Engineering Ag₂Se thermoelectrics via amorphous nano-Si₃N₄: a dual-functional strategy for enhanced zT and mechanical strength†

Liedong Zhao‡ ^a, Hailan Zhang‡^a, Jiaqi Dong^a, Guangxu Zhang^a, Qian Cao^b, Zhihai Ding^b, Shufang Wang^ac, Jianglong Wang*^a and Zhiliang Li*^ad
aKey Laboratory of High-Precision Computation and Application of Quantum Field Theory of Hebei Province, College of Physics Science and Technology, Hebei University, Baoding 071002, China. E-mail: jlwang@hbu.edu.cn; phd-lzl@hbu.edu.cn
^bXianghe Huiwen Energy Saving Technology Co., Ltd, Xianghe 065400, China
^cEngineering Research Center of Zero-Carbon Energy Buildings and Measurement Techniques, Ministry of Education, Hebei University, Baoding 071002, China
^dInstitute of Life Science and Green Development Hebei University, Baoding 071002, China

First published on 25th July 2025

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1. Introduction

Research for efficient and sustainable energy solutions has become a global focus as the energy shortage becomes increasingly severe. TE technology, with its advantages of no noise, no pollution, and high reliability, is gradually becoming an important choice for achieving sustainable energy development.^1–4 The essence of TE technology lies in improving the TE performance of materials, whose efficiency is usually characterized by the dimensionless figure of merit zT, defined as zT = σS²T/κ_tot, where σ, S, T, and κ_tot represent the electrical conductivity, Seebeck coefficient, absolute temperature, and thermal conductivity, respectively.^5,6 Bi₂Te₃-based alloys, as the classic representatives of near-room-temperature TE materials, have been extensively employed in commercial TE power generators and refrigerators. Over the past few decades, researchers have successfully elevated the zT of p-type Bi₂Te₃ to 1.7 by manipulating the stoichiometric ratio,⁷ doping,⁸ and optimizing nanostructures.⁹ However, n-type Bi₂Te₃ is constrained by its relatively poor intrinsic thermoelectric properties. The inherent brittleness of Bi₂Te₃ significantly impedes its further advancement and application. In recent years, research on non-telluride compounds with high thermoelectric performance and high mechanical properties has been ongoing.

In the search for alternative TE materials, Ag₂Se has emerged as a promising candidate material to replace n-type Bi₂Te₃, owing to its outstanding near-room-temperature TE performance, environmental advantage of no tellurium, and excellent mechanical properties. Ag₂Se is a typical “electron crystal, phonon glass” material,¹⁰ characterized by high σ, low κ, and high carrier mobility (μ), showing excellent TE conversion capability. Ag₂Se has two crystal phases, α-Ag₂Se (orthorhombic phase) at lower temperatures and β-Ag₂Se (cubic phase) at higher temperatures, with a phase transition at 406 K.¹¹ α-Ag₂Se, with inherent low lattice thermal conductivity (κ_l) and relatively excellent electrical properties,¹² has significant TE potential at room temperature. Although there have been numerous studies attempting to improve the TE performance of Ag₂Se by manipulating the stoichiometric ratio,^13,14 alloying,^13,15 and doping,^16,17 these methods still have a lot of limitations. While manipulating the stoichiometric ratio can reduce Ag precipitation and inhibit the formation of metastable phases, thereby reducing n and improving μ, the variability in synthesis conditions among laboratories hampers the reproducibility of results.¹⁸ Alloying can regulate n and improve mechanical properties, but often leads to a significant decrease in μ and may cause phase separation, resulting in a low zT compared to pure Ag₂Se.¹⁹ The limited solubility of Ag₂Se poses challenges for heterovalent doping, leading to non-uniform distribution and increased local defect concentration, which in turn affects σ and TE performance.²⁰ Research studies indicate that incorporating nanoscale second phases is a promising strategy to enhance the TE performance of Ag₂Se. This approach can induce energy filtering effects to enhance S without significantly reducing σ. The nanocrystalline precipitates can also enhance interface phonon scattering and reduce κ_l. However, current research predominantly focuses on crystalline nanoscale materials,²¹ with less exploration of amorphous nanoscale materials.²² The disordered structure of amorphous materials significantly impedes the propagation of phonons, resulting in frequent scattering events that diminish the κ_l.²³ Furthermore, the mechanical flexibility of amorphous materials surpasses that of crystalline counterparts, endowing them with a unique advantage in the fabrication of flexible TE devices. Specifically, amorphous nano-Si₃N₄, characterized by its reduced κ and outstanding mechanical properties, can act as a nanoscale material to elevate the TE efficiency of Ag₂Se.

In this study, Ag₂Se crystals are synthesized using a microwave-assisted method. The impact of synthesis temperature on the TE is comprehensively investigated. Subsequently, amorphous nano-Si₃N₄ is incorporated into the optimal sample (200 °C). It is observed that Si₃N₄ incorporation can significantly diminish the κ_l while preserving a satisfactory electrical performance, leading to a high zT of 0.95 at 388 K. Simultaneously, the Vickers hardness increases to 0.30 GPa. Various characterization techniques are employed to elucidate the intrinsic mechanisms of the enhanced TE.

2. Experimental section

2.1. Sample synthesis

A straightforward microwave-assisted method is used to synthesize Ag₂Se powder. Typically, 0.0544 mol of silver acetate (CH₃COOAg, AR) and 0.0272 mol of sodium selenite pentahydrate (Na₂SeO₃·5H₂O, ≥98%) are separately dissolved in 10 mL of ammonia solution (NH₃·H₂O) and 20 mL of deionized water, respectively. The resulting mixture is transferred to a 250 mL polytetrafluoroethylene autoclave, to which an appropriate amount of hydrazine hydrate solution (N₂H₄·H₂O) is added dropwise, with 50 mL of ethylene glycol used as the solvent. The solution is then heated and stirred in a microwave-assisted synthesis apparatus at the set temperature for 8 min. Afterward, the product is washed several times with deionized water and anhydrous ethanol using centrifugation at 8000 rpm. The sample is subsequently dried in a vacuum for 12 h to yield powdered Ag₂Se. The Ag₂Se powder is placed into a 12 mm diameter graphite mold and pressed into a thin sheet at 400 °C, 50 MPa for 10 min in an SPS system. For the powder synthesis, the microwave heating temperatures are set to 120 °C, 200 °C, and 240 °C, and the resulting samples are labeled as samples 1, 2, and 3, respectively. The synthesis of the Ag₂Se based composites with amorphous nano-Si₃N₄ followed a similar procedure. Specifically, 0.015 g, 0.025 g, and 0.035 g of amorphous nano-Si₃N₄ (99.9%, ∼20 nm) are uniformly mixed with 5 g of sample 2 in a quartz mortar, then loaded into a 12 mm diameter graphite mold for SPS.

2.2. Microstructural characterization and TE property measurement

The crystal phases and microstructures of the samples are characterized by X-ray diffraction (XRD, D8 Advance, Bruker, Germany), field emission scanning electron microscopy (SEM, Nova Nano SEM450, FEI, USA) and aberration-corrected transmission electron microscopy (JEM-ARM200F, JEOL, Japan). The elemental chemical valence state is revealed by X-ray photoelectron spectroscopy (XPS, ESCALAB 250Xi, Thermo Fisher Scientific Inc., USA). The temperature-dependent σ and S are evaluated using an LSR3-1000 Seebeck coefficient/electrical resistance measurement system. The Hall coefficient is measured by the van der Pauw method in a reversible magnetic field of 1.5 T. The κ_tot is calculated using the equation: κ_tot = λC_pρ, where λ, C_p, and ρ are the thermal diffusion coefficient, specific heat capacity, and density, respectively. λ is evaluated using a laser flash apparatus (LFA 1000, LINSEIS, Germany). C_p is calculated using the Dulong–Petit law, and ρ is measured according to the Archimedes principle. Both the TE and the Hall test are conducted along the direction of the SPS pressing force. Vickers hardness is measured three times at a load of 9.8 N using a measurement system (VMHK-30, Japan). Notably, the experimental error for all thermoelectric performance measurements is 7%.

2.3. Band-structure simulation

Density functional theory calculations are performed using the Vienna Ab initio Simulation Package (VASP) based on the projector-augmented wave (PAW) method.^24,25 The exchange–correlation functional is treated using the Perdew–Burke–Ernzerhof generalized gradient approximation.²⁶ Orthorhombic phase Ag₂Se supercells (Ag₃₂Se₁₆) are employed to investigate the changes in the band structures of Ag₂Se and Ag₂Se_1−xN_x samples, respectively. The structures are fully optimized until the Hellmann–Feynman force on each atom is less than 0.01 eV Å⁻¹. The plane-wave function basis set is used to expand the wave functions, with an energy cutoff of 500 eV. Since the generalized gradient approximation tends to underestimate the band gap, the modified Becke–Johnson (mBJ) method²⁷ is also employed, where the CMBJ parameter is taken as 1.095 to fit the experimental band gap of ∼0.07 eV.²⁸ The electron localization function (ELF) and difference charge density diagrams²⁹ of Ag₂Se_1−xN_x are calculated using the Ag₃₂Se₁₅N supercell structure.

3. Results and discussion

To identify the phase composition of the synthesized samples, XRD analysis is conducted on the bulk materials after SPS (Fig. S1, ESI†). The results indicate that all major peaks align well with the standard peaks of orthorhombic Ag₂Se (space group: P2₁2₁2₁, PDF no. 24-1041). However, diffraction peaks corresponding to elemental Ag are observed for sample 1 with (111) and (200) planes, and for sample 3 with the (111) plane. In contrast, all diffraction peaks for sample 2 matched the standard α-Ag₂Se reference pattern without exhibiting any additional peaks.

Fig. 1 presents the TE properties of Ag₂Se samples synthesized at different temperatures. Fig. 1a shows that the σ value of all samples increases from 303 K to 388 K, illustrating the thermal excitation behavior of semiconductors. As the synthesis temperature increases, the σ of all samples first decreases and then increases, while S exhibits the opposite trend, initially increasing and then decreasing. Sample 2 achieves its maximum S of 150.63 μV K⁻¹ at 303 K, as shown in Fig. 1b. To further elucidate the reasons behind the changes in σ and S, Hall tests are conducted, as shown in Fig. S2 (ESI†). It can be observed that the relatively higher σ of samples 1 and 3 is primarily attributed to their elevated n.

The PF of all samples remains relatively stable between 303 K and 388 K (Fig. 1c). Notably, sample 1 maintains the highest PF across the temperature range, achieving a peak of 40 μW cm⁻¹ K⁻² at 303 K, primarily attributed to the high σ. Fig. 1d displays the trend of κ_tot as a function of temperature. κ_tot increases with increasing temperature, with a more pronounced increase observed for samples 1 and 3 compared to sample 2, primarily due to the presence of elemental Ag with high κ_tot. Fig. 1e shows the variation in zT with temperature for all samples. Between 303 K and 388 K, the zT of sample 2 increases with increasing temperature, whereas the zT of samples 1 and 3 decreases, mainly due to the abnormal increase in κ_tot at high temperatures, which negatively impacts the TE performance. Further analysis of the average zT value (zT_avg) reveals that sample 2 has the highest zT_avg of 0.73, followed by sample 3 with zT_avg = 0.62, and sample 1 with zT_avg = 0.50.

To further optimize the TE performance, sample 2, which exhibited the highest zT_avg, is selected and incorporated with varying amounts of amorphous nano-Si₃N₄, specifically Ag₂Se–x wt% Si₃N₄ (x = 0, 0.3, 0.5, 0.7). To examine the form of amorphous Si₃N₄ in the Ag₂Se matrix, XRD and XPS analyses are conducted. As shown in Fig. 2a, all major peaks align well with the standard peaks of α-Ag₂Se, and no peak corresponding to amorphous Si₃N₄ is observed. This absence is primarily due to the amorphous nature of Si₃N₄, though subsequent XPS and TEM analyses confirmed its presence. In Fig. 2b, the peaks at binding energies of 375 eV and 369 eV correspond to the Ag⁺ 3d_3/2 and Ag⁺ 3d_5/2 orbitals, respectively.³⁰ In Fig. 2c, the peaks at 55.4 eV and 54.6 eV correspond to Se²⁻ 3d_3/2 and Se²⁻ 3d_5/2 orbitals.³⁰ Fig. 2d shows peaks at 102.8 eV and 102.34 eV, which correspond to Si⁴⁺, confirming the presence of Si₃N₄ in the Ag₂Se matrix.³¹

Fig. 2e illustrates the charge density difference for Ag₂Se_1−xN_x, with an isosurface level of 0.008. The charge distribution of each atom in the crystal structure is calculated, revealing that the charge contributions from the Ag cation is ∼0.23 e⁻, and those from Se and N anions are ∼0.43 e⁻ and ∼0.91 e⁻, respectively. Notably, the higher electron acquisition ability from N suggests that n can be regulated by introducing additional acceptor energy levels. Fig. 2f presents the ELF diagram of Ag₂Se_1−xN_x, demonstrating the presence of ionic bonding between Ag and N with stronger electron localization compared to that between Ag and Se. First-principles calculations reveal that the binding energy of Ag₂Se_1−xN_x (∼−147.67 eV) is lower than that of Ag₂Se (∼−146.10 eV), confirming that the structure of Ag₂Se_1−xN_x is more stable and suggests higher feasibility of N doping.

To investigate the microstructure of Ag₂Se–x wt% Si₃N₄, the sample with x = 0.5 is selected for TEM analysis (Fig. 3a), which revealed the distribution of nano-inclusions within the Ag₂Se matrix. Fig. 3b shows the energy dispersive X-ray spectroscopy (EDS) results from the magnified region of Fig. 3a, confirming that the nano-inclusions are amorphous Si₃N₄. Additionally, a portion of Si₃N₄ decomposes, allowing N to diffuse into the Ag₂Se matrix, while Si precipitates. Furthermore, as shown in Fig. 3c and d, the additionally incorporated Si₃N₄ primarily resides at the grain boundaries of the Ag₂Se crystals.

To investigate the influence of the incorporation of amorphous Si₃N₄ on the TE properties of Ag₂Se, the electrical properties are measured (Fig. 4). Fig. 4a illustrates the variation of σ with temperature for Ag₂Se–x wt% Si₃N₄. In the temperature range of 303 K to 388 K, the σ of all samples increases gradually with temperature, with that of the Ag₂Se matrix reaching a maximum value of 1388.86 S cm⁻¹ at 388 K. Notably, within the range of 303 K to 388 K, the σ of all amorphous Si₃N₄ incorporated samples is lower than that of the pure Ag₂Se matrix, suggesting that the n or μ in the amorphous Si₃N₄ incorporated samples is reduced. Fig. 4b shows the variation of S for all samples. The negative values indicate that all samples are n-type semiconductors. Within the range of 303–388 K, the absolute value of S decreases gradually as the temperature increases, reaching a minimum of 131.94 μV K⁻¹ at 388 K, primarily due to the increase of n resulting from electron thermal excitation. The S of all amorphous Si₃N₄ incorporated samples is higher than that of the pure Ag₂Se matrix. This may be attributed to a reduction in n or an increase in carrier effective mass (m*). S can be expressed as: , where k_B is the Boltzmann constant, e is the elementary charge, h is Planck's constant, and m* is the carrier effective mass. To further investigate the changes in σ and S, n and μ are measured using the Hall effect at 303 K, as shown in Fig. 4c. As the amorphous Si₃N₄ content increases, the n and μ decrease simultaneously. The n and μ exhibit a concurrent reduction with the increase of amorphous Si₃N₄ content, consequently leading to a decline in σ. First-principles calculations reveal that the m* of Ag₂Se is approximately 0.89 m₀ (m₀ is the charge mass), while that of Ag₂Se_1−xN_x reaches about 1.02 m₀. The decreased n combined with increased m* collectively leads to an enhancement of S. Fig. 4d displays the variation of the PF for all samples. Within the range of 303–388 K, the PF values of Si₃N₄ incorporated samples decrease slightly compared to the Ag₂Se matrix sample. This result is due to the combined effects of σ and S. In addition, to evaluate the stability of the samples, a cyclic test is conducted on the electrical properties of Ag₂Se–0.5 wt% Si₃N₄, as illustrated in Fig. S2 (ESI†).

To explain the reasons for the change of n, the band structures of Ag₂Se and Ag₂Se_1−xN_x are obtained through first-principles calculations, as shown in Fig. 5. As shown in Fig. 5a and b, under heavy doping conditions, Ag₂Se_1−xN_x exhibits a wide bandgap (∼0.251 eV) compared to Ag₂Se (∼0.07 eV), and the Fermi level crosses the valence band, indicative of p-type degeneracy. Furthermore, Fig. 2c and the projected energy bands of each element in Fig. 5d–f demonstrate that N doping introduces impurity levels, forming a negative charge center and reducing the n. This suggests that the primary mechanism for the diminished n is the formation of negative charge centers after N substitutes Se sites, which shifts the Fermi level toward the valence band.

Fig. 6 examines the impact of the incorporation of amorphous Si₃N₄ on the thermal properties of Ag₂Se. Fig. 6a shows that the κ_tot of all samples increases with temperature, and the κ_tot of the amorphous Si₃N₄-incorporated samples is significantly lower than that of the Ag₂Se matrix. In general, the κ_tot of TE materials consists of electronic thermal conductivity (κ_e) and lattice thermal conductivity (κ_l), expressed as κ_tot = κ_e + κ_l, where κ_e is derived from the Wiedemann–Franz law: κ_e = LσT, with L representing the Lorenz constant. Fig. 6b illustrates the temperature dependence of κ_e. As temperature increases, κ_e gradually increases. Simultaneously, the incorporation of amorphous Si₃N₄ leads to a reduction in κ_e across the entire temperature range, due to the decrease in σ. Fig. 6c presents the temperature dependence of κ_l. As the temperature increases from 303 K to 388 K, κ_l initially decreases and then increases with increasing amorphous Si₃N₄ content. The incorporation of amorphous Si₃N₄ introduces a substantial number of dislocations and correspondingly generates pronounced strain fluctuations at the Ag₂Se–Si₃N₄ interface (Fig. 6e–i), thereby enhancing phonon scattering. This effect is the primary cause of the observed decrease in κ₁. For the sample with x = 0.7, κ_l shows an anomalous increase, suggesting that when the concentration of Si₃N₄ reaches a critical value (approximately x = 0.7 wt%), Si₃N₄ forms agglomerates (Fig. S4, ESI†), and the κ of amorphous Si₃N₄ (2–8 W m⁻¹ K⁻¹)³² has an important effect on Ag₂Se–0.7 wt% Si₃N₄. Similar phenomena have been reported in other studies.^21,33,34 As a result of the combined reduction in both κ_e and κ_l, the sample with x = 0.5 achieves the lowest κ_tot, ∼0.70 W m⁻¹ K⁻¹ at 303 K, representing a ∼32.0% decrease compared to the pure Ag₂Se matrix. In comparison with the κ_tot and κ_l of Ag₂Se in the state-of-the-art studies^{13,21,35–38} (Fig. 6d), one of the lowest values is achieved, underscoring the beneficial role of amorphous nano-Si₃N₄ in reducing the κ of Ag₂Se.

To assess the TE performance of the samples, the zT values for all samples are calculated (Fig. 7a). In the temperature range of 303–388 K, the value of zT initially increases and then subsequently declines as the concentration of amorphous Si₃N₄ is increased. The sample with x = 0.5 exhibits the best TE performance, with a zT of 0.95 at 388 K, followed by x = 0.3 and x = 0.7, with zT values of 0.91 and 0.85, which are higher than that of the pure Ag₂Se matrix (∼0.73). To further evaluate the TE performance across the entire temperature range, the zT_avg for all samples within the range of 303 K to 388 K is calculated (Fig. 7b). These results are compared with state-of-the-art studies on the synthesized Ag₂Se, demonstrating that our study is at an intermediate level.

To evaluate the mechanical properties, Vickers hardness tests are conducted on all samples. The tests are performed under a 9.8 N load for 10 s and repeated three times, and the Vickers hardness values are recorded by measuring the diagonal length of the square indentation on the material's surface.

As the amorphous Si₃N₄ content increases, the Vickers hardness values of the samples increase gradually (Fig. 8a). The Vickers hardness of the pure Ag₂Se matrix is ∼0.26 GPa, while the sample with 0.7 wt% Si₃N₄ exhibited a hardness of ∼0.33 GPa, representing a ∼26.9% improvement compared to the Ag₂Se matrix. The increase in Vickers hardness is primarily attributed to the distribution of amorphous Si₃N₄ on the grain boundaries, which inhibits crack propagation,⁴⁰ as shown in Fig. 3c. Fig. 8b shows a gradual increase in compressive strength with increasing amorphous Si₃N₄ content. Moreover, the sample with 0.7 wt% Si₃N₄ exhibits the highest yield strength, reaching 116 MPa. Comparative analysis with state-of-the-art thermoelectric materials indicates a modest advantage in our study (Table 1). These results demonstrate that the incorporation of amorphous Si₃N₄ effectively enhances the mechanical properties of Ag₂Se.

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4. Conclusion

This study presents an economical and efficient approach to synthesizing Ag₂Se powder using a microwave-assisted method and significantly improves the TE properties by incorporating amorphous nano-Si₃N₄. Specifically, the incorporation of amorphous Si₃N₄ not only reduces the κ_l of Ag₂Se, but also enhances the mechanical properties. For the Ag₂Se–0.5 wt% Si₃N₄ sample, a remarkable zT of 0.90 is achieved at 303 K, while the average zT of 0.92 is maintained across 303–388 K. Moreover, the Vickers hardness increased from 0.26 GPa to 0.30 GPa due to the possible pinning effect of crack propagation on the interface. These findings suggest that the incorporation of amorphous nano-Si₃N₄ effectively enhances both the TE and mechanical properties of Ag₂Se, providing a foundation for its application in TE devices. Furthermore, this method offers valuable insights for improving the TE and mechanical properties of other materials, highlighting the significant potential of amorphous nanomaterials in optimizing TE materials.

Conflicts of interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Data availability

All data supporting the findings of this study are available within the article and its ESI.† Additional raw data, including experimental details, characterization results, and computational inputs/outputs, are available from the corresponding author upon reasonable request.

Acknowledgements

The authors acknowledge the funding support of the Hebei Provincial Department of Science and Technology (236Z4403G), the Research Innovation Team Project of Hebei University (150000321008), and the Science Research Project of Hebei Education Department (Grant No. JZX2024008).

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Footnotes

† Electronic supplementary information (ESI) available. See DOI: https://doi.org/10.1039/d5tc01049g

‡ Liedong Zhao and Hailan Zhang contributed equally to this study.

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