor PF = S²σ), and κ is the thermal conductivity. Over decades of development, tellurium-bearing systems such as Bi₂Te₃,^4,5 GeTe,^6,7 and PbTe⁸ have been established as the state of the art for thermoelectric generators (TEGs) and coolers (TECs). However, their large-scale application remains constrained by two critical factors: the scarcity of tellurium, which hinders mass production, and the inherent rigidity of these alloys, which prevents effective integration on curved or irregular surfaces, such as pipelines or engine casings, for direct waste-heat recovery.

In response, a new category of flexible thermoelectrics has emerged. Organic–inorganic composites have demonstrated remarkable stretchability and mechanical compliance⁹ but often at the expense of thermoelectric performance. By contrast, fully inorganic systems exhibit intrinsic ductility while retaining moderate efficiency; notable among them are tellurium-free Ag₂Se-based alloys.¹⁰ Ag₂Se has been recognized for decades as a promising room-temperature thermoelectric material, yet bulk cooling or generator devices remain rare. The primary obstacle lies in its first-order phase transition near 400 K, which complicates device design by strongly affecting its transport properties.

Given that Ag₂Se-based alloys are inherently more ductile than conventional thermoelectrics,¹¹ the key challenge is to further enhance their zT. Because zT depends on both the PF and κ, optimization is inherently difficult due to their coupled nature. Extrinsic doping with foreign elements has long been the dominant approach for tuning carrier concentration,^12,13 but this strategy risks altering the chemical environment of the host lattice and inducing undesirable strain. Here, we adopt an intrinsic approach by adjusting the Ag : Se stoichiometric ratio, enabling controlled carrier modulation without external dopants. Three silver chalcogenides were synthesized—Ag₂Se, Ag₂Se_1.04 (SeAg₂Se), and Ag_2.02Se (AgAg₂Se)—which, when superimposed on the Ag–Se phase diagram, fall in the Ag₂Se, Se + Ag₂Se, and Ag + Ag₂Se phase regions, respectively. Despite their minor compositional differences, these alloys display strikingly distinct mechanical responses under compression: SeAg₂Se achieves an optimal balance, combining precipitation hardening (which enhances compressive strength) with a dual-phase microstructure in which soft Se precipitates improve elongation relative to intrinsic Ag₂Se. To further probe mechanical behavior across the phase transition, we performed the first strain–temperature (S–T) measurements on this ductile system under a constant external load during heating. Remarkably, intrinsic doping altered the strain response, shifting from plasticity-like in Ag₂Se and SeAg₂Se to elasticity-like & pseudo-reversible behavior in AgAg₂Se as the phase transition was crossed.

Together with the improved thermoelectric performance identified in SeAg₂Se, these results demonstrate that subtle intrinsic doping not only enhances zT but also resolves the long-standing trade-off between mechanical strength and ductility. This work establishes a direct correlation between mechanical properties and thermal–electrical transport, laying the groundwork for the design of high-performance, flexible, and ductile thermoelectric generators and coolers.

Results and discussion

To examine how stoichiometry affects material properties, we synthesized three alloys with nominal compositions of Ag₂Se, Ag₂Se_1.04 (SeAg₂Se), and Ag_2.02Se (AgAg₂Se). When plotted on the enlarged Ag–Se phase diagram redrawn from ref. 14, the nominal compositions (open triangles, Fig. 1a) reveal a systematic phase evolution with increasing Se content, shifting from Ag + Ag₂Se to Ag₂Se and finally to Se + Ag₂Se. As shown in Fig. 1a, excess Se or Ag is expected to occupy interstitial sites within the Ag₂Se lattice, where such compositional fluctuations may drive the formation of nanoclusters or even secondary phases. Building on this structural insight, the mechanical properties were subsequently evaluated through compression experiments (Fig. 1b), with small cross symbols at the end of the curves indicating specimen failure. The inset presents both a schematic illustration and an optical image of the specimen before and after compression.

Fig. 1 Phase evolution and mechanical response of Ag₂Se-based alloys. (a) Enlarged Ag–Se phase diagram^10,14 showing the nominal compositions of Ag₂Se, Se-rich Ag₂Se_1.04 (SeAg₂Se), and Ag-rich Ag_2.02Se (AgAg₂Se), marked as open triangles. The inset shows a schematic illustration of the SeAg₂Se and AgAg₂Se lattices, where excess Se or Ag may occupy interstitial sites. (b) Compression stress–strain curves of the three alloys, with small cross symbols marking specimen failure. The inset shows a schematic and an optical image of the specimen before and after compression. (c) Temperature-dependent strain curves of Ag₂Se, Se-rich Ag₂Se_1.04, and Ag-rich Ag_2.02Se recorded upon heating from room temperature RT to 423 K and then cooling back to RT.

The compression stress–strain curves of Ag₂Se, SeAg₂Se, and AgAg₂Se at room temperature exhibit markedly different responses. For a more quantitative comparison, the 0.2% yield stress σ_0.2, maximum stress σ_max, and elongation at fracture ε were extracted and are summarized in Table 1. Remarkably, even slight deviations from stoichiometry, whether Ag-rich or Se-rich, substantially enhance σ_0.2, σ_max, and ε compared to pristine Ag₂Se. Moreover, SeAg₂Se exhibits a balanced σ–ε response, given that it possesses the largest ε with enhanced σ_0.2 and σ_max compared to pristine Ag₂Se. By contrast, the Ag-rich sample exhibits the highest σ_max but sacrifices part of its elongation relative to SeAg₂Se.

Table 1 The 0.2 yielding stress (σ_0.2), maximum stress (σ_Max), and the elongation (ε) of each specimen read from the stress–stress curves in Fig. 1b

Sample	σ0.2 (Mpa)	σmax (Mpa)	ε (%)
SeAg2Se	36.9	62.4	15.1
Ag2Se	8.6	10.2	6.9
AgAg2Se	39.6	66.6	9.9

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After compression to failure, microstructural characterization studies were conducted on Ag₂Se, SeAg₂Se, and AgAg₂Se specimens, examining side views parallel to the loading direction (Fig. S1a–f). For stoichiometric Ag₂Se and AgAg₂Se, river-like features were observed on the side views (Fig. S1b and d). In Ag₂Se, layered cleavage facets appeared, revealing a relatively brittle fracture feature, whereas the AgAg₂Se sample (Fig. S1a) exhibited a nearly crack-free surface after compression. In contrast, the SeAg₂Se specimen displayed a distinct twin-like (pseudo-twin) microstructure, highlighted by a yellow square (Fig. S1e and f), which may account for its superior mechanical robustness. These distinct deformation responses among Ag₂Se-based specimens can thus be attributed to compression-induced mechanical twinning¹⁵ and compositional segregation arising from off-stoichiometry.¹⁶

However, systematic studies on the deformation mechanisms of Ag₂Se-based thermoelectrics remain scarce, and further work is needed to elucidate their mechanical response and microstructural evolution.

To further examine the dynamic mechanical response across the phase transition, temperature-dependent compression experiments were carried out by heating the specimen under a constant load while recording the strain. This setup, schematically shown in the inset of Fig. 1c is designed to explore the deformation behavior of phase-transition thermoelectric materials, exemplified here by Ag₂Se-based alloys, under the temperature gradients typically encountered in thermoelectric generators or coolers. Here, we define the temperature-dependent constant-load strains as S–T curves. As shown in Fig. 1c, positive strain denotes compression, while negative strain indicates expansion. S–T curves of Ag₂Se, SeAg₂Se, and AgAg₂Se were recorded between room temperature and 423 K under a constant compressive stress of 2 MPa, and subsequently upon cooling, to evaluate shape deformation and recovery. Focusing on the heating S–T curves of Ag₂Se and SeAg₂Se (Fig. 1c), both alloys exhibited pronounced deformation upon cooling, indicating reduced yield strength and plastic flow. Below 400 K, the strain stabilized as strength recovered (Fig. S3). While SeAg₂Se exhibits behavior similar to Ag₂Se, its phase transition is marked by a higher compressive response, likely arising from the combined effects of Se evaporation and the α–β transition.

By contrast, AgAg₂Se shows distinct S–T curves, with minor deformation during heating, shape recovery upon cooling, and clear thermal hysteresis. The slight initial expansion likely arises from the jig of the universal testing machine or the thermal expansion of α-Ag₂Se. Following the slight expansion, a pronounced tensile response emerged near 403 K, with deformation saturating at ∼1% strain as the phase transition completed. On cooling, AgAg₂Se recovered its shape with minor hysteresis and negligible plastic deformation strain, reflecting a higher yield stress than that of Ag₂Se and SeAg₂Se. To further probe their mechanical stability, S–T tests were extended to 500 K (Fig. S3). The results closely match those in Fig. 1c; AgAg₂Se specimens retained excellent mechanical integrity at elevated temperature, whereas Ag₂Se and SeAg₂Se exhibited pronounced plastic deformation due to reduced strength and dislocation slip.

These results reveal that self-doping has a marked influence on the mechanical response, and to the best of our knowledge, represent the first report of high-temperature strain behavior in semiconducting silver chalcogenides. The temperature-dependent σ, S, and κ are likewise strongly affected by defect types, which are typically governed by self-doping. As shown in Fig. 2a–f, the temperature-dependent thermoelectric properties differ significantly among AgAg₂Se, Ag₂Se, and SeAg₂Se, despite their similar chemical compositions. Discontinuities observed across the phase transition arise from limitations of the measurement techniques; therefore, data within the transition region are omitted.

Fig. 2 Temperature dependence of the (a) electrical conductivity σ, (b) Seebeck coefficient S, (c) power factor PF, (d) heat capacity C_p, (e) total/lattice thermal conductivity κ/κ_L, and (f) figure of merit, zT for Ag₂Se, SeAg₂Se, and AgAg₂Se.

In the temperature range of 300–418 K, the σ(T) and S(T) curves of AgAg₂Se and Ag₂Se are nearly identical, whereas SeAg₂Se exhibits a lower σ(T) and a higher S(T), as shown in Fig. 2a and b. This distinction aligns with the carrier concentration n_H, as shown in Table S1, where AgAg₂Se and Ag₂Se share a comparable n_H of 4 × 10¹⁸ cm⁻³, but SeAg₂Se exhibits a slightly lower n_H of 3 × 10¹⁸ cm⁻³ at 300 K, leading to its larger S(T) and smaller σ(T). In contrast, upon entering the high-temperature β phase (above 418 K), SeAg₂Se and Ag₂Se converge to a low σ(T), whereas AgAg₂Se retains a distinctly higher σ(T).

A similar “grouping” trend is evident in S(T) (Fig. 2b), where AgAg₂Se resembles Ag₂Se before the phase transition, but SeAg₂Se converges toward Ag₂Se after entering the β phase. Despite their distinct σ(T) and S(T) behaviors, all three samples exhibit similar power factors (S²σ) owing to the S–σ trade-off, forming a plateau near 2.5 W m⁻¹ K⁻². Upon the α–β transition, the PF decreases abruptly, with β-Ag₂Se retaining merely 20–40% of the α-phase value.

Attention is now directed to the thermal transport behavior. The total thermal conductivity κ_T (Fig. 2e), directly correlated with the heat capacity C_p (Fig. 2d) and experimentally-determined thermal diffusivity D (Fig. S4), can be separated into lattice κ_L and electronic κ_e components. Notably, AgAg₂Se exhibits the highest heat capacity, reaching C_p = 0.284 J g⁻¹ K⁻¹ at 323 K, followed by Ag₂Se (C_p = 0.275 J g⁻¹ K⁻¹) and SeAg₂Se (C_p = 0.261 J g⁻¹ K⁻¹). In the α phase region of Ag₂Se, C_p(T) gradually increases with temperature, whereas the temperature dependence becomes nearly flat after the transition to the β phase. A similar trend is observed in the total thermal conductivity κ_T and its lattice contribution κ_L, as shown in Fig. 2e. Within the α phase region, all Ag₂Se based alloys exhibit low-lying κ_L(T), with SeAg₂Se reaching as low as 0.3 W m⁻¹ K⁻¹ at 480 K. This value is significantly lower than that of the other alloys (κ_L greater than 0.7 W m⁻¹ K⁻¹), suggesting that additional phonon scattering arises from self-doping in SeAg₂Se compared with the intrinsic composition. Because phonons are typically scattered by defects in bulk materials, nanoscale structural characterization using TEM is essential to confirm the origin of this enhanced scattering. Overall, SeAg₂Se delivers an enhanced power factor PF(T) together with a markedly reduced thermal conductivity κ(T), yielding the highest zT values across the entire measured temperature range (Fig. 2f).

It is evident that self-doping induces significant changes in the transport properties; however, the underlying mechanism remains unresolved. To clarify this, transmission electron microscopy (TEM) analyses were performed on Ag₂Se and SeAg₂Se alloys. As shown in Fig. S5b, the high-resolution TEM (HRTEM) image of Ag₂Se reveals well-defined lattice fringes without any apparent lattice defects. Indexing of the corresponding selected-area electron diffraction (SAED) pattern (Fig. S5a) identifies the [1̄01] zone axis of Ag₂Se, while the inverse fast Fourier transform (IFFT) image (Fig. S5c) from the region marked in Fig. S5a further confirms the absence of crystallographic imperfections in pristine Ag₂Se. Focusing on the structural characterization of SeAg₂Se, Fig. 3a shows the synchrotron-based powder X-ray diffraction (PXRD) pattern collected at ambient temperature. Rietveld refinement using Ag₂Se as the reference phase fits the experimental profile well, yielding a satisfactory agreement with an R_wp value of 5.792%. The PXRD patterns for SeAg₂Se and Ag₂Se are shown in Fig. S6 and exhibit excellent agreement with the reference phases.

Fig. 3 (a and b) Powder XRD patterns of SeAg₂Se at room temperature and in the range of 180–420 K (synchrotron radiation source: TPS-19A). High-resolution TEM (HRTEM) lattice image and SAED analyses of the SeAg₂Se. (c–f) HRTEM image showing Ag₂Se adjacent to elemental Se with Moiré fringes; the corresponding SAED along [100] Ag₂Se and FFT analysis of the Se phase. (g) GPA strain maps reveal the local strain distribution at SeAg₂Se. (h) STEM-EDS elemental mapping STEM-EDS elemental mapping showing the elemental distribution of Ag and Se in Ag₂Se.

Furthermore, the in situ synchrotron PXRD measurements conducted between 300 K and 450 K unambiguously confirm the α–β phase transition at approximately 418 K (Fig. 3b). Both room-temperature and variable-temperature PXRD results reveal no evidence of secondary phases, indicating the phase purity of SeAg₂Se at the macroscopic scale.

At the nanoscale, however, transmission electron microscopy (TEM) and scanning TEM (STEM) reveal distinct structural features, as shown in Fig. 3c–h. A magnified bright-field (BF) TEM image (Fig. 3c) displays pebble-like precipitates embedded within the matrix, producing pronounced Moiré fringes. The corresponding SAED pattern (Fig. 3f), acquired from the same measured region of Fig. 3c, can be indexed to the [100] zone axis of Ag₂Se, and it exhibits continuous arc-shaped diffraction spots at higher orders, signifying substantial lattice strain within the matrix. Moreover, by performing a fast-Fourier transform (FFT) from the region marked in Fig. 3e, one can conclude that the pebble-like precipitate has an equivalent diameter of approximately 30 nm(Fig. 3d). Furthermore, when the FFT (Fig. 3e) is applied to the pebble-like precipitate, the resultant diffraction pattern can be indexed to a single structure of Se oriented along the [21̄7̄] axis, suggesting that the precipitate could be of the Se phase.

The local IFFT image (Fig. 3e) further reveals a high density of dislocations and low-angle grain boundaries. These nanoscale defects collectively lead to strain hardening, as confirmed by the GPA strain mapping (Fig. 3g), which highlights pronounced lattice distortions arising from dislocation accumulation and the resultant residual stress. The improved ductility is likely associated with dislocation motion accommodated along the interfaces between Se precipitates and the Ag₂Se matrix. Moreover, the pronounced lattice distortions revealed by GPA indicate substantial local strain fields associated with dislocation accumulation. Such strain fields are expected to enhance phonon scattering, providing a plausible explanation for the reduced κ_L observed in SeAg₂Se. The STEM-HAADF image (Fig. 3h) exhibits numerous dark contrast features, indicative of regions containing elements with lower atomic numbers embedded within an otherwise homogeneous matrix. In conjunction with the corresponding FFT analysis, these dark features are identified as Se-rich nanoprecipitates. However, owing to the limited spatial resolution of the elemental mapping, the Se-rich regions cannot be clearly distinguished from the surrounding Ag₂Se matrix in Fig. 3h.

Given that intrinsic self-doping in Ag₂Se can modulate carrier concentration and defect chemistry, it is important to determine whether these effects translate into measurable improvements in device performance. To establish a quantitative link between material properties and energy conversion, bulk AgAg₂Se and SeAg₂Se were fabricated into generator-type single-leg devices using solder and silver paste, as illustrated in the inset of Fig. 4a. The devices were characterized using a commercial mini-PEM setup at variable hot-side temperatures (T_h) and a fixed cold-side temperature (T_c), enabling simultaneous measurement of output power (P_out) and heat flow (Q_t) (Fig. 4b and c). Notably, the P_out and conversion efficiency are mainly governed by the electronic transport properties of α-Ag₂Se, while any β-Ag₂Se formed locally near the hot side is limited in extent and is not expected to significantly affect the overall device performance. Under these operating conditions, the mechanical stability of the single leg is well preserved. As shown in Fig. 4b and 2b, below 393 K, SeAg₂Se exhibits a higher S, leading to a higher output power compared with AgAg₂Se. By contrast, the heat-flow behavior does not exhibit a direct correlation with lattice thermal conductivity, as the measured total heat flow includes contributions from Fourier, Peltier, and radiative heat transfer. Accordingly, the conversion efficiency (Fig. 4a), η = P_out/Q_t, was evaluated up to T_h = 393 K, just below the α–β transition temperature to avoid mechanical degradation associated with volumetric strain. Notably, SeAg₂Se exhibits higher η across the entire temperature range, reaching a peak efficiency of 1.6% and an output power of 5.81 mW (Fig. 4b), both surpassing AgAg₂Se.

Fig. 4 (a–c) The conversion efficiency, output power (P_out), and heat flow (Q_t) of SeAg₂Se and AgAg₂Se single leg as a function of hot side temperature. (d) Schematic diagram of the Z-meter measurement. (e) Comparison of maximum temperature difference achieved by promising TE materials.^17–19

The α–β transition near 418 K and the accompanying volumetric strain impose intrinsic limitations on Ag₂Se-based materials for thermoelectric power generation, where conversion efficiency scales with the temperature gradient. Although SeAg₂Se demonstrates reliable performance for small temperature gradient generators, its operational window motivates exploration toward thermoelectric cooling. The cooling capability, quantified by the Z value and the maximum temperature difference (ΔT_max), was evaluated using a commercial Z-meter. A small piece of SeAg₂Se was sandwiched between nickel wires at an ambient temperature of 289 K, as schematically shown in Fig. 4d. The ΔT_max, defined as the temperature drop of the cold side relative to 298 K (Fig. 4e and S7), reaches 49.1 K, corresponding to a cold-side temperature of 251.7 K. This value surpasses those of conventional PbTe (13.9 K),¹⁷ PbS_0.6Se_0.4 (36.9 K),¹⁸ and even state-of-the-art Bi₂Te₃ (44.0 K),¹⁹ highlighting the exceptional cooling performance of SeAg₂Se.

These results indicate that intrinsic self-doping not only optimizes the electronic transport and stabilizes the microstructure under thermal bias but also enhances device-level conversion efficiency, providing a coherent link between defect chemistry, thermoelectric transport, and functional performance.²⁰ Moreover, near-room-temperature thermoelectric materials that combine high performance with mechanical flexibility are increasingly attractive for ambient energy harvesting beyond conventional waste-heat recovery. Recent studies²¹ have shown that thermoelectrics can surpass hydrovoltaic systems in harvesting energy from water evaporation, owing to their continuous energy conversion and higher power density under ambient conditions. Herein, the mechanical robustness and low-temperature operating window of SeAg₂Se further broaden its potential for emerging ambient energy-harvesting applications, underscoring the expanding role of thermoelectrics beyond traditional waste-heat utilization.

Conclusions

This work establishes a self-doping strategy that intrinsically modulates both thermoelectric properties and mechanical behavior in flexible Ag₂Se-based bulk materials. By subtly deviating from stoichiometry, SeAg₂Se achieves a synergistic balance of thermoelectric performance and moderate ductility, arising from nanoscale Se precipitates that relieve strain and scatter phonons. The intrinsic self-doping approach simultaneously optimizes carrier concentration and defect chemistry without extrinsic impurities, leading to a superior zT of 0.7 (390 K) and an outstanding cooling performance of ΔT_max = 49.1 K. These findings reveal the strong coupling among microstructure, phase stability, and thermoelectric transport, showing that off-stoichiometric design—rather than chemical doping—can reconcile mechanical compliance with high efficiency, enabling durable, ductile, and tellurium-free thermoelectric coolers and generators.

Author contributions

I-L. Jen, W.-T. Chiu, and H.-J. Wu conceived, designed, and supervised the study. I-L. J. synthesized the samples and, together with W.-T. Chiu, K.-K. Wang, and L.-Y. Lee, performed the experimental investigation and data analysis. I-L. Jen, W.-T. Chiu, and H.-J. Wu wrote the original draft and finalized the paper. W.-T. Chiu, M. Tahara, H. Hosoda, and H.-J. Wu acquired the funding.

Conflicts of interest

There are no conflicts to declare.

Data availability

Supplementary information: experimental details, mechanical testing, XRD anaysis, the comparsion of thermoelectric properties and composition anaysis. See DOI: https://doi.org/10.1039/d5ta10274j.

Acknowledgements

The authors acknowledge the financial support from the National Science and Technology Council of Taiwan under Grants MOST 111-2628-E-A49-017-MY4, NSTC 112-2224-E-008-001, 112-2223-E-A49-003-MY5, 112-2112-M-008-028, and 112-2221-E-007-081. The authors thank Yen-Wen Chen (Instrumentation center at NSYSU) for the Focused Ion and Electron Beam System.

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