Structural stability enables high thermoelectric performance in room temperature Ag2Se

Priyanka Jood *, Raju Chetty and Michihiro Ohta *
Global Zero Emission Research Center, National Institute of Advanced Industrial Science and Technology (AIST), Umezono 1-1-1, Tsukuba, Ibaraki 305-8568, Japan. E-mail:;

Received 6th March 2020 , Accepted 29th April 2020

First published on 28th May 2020

Ag2Se is considered as an attractive candidate for use in room-temperature thermoelectric applications owing to its unique transport properties, such as glass-like thermal conductivity and good electrical conductivity. However, understanding the correlation between composition (Ag/Se ratio), defect structure, and transport properties is an important prerequisite to optimize its figure of merit (ZT). Using in-depth microscopic analysis, this study reveals the coexistence of a metastable and the main orthorhombic crystal structure in stoichiometric Ag2Se. The formation of the metastable structure was found to be detrimental to the transport properties of bulk Ag2Se. We were able to successfully inhibit its formation and stabilize the main orthorhombic structure via small anion (Se and S) excess. The compositions Ag2SeChy (y ≤ 0.01; Ch = Se, S) yielded 40–70% rise in carrier mobility with a value of 2510 cm2 V−1 s−1 at 300 K and extremely low lattice-thermal-conductivity (0.2–0.1 W m−1 K−1 over 300–375 K). This combination of transport properties yielded a room-temperature power factor of 3.2 mW m−1 K−2 and a nearly flat ZT value of ∼1.0 over the 300–375 K temperature range. Additionally, a record-high conversion efficiency (ηmax) of 3.7% was theoretically obtained for single-leg Ag2Se for a small temperature gradient of ∼80 K.


The latest report of the Intergovernmental Panel on Climate Change (IPCC)1 emphasizes the need to limit the temperature rise due to global warming to under 1.5 °C to evade catastrophic environmental hazards, and as of today, the said temperature rise stands at about 1 °C. Thus, there exists an urgent need to inhibit carbon emissions and strengthen energy management and sustainability measures to alleviate the effects of climate change. Thermoelectric devices directly convert waste heat to electrical energy, and therefore, are expected to play an important role in the development of efficient energy-management strategies.2,3 These devices are lightweight, compact, low-maintenance, and possess no moving parts. This affords them a unique advantage over other competing energy-conversion technologies.

Since maximum energy wastage occurs at temperatures below 100 °C (373 K),4,5 efforts need to be made to utilize this waste heat for thermoelectric power generation. Furthermore, room-temperature energy harvesting from ambient heat via use of thermoelectric systems is forecast to play a critical role in the growth of the Internet of Things (IoT) market,6 which is currently limited by the unavailability of non-battery-based and off grid power sources.

The efficiency of thermoelectric devices largely depends on the dimensionless figure of merit (ZT) of a thermoelectric material given by ZT = S2/ρκtotalT, where S, ρ, κtotal, and T denote the Seebeck coefficient, electrical resistivity, thermal conductivity (κtotal = κlat + κel; sum of lattice and electronic thermal conductivities) and absolute temperature, respectively. Thus, an ideal thermoelectric material is one characterized by a high power factor (S2/ρ) and a low κlat value—both of which are governed by inter-related but contradictory fundamental parameters.7 Over the past two decades, innovative approaches, such as phonon-glass electron-crystals (PGECs),8–10 nanostructuring,11–14 panascopic approach,15 band-structure,16–19 and defect structure engineering,20,21 have remarkably improved the ZT value of several high temperature thermoelectric materials, such as PbTe,15,16,18,22 SiGe,12 skutterudites,17,19 half-Heusler compounds,9 colusites,20,23 SnSe,24 SnS,25 Cu2Se[thin space (1/6-em)]14,26etc. However, none of these materials are efficient for room temperature applications since they exhibit high ZT (1.5–2.5) values exclusively at elevated temperatures (above 500 K) with room temperature ZT usually below 1.0.

Despite the progress made in thermoelectric material technology to date, Bi2Te3 alloys remain the only material appropriate for thermoelectric applications at or near room temperature. Although the performances of Bi2Te3 alloys have been strategically improved over the past 60 years, only the p-type ZT has shown drastic improvement with values reaching 1.3–1.7 (ref. 13 and 27) while the n-type ZT still remains below unity at room temperature.7,28,29 Moreover, the scarce availability of tellurium (Te) (0.001 ppm) in the earth's crust30,31 necessitates development of new Te-free thermoelectric materials for use in widespread industrial applications. Recent reports on p-type MgAgSb,30 and p-type SnS0.91Se0.09 (ref. 25) have shown promise for their use at low temperatures with ZT ∼ 0.8 and ∼0.7, respectively at 300 K. The development of a thermoelectric device usually requires both n- and p-type materials which makes the search for a high performing n-type room temperature material only imperative.

Ag2Se—an n-type chalcogenide—is an ideal candidate for use in room-temperature applications owing to its inherently low thermal conductivity κtotal (∼1 W m−1 K−1)32 and narrow band gap (∼0.04–0.2 eV),33,34 which is suggestive of a high S2/ρ value at room temperature.35 Ag2Se undergoes a phase transition from semiconducting orthorhombic to superionic cubic at approximately 407 K where Ag ions become mobile within a rigid Se lattice.36–39 The low-temperature orthorhombic Ag2Se phase demonstrates promising ZT values. However, large discrepancy in reported values (0.3–0.96 in the 300–400 K temperature range)32,40–46 (Fig. 1) and lack of consensus on establishing optimum parameters for attainment of high ZT have prevented bulk Ag2Se from being tested in device configurations.

image file: d0ta02614j-f1.tif
Fig. 1 Thermoelectric figure of merit, ZT values achieved over the 300–400 K temperature range in previous investigations concerning bulk Ag2Se32,40–43,45 along with their respective carrier concentrations (n). ZT value obtained in this study for bulk Ag2Se and that corresponding to n-type Bi2Te3-based alloy,7 p-type MgAgSb,30 and p-type SnS0.91Se0.09 (ref. 25) are also included for comparison.

In the 1960s, Ag2Se was first identified as a potential thermoelectric material with reported ZT ∼ 0.7 at 300 K.32,44 Subsequent efforts were directed towards tuning the carrier concentration of Ag2Se via doping using several elements to enhance its ZT. However, no doped composition demonstrated significant advantage over undoped Ag2Se owing to low dopant solubility in the parent compound.32,44 Four decades later, the thermoelectric potential of Ag2Se was revisited, and a high ZT of approximately unity was reported at room temperature by using excess Se to reduce the carrier concentration (n). However, no information pertaining to the corresponding stoichiometry (Ag/Se ratio) or microstructure changes due to Se excess was investigated.43,46 This high ZT value could not be reproduced in recent studies40–42,45 owing to the lack of knowledge regarding the effects of metal or anion excess on the defect structure of Ag2Se. Furthermore, the low solubility of excess Ag or Se32,44 and the difficulty associated with realizing precise control over stoichiometry,47–49 complicate the correlation between the Ag/Se ratio, n and ZT. For example, a large deviation can be observed in the maximum ZT value at room temperature reported by Alieve et al. (∼1.0),43 Lee et al. (∼0.6 for Ag1.975Se1.025),45 Mi et al. (∼0.84 for Ag2Se1.06),41 and Day et al. (∼0.6 for Ag2.0006Se)40 for nearly similar values of n ∼ 6 × 1018 cm−3 (Fig. 1). Nonetheless, recent reports on high power density(5.42 W m−2 with a 45 K temperature difference) achieved using Ag2Se-based flexible thin films50 and high ZT value (1.2) achieved for Ag2Se thin films developed using pulsed hybrid reactive magnetron sputtering51 demonstrate the scope for commercial utilization of Ag2Se.

This paper reports achievement of a high ZT value of 0.9–1 over the 300–375 K temperature range, thereby demonstrating the competitiveness of n-type bulk Ag2Se as a thermoelectric material with performance comparable and even higher to that of the state-of-the-art low temperature thermoelectric materials, such as n-type Bi2Te3,7 p-type MgAgSb,30 and p-type SnS0.91Se0.09 (ref. 25) (Fig. 1). Most importantly, the proposed study establishes parameters concerning ZT optimization in Ag2Se using correlations between structural changes, carrier transport, and Ag/Se ratio. Finally, a high theoretical efficiency ηmax = 3.7% was observed for a small temperature gradient of 80 K for a single-leg Ag2Se-based device, thereby demonstrating its utility in low-temperature applications.

Experimental section

The full details of all experiments are provided in the ESI.

Several ingots with nominal compositions given by Ag2SeChy (y = 0, 0.005, 0.01, 0.015, 0.02, 0.04, 0.06 and 0.07; Ch = Se and S) and weighing 8 g each were synthesized by mixing appropriate amounts of Ag, Se, and S in carbon-coated fused silica tubes which were then evacuated and subsequently flame-sealed. All mixtures were heated to 1273 K at a rate of 65 K h−1 prior to being held at that temperature for 12 h, and subsequently cooled to 723 K at 11 K h−1. The ingots were then annealed at 723 K for 24 h followed by cooling to room temperature in 15 h. Finally, the ingots were cut into pellets for thermoelectric-property measurement.

Crystal structures of ingots were examined via X-ray diffractometry (XRD; MiniFlex; Rigaku) using Cu Kα radiations over a 2θ range of 20–60°. Microstructures and chemical compositions of ingots were examined using scanning electron microscopy (SEM; 15 kV; Miniscope TM 3030Plus; Hitachi high-Technologies) coupled with energy-dispersive X-ray spectroscopy (EDX; Quantax 70; Bruker). Transmission electron microscopy (TEM), energy-dispersive X-ray spectroscopy (EDX), electron diffraction (ED), and scanning transmission electron microscopy (STEM) investigations were performed at JEOL, Japan, using the JEM-ARM200F atomic resolution analytical electron microscope operated at 200 kV.

Seebeck coefficient and electrical resistivity were measured simultaneously in a He atmosphere using the temperature differential and four-probe methods (ZEM-3; ULVAC-RIKO), respectively, over the 300–375 K temperature range. Relative uncertainties in determination of the Seebeck coefficient and electrical resistivity were estimated to be within 5%. The Hall coefficient (RH) was measured at room temperature using a home-built system under a magnetic field with strength of up to 2.3 T.

Thermal conductivity (κtotal) values were calculated using the expression κtotal = DCpd involving the thermal diffusivity (D), heat capacity (CP), and density (d) of the material. The D values were directly measured, whereas CP values were derived using a standard sample (Pyroceram 9606; Netzsch) by the laser flash method (LFA 457 MicroFlash; Netzsch) in an Ar gas flow (100 ml min−1) over the 300–375 K temperature range. The values of D and CP are shown in Fig. S1 and S2 of the ESI. Density values for samples were determined using the gas pycnometer method (AccuPyc II 1340; Micromeritics). The relative uncertainty in thermal conductivity measurement was estimated to be within 6%. The combined relative uncertainty in all measurements involved in ZT calculation equaled approximately 11%.

The sound velocities in the longitudinal and transverse modes were measured at room temperature using the pulse-echo method employing ultrasonic pulsers/receivers (5077 PR; Olympus), 5- and 15 MHz longitudinal-contact transducers (V110-RM and V113-RM; Olympus), 5 MHz transverse-contact transducer (V156-RM; Olympus), and digitizing oscilloscope (WaveJet300A; Teledyne LeCroy).

Three-dimensional finite-element simulations were performed using COMSOL Multiphysics equipped with a heat-transfer module to investigate power-generation characteristics of a single Ag2SeS0.01 thermoelectric element.

Results and discussion

Correlation of carrier transport with compositional and structural parameters

Typically, Ag2Se is a non-stoichiometric compound in both its low- and high-temperature phase. It is necessary to look at the phase field of the low temperature Ag2Se phase from 400 K down to room temperature.47 The low-temperature phase exists only in a very small range of homogeneity which becomes narrower with decreasing temperature. Grønvold et al.52 have reported that even a small excess (∼1%) of Se in Ag2Se alters the defect chemistry and progression of phase transition. In this study, anion excess was closely monitored, and excess concentrations of Se and S in the samples varied from 0.05% to 7%, with the purpose of investigating the defect structure and tuning the transport properties.

Fig. 2 depicts observed trends concerning room-temperature values of the Hall carrier concentration (n) and carrier mobility (μ) for all nominal compositions Ag2SeChy (y = 0–0.07; Ch = Se, S) considered in this study. The negative sign associated with the Hall (RH,Table S1, ESI) and Seebeck coefficients (S, Fig. 7) for all samples confirms the n-type carrier transport. Anion excess acts as the acceptor in n-type Ag2Se and consequently, a mere 0.05% anion excess causes the value of n to drop considerably from 6.0 × 1018 cm−3 to 3.5 × 1018 cm−3 and thenceforth remain constant irrespective of the amount of excess Se or S owing to attainment of the solubility limit of excess anions (i.e., ≤1%).44 Beyond this point, any additional Se or S will only result in related impurities, as corroborated by X-ray diffraction (XRD) data, which depicts the presence of Se impurity peaks at y ≥ 0.02 (Fig. S3, ESI) with the main phase for all samples demonstrating an orthorhombic structure with P212121 space group. The chemical state and coordination environment of Se contained in stoichiometric silver selenide (Ag2Se) and minute anion excess sample (Ag2Se1.01) were also analysed using Se K-edge X-ray absorption fine structure (XAFS) measurement which includes X-ray absorption near edge structure (XANES) spectra (shown in Fig. S4, ESI). Clearly, Ag2Se1.01 has the same chemical state and coordination environment of Se as Ag2Se, and spectra related to Se metal are not seen in Ag2Se1.01. This confirms that Se related impurities do not exist in samples for y = 0.01 and that extra anions stay in the lattice.

image file: d0ta02614j-f2.tif
Fig. 2 Trends concerning carrier concentration (n) and carrier mobility (μ) for Ag2SeChy (y = 0–0.07; Ch = Se, S) at room temperature. The lines connecting the symbols are a guide to the eye.

As observed in Fig. 2, values of μ demonstrate an unusual trend with increasing excess-anion concentration. The μ for a stoichiometric sample (y = 0) equals 1460 cm2 V−1 s−1, and small Se and S excesses of y ≤ 1% each cause this value to increase by approximately 70% (to ∼2510 cm2 V−1 s−1) and 40% (to ∼2030 cm2 V−1 s−1), respectively. Any further increase in Se or S concentration reduces μ to a value similar to that corresponding to y = 0. It must be noted that μ follows the same trend in cases of increase in both Se and S excess. Therefore, the observed trend must be governed by the same underlying mechanism. Additionally, the carrier mobility achieved in this case exceeds that observed in Bi2Te3 alloys28 by nearly five times.

To understand the reason underlying the increase in μ values due to small anion excess in Ag2Se samples, the defect chemistry in the system was investigated via an in-depth microscopic analysis. Fig. 3(a) and (b) depict scanning electron microscopy (SEM) images of Ag2Se and Ag2SeS0.01, respectively. As can be seen, triangular precipitates which are Ag phase (Fig. S5, ESI), and measuring 2–3 μm in size are homogeneously dispersed throughout the Ag2Se sample, which suggests slight Ag deficiency in the Ag2Se matrix. This is expected, since low-temperature Ag2Se demonstrates limited homogeneity.47,52 Furthermore, some Ag diffusion occurs at room temperature which could promote Ag precipitation.38 Therefore, the low μ value of the stoichiometric sample can be attributed to the impurity scattering.46 On the other hand, the sample with small anion excess (Ag2SeS0.01) demonstrates no sign of precipitation or other impurity phases. This is in agreement with the findings of Grønvold et al.52 They demonstrated, via specific-heat measurements, that 1% anion excess prevents Ag precipitation, thereby altering the progression of phase transition from orthorhombic to cubic phases. This indicates that introduction of small concentration of excess anions in the system might inhibit cationic diffusion to some extent. For cases involving larger amounts of excess anions (≥2%), SEM images (Fig. S6, ESI) depict occurrence of Se precipitation, thereby corroborating XRD data (Fig. S3, ESI). In such cases, excess Se exudes out of the ingot, thereby creating large pores around its edges (Fig. S7, ESI). Therefore, larger values of μ in samples containing small amounts of excess anions (y ≤ 0.01) can be attributed partially to the lack of Ag/Se impurities implying reduced eventuality of carrier scattering across impurity interfaces.

image file: d0ta02614j-f3.tif
Fig. 3 Scanning electron microscopy (SEM) results for fractured and polished areas of (a) Ag2Se and (b) Ag2SeS0.01 along with transmission electron microscopy (TEM) images of (c) Ag2Se and (d) Ag2SeS0.01 along the [010] zone axis with respective electron diffraction (ED) patterns as the inset.

Fig. 3(c) and (d) illustrate transmission electron microscopy (TEM) images and electron diffraction (ED) patterns along the [010] zone axis of Ag2Se and Ag2SeS0.01. As can be seen, high-contrast (dark) defect planes along the c-axis (Fig. 3(c)) indicate atomic arrangements different from those corresponding to the main orthorhombic Ag2Se structure, whereas no such defects are observed in the Ag2SeS0.01 sample (Fig. 3(d)). Streaking and diffused spots observed in the ED pattern for Ag2Se (inset to Fig. 3(c)) not only support the above mentioned statement but also suggest the occurrence of slow Ag diffusion even at room temperature.53 However, the ED pattern for Ag2SeS0.01 (inset to Fig. 3(d)) shows sharp spots, thereby confirming the existence of a relatively flawless structure.

A closer look at the Ag2Se atomic structure along the [010] direction—obtained using high-angle annular dark-field scanning transmission electron microscopy (HAADF-STEM), as depicted in Fig. 4(a) and (b), confirms the coexistence of a metastable structure (dark regions) and the main orthorhombic structure along the c-axis. Results obtained via application of the fast Fourier transform (FFT) to the orthorhombic and metastable structural regions are depicted in Fig. 4(c) and (d), respectively. Additionally, corresponding overlap and simulated patterns are depicted in Fig. 4(e) and (f), respectively, for comparison. As observed, the overlap pattern depicts spots corresponding to the orthorhombic structure along the [010] direction (red) along with additional spots for the metastable structure (green), which shares the c-plane (yellow) with the orthorhombic structure. Different crystal-structure modifications, such as tetragonal,54,55 cubic,56 triclinic,57,58 monoclinic,59,60 and the largely accepted orthorhombic,51,61,62 have been reported in the past for low-temperature Ag2Se thin films. In certain cases, more than two structural modifications have co-existed.59,63 The reason behind such a wide array of crystal structures associated with Ag2Se thin films is the difference in sample-manufacturing techniques (difficulties encountered in controlling Ag/Se ratio) and various methods of studying them. It is clear from the example of thin films, even minute stoichiometric changes in Ag2Se could trigger polymorphic transformations similar to those in other compounds, such as Cu2Se,63 Cu2Te64 and AgCuSe,63 of the same class. Low-temperature polymorphic transformations, although common in Ag2Se thin films, have seldom been reported for bulk Ag2Se. Only one report53 shows two semiconductor modifications, pseudo-orthorhombic which changes into monoclinic with small heat treatment. The FFT of our metastable structure matches perfectly with the monoclinic, pseudo-tetragonal structure reported by Günter and Keusch59 for one of their Ag2Se thin-film configurations: pseudo-tetragonal unit cell with the monoclinic space group P2(P112), a = b = 0.706 nm, c = 0.498 nm, β = 90°, Z = 4 with Se in the face-centered position. Furthermore, the number of Ag atoms in the metastable structure reported in this paper appears to be less compared to that in the orthorhombic structure. This can be seen from darker regions (less bright spots representing Ag) depicted in Fig. 4(a) and (b). EDX results, too, confirm the metastable structure to be slightly Ag deficient (Fig. S8, ESI). Therefore, the metastable structure is still silver selenide but possibly with Ag2−zSe composition. This means that the sample consisting of the metastable structure (i.e. nominally stoichiometric Ag2Se) is Ag deficient, which is also supported by Ag precipitation observed in this sample. Although Ag2Se becomes an ionic conductor with liquid-like ionic conductivity only above 407 K, the literature shows that even low temperature Ag2Se undergoes ionic diffusion in the form of cationic Frenkel disorder where Ag activity is through migration of ionized vacancies in the Ag sublattice and of interstitial Ag ions.38,65 However, this ionic activity is not large enough to make Ag2Se superionic at room temperature. Furthermore, it is also reported that in the proximity of the stoichiometric composition the concentration of the ionic defects (i.e. Ag interstitials and Ag vacancies) changes considerably with even a minor change in stoichiometry.38 It can be implied that the Ag diffusion in Ag2Se makes the orthorhombic lattice unstable which then has to compensate in energy by inserting a metastable structure (monoclinic) to attain a system in equilibrium. Therefore, the formation of the metastable structure is most likely initiated by the movement of Ag atoms from one site to another and followed by all the atoms shifting to the next stable column, as shown schematically in Fig. 5.

image file: d0ta02614j-f4.tif
Fig. 4 High-angle annular dark-field scanning transmission electron microscopy (HAADF-STEM) images of Ag2Se along the [010] axis in (a) medium and (b) high resolutions with the structural model of the orthorhombic region superimposed on the high-resolution image in (b)—green and grey spheres represent Se and Ag atoms, respectively. Fast Fourier transform (FFT) results concerning orthorhombic (O) and metastable (M) regions are depicted in (c) and (d), respectively. Overlapping FFT results of two structures are depicted in (e) with red and green spots denoting orthorhombic and metastable structures, respectively, along the [010] direction and sharing the c-plane (yellow). The simulated diffraction pattern of orthorhombic Ag2Se along the [010] axis is depicted in (f).

image file: d0ta02614j-f5.tif
Fig. 5 Schematic describing the possible transition from the orthorhombic structure (solid ovals) to the metastable structure (dashed ovals) due to the activity of Ag atoms (grey spheres) from one site to another in stoichiometric Ag2Se.

The sample with minute anion excess—Ag2SeS0.01—is clear of any metastable structure formation. However, dark spherical regions can be observed throughout the sample structure, as depicted in the HAADF-STEM image along the [010] zone axis (Fig. 6(a)). These dark regions resemble voids, and can be similarly observed along the [011] zone axis (Fig. 6(b)). FFT results concerning the main matrix (inset to Fig. 6(b)) confirm the existence of only the orthorhombic structure. These voids, measuring approximately 2 nm in diameter and placed 15 nm apart (on average), are thermally stable and remain intact on heating until the occurrence of phase transition at ∼407 K, beyond which point the crystalline structure should transform to the cubic form. The STEM image (Fig. 6(d)) captured at 405 K (just before the phase transition) confirms the above statement.

image file: d0ta02614j-f6.tif
Fig. 6 HAADF-STEM images of Ag2SeS0.01 along (a) [010] and (b) [011] zone axes along with corresponding FFT in the inset; (c) high-resolution HAADF-STEM image with voids indicated by white arrows along the [011] zone axis; (d) HAADF-STEM image captured at 405 K along the [011] zone axis.

The transformation from one crystalline structure to another or coexistence of the metastable and main structures (as in this case) usually occurs owing to similarities between the two crystal structures and their respective densities.63 One strategy to stabilize a single-crystal structure involves using partial cation–cation or anion–anion exchange to alter the nature of atomic bonds and cation mobility within the main lattice.63,66,67 Application of high pressure68 and reduction in crystal size69 have also been reported to tune polymorphic transitions within such systems. In the present case, minute anion excess resulted in stabilization of the orthorhombic structure along with void generation owing to redistribution of Ag atoms and vacancies. High μ values observed for samples with minute anion excess (Ag2SeChy (y ≤ 0.01; Ch = Se, S)) (Fig. 2) can, therefore, be easily correlated with the lack of a metastable structure as well as Ag or Se impurities, both of which are likely a consequence of restricted cationic diffusion. The voids cast no negative impact on carrier transport. Although the microscopy study was not performed on the Se excess samples, we believe that minute anion excess (≤1%), whether it is Se or S would provide the same results in terms of limiting the cationic diffusion and related defects (and therefore, non-existence of metastable structure), which is confirmed by the similarity in carrier concentration and mobility trends between Ag2SeS0.01 and Ag2Se1.01 samples. At this point, it is difficult to state whether samples with higher excess-anion concentrations demonstrate metastable structure formation because TEM and STEM analysis was not performed on them. Finally, as this paper was being reviewed, temperature dependent structural variations in Ag2Se and Ag2SeS0.01 were reported.70 The metastable structure formed alongside the main orthorhombic structure in Ag2Se was found to exist from room temperature until phase transition to the cubic phase around 407 K. However, no metastable structure was formed in the Ag2SeS0.01 sample, proving that minute anion excess is capable of stabilizing the orthorhombic structure throughout the temperature range of interest (300–400 K).

Thermoelectric properties

Fig. 7 depicts trends concerning the temperature dependence of electrical resistivity (ρ) and Seebeck coefficient (S) in samples containing excess Se (Ag2Se1+y (y = 0–0.06)) and S (Ag2SeSy (y = 0–0.02)) over the 300–375 K temperature range. As can be observed, values of ρ (Fig. 7(a) and (b)) and S (Fig. 7(c) and (d)) of the stoichiometric sample decrease with temperature rise, thereby indicating typical semiconductor behavior in agreement with the extant literature.40,41,45 Addition of a minute amount of Se (y = 0.005 and 0.01; Fig. 6(a)) or S (y = 0.01; Fig. 6(b)) results in a nearly temperature-independent trend in ρ values. This clearly points to a difference in scattering mechanisms between the stoichiometric sample and the samples with minute anion excess. Further anion addition (y ≥ 0.02) increases the temperature dependency of ρ, revealing a similar trend to the stoichiometric sample.
image file: d0ta02614j-f7.tif
Fig. 7 Temperature dependence of the (a and b) electrical resistivity (ρ), (c and d) Seebeck coefficient (S), and (e and f) power factor (S2/ρ) for Ag2Se1+y (y = 0–0.06) and Ag2SeSy (y = 0–0.02) samples, respectively. The straight lines connecting the symbols in all the plots are a guide to the eye.

The energy band gap (Eg) can be roughly estimated as the slope of ln[thin space (1/6-em)]ρ versus 1/2kBT, where kB denotes the Boltzmann constant.41,62 As observed, estimated values of Eg in the range of 0.06–0.20 eV (as depicted alongside ρ plots in Fig. 7(a) and (b)) vary with stoichiometry. This large variation is consistent with that reported in the extant literature,33,34 however the reason behind it was never fully explored in the past. Changes in the microstructure, defects and dislocations, and stoichiometry were said to account for the different Eg values observed by different authors.62,71 In this study, the smallest value of Eg (0.06 eV) was observed in samples containing small amounts of excess Se and S (y ≤ 0.01), whereas the highest Eg value (0.20 eV) was observed for the stoichiometric sample. Since a stable orthorhombic structure (without metastable-structure formation) yields a three times smaller value of Eg compared to the sample with the metastable structure, it implies that the band gap pertaining to the metastable structure significantly exceeds that corresponding to the orthorhombic structure. This difference in band gaps can result in a large offset between the corresponding conduction bands causing strong electron scattering, as observed in the case of stoichiometric Ag2Se. The higher anion excess samples (y ≥ 0.02) exhibit Eg values (0.08–0.10 eV) higher than the minute anion excess samples (0.06 eV) but smaller than the stoichiometric one (0.20 eV). Although these samples (y ≥ 0.02) were not investigated using TEM and STEM, their carrier mobility, temperature dependence of ρ, and Eg being similar to that of the stoichiometric sample suggests the presence of a metastable structure to some extent. Additionally, their transport properties are likely influenced by Se based impurities as well.

Owing to counter balancing of the low n and high μ values in samples containing small amounts of excess Se (0.005 ≤ y ≤ 0.01), the value of ρ remains identical to that corresponding to stoichiometric Ag2Se (∼7 μΩ m) at room temperature and demonstrates a slight reduction (to ∼6 μΩ m) as the temperature increases to 375 K (Fig. 7(a)). On the other hand, stoichiometric Ag2Se demonstrates a greater reduction in ρ to ∼4 μΩ m at 375 K. Samples containing higher amounts of excess Se (y ≥ 0.02) demonstrate 30–90% higher values of ρ at room temperature compared to samples with y ≤ 0.01 owing to the low values of n and μ. For instance, y = 0.04 has ρ ∼ 13 μΩ m at room temperature. Samples with S addition demonstrate a trend similar to that observed for samples containing excess Se, albeit with slightly higher resistivity values (Fig. 7(b)). For example, addition of 1% S demonstrates a higher value of ρ (∼9 μΩ m) at room temperature compared to 1% excess Se (∼7 μΩ m).

Values of the Seebeck coefficient (S) for all excess-anion samples demonstrate a temperature-independent trend (Fig. 7(c) and (d)) with values of the order of −140 to −170 μV K−1 at 300 K, which are higher compared to that observed for stoichiometric Ag2Se (∼−130 μV K−1 at 300 K) owing to the lower values of n for the former. The value of S for the stoichiometric sample demonstrates a sharp reduction from ∼−130 μV K−1 at 300 K to ∼−90 μV K−1 at 375 K. Although the value of n is similar for all excess-anion samples, samples with y ≤ 0.01 demonstrate slightly lower values of S compared to those with y ≥ 0.02. This could be attributed to differences in the scattering mechanism caused by impurity precipitation and generation of metastable structural interfaces in the latter.

Fig. 7(e) and (f) depict the temperature dependence of the power factor (S2/ρ) for samples containing excess Se (Ag2Se1+y (y = 0–0.06)) and S (Ag2SeSy (y = 0–0.02)), respectively, over the 300–375 K temperature range. With minute Se excess (y = 0.01), the value of S was observed to increase while that of ρ was maintained low. This results in a very high value of S2/ρ (∼3.2 mW m−1 K−2) across the entire temperature range considered. This corresponds to a 45% improvement over stoichiometric Ag2Se (S2/ρ ∼ 2.2 mW m−1 K−2 at 300 K and ∼2.0 mW m−1 K−2 at 375 K). Likewise, samples containing excess S (y = 0.01) also demonstrated higher values of S2/ρ (∼2.4 mW m−1 K−2 at 300 K and ∼2.6 mW m−1 K−2 at 375 K) compared to the stoichiometric sample. However, the observed increase in this case is comparatively smaller owing to higher ρ values. S2/ρ values for Ag2Se observed in this study at room temperature are, to the best of the authors' knowledge, the highest ever reported for Ag2Se and only surpassed by Ferhat and Nagao's46 Ag2Se (S2/ρ ∼ 3.5 mW m−1 K−2) owing to its remarkably high μ = 11[thin space (1/6-em)]610 cm2 V−1 s−1. Furthermore, these S2/ρ values are comparable, and in some cases, even exceed those reported at room temperature for conventional Bi2Te3 (ref. 28) alloys and other high-performance thermoelectric materials, such as PbTe,22 SiGe,72 MgAgSb,30 and half-Heusler compounds.9 It was experimentally determined32 that p-type doping is scarcely possible in Ag2Se primarily because of very low solubility of foreign dopants. In this regard, the most accessible approach to improve the S2/ρ is to focus on optimizing carrier mobility. Although high mobility in Ag2Se is mainly due to the low effective mass of electrons (0.1–0.3 eV),34 however as we show here, μ (and S2/ρ) can be further improved by targeting the metastability.

Fig. 8(a) and (b) depict temperature dependencies of the total (κtotal) and lattice (κlat) thermal conductivities of the Ag2Se1+y (y = 0–0.06) and Ag2SeSy (y = 0–0.02) samples, respectively. As can be seen, the κtotal value for the stoichiometric sample increases from ∼1.2 W m−1 K−1 at 300 K to ∼2.0 W m−1 K−1 at 375 K. Samples with excess anions—both Se and S— regardless of the concentration, demonstrate only a slight increase in κtotal values with temperature from ∼1.0 W m−1 K−1 at 300 K to ∼1.2 W m−1 K−1 375 K, on average. The κlat value was obtained by subtracting that of the electronic component (κel) from κtotal, and κel was calculated using the relationship κel = LT/ρ, where L denotes the Lorenz number calculated using the single parabolic band model (SPB) with reasonable approximation.73 Consistent with the extant literature,40 all L values lie within 10% of 1.8 × 10−8 V2 K−2 (Fig. S9, ESI). Major reduction in κtotal value observed upon addition of Se or S is attributed to a decrease in κel (Fig. S10, ESI). The lowest κtotal values were obtained for samples with large anion excess (y ≥ 0.02) owing to their low values of n and μ. The value of κel constitutes about 50–90% of that of κtotal for all samples, especially as the temperature rises to 375 K; additionally, the increasing trend of κtotal can be attributed to κel, since κlat undergoes a slight decrease with reduction in temperature. The κtotal of Ag2Se is clearly more sensitive to changes in the carrier spectrum compared to the phonon spectrum.43 This makes it even more critical to tune the defect structure of Ag2Se that governs carrier transport to not only enhance S2/ρ but also reduce κtotal.

image file: d0ta02614j-f8.tif
Fig. 8 Temperature dependence of total and lattice thermal conductivities (κtotal and κlat, respectively) for (a) Ag2Se1+y (y = 0–0.06) and (b) Ag2SeSy (y = 0–0.02); (c) trend concerning μ/κlat for all compositions Ag2SeChy (y = 0–0.07; Ch = Se, S) along with calculated phonon mean free path (l). The lines connecting the symbols in all the plots of (a) and (b) are a guide to the eye.

Values of κlat for all compositions (Fig. 8(a) and (b)) lie below 0.5 W m−1 K−1, which is significantly lower compared to that for most state-of-the-art thermoelectric materials,22,28,30,74 thereby demonstrating a typical characteristic of disordered crystals.75,76 Another interesting point is the absence of any bipolar contribution to thermal conductivity (usually identified by an upturn in κlat) in the measured temperature range despite such a low band gap. The effective mass (0.75 me) of holes (minority carriers) is much larger than the electron effective mass (0.1–0.3 eV),34 which implies a considerably lower hole mobility than electron mobility and therefore, mostly electrons contribute to the overall conduction. The κlat value for stoichiometric Ag2Se reduces from approximately 0.5 W m−1 K−1 at 300 K to 0.2 W m−1 K−1 at 375 K. Strangely, minute anion excess (y = 0.01) results in the smallest κlat value (0.2 W m−1 K−1 at 300 K) among all samples, and at 375 K, this value further reduces to approximately 0.1 W m−1 K−1, despite a relatively flawless structure and absence of Ag or Se impurities. In Ag2Se, the mean free path of electrons (λ) is generally much larger than the phonon mean free path (for instance, λ = 57 nm for n = 5.85× 1022 cm−3 at 300 K[thin space (1/6-em)]48), thereby facilitating individual manipulation of both transports. As predicted before and confirmed via findings in this study (Fig. 8(c)), the value of μ/κlat can be increased by controlling the nature of defects. The μ/κlat value for samples containing minute anion excess (y ≤ 0.01) equals more than twice that for all other compositions. This is because electron transport in y ≤ 0.01 samples is facilitated whilst maintaining low thermal conductivity. To further examine the reason behind the high values of μ/κlat in samples with small anion excess, ultrasonic pulse-echo measurements were performed, and the longitudinal (vl) and transverse (vt) sound velocities for the stoichiometric (Ag2Se), minute anion excess (Ag2SeS0.01), and large anion excess (Ag2SeS0.015, Ag2SeS0.02) samples were evaluated. The average sound velocity (va) was subsequently calculated using the expression

image file: d0ta02614j-t1.tif(1)

Room temperature values of vl, vt, and va are listed in Table 1. The value of κlat is a function of the volumetric heat capacity at constant pressure (Cv), average sound velocity (va), and mean free path of phonon (l), and can be expressed as κlat = 1/3Cvvalp. In this study, Cv was considered equal to Cp. Estimated values of l are depicted in the inset plot in Fig. 8(c). The longitudinal speed of sound of our Ag2Se (vl = 3270 ms−1) was observed to be comparable to that in Cu2Se75 (vl = 3350 ms−1), whereas the corresponding transverse speed of sound (vt = 1250 ms−1) was found to be lower compared to that in Cu2Se (vt = 1870 ms−1). Both the Ag2Se and Cu2Se systems become superionic above 400 K. The much lower vt in Ag2Se indicates significant softening of shear modes76 owing to the higher levels of disorderliness caused by cation diffusion compared to other compounds of the same class, such as Cu2Se or Cu7PSe6.75 Both vl and vt (3360 ms−1 and 1390 ms−1, respectively for Ag2SeS0.01) slightly increase with increase in anion concentration above the stoichiometric composition.

Table 1 Values of room-temperature lattice parameters—a, b, and c, average sound velocity (va), Gruneisen parameter (γ), and Young's modulus (E) for Ag2SeSy (y = 0, 0.01, 0.02)
Samples Ag2Se Ag2SeS0.01 Ag2SeS0.02
a (Å) 4.3311(7) 4.3284(9) 4.3295(7)
b (Å) 7.0650(3) 7.0610(3) 7.0630(4)
c (Å) 7.7670(2) 7.7650(3) 7.7650(2)
v l (m s−1) 3270 3360 3320
v t (m s−1) 1250 1390 1280
v a (m s−1) 1420 1570 1450
l p (nm) 0.44 0.23 0.48
Γ 2.8 2.6 2.8
E (GPa) 36 44 38

Values of the Young's modulus (E), which is indicative of the strength of a material's atomic bonds, and Gruneisen parameter (γ), which indicates the degree of anharmonicity in the bonding arrangement, were also evaluated (as listed in Table 1) using the following expressions.

image file: d0ta02614j-t2.tif(2)
image file: d0ta02614j-t3.tif(3)

In the above expressions, d denotes material density and vp denotes the Poisson ratio given by

image file: d0ta02614j-t4.tif(4)

As observed in Table 1, the Ag2SeS0.01 sample demonstrates highest values of vl (3360 ms−1), vt (1390 ms−1), and E (44 GPa) among all samples considered. This implies existence of stronger interatomic bonding within the Ag2SeS0.01 structure owing to the higher structural order (absence of a coexisting metastable structure). Furthermore, Ag2SeS0.01 also exhibits a slightly lower value of γ (2.6) compared to other compositions (2.8), thereby suggesting smaller Ag–Se bond anharmonicity. These results corroborate the idea that samples with minute anion excess (y ≤ 0.01) reduce disorder in the Ag2Se structure by inhibiting cationic diffusion.52 The value of γ for Ag2Se, in general, far exceeds that for other conventional thermoelectric materials, such as PbTe (∼1.45),77 which is one of the reasons for its glass-like κlat. Despite the lower anharmonicity and disorderliness, the Ag2SeS0.01 sample demonstrates the smallest l (inset plot in Fig. 8(c)). The value of l for stoichiometric Ag2Se equals ∼0.5 nm, which reduces to ∼0.2 nm upon addition of excess anions (up to y = 0.01) and subsequently jumps to ∼0.5 nm for larger concentrations of excess anions (y = 0.015, 0.02). The l for Ag2Se (with the metastable structure) being larger than that for Ag2SeS0.01 (no metastable structure), suggests that the interfaces between orthorhombic and metastable structure in the former do not provide significant phonon scattering. Lattice parameter values calculated exclusively using the orthorhombic structure with space group P212121 (Table 1) are slightly smaller for the y = 0.01 sample (a = 4.3284(9) Å, b = 7.0610(3) Å, and c = 7.7650(3) Å) compared to those corresponding to the stoichiometric sample (a = 4.3311(7) Å, b = 7.0650(3) Å, and c = 7.7670(2) Å). This indicates that the lower value of l in samples with minute anion excess arises from possible changes in crystal chemistry,78 including reduction in interatomic distances and/or increase in the number of atoms within the lattice owing to the absence of a metastable structure. This additionally supports the authors' previous hypothesis of cation deficiency in metastable structures. The phonon mean free path in silver selenide is of the order of interatomic distances,79,80 therefore more Ag atoms occupying lattice sites would surely enhance the phonon scattering. The low lattice thermal conductivity (0.3–0.6 W m−1 K−1) in Cu2−δSe,81 which belong to the same class of superionic compounds as Ag2Se, comes from low energy multi-Einstein optic modes which originate from the slightly localized motions of confined copper ions. Large differences in the crystal and physical properties of Cu2−δSe exist depending on the amount of Cu deficiencies. A similar mechanism and composition dependence of thermal conductivity can be expected for Ag2Se as well. An in-depth modelling study along with neutron scattering measurements would be beneficial to understand the phonon transport in silver selenide systems. Voids observed in the y = 0.01 sample may also play a role in phonon scattering. In summary, a high value of μ/κlat is realized in Ag2Se samples with minute anion excess (≤1%) owing to the existence of stronger interatomic bonding and lower structural disorder, which enhances carrier transport, along with preferable changes in the overall crystal geometry, thereby promoting phonon scattering.

Figure of merit (ZT) and theoretical conversion efficiency

As discussed earlier, samples containing small amounts of excess anions (y ≤ 0.01) demonstrate a very high value of S2/ρ whilst reducing the κlat value in Ag2SeChy (Ch = Se, S) system. This ideal combination of electrical and thermal transport properties yields a high value of ZT—of the order of 0.9–1.0 for samples containing excess Se and 0.8–0.9 for those containing S in the 300–375 K temperature range (Fig. 9(a) and b). It should be noted that flat high ZT achieved here is interesting for module development and for practical applications because thermoelectric module efficiency depends on the average ZT value over the entire operating-temperature range. ZT values realized in this study at room temperature exceed those of state-of-the-art n-type Bi2Te3[thin space (1/6-em)]33—the only commercially available thermoelectric material, at present, for use in room-temperature applications.
image file: d0ta02614j-f9.tif
Fig. 9 Temperature dependence of thermoelectric figure of merit (ZT) for (a) Ag2Se1+y (y = 0–0.06) and (b) Ag2SeSy (y = 0–0.02); (c) comparison between maximum power-generation efficiencies of single-leg of our n-type Ag2Se (simulated), our n-type Ag2SeS0.01 (simulated), p-type MgAgSb30 (experimental), and p-type SnS0.91Se0.09[thin space (1/6-em)]25 (simulated) as a function of temperature gradient. The experimental module efficiency of Bi–Te-based module (manufactured by KELK Ltd82) is included for comparison. The straight lines connecting the symbols in all the plots of (a) and (b) are a guide to the eye.

We determined the theoretical efficiency (η) of the Ag2Se single-leg developed in this study via three-dimensional finite-element simulations performed using COMSOL Multiphysics equipped with a heat-transfer module (Fig. S11, ESI). As depicted in Fig. 9(c), a maximum efficiency ηmax of 3.7% was realized for hot- and cold-side temperatures (Th and Tc, respectively) of 378 K and 297 K (ΔT ∼ 80 K), respectively, and this value of ηmax is 60% higher than that obtained for Ag2Se (2.3%) and also exceeds that of the commercial Bi–Te module.82 Additionally, the n-type Ag2SeS0.01 composition considered in this study demonstrates a simulated ηmax value comparable to that of emerging materials, such as p-type MgAgSb (experimental ηmax of ∼3.2%)30,83 and p-type SnS0.91Se0.09 (simulated ηmax ∼ 3.4%)25 for ΔT ∼ 80 K.

Finally, an attempt was made in this study to experimentally investigate power-generating characteristics (using a mini-PEM84) of a single-leg Ag2SeS0.01 with Au electrodes. As observed, for Th = 378 K and Tc = 297 K, a maximum output power (Pmax) of ∼3 mW was obtained. This is far lower compared to the simulated value of ∼9 mW owing to the use of an unoptimized configuration, as can be inferred from spikes observed in the value of the contact resistance across interfaces between the Au electrodes and Ag2SeS0.01 element (Fig. S12, ESI). An active study concerning the identification and utilization of an ideal diffusion barrier for Ag2SeS0.01 is currently underway to facilitate realization of the full potential of the Ag2Se system with regard to thermoelectric module development.


Ag2Se, with its remarkable thermoelectric properties, can be considered an ideal candidate for use in room-temperature energy-conversion and waste-heat-recovery applications. The only drawback associated with its widespread utilization is the inconsistency of its figure of merit ZT due to the unoptimized crystal structure and chemical composition. The proposed study presents an effective strategy to achieve high ZT values by (1) revealing structural transformations in bulk stoichiometric Ag2Se at room temperature and (2) stabilizing the main orthorhombic structure, via addition of minute anion excess. Through this study we can conclude that to achieve good thermoelectric performance in Ag2Se systems, it is necessary to focus on improving the carrier mobility along with tuning the carrier concentration. One way to achieve this is by avoiding the formation of metastable structures and subsequently Ag or Se based impurities. A significant enhancement (up to 70%) in carrier mobility was realized in this study for Ag2SeChy (y ≤ 0.01, Ch = Se, S) compositions along with very low lattice thermal conductivity values (0.2–0.1 W m−1 K−1 over the 300–375 K temperature range) owing to the optimization of the defect structure. Thus, impressive ZT values (0.9–1.0) over the 300–375 K temperature range were achieved. A record high conversion efficiency of approximately 3.7% was theoretically estimated for a single-leg Ag2SeS0.01 composition for a very low operating temperature difference of ∼80 K, thereby highlighting the promise the proposed system holds. Future directions and challenges include detailed investigation of the proposed system's mechanical properties and at the device level, optimization of the diffusion barrier for reducing contact resistance between Ag2Se and electrodes.

Conflicts of interest

The authors declare no competing financial interest. M. O. is cofounder and technical advisor of Mottainai Energy Co., Ltd. Mottainai Energy Co., Ltd. does not fund the work or participate in its execution.


The authors express thanks to Mr Ichiro Okumura (AIST) for his assistance in preparing the Ag2Se-based ingots and thermoelectric property measurements, and Mr Nayuki Keiichiro (JEOL) for TEM, STEM and discussions on the crystal structure. The material development and characterization were supported by Development of Thermal Management Materials and Technology funded by the New Energy and Industrial Technology Development Organization (NEDO) and The Thermal & Electric Energy Technology Foundation (TEET). The simulation of power generating characteristics was supported by the International Joint Research Program for Innovative Energy Technology funded by the Ministry of Economy, Trade and Industry (METI).


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Electronic supplementary information (ESI) available: Experimental details, thermal diffusivity, heat capacity, density, Hall coefficient, room temperature XRD, X-ray absorption fine structure (XAFS) measurement, Lorenz number, electronic thermal conductivity, SEM of ingot surfaces, and EDX of the metastable structure. Simulated thermoelectric conversion parameters (using COMSOL) and electrical output power measurements of single leg Ag2SeS0.01. See DOI: 10.1039/d0ta02614j

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