Superior flexibility merges high power density in single-crystal Bi₂Te₃ film thermoelectric generators

Abstract

Developing high-performance, mechanically robust power sources is critical for wearable microelectronic networks. Flexible thermoelectric technology offers a promising solution, but the central challenge remains the synergistic optimization of mechanical flexibility and functional performance in high-efficiency materials. Here, we report an antisite defect suppression strategy to resolve these conflicting demands in Bi₂Te₃ single-crystal thin films. By utilizing Se alloying, we tailor interplanar energetics to improve yield strength while enabling an unusual microcrack propagation mechanism that retains superior plasticity. This defect engineering approach also optimizes carrier mobility, leading to ultrahigh power factors of 50.6 for n-type and 48.2 μW cm⁻¹ K⁻² for p-type single-crystal films. A flexible thermoelectric generator fabricated from these films demonstrates robust bendability over 10,000 cycles and achieves a record power density of 805.0 W m⁻² under a temperature difference of 79.6 K in natural cooling conditions. This study highlights intrinsic defect engineering’s transformative potential for next-generation durable, high-power flexible thermoelectric generators.

This work demonstrates an antisite-defect suppression strategy for Bi2Te3 single-crystal thin films, enabling flexible thermoelectric generators that deliver high power output and long-term bending durability for wearable microelectronic applications.

Introduction

With an ever-surging demand for wearable and portable electronics, sustainable and stable charging, sensing and cooling technologies have garnered growing interest¹. Flexible thermoelectric generators (f-TEGs) show great promise in these fields given that they enable close adhesion to non-planar heat sources and direct conversion between thermal and electrical energy^2–4. The energy conversion efficiency of f-TEGs is determined by the dimensionless figure of merit ZT for materials, ZT = S²σT/κ, here S, σ, κ, and T, are the Seebeck coefficient, electrical conductivity, thermal conductivity, and absolute temperature, respectively⁵. Beyond conversion efficiency, the actual output power of practical f-TEGs is strongly dependent on the material’s power factor (PF = S²σ)^6,7. Meanwhile, excellent mechanical flexibility remains an essential requirement for targeting flexible applications⁸. Conventional inorganic thermoelectric materials offer high performance but suffer from intrinsic brittleness, precluding bending for flexible applications⁹, while organic counterparts exhibit innate flexibility yet have substantially inferior thermoelectric properties⁴. Therefore, realizing both excellent thermoelectric performance and satisfactory mechanical flexibility poses a key challenge for the fabrication of high-performance f-TEGs¹⁰.

Bismuth telluride (Bi₂Te₃) stands as a benchmark inorganic thermoelectric material at room temperature owing to its high thermoelectric performance¹¹. However, its inherent rigidity restricts its practical applications in flexible electronics⁹. To improve its flexibility, researchers have explored fabrication methods such as magnetron sputtering and vacuum thermal evaporation to fabricate Bi₂Te₃-based polycrystalline thin films. Yet the PF of these thin films is obviously lower than that of bulk materials^12–14. Besides, they also suffer from poor flexible stability, with their electrical resistance increasing by more than 10% after 1000 cycles^13–15. Thus, improving the TE performance and flexibility of Bi₂Te₃-based films calls for more innovative strategies.

Recently, a method of directly exfoliating Bi₂Te₃-based single crystal films is developed¹⁶, with the resulting p-type and n-type films both exhibiting a power factor exceeding 40 μW cm⁻¹ K⁻². Such performance attests to the films’ strong competitiveness relative to the state-of-the-art flexible thermoelectric films. However, extraordinary room-temperature plasticity is found in Bi₂Te₃ single crystals owing to the presence of intrinsic antisite defects^17–19. This endows materials with excellent processibility, but also leads to a reduction in yield strength. As for thin films, low yield strength can result in a poor flexibility as evaluated by the flexibility figure of merit f_FoM, expressed as f_FoM = σ_y/E, where σ_y and E are yield strength and elastic (Young’s) modulus, respectively²⁰. Notably, this is particularly true for single-crystalline thin-film materials that rely on elastic deformation to achieve flexibility. Therefore, it is considerable to enhance the yield strength by suppressing antisite defects, thereby improving the flexibility of Bi₂Te₃ single-crystal thin films. In addition, antisite defects can disrupt the lattice charge balance to generate free carriers and alter carrier mobility, thereby governing the associated electrical properties^21–23. Therefore, the manipulation of antisite defects potentially enables the synergistic enhancement of both flexibility and TE properties of Bi₂Te₃-based single crystal films.

In this work, we systematically reveal that suppressing the formation of the intrinsic antisite defect can simultaneously enhance the flexibility and TE performance of Bi₂Te₃ single crystal films. The enhanced flexibility is achieved by increasing yield strength, while TE performance enhancement stems from optimized carrier concentration and increased carrier mobility. By Se alloying, the formation energy of antisite defects increases, leading to a reduction in the equilibrium concentration of antisite defects. This enhances the electron interaction and interplanar separation energy of the (0 $\overline{1}$ 10) plane, with the latter contributing to the improved yield strength and intrinsic flexibility of the material, while the alternating propagating microcracks induced by mechanical stress counterintuitively retain its plasticity simultaneously. (Fig. 1a, b). Meanwhile, Se alloying tunes the carrier concentration to an optimal range and weakens carrier scattering process, resulting in enhanced carrier mobility. As a result, exceptional power factor of 50.6 μW cm⁻¹ K⁻² and 48.2 μW cm⁻¹ K⁻² are achieved in n-type and p-type Bi₂Te₃ films exfoliated from the corresponding crystals, respectively (Fig. 1c). Our Bi₂Te₃-based single crystal flexible TE generator realizes a record-high power density of 805.0 W m⁻² at ΔT = 79.6 K even at a natural cooling condition (Fig. 1d). More importantly, the electrical resistance variation of the flexible TE generator after 10,000 bending cycles is below 5% (Fig. 1e and Supplementary movie 1), indicating excellent stability for flexible applications. Our findings demonstrate that manipulating intrinsic defect is an effective approach to concurrently enhance the flexibility and TE performance of inorganic thermoelectric materials, which accelerates the development of self-powered wearable electronics.

Fig. 1. High performance single-crystal Bi₂Te₃-based materials and f-TEGs.

a Schematic diagram illustrating the mechanism of the antisite defects-manipulation strategy. b The yield strength and elastic modulus of the Se alloyed single-crystal Bi₂Te₃ and typical TE materials^26–30. c Power factor and compressive strain at room temperature of thermoelectric materials including the Se-alloyed single-crystal Bi₂Te₃, Bi₂(Te,S)₃, Bi₂(Te,Se)₃, Mg₃(Sb,Bi)₂ and AgCu(Te,Se,S) systems^8,29,31–33. d The maximum power density (PD_max) of the single-crystal Bi₂Te₃ film generator compared with previously reported studies^14,34–39. e Relationship between relative resistance change (R/R₀) and bending cycles for the film generator in this work and those reported previously^16,40–48.

Results

Microstructure characterizations

Leveraging the distinct differences in electronegativity and atomic radius between Bi₂Se₃ and Bi₂Te₃, we adopted Se alloying to increase the formation energy of antisite defects in Bi₂Te₃. As calculated results, the formation energy of Bi_Te antisite defects in Bi₂Te₂Se is significantly higher than that in Bi₂Te₃, confirming the feasibility of reducing antisite defect concentration of Bi₂Te₃ through Se alloying (Fig. 2a). To validate this, as well as the mechanical and TE properties, Bi₂Te₃ and Bi₂Te_2.7Se_0.3 single crystals were grown via the modified Bridgman method and are shown in Fig. 2b. The mirror-like cleavage planes attest to the superior crystallographic integrity and high quality of the crystals. The X-ray diffraction (XRD), backscattering electron (BSE) images, and energy-dispersive spectroscopy (EDS) mappings collectively verify the absence of impurity phases in the Bi₂Te₃ and Bi₂Te_2.7Se_0.3 crystals (Figs.S1–S10). To quantitatively determine the defects evolution in Bi₂Te₃ and Bi₂Te_2.7Se_0.3, the synchrotron XRD (SR-XRD) is employed combined with Rietveld refinement (Fig. 2c). For the Bi₂Te₃ sample, partial occupation of Te2 sites by Bi atoms was detected, resulting in a Bi_Te antisite defects concentration of 2.0 × 10²⁰cm⁻³. Upon Se alloying, the concentration decreases to 1.4 × 10²⁰cm⁻³ in the Bi₂Te_2.7Se_0.3 single crystal (Fig. 2c, S11 and Tables S1-S2). To clarify the inherent correlation between antisite defect concentration and microstructure of Bi₂Te₃ and Bi₂Te_2.7Se_0.3, we carried out atomic-resolution scanning transmission electron microscopy (STEM) analysis (Figs. 2d–g). High-density and diverse microstructures are observed in the Bi₂Te₃ crystal, while such features are substantially less abundant in the Bi₂Te_2.7Se_0.3 crystal. Geometric phase analysis (GPA) of the STEM images further reveals reduced disordered strain distributions in Bi₂Te_2.7Se_0.3 compared to Bi₂Te₃. The more ordered microstructure of Bi₂Te_2.7Se_0.3 is consistent with its lower antisite defect concentration.

Fig. 2. The strengthening and toughening of Bi₂Te₃ single crystal materials induced by restraining antisite defects.

a The formation energy of Bi_Te antisite defects for Bi₂Te₃ and Bi₂Te₂Se. b The optical images of Bi₂Te₃ and Bi₂Te_2.7Se_0.3 single crystals. c The synchrotron radiation XRD refinement results and the antisite defect concentration of Bi₂Te₃ and Bi₂Te_2.7Se_0.3 single crystals. d–g HRTEM images and geometric phase analysis (GPA) images of Bi₂Te₃ and Bi₂Te_2.7Se_0.3 single crystal samples. Three-point bending results along the c axis (h) and optical images (i) of Bi₂Te₃ and Bi₂Te_2.7Se_0.3 single crystals before and after testing. Compressive results along a-axis (j) and optical images (k) of Bi₂Te₃ and Bi₂Te_2.7Se_0.3 single crystals before and after testing. l Schematic diagrams of the crystal structure of the perfect Bi₂Te₃ (PBT), the antisite-defective Bi₂Te₃ (ABT) and the Se-alloyed Bi₂Te₃ (BTS). The simulated stress-strain curves of three-point bending (m) and compression along the a-axis (n) for the PBT, ABT and BTS.

Mechanical properties

As seen from the three-point bending results, pristine Bi₂Te₃ possesses a low bending strength of 9.2 MPa and an elastic modulus of 10.9 GPa, exhibiting typical plastic deformation behavior. In sharp contrast, Bi₂Te_2.7Se_0.3 shows a significantly enhanced bending strength of 54.3 MPa, which is more than five times higher than that of pristine Bi₂Te₃, and a barely altered elastic modulus of 9.9 GPa. (Fig. 2h, i and S12–S13). Furthermore, the compressive results along the a/c axis also prove that the significantly enhanced yield strength of Bi₂Te_2.7Se_0.3 without sacrificing its plasticity (Fig. 2j, k and S14–18). The f_FoM values, calculated as 8.5 × 10⁻⁴ for pristine Bi₂Te₃ and 4.9 × 10⁻³ for Bi₂Te_2.7Se_0.3, indicate that the increased yield strength should translate into markedly improved intrinsic bending flexibility of the single crystal. All above mechanical measurements were performed over multiple repeated trials to verify the reliability of the obtained performance data.

To clarify the underlying mechanism through which Se alloying improves the mechanical properties of Bi₂Te₃, molecular dynamics (MD) simulations based on machine learning potential (MLP) were performed. We constructed three supercell models including perfect Bi₂Te₃ (PBT), antisite-defective Bi₂Te₃ (ABT), and Se-alloyed Bi₂Te₃ (BTS) (Fig. 2l). Analysis of the simulated bending and compression stress-strain curves indicates that the yield strength of the defect-free PBT model is marginally inferior to that of the BTS counterpart, while both substantially outperform the antisite-defective ABT model in terms of this key mechanical parameter (Figs. 2m, n, S19–S20). Our simulation results further confirm that intrinsic antisite defects act as the dominant factor leading to the compromised yield strength of Bi₂Te₃. Consequently, the enhanced yield strength achieved by Se alloying predominantly stems from the efficient suppression of these antisite defects.

The side-view SEM images of Bi₂Te₃ crystals after bending and compression are shown in Fig. 3a, c respectively. While plasticity-induced bulk deformation is clearly visualized throughout the material, localized fracture occur exclusively along (0 0 l) cleavage planes. In stark contrast, crack propagation in bent Bi₂Te_2.7Se_0.3 crystals adopts a zigzag, stair-like pattern, rather than propagating along the layer-parallel cleavage paths seen in pure Bi₂Te₃ (Fig. 3b, d and S21-S22). Such bulk deformation is barely observable. For compressed Bi₂Te_2.7Se_0.3 crystal, extensive microcrack networks are widely spread across the crystal interior. These microcrack networks effectively dissipate stress accumulated during deformation and act as direct evidence of retained plastic capacity²⁴. Based on SR-XRD data, Rietveld refinement was utilized to obtain the electron density distribution (EDD) of (0 0 1), (0 1 5), and (0 $\overline{1}$ 10) planes, which possess the largest interplanar spacings among the major diffraction planes of the Bi₂Te₃-based crystals. The EDD of (0 0 1) and (0 1 5) planes barely change when Se alloying, while (0 $\overline{1}$ 10) plane increases significantly (Figs. 3e–h, S23). This indicates that the lattice electronic interaction of the (0 $\overline{1}$ 10) plane in the Bi₂Te_2.7Se_0.3 single crystal is enhanced owing to the reduced antisite defect concentration. The interplanar separation energy (E_sep) derived from the first principles calculations shows that the E_sep of the (0 $\overline{1}$ 10) plane of PBT and BTS rises remarkably, while the E_sep of (0 0 1) and (0 1 5) planes remains unchanged (Fig. 3i, j). This suggests the strengthening of interlayer chemical bonding of the (0 $\overline{1}$ 10) plane. The dominant role of the strengthened (0 $\overline{1}$ 10) plane on deformation mechanism during bending and compression is further demonstrated by the MD simulations. Local atomic configuration and strain analysis reveal that localized strain concentration occurs on the (0 0 1), (0 1 5) and (0 $\overline{1}$ 10) crystal planes of ABT under applied stress, with such strain behavior confined only to the (0 0 1) and (0 1 5) planes for PBT and BTS. Combined with the strain analysis and atomic trajectory results (Figs. S24-S36), ABT exhibits multiple slip paths, whereas such paths in BTS are primarily confined to the (0 0 1) and (0 1 5) planes (Fig. 3k, l). The enhanced E_sep of the crystal planes reduces the number of slip planes involved in plastic deformation and thus improves the strength. Nevertheless, the microcrack network conversely facilitates stress dissipation and thereby sustains the plastic deformability of the material. We further performed STEM to investigate the atomic arrangement of bent Bi₂Te₃ and Bi₂Te_2.7Se_0.3 crystals. Consistent with the simulation results, strain along the (0 $\overline{1}$ 10) crystallographic plane is observed in Bi₂Te₃ crystals, whereas strain in Bi₂Te_2.7Se_0.3 is restricted exclusively to the (0 0 1) and (0 1 5) planes (Figs. 3m, n and S37). Notably, the atomic trajectories of BTS align well with the side-view SEM observations of compressed Bi₂Te_2.7Se_0.3 crystals, both of which are consistent with the bending-induced deformation behaviors. This agreement further corroborates the structural evolution characteristics associated with the deformation process (Fig. 3o, p). In summary, Se alloying enhances the interplanar interactions of the (0 $\overline{1}$ 10) plane in Bi₂Te₃ and suppresses slip along this plane. Precisely due to the restriction of slip on this specific plane, microcracks are induced and propagate alternately in an ordered manner. This process tunes mechanical performance via controllable crack deflection and strain energy dissipation, ultimately realizing synergistic improvements in the material’s yield strength, toughness and intrinsic flexibility.

Fig. 3. The intrinsic origin of strengthening and toughening in the Se-alloyed Bi₂Te₃ single crystal.

a–d SEM images of the Bi₂Te₃ and Bi₂Te_2.7Se_0.3 single crystal after three-point bending and compressing along a-axis. e–h The charge density distributions of the Bi₂Te₃ and Bi₂Te_2.7Se_0.3 single crystal of the (0 1 5) and (0 $\overline{1}$ 10) crystal planes derived from the synchrotron radiation XRD. i. Schematic diagrams of the (0 0 1), (0 1 5) and (0 $\overline{1}$ 10) planes in Bi₂Te₃ crystal structure. j The calculated separation energy (E_sep) for (0 0 1), (0 1 5) and (0 $\overline{1}$ 10) crystal planes of ABT_, PBT and BTS. Simulated local atomic configuration and strain of ABT, PBT and BTS under k three-point bending and (l) compressing along c a-axis. m High-angle annular dark-filed (HAADF) images of the Bi₂Te₃ and Bi₂Te_2.7Se_0.3 single crystal after bending and n their corresponding inverse fast Fourier transformation (IFFT) images projected on (0 0 l) planes. o Atomic trajectories of the compressed BTS and (p) SEM images of side view of Bi₂Te_2.7Se_0.3 crystal after compression.

To further validate this strengthening effect achieved by suppressing antisite defects in Bi₂Te₃-based single crystals, we took p-type Bi_0.5Sb_1.5Te₃ material as another case. The calculated defect formation energies demonstrate that Se doping raises the energy barrier for antisite defect formation over a broad Fermi level range (Fig. 2a), thus indicating that Se exerts a consistent antisite defect suppression effect under both p-type and n-type conditions. Therefore, Bi_0.5Sb_1.5Te₃ and Bi_0.5Sb_1.5Te_2.9Se_0.1 single crystals were grown, and compression as well as bending tests were performed on both materials. Similar to the n-type Bi₂Te₃, Bi_0.5Sb_1.5Te_2.9Se_0.1 displays simultaneous enhancements in yield and bending strength along the a and c crystallographic axes, with both values exceeding those of Bi_0.5Sb_1.5Te₃ (Figs. S13, S17, S21–22 and S38–S43). As a result, regulating defect concentrations through defect engineering can improve mechanical strength, which provides a feasible strategy to enhance the flexibility of other inorganic thermoelectric semiconductors.

Thermoelectric properties

Owing to the absence of grain boundaries, the pristine Bi₂Te₃ and Bi_0.5Sb_1.5Te₃ crystals exhibit large carrier mobility (μ_H) of 277.3 cm²V⁻¹ s⁻¹ and 220.3 cm²V⁻¹ s⁻¹, which are much higher than that of the deposited films (Fig. 4b). After Se alloying, the carrier concentration (n_H) decreases into an appropriate range, which further increases the μ_H. Benefiting from the optimized carrier concentration and the increased mobility, the PFs of Bi₂Te_2.7Se_0.3 and Bi_0.5Sb_1.5Te_2.9Se_0.1 crystals reach 50.6 μW cm⁻¹ K⁻² and 48.2 μW cm⁻¹ K⁻² at 300 K, respectively (Fig. S44). Leveraging the intrinsic layered cleavage property of Bi₂Te₃-based single crystals, the bulk single crystals in this work can be directly processed into single-crystal thin films via mechanical exfoliation, which further broadens the application prospects of these high-performance thermoelectric materials in flexible thermoelectric generators (Fig. 4a and S45-46). The detailed exfoliation procedure is described in the “Methods” section. The carrier mobility and power factors of the exfoliated Bi₂Te_2.7Se_0.3 and Bi_0.5Sb_1.5Te_2.9Se_0.1 single-crystal thin films are well consistent with those of their bulk counterparts (Fig. 4c, S44 and S47-48). Furthermore, Se alloying also suppresses lattice thermal conductivity effectively through intensified phonon scattering (Figs. S44 and S49). Finally, the peak ZT values of 1.08 at 348 K and 1.16 at 323 K are achieved in our plasticity-enhanced Bi₂Te_2.7Se_0.3 and Bi_0.5Sb_1.5Te_2.9Se_0.1 crystals, respectively (Fig. S50). These thermoelectric performance rival those of state-of-the-art inorganic plastic and flexible thermoelectric materials (Fig. S51). The Se alloying concentration also needs to be controlled within a certain range, as further increasing the Se concentration leads to degradation of thermoelectric performance. (Figs. S52, 53). Beyond the optimization of thermoelectric transport properties, Se alloying markedly boosts the long-term thermal stability of Bi₂Te₃ single-crystal thin films under continuous serving operation in air. After 30-day annealing at 348 K in air condition, the Bi₂Te_2.7Se_0.3 film retains a power factor of 44.9 μW cm⁻¹ K⁻², rather than experiencing significant degradation as seen in pristine Bi₂Te₃ film. This robust performance lays a solid material foundation for the long-term stable operation of flexible thermoelectric generators. (Fig. S54).

Fig. 4. Extraordinary TE performance and superior flexibility of the Se-alloyed Bi₂Te₃ single crystals thin films and the film generator.

a Schematic diagram of the exfoliation process for single-crystal thin films. b Carrier mobility and concentration of the single crystal Bi₂Te₃-based materials and previously reported polycrystalline samples^{16,34,49–51}. c Temperature-dependent power factor (PF) of the single crystal Bi₂Te₃-based films and previously reported works^16,34, error bars denote the standard deviation obtained from repeated measurements of multiple samples. d The relations between bending radius and resistance variation for single crystal Bi₂Te₃-based films with thicknesses of 10 μm and 20 μm, respectively. The insets display the pictures of bent single-crystal films. e Simulated temperature contour maps of film generators as affected by thickness and cooling conditions. f Variation of the maximum power density (PD_max) with film thickness under different cooling conditions for ΔT = 80 K and 100 K. g Output voltage (V) and the maximum output power (PD_max) of the single crystal Bi₂Te₃-based film generator under natural cooling condition in this work. The inset shows a digital image and a thermal image.

Flexible TE generator

To preserve stable TE performance for deformable applications, flexible thin-films must fundamentally maintain recoverable atomic configurations upon mechanical deformation. To meet this criterion, f-TEGs are required to operate within the elastic regime with a large permissible elastic bending strain. This capability is determined by the critical bending radius of flexible materials, which is inherently governed by their thickness and mechanical flexibility. In this work, the critical bending radii of Bi₂Te₃, Bi₂Te_2.7Se_0.3, Bi_0.5Sb_1.5Te₃, and Bi_0.5Sb_1.5Te_2.9Se_0.1 single crystals films with the thickness of 20 μm and 10 μm were studied by measuring their resistance as a function of bending radius. As the bending radius gradually decreases, all films initially exhibit only a slight increase in electrical resistance, followed by a sharp increase once the critical bending radius is exceeded (Fig. 4d and S55). The mild rise in electrical resistance signals elastic deformation of the films, whereas the abrupt resistance surge stems predominantly from continuous crack propagation and plastic deformation. The transition point corresponds to the critical bending radius (Fig. S56). For 20 μm-thick films, Bi₂Te_2.7Se_0.3 film exhibits a critical bending radius of 4.8 mm, smaller than 6.2 mm of the pristine Bi₂Te₃. At a reduced thickness of 10 μm, the critical bending radii of these two films further decline to 3.4 mm and 5.3 mm, respectively. Notably, Bi_0.5Sb_1.5Te_2.9Se_0.1 film delivers an even smaller critical bending radius of only 2.8 mm at 10 μm thickness. The reduced critical bending radius of the films confirms that Se alloying enhances the intrinsic mechanical flexibility of Bi₂Te₃-based films at fixed thickness. Meanwhile, this improved mechanical capability also enables superior bending conformability and expands the application coverage of f-TEGs, a pivotal prerequisite for their practical integration into flexible and wearable thermoelectric systems (Fig. S57).

Besides, reducing the thickness of the Bi₂Te₃-based single-crystal films increases the thermal resistance, facilitating the formation of a stable temperature gradient between the hot and cold junctions even without active cooling. As illustrated in the simulated temperature contour maps (Fig. 4e, S58), under natural convection, the 10 μm-thick film generator exhibits a more pronounced temperature gradient across its hot and cold ends compared to the 60 μm-thick counterpart. Notably, the overall temperature difference of the 10 μm generator under natural convection shows negligible deviation from the ∆T achieved under active cooling conditions. It is worth noting that at a film thickness of 10 μm and ∆T = 80 K, the generator attains a high simulated power density of 1113.0 W m⁻² (Figs. S59, 60). Furthermore, under passive cooling conditions, the 10 μm-thick film generator theoretically maintains a high power density of 1003.5 W m⁻², which is comparable to the power density obtained under active cooling condition (Fig. 4f and S61).

To validate the simulation predictions, we fabricated two film generators using above p-type and n-type single-crystal films with thickness of 10 μm and 20 μm, respectively (Figs. S44-45, S62-64). Under active cooling conditions (∆T = 83.6 K), the 10 μm-thick generator achieves a P_max of 154.0 μW (Fig. S65). For comparison, under passive cold-end heat dissipation, the same 10 μm-thick film generator delivers 138.5 μW (∆T = 79.6 K), demonstrating a record high power density of 805.0 W m⁻², which corresponds to a specific power density of 8.4 μW cm⁻¹ K⁻² (Fig. 4g and S66, 67). The relations between ∆T and power density are basically repeated for the 10 μm-thick film generator with and without cooling. To further verify the film generator’s practical operational reliability, we further carried out a 7-day continuous durability test at a fixed temperature difference of 40 K, during which its output voltage remained steadily at ~39 mV without obvious performance degradation after prolonged operation (Fig. S68). Overall, endowed with favorable power generation capacity and robust long-term service stability, the generator delivers superior comprehensive performance and exhibits promising prospects for flexible electronics fields (Figs. S69–71).

Discussion

In summary, we have demonstrated that the reduction of antisite defect concentration in Bi₂Te₃ crystal enables the synergetic enhancement of flexibility and TE performance. Se alloying reduces the antisite defect concentration, strengthens interplanar interactions, induces microcracks to alternatingly propagate, thus simultaneously enhancing the strength and inherent flexibility of the material. Meanwhile, Se alloying leads to an optimal carrier concentration and enhances carrier mobility. Finally, n-type and p-type Bi₂Te₃ films exfoliated from their corresponding crystals realize ultrahigh PF of 50.6 and 48.2 μW cm⁻¹ K⁻² at room temperature, respectively. A record-high power density of 805.0 W m⁻² is achieved in our flexible TE generator at ∆T of 79.6 K under natural cooling conditions, while the generator exhibits a resistance variation of <5% over 10000 bending cycles, indicating reliable operational stability in flexible conditions. Our work presents a strategy for the synergistic enhancement of flexibility and TE performance in inorganic TE semiconductor through defect engineering, accelerating the development of self-powered wearable electronics.

Methods

Materials synthesis

High-purity raw materials, including Bi (bulk, 99.99% from Alfa Aesar), Te (bulk, 99.99% from Alfa Aesar), Se (bulk, 99.99% from Alfa Aesar), Sb (bulk, 99.99% from Alfa Aesar) and BiBr₃ (powder, 99.99% from Alfa Aesar) were accurately weighed based on the nominal composition of Bi₂Te₃, Bi₂Te_2.7Se_0.3, Bi_0.5Sb_1.5Te₃ and Bi_0.5Sb_1.5Te_2.9Se_0.1 in a glove box. These materials were then loaded into vacuum-sealed quartz tubes. The quartz tubes with materials were heated to 1073 K and kept at that temperature for 8 h, followed by natural cooling to room temperature. The quartz tubes with materials were placed into the single crystal pulling furnace. The temperature was raised to 933 K and held for 30 h, after which the furnace was cooled down to room temperature. The moving rate of the furnace chamber was 5 mm/h (the holding time is determined by the moving distance of the furnace chamber and the moving rate). The obtained dense bulk samples were cut into specific strips using a diamond wire cutting machine to measure their mechanical and electrical properties. The dimensions of the bending test samples were ~1.5 × 3 × 11 mm³, while those of the compression test samples were about 2 × 2 × 4 mm³. Both the bending test and compression test were conducted using an Instron 5566 universal testing machine at a loading rate of 0.1 mm·min⁻¹.

Machine learning potential molecular dynamics (MD) simulations

In this work, a machine-learning interatomic potential for the Bi-Te-Se system was constructed using the DPGEN-DeepMD-kit workflow. First, representative atomic configurations were labeled by a plane-wave DFT method to obtain reference energies, atomic forces, and stress tensors, forming the initial training dataset. The initial configurations included:

1. distorted crystal structures under various strain states (tension, compression, and shear);

2. NVT/NpT sampling at different temperatures (50–700 K);

3. local structures containing Se dopants and Bi-Te/Se antisite defects.

On this basis, an active-learning loop in DPGEN (exploration, labeling, training, and model-deviation analysis) was repeatedly performed to enrich the dataset:

1. MD explorations with the current potential were carried out under various stress, temperature, and defect conditions (exploration);

2. configurations exhibiting large model deviation were re-labeled by DFT (labeling) and added to the training set;

3. Multiple DeepMD models were trained iteratively (training) until the model deviation converged in the target state space.

The final Deep Potential model, after convergence in DeepMD-kit, was exported and coupled to LAMMPS as a frozen model, and then employed for large-scale three-point-bending and compression MD simulations.

The three-point bending model consists of 1,080,000 atoms with dimensional ratios of 6:1.75:1, whereas the compression model consists of 26,910 atoms with a ratio of 1:1:1, so that the stress state is close to homogeneous bulk compression. The atomic radius ratio of Bi, Te, and Se was set to 1.46:1.38:1.20, reflecting their relative sizes at lattice sites.

The bulk initial structure was generated by replicating the Trigonal R3̅m unit cell along three crystallographic directions to form large supercells, which were then used as the basis for the bending and compression models. To study the effect of Se doping, for each Se concentration, 10% of the Te atoms were randomly replaced by Se atoms, producing statistically homogeneous solid-solution configurations. Antisite defects were introduced by randomly exchanging Te/Se atoms with their nearest-neighbor Bi atoms, thereby mimicking Bi-Te/Se antisite disorder and its impact on local structure and mechanical response. The ABT model in this work incorporates two distinct concentrations of antisite defects, namely 3.3% and 10%.

All molecular dynamics simulations were conducted in LAMMPS using the DeepMD potential, with periodic boundary conditions applied in all three dimensions. Prior to mechanical loading, each system was equilibrated under isothermal–isobaric (NpT) conditions at 1013.25 mbar and 300 K, with a timestep of 1 fs and a total relaxation duration of 100 ps to ensure full thermodynamic equilibrium.

Characterizations

The phase identification was detected by the X-ray diffraction (XRD, EmpyreanX, Netherlands) with Cu Kα (λ = 1.5406 Å) radiation.

The HELIOS Nanolab 600i SEM and Zeiss Merlin Compact SEM, equipped with energy-dispersive X-ray spectroscopy (EDS), were utilized for micromorphological characterization and element distribution identification.

It is worth noting that all thermoelectric properties were measured along the direction parallel to the (00 l) crystal plane of the Bi₂Te₃ single crystal. The ZEM-3 (Ulvac-Riko, Inc., Japan) was adopted to test the electrical properties, including electrical conductivity, Seebeck coefficient and power factor. The thermal conductivity was obtained by the calculation of κ = DρC_p, where D is the thermal diffusivity measured by the laser flash method (LFA-457, Netzsch, Germany), ρ is the density measured by the Archimedes method, and C_p is the heat capacity obtained through Dulong–Petit law. The carrier concentration(n_H) and mobility (µ_H) were calculated by the formula n_H = 1/(e·R_H), and µ_H = σ·R_H, where R_H is the Hall coefficient acquired by the van der Pauw technique under a 1.5 T magnetic field. Transmission electron microscopy (TEM, FEI Talos F200X, America) was used to characterize microstructure.

Synchrotron X-ray diffraction (XRD) measurements of the Bi₂Te₃ powder sample were conducted at the BL17B beamline of the Shanghai Synchrotron Radiation Facility (SSRF), using a monochromatic X-ray beam with an energy of 18 keV (corresponding to a wavelength of 0.688 Å) and a PILATUS 3 CdTe 2 M detector. XRD patterns were collected over a 2θ range of 2°−60.46°, with a step size of 0.034° and an exposure time of 10 s per step. The obtained two-dimensional diffraction images were radially integrated into one-dimensional XRD patterns using the FIT2D software. Subsequent phase identification and Rietveld refinement were carried out using the Full Prof Suite program, with the JCPDS card No. 01-072-1836 referenced for the Bi₂Te₃ phase.

Calculation methods

The entire DFT calculation process adopts the Vienna ab initio Simulation Package (VASP) based on the Perdew-Burke-Ernzerhof functional in the generalized gradient approximation and the projected augmented wave pseudopotential. The pseudopotentials of bismuth (Bi), tellurium (Te) and selenium (Se) explicitly treat the valence electrons with configurations of 6s²6p³, 5s²5p⁴, and 4s²4p⁴, respectively. The atomic motion was determined by the conjugate gradient algorithm (GG). We set 1 × 10⁻⁶eV and 1 × 10⁻²eV/Å as the convergence criteria for the electron self-consistent field and force, respectively. The dispersion interaction was approximated by the DFT-D3 method to describe the vdW interaction. To obtain electronic transport properties, we employed the BoltzTraP2 package and implemented the Monkhorst-Pack uniform k-point samplings with as dense a k-mesh of 21 × 21 × 21 as possible for self-consistent calculations.

Methodological details of single-crystal thin film exfoliation

Firstly, bulk single crystal ingots synthesized via the vertical Bridgman method are ultrasonically cleaned in anhydrous ethanol and acetone for 5–10 min respectively and dried to remove surface contaminants. Secondly, the crystal ingot is fixed, and the (001) cleavage plane is confirmed by a stereomicroscope and X-ray diffraction. Under a microscope, the tip of flat tweezers is precisely aligned with the confirmed cleavage direction. Initial microcracks along the cleavage plane are generated at the crystal edge through vertical pressing followed by horizontal prying. Then a blade is inserted to pry the crystal slowly and stably upwards, enabling cracks to propagate along the cleavage plane with the lowest surface energy, and bulk single crystal flakes with fresh and flat cleavage surfaces can be separated. Afterward, 3 M adhesive tape is tightly attached to the fresh cleavage surface of cleaned bulk flakes with appropriate uniform pressure. A single exfoliation process is realized by peeling off the tape steadily at a 45° oblique angle with a constant speed lower than 2 mm/s, obtaining thin films with micrometer-level thickness.

To guarantee consistent film thickness in each exfoliation operation, quantitative multi-parameter restriction and standardized control are implemented throughout the exfoliation process, and specific measures are summarized below:

(1) All bulk single crystals are processed into unified dimensions of 3 mm × 10 mm on the cleavage plane. Surface impurities and uneven surface layers are completely removed to ensure identical initial states of all raw materials.

(2) The same type of low-viscosity adhesive tape is adopted. Constant pressure provided by a 100 g weight, fixed 45° peeling angle and uniform peeling speed below 2 mm/s are applied for all single exfoliation processes, minimizing discrepancies caused by manual operation.

(3) Optical microscopy is applied for rapid preliminary screening based on the optical contrast of thin films after exfoliation. Scanning electron microscopy (SEM) cross-section characterization is further used for sampling and accurate thickness measurement. The thickness distribution of each batch is statistically analyzed, ensuring the relative thickness deviation within each batch is no more than 10%. This strategy realizes the stable and repeatable fabrication of thin films with uniform thickness.

Thin-film generator fabrication

n-type and p-type thin films with a thickness of ~10 μm were exfoliated from the as-prepared crystals. These thin films were cut into long strips, which served as thermoelectric legs. The width and length of each strip were about 3.0 mm and 10.0 mm, respectively. The n-type and p-type legs were electrically connected in series and thermally connected in parallel using Ag foils to assemble a 3-couple Bi₂Te_2.7Se_0.3/Bi_0.5Sb_1.5Te_2.9Se_0.1 Π-shaped thin-film thermoelectric generator. The Ag foils and thermoelectric legs were bonded together using silver paste and gallium-indium (GaIn) alloy. This thin-film generator features ultralow interfacial contact resistance, with its N-type Bi₂Te_2.7Se_0.3 and P-type Bi_0.5Sb_1.5Te_2.9Se_0.1 thermoelectric legs showing specific contact resistances of 3.58 mΩ cm² and 8.14 mΩ cm² at the film-Ag interfaces, respectively, of which the resistance values experience negligible increments upon annealing and reveal no detectable elemental interdiffusion across the interface. All substrates of the generator were polyimide (PI) films, and the performance of this thermoelectric generator was tested using a home-built instrument.

Author contributions

Y.-K. Z. and J.-T. N. designed this work. J.-T. N. and Y.-K. Z. prepared the materials and measured the properties. X. Dong, J.-B. N. and Y. Gong provided the first principles calculations and the molecular dynamics simulations. J.-T. N., P.-Y. Z., L. Z. and Z. Du evaluated the mechanical and thermoelectric properties. Y.-K. Z., J.-T. N. and M. Guo analyzed the TEM results. D. Luo provided the simulation of thin film generator. J.-T. N., Z. Guo, M. Liu and H. M. fabricated the power generation module. All authors discussed the results and contributed to the data analysis. J.-T. N., Y.-K. Z. and M. Liu wrote and edited the manuscript. Y.-K. Z., F. Guo, Z. Liu and J. S. supervised the whole project.

Peer review

Peer review information

Nature Communications thanks Chaochao Dun and the other anonymous reviewer(s) for their contribution to the peer review of this work. A peer review file is available.

Funding

This work was funded by the National Natural Science Foundation of China (Nos. U23A20556, 52602005, 523B2020, 524B2021 and 525B2026), the China Postdoctoral Science Foundation (2025M784362 and 2025M774303), the National Key Research, and the Fundamental Research Funds for the Central Universities (HIT.DZJJ.2025003).

Data availability

The data generated in this study are available within the published article, its Supplementary Information, and the Source Data file provided with this article. Source data are provided with this paper.

Code availability

All code and software utilized in the manuscript are publicly accessible from established open-source repositories, and no custom-developed code or software has been employed in this work. The publicly accessible DPGEN-DeepMD-kit workflow was adopted to obtain the available potential function for MD calculations. All required files for MD calculation process have also been uploaded on Zenodo (https://doi.org/10.5281/zenodo.21898917)²⁵.

Competing interests

The authors declare no competing interests.

Supplementary information

The online version contains supplementary material available at https://doi.org/10.1038/s41467-026-77574-1.