Introduction

With the rapid development of portable electronics, a powerful, flexible, and durative power supply is urgently demanded. A direct generation of electricity using body or environmental heat by thermoelectricity provides a sustainable solution to this demand, in addition to the technical merits of safety, silence, reliability, and operation under all weather conditions1,2.

A high power output is the primary criteria for practical thermoelectric generators, which is determined by the thermoelectric power factor (PF = S2/ρ) with S and ρ being the Seebeck coefficient and resistivity, respectively. Many successful strategies offered guidelines for advancing thermoelectrics power factor3,4,5,6,7,8,9. These strategies, however, generally built upon the periodicity of atomic arrangements, which are usually limited in inorganic components that are typically rigid. This leaves the key challenge for wearable demands to make powerful thermoelectrics flexible since known inherently flexible organic and their composites are much inferior in performance10,11,12,13. Reported works on flexible thermoelectrics exhibit limited flexibility, with no safe bending times >1000 so far14,15,16,17,18.

Many studies19,20,21,22 on making thermoelectrics flexible were motivated by plasticity/ductility, which indeed ensured a large flexibility of no breakage. However, this may unsecure the recoverability of thermoelectric performance, since any irreversible atomic reconstructions due to plastic deformations lead to unrecoverable electronic and thermal transport properties.

Mechanically, elastic bendability offers a solution for fully recoverable flexible thermoelectrics, because it not only ensures safely permitted strains free of plasticity and breakages but also enables the reservation of initial functionalities after bendings. The maximum elastic strain (εEmax) is then the key material property measuring both recoverable bendability and recoverable thermoelectric performance, an enhancement of which is fundamentally needed for advancing flexible inorganic thermoelectric generators.

Intrinsic εEmax of a material is proportional to the Poisson’s ratio (v) via εEmax∝1/(1-v)23, since a large v enables a large corresponding transverse stress to help energy consumption under a longitudinal stress. This suggests a guidance for the selection of thermoelectric materials having a large v for flexible applications. Extrinsic factors further enabling a εEmax-enhancement can be often realized by refining grains and creating dislocations24, indicating the commonly used strategy in metals25,26,27 and ceramics28,29 of plastic processing as an effective pathway for advancing flexible inorganic thermoelectrics.

Results and discussion

These motive the current work to focus on Ag2Se foils for robust flexible thermoelectric applications, not only intrinsically due to its largest v among inorganic thermoelectrics (Fig. S1 and Table S1), but also because of its plasticity allowing plastic processing for extrinsic dislocation creation and grain refinement. Surely, the highest thermoelectric power factor secured in Ag2Se30 among silver chalcogenides31,32 guarantees its highest power output. Existing works on flexible Ag2Se-based thermoelectric generators largely comes from the involvement of flexible organic components as either substrates2,14,15,18 or additions19,33.

A multi-pass hot rolling technique is utilized in this work, leading to an impressive density of dislocations reaching 1014 m−2 with a Burger’s vector along the [001] direction as well as refinement of the grains from hundreds of micrometers down to just twenty micrometers, as evidenced by the electron backscatter diffraction (EBSD) observations34,35 (Figs. 1, S2). Both of them significantly enhance the elasticity of the obtained Ag2Se foils. Eventually, the multi-pass hot-rolled device of 36 μm thick, a typical thickness for flexible thermoelectric generators14,15,16,17,36, survives at least 1,000,000-time elastic bending at a tiny bending radius of ~3 mm, without observable degradations in the high power output reserved from bulks. Both the output power density and the bendability are significantly superior to that of reported flexible thermoelectric devices of polycrystals, allowing a full applicability of a human body.

Fig. 1: Fabrication, mechanical properties and microstructures.
figure 1

Schematic of hot-rolling process (a) for Ag2Se foils. Stress versus strain of three-point bending test for Ag2Se ingot and rolled foil (b). Electron back-scattering diffraction (EBSD) images and zoomed-in ones showing dense dislocations with statistic analyses in the rolled foil (c). The inverse pole figures show a [013] grain orientation (d) and a Burger’s vector along [001] (e, black arrows).

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Hot rolling is a well-established and cost-effective plastic processing technique, which allows a feasible approach to deform and thin inorganic thermoelectrics at appropriate temperatures. Ag2Se undergoes an orthorhombic to cubic structural transition at 407 K upon warming37, of which the atomic rearrangement could facilitate the hot-rolling process at nearby temperatures. Note the ductility of silver sulfide was attributed to the uncleavable slipping of sub-lattice units31.

The details of the synthesis, characterizations, and property measurements of Ag2Se, are shown in the Supplementary. When Ag2Se is heated up to 150 °C, slightly higher than the orthorhombic-cubic phase transition temperature, it becomes very soft for an easy multi-pass rolling with various thickness down to ~30 μm (Fig. S3). Indeed, a 36 μm thick device focused on here shows a safe bending at a radius of 3 mm for at least 1,000,000 times, as further confirmed by the unchanged thermoelectric properties (Figs. S4, 2). This can be understood by the largely enhanced εEmax of ~0.8% in rolled Ag2Se foil (Fig. 1b), because it is larger than the needed strain of ~0.6% (εEmax = t/2rb with a bending radius of rb and a thickness of t)38. Since both minimum rb and safe bending times are critical parameters for measuring the elastic bendability, a factor B of bending radius to bending times ratio for the Ag2Se device in this work is significantly smaller than those reported (Fig. 2d).

Fig. 2: Bendability of hot-rolled thermoelectric Ag2Se.
figure 2

The 36 μm thick device in this work shows unchanged resistance (a), Seebeck coefficient (b) and power factor with a statistical analysis (c) upon 1,000,000-time bending at a radius of 3 mm, ensuring its extraordinary elastic B-ratio of bending radius to bending times (d), with a comparison to that of ever-reported flexible devices2,16,17,18,19,33,36,39,40,41,42,43,44,45,46,48,49,50,51,52,53,54,55,56,57.

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X-ray diffraction (XRD, Fig. S5) results indicate a preferred [013] orientation of Ag2Se foils after rolling, and the orientation factor F[013] is about 0.5 (Table S2). Scanning electron microscopy (SEM) observations and energy dispersive spectroscopy (EDS) analyses ensure the compositional homogeneity (Fig. S6). Importantly, thermoelectric performance of hot-rolled foils is quite reproducible with nearly isotropic properties30 (Fig. S7–S8). The existence of dense dislocations and the increase in carrier concentration lead to a decrease in carrier mobility in the rolled Ag2Se foils, which further result in a comparable resistivity but a lower Seebeck coefficient (thus a lower power factor particularly at T > 340 K, Fig. S9).

A low device contact resistance (Rc) is important to realize the full potential of high-performance thermoelectric materials. Silver paste is usually used for thin-device assembly. To further minimize Rc, the silver foil of 0.1 mm thick is used as an electrode in this work, and Au is deposited on both ends of the hot-rolled Ag2Se foils to ensure ohmic metallic contacts with the electrode. With the excellent machinability of both Ag2Se and elementary silver, a firm touching is achieved by bolts and nuts (the inset of Fig. 3a). Uniform mechanical pressure on the foil module is ensured by applying small torque deviation of ~0.0185 ± 0.0005 Nm to the bolts (Fig. S10). The internal resistance (Rin) for single-leg foil device with the size of 5 × 5 × 0.036 mm3 was measured by the four-probe technique across the contacts along multiple parallel paths for averaging (Fig. 3a). The resulting interfacial contact resistivity (ρc) at both ends are only ~2.0 and ~2.1 mΩ·cm2, respectively, being significantly lower than those of reported flexible film devices15,16,18,33,39,40,41,42,43,44,45,46,47 (Fig. 3b and Table S3). The consistence between the measured total device resistance of 2.7 Ω and the summation of materials (2.4 Ω) and contact components (0.02 Ω × 12 = 0.24 Ω for 12 in total contacts of ~0.02 Ω each), suggests both good accuracy in ρc-determination and uniformity in resistance distribution among contacts.

Fig. 3: Device properties.
figure 3

Scanning resistance (R) (a) indicates an extremely low interfacial resistivity for flexible film devices of polycrystals (b), enabling a superior power density (c) and specific power density (d), with a comparison to those of ever-reported flexible devices2,15,16,17,18,19,33,39,40,41,42,43,44,45,46,47,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73.

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Six n-type Ag2Se legs of 20 × 5 × 0.036 mm3 are assembled in this way, paring with copper wires of a positive but quite close to zero Seebeck coefficient, for a device (Fig. S11). Both the output voltage and power at interested temperature gradients are quite comparable to the predictions according to the material properties (Fig. S12). Eventually, a maximum output power (Pmax) up to 180 μW is reached at ΔT ~ 69 K (Fig. S13), corresponding to a power density (Pdmax, power divided by the cross-section area of thermoelectric materials) as high as 167 W/m2 (Fig. 3c). Moreover, the specific power density (PdmaxL/ΔT2, with L being the leg length) of the device in this work is outstanding (Fig. 3d). Using instead an better performing material, tape-supported single-crystalline Bi2Te3-based thin films48 showed an even higher power density. Limiting the deformations to be elastic and further strengthening its elasticity (Fig. S14) are expected to enable extra robust bendability, performance recoverability, free-standability and mass-producibility. Fig. S15 shows a demonstration of outputting an open-circuit voltage of 4.2 mV under a ΔT of ~8 K.

In summary, the fact that elastic bending fundamentally allows recoverability, in principle offers an additional opportunity of flexibility even in inorganics with rigidity. This work demonstrates in elasticity-strengthened Ag2Se of an intrinsic large Poisson’s ratio, and extrinsic dense dislocations and refined grains, a successful realization of safe bending at a 3 mm radius for at least 1,000,000 times while retaining an extraordinary power output, through a facile hot-rolling technique. This concept is believed to be equally applicable in other materials/devices for topping up functionalities with robust bendability.

Methods

Experimental details of materials and methods are shown in Supplementary Information.