Phase-controlled molecular beam deposition unlocks flexible MgAgSb thermoelectrics with exceptional performance

Domain: neuroscience
Published: 2026-02-12
Editorial outcome: minor_revision

Abstract
Flexible thermoelectric materials hold great promise for sustainable energy supply in flexible electronics. However, beyond the long-standing champion Bi2Te3-based flexible films, high-performance alternatives remain scarce. Here, we report a promising flexible thermoelectric material based on eco-friendly MgAgSb, a bulk-proven high-performance system whose development in flexible form has long been hindered by its intrinsic brittleness and phase complexity. Using molecular beam deposition, we manage to precisely stabilize MgAgSb within its α-phase range and finely control its stoichiometry. As a result, we successfully fabricate the α-MgAgSb film with exceptional performance, achieving a room temperature zT of 0.8 and a peak power factor of 19.3 μW cm-1 K-2, ranking among the promising flexible thermoelectric materials developed. Moreover, the α-MgAgSb film is revealed to exhibit notable flexibility and stability under repeated bending and heating. Leveraging this high-performance stable α-MgAgSb film, the flexible thermoelectric device delivers a maximum normalized power density of 4.9 μW cm-2 K-2. This work opens a pathway for flexible MgAgSb applications and offers strong potential for realizing self-powered flexible technologies.

Introduction
Flexible electronics are emerging technologies that enable advancements in wearable devices, healthcare monitoring, and soft robotics, while also opening new possibilities for applications in high-temperature environments above 373K, such as aerospace surface monitoring and engine diagnostics1. However, continuously and maintenance-free powering of electronic components within flexible devices remains a critical challenge2. Thermoelectric (TE) devices, which can directly harvest heat from surfaces and the environment to generate sustainable electrical energy, offer a promising alternative to traditional batteries3–5. Typically, TE devices consist of n-type and p-type TE materials connected in series to convert heat into electricity, and their conversion efficiency is fundamentally determined by the dimensionless figure of merit (zT) of the constituent TE materials6. zT is defined as zT = S2σT/κ = PF × T/κ, where S is the Seebeck coefficient, σ is the electrical conductivity, κ is the total thermal conductivity, PF (= S2σ) is the power factor, a metric of electrical performance. It means that achieving high zT requires materials with both a high PF and a low κ. Beyond high TE performance, in the context of flexible thermoelectrics, the mechanical flexibility of TE materials and devices is also a key prerequisite7,8.

However, flexibility and TE performance are two different material attributes. Achieving both high flexibility and high TE performance in a single material remains highly challenging, making suitable candidates for flexible thermoelectrics extremely scarce9. Organic thermoelectric (TE) materials offer excellent flexibility due to their molecular and polymeric structures, but suffer from low electrical performance10. Although significant efforts have been devoted to enhancing systems such as PEDOT: PSS11–13, PANI14, SWCNT15,16, and PMHJ17, their zT and PF values remain far below those of inorganic TE materials. Hybridizing organics with inorganics can provide moderate performance and flexibility, but weak interfacial bonding and still-inferior TE properties hinder practical use18,19. To date, inorganic TE compounds remain the leaders in TE performance, with materials such as SnSe and GeTe achieving zT values exceeding 220–24. However, their brittleness limits flexible applications.

Reducing the dimensional size of materials to the micro- or nanoscale is an effective approach to endow brittle materials with flexibility through either top-down or bottom-up methods9,25–27. Top-down processing is often limited by their intrinsic brittleness. Only a few inorganic compounds, including Ag2(S, Se, Te)9,26,28, Mg3(Sb, Bi)229, single-crystalline Bi2Te330 and some van der Waals compounds31 exhibit intrinsic plasticity that enables safer deformation and flexible device fabrication32–34. In most cases, bottom-up synthesis of thin films (e.g., by printing or various deposition) is preferred, offering flexibility and tunability35,36. Currently, research on thin-film-based flexible inorganic TE materials has mainly focused on Bi2Te337–39 and Ag2Se40–42 due to their superior room temperature TE performance. For instance, p-type Bi0.3Sb1.7Te3 can achieve a zT value exceeding 1 at room temperature43, while n-type Ag2Se exhibits a comparable performance under similar conditions40. However, their performance deteriorates rapidly at elevated temperatures, posing an obstacle for their applications in flexible devices operating above 373K. Furthermore, the toxicity of Te/Se and the scarcity of Te impose additional limitations on their practical deployment44.

In contrast, α-MgAgSb is an eco-friendly and high-performance TE material, exhibiting zT values of ~0.8 at room temperature and peak values of around 1.3 above 473K45. Its intrinsically high PF across the working temperature range stems from its high band degeneracy, while its complex crystal structure results in its intrinsically low lattice thermal conductivity46,47. These merits make α-MgAgSb one of the most promising p-type TE materials near room temperature, particularly as a potential substitute for p-type (Bi, Sb)2Te3 in power generation. However, the TE performance of α-MgAgSb is highly sensitive to impurities such as Ag3Sb48, and α-MgAgSb will also undergo phase transitions to β- and γ-MgAgSb at elevated temperatures, complicating the fabrication of high-performance α-MgAgSb. Many processing optimizations have been reported to improve the phase purity and reliability of bulk α-MgAgSb, advancing its use in rigid TE devices45,49.

Despite these encouraging developments, studies on α-MgAgSb have so far been limited to rigid bulk forms, leaving its application in flexible thermoelectrics largely unexplored.

α-MgAgSb is intrinsically brittle, making it particularly difficult to impart flexibility through top-down processing methods. A more promising route is to fabricate α-MgAgSb thin films via bottom-up approaches. However, the complex phase behavior of MgAgSb poses significant challenges for film fabrication, and achieving flexible α-MgAgSb films with high performance remains elusive. In previous work, Wang et al.50 prepared flexible MgAgSb-based films by solution-casting mixtures of α-MgAgSb powder with graphene and PEDOT:PSS. However, the presence of multiple phases and interfaces in such inorganic/organic composites led to TE performance far below that of bulk α-MgAgSb. Besides, Oueldna et al. attempted to co-deposit Mg, Ag and Sb using magnetron sputtering. However, regardless of how the initial composition ratio was adjusted, the resulting films failed to form pure α-MgAgSb as the main phase51,52. At present, despite the promising TE potential of α-MgAgSb, a phase-pure and high-performance α-MgAgSb film suitable for flexible TE devices has not yet been realized.

In this work, we employ molecular beam deposition to precisely stabilize MgAgSb within its α-phase range and finely tune its stoichiometry. This deposition technique provides a quasi-equilibrium growth environment that favors the formation of phase-pure α-MgAgSb while suppressing secondary phases. Consequently, we successfully obtain the flexible inorganic α-MgAgSb thin film with exceptional TE performance, achieving a zT value of 0.8 at room temperature and a peak PF of 19.3 μW cm−1 K-2 at 473K, placing these films among the promising flexible p-type TE candidates beyond Bi2Te3. Using this technique, we further investigate the impact of stoichiometric deviations and find that slight deficiencies in composition degrade the TE performance of α-MgAgSb. Furthermore, we demonstrate that the fabricated α-MgAgSb film exhibits notable flexibility and thermal stability, maintains performance after 1000 bending cycles and repeated thermal cycling between 373K and 473K. Finally, we fabricate a flexible thermoelectric device based on these films, realizing an estimated normalized power density of 4.9 μW cm-2 K-2, suggesting their strong practical potential. This work marks an important step in the exploration of flexible α-MgAgSb and provides valuable insights for integrating MgAgSb-based thermoelectrics in flexible electronics.

Results
High-performance flexible α-MgAgSb film
MgAgSb exhibits three polymorphs over different temperature ranges: α-MgAgSb, β-MgAgSb, and γ-MgAgSb. Among them, only α-MgAgSb shows high TE potential with large zT values, whereas both β- and γ-MgAgSb display poor performance. A recent study has demonstrated that β-MgAgSb can be strategically utilized in α/β-segmented junctions to enhance power output while maintaining conversion efficiency53. However, the formation of β- or especially γ-MgAgSb within the MgAgSb matrix will degrade its overall TE performance. As shown in Fig. 1a, γ-MgAgSb forms from β-MgAgSb upon heating, accompanied by the precipitation of Ag3Sb and Sb. Once γ-MgAgSb, Ag3Sb, and Sb appear, they remain even after cooling to room temperature, which not only deteriorates MgAgSb performance but also complicates the synthesis of high-quality MgAgSb. This issue is particularly critical for film fabrication. Magnetron sputtering, a commonly used deposition technique, has consistently failed to produce high-performance α-MgAgSb films because of extensive impurity formation. Typically, during sputtering, energetic atoms, ions, and excited species with high kinetic energies and fluctuating fluxes lead to non-uniform nucleation and far-from-equilibrium growth, making the formation of secondary phases easy. These problems are particularly severe for MgAgSb due to the above-mentioned complex phase behavior. In addition, the high vapor pressure and reactivity of Mg under the relatively low vacuum of the sputtering chamber result in Mg loss and undesired reactions during deposition, which further disturb the stoichiometry and hinder precise phase control, making it difficult to fabricate high-performance MgAgSb films.

To achieve a high-performance α-MgAgSb film, precise phase control during deposition is essential. First, the reaction temperature must be strictly maintained below 573K to keep MgAgSb within the α-phase stability range. Second, the deposited Mg, Ag and Sb atoms need to thoroughly react under near-equilibrium conditions. Third, a high-vacuum environment is required to prevent oxidation and undesirable reactions of Mg. Based on these requirements, we employed molecular beam deposition (Fig. 1b), which offers ideal growth conditions for the MgAgSb film. In this process, low-energy neutral Mg, Ag and Sb atoms arrive at the substrate in well-collimated molecular beams under ultra-high vacuum. The slow and gentle deposition enables controlled surface diffusion and reaction of these atoms under quasi-equilibrium conditions, forming α-MgAgSb when the substrate temperature is maintained at 523K. It is worth noting that although a molecular beam epitaxy system was used, the substrate was a flexible polyimide rather than a conventional single-crystalline substrate, which enables both film growth and mechanical flexibility. Supplementary Fig. S1 shows the X-ray diffraction (XRD) patterns of the molecular-beam-deposited films, which match well with the corresponding powder diffraction patterns of the α-MgAgSb phase, confirming that flexible α-MgAgSb films were successfully obtained on polyimide substrates (Fig. 1c).

Importantly, as shown in Fig. 1d, the flexible MgAgSb films exhibit an excellent room-temperature zT of 0.8. Although this value is slightly lower than that of state-of-the-art p-type Bi2Te3-based flexible materials, it is significantly higher than those of other reported flexible TE films. Moreover, as shown in Fig. 1e, the α-MgAgSb film shows an increasing PF, reaching a maximum of 19.3 μW cm−1 K−2 at 473K. This temperature-dependent enhancement leads to a high average power factor (PFavg) of 17.2 μW cm−1 K−2 over the range of 293–523K (Fig. 1f). The exceptional performance (zT and PF) of α-MgAgSb in this work can be attributed to the successful synthesis of high-purity α-MgAgSb. Intrinsically, the favorable band structure of high band degeneracy, as well as large anharmonicity and weak chemical bonding in α-MgAgSb, enables its high PF and zT compared to other materials. These results highlight the strong potential of flexible α-MgAgSb films for TE applications even beyond room temperature.

Elemental deficiency effects on TE performance
MgAgSb is known to be highly sensitive to stoichiometry54. Molecular beam deposition provides an ideal platform to investigate how stoichiometric deviation affects the TE performance of flexible MgAgSb film. By carefully adjusting the flux rate of Mg, Ag and Sb (Supplementary Fig. S2 and Supplementary Table S1), we intentionally introduced a 5% deficiency in each element to allow a clearer observation of the effects of non-stoichiometry on the TE properties of MgAgSb thin films, producing Mg-deficient, Ag-deficient, and Sb-deficient films, respectively. XRD patterns confirmed that all these films remain primarily in the α-MgAgSb phase (Supplementary Fig. S3). The TE performance of these films was systematically measured over a temperature range of 303K to 523K to assess the impact of these deficiencies, with the corresponding thickness data shown in Supplementary Fig. S4. As shown in Fig. 2a, Sb and Ag deficiencies lead to higher resistivity ρ of the films, whereas Mg deficiency decreases ρ. Figure 2b shows the S of these films, and the S increases in the Sb-deficient, slightly decreases in Ag-deficient films, and drops markedly in the Mg-deficient film. Consequently, all deficient films exhibit lower PF than the stoichiometric film (Fig. 2c), underscoring the critical role of precise phase and composition control in achieving high-performance α-MgAgSb films.

To further elucidate the impact of elemental deficiencies on charge transport, we measured the Hall carrier concentration nH and mobility μH of each α-MgAgSb film at room temperature. As shown in Fig. 2d, the stoichiometric film exhibits an nH of 3.9 × 1019 cm−3 and a μH of 53 cm2 V−1 s−1, values consistent with those reported for high-performance bulk α-MgAgSb55. For the element-deficient films, Sb deficiency is observed to reduce the room-temperature nH, which may arise from the formation of Sb vacancies (V3+Sb). These vacancies act as electron donors, leading to a decreased nH and consequently an increased S according to the Pisarenko relation. In the case of Ag deficiency, Ag vacancies (V−Ag) may be induced, increasing nH, as reflected by the decreasing trend of S over a broad temperature range. In contrast, Mg deficiency markedly increases nH due to the formation of Mg vacancies (V2−Mg) and Ag-Mg antistites defects (AgMg)56,57, resulting in a much lower S. Notably, μH decreases uniformly in all deficient films, primarily due to enhanced carrier scattering from point defects and possible secondary phases associated with non-stoichiometry. The reduced μH intrinsically deteriorates electrical transport, resulting in all deficient films exhibiting lower PFs than the non-deficient sample. Since charge transport is also strongly influenced by the electronic band structure, we further investigated how elemental deficiencies modify the band structure of α-MgAgSb. As shown in Fig. 2e, Ag and Mg deficiencies exert little influence on the valence band maximum (VBM) between the X and Γ points, whereas Sb deficiency significantly distorts the VBM. This distortion likely explains the pronounced reduction in mobility observed in Sb-deficient films. Overall, among the various elemental deficiencies, Sb deficiency is the most detrimental, leading to both the lowest carrier nH and μH, and thus causing the greatest degradation in electrical performance, with the PF of the Sb-deficient film being only half that of the non-deficient film.

In addition to electrical performance, the cross-plane thermal conductivity κ of these films was measured at room temperature using the time-domain thermoreflectance method and is presented in Supplementary Figs. S5, S6 and Supplementary Table S2. All films exhibit lower κ compared to reported bulk values. The non-deficient MgAgSb film shows a κ of 0.61 W m−1 K−1, while the deficient films show even lower values. Benefiting from the ultralow κ and relatively high PF, the non-deficient flexible MgAgSb film achieves a room-temperature zT of approximately 0.8, which is comparable to that of state-of-the-art MgAgSb bulk. However, despite the lower κ values in element-deficient films, all of them exhibit reduced zT values. In particular, the zT of the Sb-deficient film drops to around 0.5 at room temperature (Supplementary Fig. S7), primarily due to its pronounced decline in PF.

Microstructure, stability and flexibility of α-MgAgSb film
MgAgSb is intrinsically a low κ system. The α-MgAgSb films fabricated by molecular beam deposition exhibit lower κ than most conventional bulk α-MgAgSb, as noted in the previous section55. To elucidate the origin of their low κ, we examined the microstructures of stoichiometric and element-deficient films using scanning electron microscopy (SEM). As shown in Fig. 3a and Supplementary Figs. S8, S9, the stoichiometric, Ag‑deficient, and Mg‑deficient films display uniform and compact surfaces, whereas the Sb‑deficient film shows poor and uneven crystal quality, indicating that Sb deficiency is unfavorable for the growth of α-MgAgSb crystals. Notably, the grains in all films are nanosized; for example, the stoichiometric film has grain sizes of about 60-90 nm, as displayed in Fig. 3b. The nanoscale grain structure reveals the polycrystalline nature of the films. Together with the absence of obvious preferred orientation in the XRD patterns (Supplementary Fig S1), the films are therefore expected to exhibit nearly isotropic TE properties, even though S and σ were measured in-plane, while κ was measured cross-plane. These nanoscale grains result from the low deposition temperature, which limits atomic diffusion and grain growth. To further investigate compositional uniformity, we also applied the energy-dispersive X-ray spectroscopy (EDS) analysis. As shown in Fig. 3c and Supplementary Figs. S10–S12, Mg, Ag and Sb are homogeneously distributed in the stoichiometric, Ag-deficient, and Mg-deficient films. In contrast, the Sb-deficient film contains Mg-rich regions (Supplementary Fig. S12), evidencing impurity formation.

To gain deeper insight into the impact of elemental deficiencies on thermal transport, we have decomposed the total thermal conductivity into its electronic and lattice components (Supplementary Note S1 and Supplementary Fig. S13). It is evident that Sb deficiency leads to an increase in lattice thermal conductivity (κL), whereas Mg deficiency results in a pronounced reduction in κL. In comparison, Ag deficiency has a relatively minor influence on κL. The increased κL observed in Sb-deficient films likely originates from the formation of Mg-rich metallic secondary phases, as evidenced in Supplementary Figs. S9 and S12. In contrast, the presence of Mg vacancies and Ag-Mg antisite defects in Mg-deficient films enhances phonon scattering, thereby reducing κL48. Notably, although all these films exhibit a reduced κL compared with bulk samples due to enhanced phonon scattering from nanoscale grains, such nanoscale grains can also induce carrier scattering, leading to a relatively lower carrier mobility than that of bulk counterparts49 and consequently relatively low zT values.

Overall, stoichiometric films exhibit the best TE performance among α-MgAgSb thin films, and even slight Sb deficiency should be avoided whenever possible. In addition to high performance of the stoichiometric films, thermal stability and mechanical stability are essential for their practical applications in flexible electronics38. We first evaluated the thermal stability of the film under repeated measurements at 373K and 473K (the temperature of peak PF). As shown in Fig. 3d, the electrical transport properties, including the S, σ, and PF, remain unchanged, demonstrating excellent thermal stability under elevated-temperature operation. This stability can be attributed to the intrinsic phase stability of α-MgAgSb, which is thermodynamically stable over a broad temperature range and does not undergo phase transitions or decomposition within the temperature window investigated in this work58. We then assessed the flexibility of the α-MgAgSb film by subjecting it to repeated bending at a fixed bending radius of 10 mm, corresponding to an applied strain of approximately 0.75% (Supplementary Note S2 and Fig. 3e). The ratios of S/S0, σ/σ0, and PF/PF0 (where S0, σ0, and PF0 are the initial values) are found to remain nearly constant with increasing bending cycles. Remarkably, after 1000 bending cycles, the PF of the film retains 96% of its initial value within a 5% measurement error. The surface morphology after 1000 bending cycles (Supplementary Fig. S14) shows few cracks. These results confirm the excellent flexibility and durability of the α-MgAgSb film. This high flexibility arises from the small film thickness (about 180 nm), which allows large elastic bending strains25, together with the intrinsically flexible polyimide substrate that redistributes bending-induced stress and reduces the effective strain in the film. Consequently, the α-MgAgSb films show strong potential for flexible TE power generation under practical operating conditions, including applications requiring mechanical compliance and thermal robustness.

High-performance flexible α-MgAgSb TE device
To evaluate the practical potential of the flexible α-MgAgSb film, we fabricated a flexible TE device consisting of nine MgAgSb legs electrically connected in series using Ag interconnects (Fig. 4a). For power generation, one side of the flexible TE device is heated, enabling in-plane heat flow. Based on this configuration, we measured the open-circuit voltage (Voc) generated by the TE device and the output power under different hot-side temperatures with varying loading current (I). As shown in Fig. 4b, when the hot-side temperature is 393K (estimated ΔT=16K), the Voc reaches 40 mV. As the hot-side temperature increases to 513K (estimated ΔT=40K), the Voc rises to 66 mV. The relationship between Voc and ΔT is shown in Supplementary Fig. S15, clearly demonstrating that Voc of TE device increases with ΔT. Based on the measured output voltage and current, the output power was calculated. The maximum output power (Pmax) is achieved when the internal resistance of the device matches the external load resistance, as shown in Supplementary Fig. S16. Consequently, a normalized power density (Pmax/AΔT2) of 4.9 μW cm−2 K−2 is obtained at a hot-side temperature of 513K. As shown in Fig. 4c and Supplementary Table S3, the normalized power density achieved in this work ranks among the leading values ever reported for flexible in-plane TE devices based on other material systems, highlighting the excellent potential of α-MgAgSb for flexible energy conversion applications. Notably, the device operates reliably at elevated temperatures up to 513K, making it suitable not only for wearable electronics but also for practical applications such as aerospace surface monitoring, engine diagnostics, and smart factories, where moderate temperature gradients are available.

To further reveal the flexibility of the device, we measured the output voltage and output power under bending conditions, as shown in Supplementary Fig. S17. At a hot stage temperature of 513K, the Voc is 58 mV, and the Pmax reaches 0.36 μW. It should be noted that the flexible TE device was mounted on the curved surface of a carbon pillar rather than directly on a flat heating stage, resulting in a different effective hot-side temperature on the device and, consequently, variations in the measured output voltage and power. In addition to testing under curved-surface conditions, we further evaluated the mechanical flexibility of the flexible MgAgSb TE device through repeated bending tests. Unlike a single TE film, a TE device includes additional electrical contacts, making such tests essential. As shown in Fig. 4d, after 1000 bending cycles with a fixed bending radius of 10 mm, the device’s internal resistance R increased only slightly by about 6% compared to its initial internal resistance R0. Meanwhile, the Pmax/A after 1000 bending cycles remained almost unchanged compared to its initial value (Fig. 4e). These results demonstrate the excellent flexibility and reliability of the device for potential practical flexible TE applications. To further illustrate its potential, we tested the device under finger-induced temperature gradients. As shown in Fig. 4f, g, the device generated an output voltage of about 3.0 mV and a maximum output power of 0.88 nW when placed on the side or tip of a finger, highlighting its promise for wearable technology and paving the way for flexible TE devices as sustainable power sources for flexible electronics59.

In summary, by succeeding to precisely stabilizing MgAgSb within its α-phase range and finely controlling its composition using advanced molecular beam deposition, we have successfully fabricated high-performance flexible α-MgAgSb films. This flexible α-MgAgSb film achieves a zT value of 0.8 at room temperature and a PF of 19.3 μW cm−1 K−2 at 473K, surpassing most flexible TE materials and second only to the long-standing champion, flexible Bi2Te3 films. Notably, the PF of flexible α-MgAgSb film increases with temperature, leading to an excellent average PF of 17.2 μW cm−1 K−2 in the 293–523K range. This measured increase in PF with temperature, together with the expected decrease in thermal conductivity at elevated temperatures due to enhanced phonon scattering, suggests that zT values exceeding 0.8 may be achievable at higher temperatures. Beyond its high performance, the flexible α-MgAgSb film shows remarkable thermal stability and mechanical flexibility under thermal and bending cycles. Finally, a flexible TE device comprising nine α-MgAgSb film legs is demonstrated to exhibit an estimated normalized power density of 4.9 μW cm−2 K−2, demonstrating strong potential for power generation in flexible electronics. In future studies, strategies such as grain enlargement and doping could be explored to further enhance TE performance, as the current films still underperform compared with optimized bulk materials. Moreover, developing scalable, large-area fabrication routes and integrating these films into flexible device architectures will be crucial for more practical applications. Nevertheless, this work opens a new pathway for flexible applications of α-MgAgSb and represents an important step toward self-powered flexible technologies.

Methods
Film fabrication
All flexible α-MgAgSb films were deposited on a polyimide substrate using a molecular beam epitaxy system (EV-500, Eiko). The base pressure in the chamber was 10⁻⁸ Pa, and the working pressure was maintained in the 10-7 Pa range during deposition. Mg, Ag, and Sb of 4N purity were placed in separate Knudsen cells and heated to the specified temperatures. The evaporation rate of each element was determined using a retractable quartz crystal microbalance (QCM) thickness monitor (Q-pod, Inficon), located at the substrate position. The substrate was heated from the back of the sample stage. A thermocouple measured the temperature between the sample holder and the heater, which controlled the heater power to keep a specified temperature. The actual substrate temperature was consistent with the set temperature when the temperature was below 773K. The polyimide substrate was immersed in acetone and subjected to ultrasonic cleaning for 30 minutes to remove surface organic contaminants and dust before being transferred into the vacuum chamber. It was heated to 523K and held for 30 minutes to remove residual impurities before deposition. The α-MgAgSb films were prepared by co-depositing Mg, Ag, and Sb with a 1:1:1 flux ratio, monitored by a QCM, at a substrate temperature of 523K. Compositional analysis was performed by EDS on films deposited on Al2O3 substrate under the same conditions as those on polyimide. As shown in Supplementary Fig. S18 and Supplementary Table S4, the film composition closely matches the intended 1:1:1 ratio. Based on this result, off-stoichiometric films were fabricated by individually reducing the flux of each element by 5% during deposition. EDS analysis further confirms a ~5% Sb deficiency in the corresponding film (Supplementary Fig. S18 and Supplementary Table S4). The films were deposited at a rate of 6 nm per minute for 30 min with the substrate rotating at 5 rpm, resulting in a thickness of approximately 180 nm.

Characterization
The phase composition and crystallinity of the stoichiometric MgAgSb film were examined using XRD and grazing incidence XRD (GIXRD). XRD measurements were performed on a Rigaku MiniFlex diffractometer with a Cu Kα+β source, while GIXRD was carried out using a Rigaku TF-XRD system equipped with a Cu Kα source. Both techniques reveal the characteristic diffraction peaks of the α-MgAgSb phase. Because GIXRD measurements are more time-consuming, conventional XRD, which provides reliable and efficient phase identification, was used for all element-deficient films. The surface morphology of films was analyzed using scanning electron microscopy (SEM) (Hitachi High-Tech/S-4800), and the component was analyzed using energy dispersive spectroscopy (EDS) (Hitachi High-Tech/TM-3000). The film thicknesses were measured using a surface profiler system (Bruker Dektak 6M) by the step method. The step was created from an uncovered area of the substrate to the film surface. The measurement uncertainty was within 10 nm. Hall carrier concentration and mobility at 300K were measured using a four-probe Hall system (Biorad H5580) under a magnetic field of 0.45 T using the van der Pauw method, which is suitable for samples of arbitrary geometry. The probes were placed at the corners of the film, and the insulating substrate did not affect the measurements. Multiple measurements were performed to ensure stable contacts, with an uncertainty of approximately 1%. The electric conductivity and Seebeck coefficient of thin films were measured using a ZEM-3 (Advance Riko) apparatus in a He atmosphere, with samples having lateral dimensions of 10 mm × 3 mm. Multiple measurements confirmed good reproducibility of the film fabrication, with variations within approximately 5% (Supplementary Fig. S19). The cross-plane thermal conductivity of the samples was measured using the picosecond time-domain thermoreflectance (TDTR) instrument (PicoTR, PicoTherm) in a front-heating/front-detection configuration. Prior to the measurements, a ~100 nm-thick Pt layer was sputtered onto the thin-film surfaces by using a DC sputtering system to serve as a transducer. A 1550 nm infrared pulsed laser with a repetition frequency of 20 MHz and a pulse duration of 0.5 ps was used as a heat source. A 780 nm probe laser was used to detect the thermoreflectance signal. The picosecond TDTR system was customized to reduce the spot size of the probe laser to ca. 5 μm as described elsewhere60. The improved mirror image method for fitting all the range of pulse interval was used to determine the thermal conductivity value61,62. In Supplementary Fig. S5, the measured thermoreflectance signals are shown together with the fitted curves. The interfacial thermal resistance (ITR) between the MgAgSb film and the Pt layer is extracted to be smaller than 1.0 × 10-8 m2 KW-1 for all films (Supplementary Table S2), indicating that the possible error introduced in film thermal conductivity is at most about 3%. The specific heat of all films was calculated based on the Dulong-Petit law, with a 5% elemental deficiency taken into account for the deficient films. The uncertainty in the measured total thermal conductivity is estimated to be within 8%.

Flexible TE device fabrication and measurement
To fabricate a nine-leg flexible thin-film thermoelectric generator, nine rectangular α-MgAgSb thermoelectric legs (6 mm in length, 2 mm in width, and 400 nm in thickness) were deposited on a PI substrate using a stainless-steel shadow mask. Thereafter, Ag interconnects with a thickness of 100 nm were deposited in MBE at room temperature to electrically connect the nine pairs of thermoelectric legs. The α-MgAgSb legs were fabricated using the same thin-film deposition procedure described above, with the deposition time extended to achieve a thickness of 400 nm. To evaluate the performance of the flexible thin-film thermoelectric generator, the device was mounted at the edge of a heating stage, with one side in contact with the stage and the other side exposed to air. By controlling the stage temperature, different temperature gradients across the two ends of the thermoelectric legs were established. The TE device performance was evaluated using a KEITHLEY 2400 Source Measuring Unit, which measured the I-V characteristics to calculate the power output of the TE device.

First-principles calculations
The electronic band structures of α-MgAgSb with and without elemental deficiencies were calculated using the Vienna ab initio Simulation Package (VASP) software. The generalized gradient approximation of Perdew-Burke-Ernzerhof (GGA-PBE) combined with the modified Becke-Johnson (mBJ) exchange-correlation functional was employed63,64. After full geometry relaxation, self-consistent static calculations were performed on 64-atom α-MgAgSb unit cell (Mg16Ag16Sb16) and on deficient structures, namely Mg15Ag16Sb16, Mg16Ag15Sb16, Mg16Ag16Sb15 for Mg-, Ag- and Sb-deficient cases at the 16i, 8e, 16i Wyckoff sites, respectively. A plane-wave energy cutoff of 500 eV was used, and the Hellmann-Feynman force on each atom energy was converged below 0.001 eV·Å−1, with an electronic convergence criterion of 10-8 eV. The resulting band structures were unfolded back to the primitive cell using VASPKIT for subsequent analysis65.

TE device evaluation
The temperature difference across the flexible TE device during heating is calculated by using ΔT=Voc/SNleg, following literature methods9,29,32. This approach could reflect the effective temperature difference experienced by the device, where Voc is the open-circuit voltage of the device under temperature difference, S is the Seebeck coefficient of the p-type leg at the hot-side temperature, and Nleg is the number of TE legs in the device. The Seebeck coefficient at the cold side differs from that at the hot side, which will introduce some uncertainty in ΔT. However, for the maximum temperature gradient of ~40K, this difference is within 6%. Considering the instrumental uncertainty in Seebeck coefficient measurements, the overall uncertainty in the estimated ΔT will be within 10%. The output power density is calculated by using P=V·I/A, where A is the cross-sectional area perpendicular to the direction of heat flow in the device. The normalized maximum power density is calculated as Pmax/AΔT2 with an estimated uncertainty of approximately 12%.

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "The authors report the fabrication of flexible, phase-pure α-MgAgSb thin films that exhibit high thermoelectric performance (zT ≈ 0.8 at 300 K; PF ≈ 19.3 µW cm-1 K-2 at 473 K), achieved through molecular-beam deposition. The study highlights the stabilization of the α-phase, controlled stoichiometry, and good mechanical robustness, representing a substantial improvement over traditional Bi2Te3-based flexible films. However, the manuscript requires significant improvement in its overall organization and in the interpretation of the experimental data. The following comments should be addressed to facilitate further consideration of the manuscript.\n1. The introduction is too lengthy and should focus more directly on the main research gap, specifically regarding the phase-pure, high-performance flexible α-MgAgSb films. The background information on organic and hybrid thermoelectrics, as well as the discussion on plasticity and size-reduction strategies, can be significantly condensed. When referring to other example systems, their key limitations should be stated briefly and clearly. The authors should avoid subjective terms such as “excellent”, “best”, or “unprecedented”, and should appropriately qualify their claims of novelty. Additionally, the overall text should be carefully revised for grammar and clarity.\n2. The reported zT at 300 K is impressive for a flexible film, but it is still lower than that of Bi2Te3. The power factor is also comparatively low; therefore, the authors should emphasize the zT at 300 K and the higher PF at 473 K while ensuring a fair comparison at the same temperature. The discussion lacks an analysis of the underlying transport mechanisms and how they relate to the observed increases in PF and zT. Although Figures 1d–f are presented clearly, the authors should provide a brief explanation of how the transport mechanisms in α-MgAgSb differ from those in the comparison materials to offer a more comprehensive physical interpretation.\n3. The increase in Seebeck coefficient for the Sb-deficient samples is likely due to a reduction in hole concentration, which can be demonstrated using the using the S–nH relation. The authors should also provide a brief explanation for why all deficient films exhibit lower PF, even though some show a reduced κ. In the thermal conductivity analysis, it is important to address the potential influence of interfacial thermal resistance between the MgAgSb film and the Pt transducer, as this can significantly affect TDTR measurements in ultrathin films. Additionally, using a fixed specific heat may introduce systematic errors, especially for nanostructured or off-stoichiometric samples. This assumption should either be justified or its uncertainty should be estimated. The analysis would improve by separating and discussing the contributions of electronic and lattice contributions to κ, which would help clarify the roles of carrier and phonon transport.\n4. Isotropy must be demonstrated by directional measurements or validated by calculations, rather than relying solely on grain size. The statement “nanoscale grains suggest isotropic TE performance” is speculative and should be supported by appropriate references. The authors need to clarify the dual role of nanoscale grains, explaining how they reduce κ via enhanced phonon scattering while potentially degrading electrical transport through grain-boundary scattering. While the bending test is useful, it has its limitations. If possible, the strain should be estimated based on the bending radius and the thickness of the film/substrate. Additionally, post-bending SEM images should be provided to confirm the absence of cracks, delamination, or failures in interconnects. The authors should also specify the temperature difference used for device performance normalization and discuss the associated uncertainties to ensure a fair comparison between devices.\n5. The conclusion is somewhat repetitive and relies too heavily on phrases such as “for the first time”, “excellent”, and “unprecedented”. The statement that zT may exceed 1 at higher temperatures is speculative, as no data beyond 523 K are provided; the authors should clarify the basis for this expectation. While the discussion of device performance is clear, the term “unprecedented” should be avoided unless it is backed by a direct numerical comparison with the best-performing flexible devices in the literature. Instead of concluding with repeated praise, the conclusion would be stronger if it included a more forward-looking perspective on future studies.\n6. In the Film fabrication section, the temperature control needs to be described more precisely. Since the stabilization of the α-MgAgSb phase is highly sensitive to temperature, it is important to specify the actual substrate temperature range rather than just the set temperature. The authors state that deposition time was adjusted to obtain ~180 nm films, but they do not provide information on the deposition rate or thickness uniformity. Small variations in Mg flux can lead to the formation of secondary phases, making these details crucial. Although QCM flux monitoring is mentioned, it remains unclear whether post-deposition compositional analysis, such as EDS or XPS quantification, was performed to confirm the stoichiometry of the films. Given the sensitivity of MgAgSb to the flux ratio, it is essential to state the nominal atomic flux ratio (e.g., Mg:Ag:Sb = 1:1:1) and to explain how this ratio was adjusted for stoichiometric versus element-deficient films.\n7. In the Characterization section, the authors should specify whether XRD was performed in grazing-incidence mode, which is more appropriate for ~180 nm films on polymer substrates. Regarding thickness measurement, the step-profile method is acceptable; however, the procedure for creating the step and the associated uncertainty should be clearly stated. The description of the Hall measurement is incomplete; it should include details about the magnetic field strength and the measurement geometry. Additionally, issues such as contact stability and the influence of the substrate should be briefly addressed. For the ZEM-3 measurements, the authors should provide the sample dimensions used in the measurement fixture and include a concise statement on data reproducibility across multiple samples to confirm the reliability of the reported results.", "reviewer_2": "In this manuscript, the authors present high-performance MgAgSb-based flexible thermoelectric film and device. By employing molecular beam deposition and finely manipulating the composition, they successfully achieved a phase-pure α-MgAgSb film, leading to a high power factor. The as-fabricated device also demonstrates a high normalized output power density. This work makes a great contribution to the development of high-performance flexible thermoelectrics with an unusual way. The manuscript is well organized, and the experimental results convincingly support the discussion and conclusions. I would like to recommend this work after addressing the following comments:\n1. Besides molecular beam deposition, are there any other feasible methods to fabricate MgAgSb thin films? Since molecular beam epitaxy is a complex and expensive equipment that may limit scalability.\n2. Although a phase-pure film was obtained, the reported power factor is still slightly lower than that of the corresponding bulk material. Please give some explanations.\n3. The authors report that a 5% elemental deficiency results in a noticeable degradation of thermoelectric performance. Since this deficiency is relatively large, it would be interesting to know whether smaller deviations in composition might have a different impact on the film properties.\n4. In the device measurement, the hot-side temperature reached up to 513 K. This temperature appears higher than what is typically expected for flexible electronic device applications. Would that be harmful to the flexible device?\n5. In Fig. 4f, a finger touch generates an open-circuit voltage of about 3 mV. Recent studies have reported practical evaluations of power density for flexible thermoelectric generators under similar human-body heat conditions (e.g. Chem. Mater. 31 2019, 5238-5244.). Could the authors estimate or calculate the corresponding output power density based on the device resistance?\n6. There exist some typos, e.g. “A more promising route is to fabricate α-MgAgSb thin films via through bottom-up approaches.” The authors should carefully scrutinize the manuscript to avoid similar mistakes.", "reviewer_3": "MgAgSb bulk materials and films have been studied in some references. In the manuscript, the authors were able to precisely control the chemical composition and phase composition of the prepared MgAgSb films and obtained the excellent thermoelectric properties. The flexibility of the prepared films and the output characteristics of thermoelectric devices assembled by studied films in the manuscript also have been studied. This is a meaningful study. However, the manuscript lacks in-depth characterization of the microstructure for the deposited films and in-depth theoretical analysis for the experimental results. Some problems are following:\nProblems:\n1. The sample lacks an in-depth observation of its microstructure. Is there any method to characterize the vacancies of the atoms in the lattice? This is a difficult problem. If possible, Try to do it.\n2. Please elaborate in detail on the sources of the main charge carriers (holes) in the p-type MgAgSb films. Analyze the essence of the change in carrier concentration and mobility when the atomic vacancies in the MgAgSb lattice have appeared. At the same time, discuss the fundamental reason for the variation of Seebeck coefficient and thermal conductivity with the occurrence of the atomic vacancies in the MgAgSb lattice.\n3. Fig.3 (d),(e) showed the excellent stability and flexibility of α-MgAgSb film. Please provide a reasonable theoretical explanation for this result.\n4. In order to more clearly express the output characteristics of the thermoelectric device, please provide a figure showing the relationship between the open-circuit voltage and the temperature difference.\n5. In page 11 line 278-279: “As shown in Fig. 4c and table S3, the performance achieved in this work is unprecedented in terms of maximum power output density demonstrated,…” and Fig.4(c): Here, because the temperature difference affects the maximum power output density of the thermoelectric device, using the maximum power output density in comparison with other references is meaningless. However, the comparison of the normalized power density for different materials is meaningful. The comparison of the maximum power output density shown in Fig. 4(c) needs to be deleted.\n6. To better understand the output characteristics of the thermoelectric device, please provide the external resistance and the internal resistance of the thermoelectric device corresponding to the maximum output power obtained under different temperature differences in Fig.4(b) and in the manuscript.\n7. In order to clearly illustrate the influence of flexibility on the output characteristics of the thermoelectric device, please mark the bending conditions in Fig.S15.\n8. In page 12 line 284-285: “At a hot-side temperature of 513 K, the V is 60 mV, and the P reaches 0.4 μW.” Here, from Fig.S15, the maximum power output density does not reach 0.4 μW. Please carefully check the data. Under this bending condition, what is the internal resistance of the thermoelectric device? What is the reason for the difference between its internal resistance under this bending condition and without bending? Under the bending conditions, at the same temperature difference, both its open-circuit voltage and maximum output power are lower than those of the thermoelectric device under no bending conditions? Why is this so? Please provide a reasonable explanation.\n9. On temperature difference evaluation of TE device, Why not use the thermocouple measurement but instead of calculation using the formula ΔT=Voc/S ∙ Nleg? Does it have any advantages over the measured values?\nOther problems\n1. In page 11 line 274-275: “As shown in Fig. 4b, when the hot-side temperature is 393 K, the V reaches 40 mV, generating an output power of 0.17 μW…” Here, the “output power” should be “maximum output power”?\n2. According to the custom, in order to clearly convey the meaning of the data in the figure, the horizontal and vertical axes of Fig.4(b) should be labeled with \"output current\" and \"output voltage\" or \"output power\".\n3. In fact, the output voltage and output power of the thermoelectric device depend on the temperature difference. In Fig.4(b) and S15, it is more appropriate to use the temperature difference instead of the hot plate temperature to describe the data in figures.\n4. In the manuscript, to avoid any confusion, please use different symbols to represent the output voltage and the open-circuit voltage. And in the statements, please replace \"V\" and \"P\" with \"output voltage\" and \"output power\" respectively.\n5. In Fig. 4(e), what parameter does TN represent?"}, "author_response": "Dear reviewers,\nThank you very much for your valuable comments on our manuscript, which helps\nimprove the quality of this work. The point-to-point reply is listed below and the\nmanuscript is revised accordingly. We hope you will find the revised manuscript can be\nsuitable for publication.\nSincerely yours,\nTakao Mori\nReviewer #1 (Remarks to the Author):\nComment: The authors report the fabrication of flexible, phase-pure α-MgAgSb thin\nfilms that exhibit high thermoelectric performance (zT ≈ 0.8 at 300 K; PF ≈ 19.3 µW\ncm-1 K-2 at 473 K), achieved through molecular-beam deposition. The study highlights\nthe stabilization of the α-phase, controlled stoichiometry, and good mechanical\nrobustness, representing a substantial improvement over traditional Bi Te -based\n2 3\nflexible films. However, the manuscript requires significant improvement in its overall\norganization and in the interpretation of the experimental data. The following comments\nshould be addressed to facilitate further consideration of the manuscript.\nResponse: Thank you very much for your thorough and constructive review of our\nwork. We sincerely appreciate your valuable comments regarding the need to improve\nthe overall organization of the manuscript and the interpretation of the experimental\ndata. In response, we have revised the manuscript accordingly. We believe these\nrevisions have improved the clarity, rigor, and completeness of the manuscript. Below,\nwe provide point-by-point responses to your detailed comments.\nComment 1: The introduction is too lengthy and should focus more directly on the\nmain research gap, specifically regarding the phase-pure, high-performance flexible α-\nMgAgSb films. The background information on organic and hybrid thermoelectrics, as\nwell as the discussion on plasticity and size-reduction strategies, can be significantly\ncondensed. When referring to other example systems, their key limitations should be\nstated briefly and clearly. The authors should avoid subjective terms such as “excellent”,\n“best”, or “unprecedented”, and should appropriately qualify their claims of novelty.\nAdditionally, the overall text should be carefully revised for grammar and clarity.\nResponse: Thank you for the insightful suggestions regarding the condensation and\nfocus of the Introduction. In response, we have reorganized this section to more clearly\nhighlight the key research gap related to achieving phase-pure, high-performance\nflexible α-MgAgSb films. The background discussions on organic and hybrid\nthermoelectrics, as well as plasticity and size-reduction strategies, have been\nsignificantly condensed, and references to other systems now briefly and clearly state\ntheir main limitations. Subjective expressions have also been removed, and the wording\nhas been adjusted to appropriately qualify claims of novelty. The revised sections on\nPages 2-4 are highlighted in yellow for ease of reference. In addition, the entire\nmanuscript has been carefully revised to improve grammar, clarity, and conciseness.\nComment 2: The reported zT at 300 K is impressive for a flexible film, but it is still\nlower than that of Bi Te . The power factor is also comparatively low; therefore, the\n2 3\nauthors should emphasize the zT at 300 K and the higher PF at 473 K while ensuring a\nfair comparison at the same temperature. The discussion lacks an analysis of the\nunderlying transport mechanisms and how they relate to the observed increases in PF\nand zT. Although Figures 1d–f are presented clearly, the authors should provide a brief\nexplanation of how the transport mechanisms in α-MgAgSb differ from those in the\ncomparison materials to offer a more comprehensive physical interpretation.\nResponse: Thank you for this valuable comment. We agree that fair and temperature-\nconsistent comparisons are essential. In response, we have revised the manuscript to\nexplicitly associate the reported thermoelectric performance with the corresponding\noperating temperatures, ensuring an accurate and balanced comparison. The revised\npart is highlighted on Page 6: “… the flexible MgAgSb films exhibit an excellent room-\ntemperature zT of 0.8. Although this value is slightly lower than that of state-of-the-art\np-type Bi Te -based flexible materials, it is significantly higher than those of other\n2 3\nreported flexible thermoelectric films. Moreover, as shown in Figure 1e, the α-MgAgSb\nfilm shows an increasing PF, reaching a maximum of 19.3 μW cm-1 K-2 at 473 K. This\ntemperature-dependent enhancement leads to a high average power factor (PF ) of\navg\n17.2 μW cm-1 K-2 over the range of 293-523 K (Figure 1f).”\nWe also appreciate your suggestion to strengthen the physical interpretation of the\nobserved performance. Beyond the successful synthesis of phase-pure α-MgAgSb, its\nhigh thermoelectric performance is intrinsically linked to its favorable electronic\nstructure, including high band degeneracy, along with large lattice anharmonicity and\nweak chemical bonding. These characteristics distinguish α-MgAgSb from the\ncomparison materials and contribute to its high PF and zT. A brief discussion has been\nadded on Page 6: “The exceptional performance (zT and PF) of α-MgAgSb in this work\ncan be attributed to the successful synthesis of high-purity α-MgAgSb. Intrinsically, the\nfavorable band structure of high band degeneracy, as well as large anharmonicity and\nweak chemical bonding in α-MgAgSb enables its high PF and zT compared to other\nmaterials.”\nComment 3: The increase in Seebeck coefficient for the Sb-deficient samples is likely\ndue to a reduction in hole concentration, which can be demonstrated using the S-n\nH\nrelation. The authors should also provide a brief explanation for why all deficient films\nexhibit lower PF, even though some show a reduced κ. In the thermal conductivity\nanalysis, it is important to address the potential influence of interfacial thermal\nresistance between the MgAgSb film and the Pt transducer, as this can significantly\naffect TDTR measurements in ultrathin films. Additionally, using a fixed specific heat\nmay introduce systematic errors, especially for nanostructured or off-stoichiometric\nsamples. This assumption should either be justified or its uncertainty should be\nestimated. The analysis would improve by separating and discussing the contributions\nof electronic and lattice contributions to κ, which would help clarify the roles of carrier\nand phonon transport.\nResponse: Thank you very much for your careful reading and insightful questions. We\napologize that this discussion was not sufficiently explicit in the original manuscript.\nWe agree that the reduced carrier concentration will lead to the enhanced Seebeck\ncoefficient observed in Sb-deficient samples, following the Pisarenko relation. This\nexplanation has now been explicitly added on Page 7: “For the element-deficient films,\nSb deficiency is observed to reduce the room-temperature n , which may arise from the\nH\nformation of Sb vacancies (V 3+). These vacancies act as electron donors, leading to a\nSb\ndecreased n and consequently an increased S according to the Pisarenko relation.”\nH\nRegarding the lower PF observed in all element-deficient films, our results show that\nthese films exhibit reduced carrier mobilities compared with the stoichiometric film\n(Figure 2d). This reduction arises from enhanced carrier scattering by point defects and\npossible secondary phases induced by non-stoichiometry, which deteriorates intrinsic\nelectrical transport and leads to a decreased power factor. Additional discussion of this\npoint has been included on Page 8 of the revised manuscript: “Notably, μ decreases\nH\nuniformly in all deficient films, primarily due to enhanced carrier scattering from point\ndefects and possible secondary phases associated with non-stoichiometry. The reduced\nμ intrinsically deteriorates electrical transport, resulting in all deficient films\nH\nexhibiting lower PFs than the non-deficient sample.”\nIn addition to the electrical transport analysis, we have further examined the thermal\ntransport properties of the films. Regarding the potential influence of interfacial thermal\nresistance (ITR) between the MgAgSb film and the Pt transducer layer, we\nacknowledge that this factor can affect the accuracy of TDTR measurements. Therefore,\nwe analyzed ITR values for all samples and summarized them in Table R1, where the\nITR was extracted from the thermoreflectance signals. The ITR values for all films are\nsmaller than 1.0 × 10-8 m2 K W-1, indicating that the possible error introduced in the\nextracted film thermal conductivity is at most about 3%. Consequently, the influence of\nITR is minor. This clarification has been added to the Methods section on Page 16:\n“The interfacial thermal resistance (ITR) between the MgAgSb film and the Pt layer is\nextracted to be smaller than 1.0 × 10-8 m2 K W-1 for all films (Table S2), indicating that\nthe possible error introduced in film thermal conductivity is at most about 3%.”\nRegarding the heat capacity C , we revised and quantitatively evaluated the effect of\np\noff-stoichiometry by accounting for the deficiency of each element in the formula unit\nand applying the Dulong-Petit law. The results show that the previously used constant\nC introduces an error of less than 1%. Additional factors, such as thermal expansion\np\nand nanostructuring, may also influence the heat capacity but are difficult to quantify\nprecisely. Based on the above, by considering both the ITR effects and the revised heat\ncapacity (Table R1), we estimate that the overall uncertainty in the total thermal\nconductivity is within 8%. This discussion has been added to the revised manuscript on\nPage 16: “The specific heat of all films was calculated based on the Dulong-Petit law,\nwith a 5% elemental deficiency taken into account for the deficient films. The\nuncertainty in the measured total thermal conductivity is estimated to be within 8%.”\nTable R1. Thermal properties of the flexible MgAgSb films.\nSample C Thermal ITR Uncertainty\np\nconductivity(W\n(J g-1 K-1) (m2 K W−1) (%)\nm-1 K-1)\nMgAgSb 0.295 0.611 8.8 × 10−9 4.72\nMg-deficient 0.291 0.566 1.0× 10−8 7.05\nAg-deficient 0.296 0.559 9.4× 10−9 6.12\nSb-deficient 0.297 0.541 9.2× 10−9 6.38\nWe apologize for not previously including a separate analysis of the electronic and\nlattice contributions to the thermal conductivity, and we appreciate your thoughtful\nsuggestion. In response, we have now decomposed the total thermal conductivity into\nits electronic and lattice components in the revised Supporting Information, as shown\nin Figure S13. The results indicate that Mg-deficient films exhibit an obvious drop in\nlattice thermal conductivity, which can be attributed to enhanced phonon scattering\ncaused by Mg vacancies and Ag-Mg antisite defects (J. Mater. Chem. A 2022, 10,\n21716-21726; Interdiscip. Mater. 2025, 4, 719-727). In contrast, Ag deficiency has a\nrelatively minor effect on the lattice thermal conductivity. Sb-deficient films show a\nslightly increased lattice thermal conductivity, which is likely due to the formation of\nMg-rich metallic secondary phases, as evidenced in Figures S9 and S12. This additional\nanalysis provides insight into the roles of different elemental deficiencies in governing\nphonon transport in the films. To address this, we have also added a related discussion\non Page 10: “To gain deeper insight into the impact of elemental deficiencies on thermal\ntransport, we have decomposed the total thermal conductivity into its electronic and\nlattice components (Note S1 and Figure S13). It is evident that Sb deficiency leads to\nan increase in lattice thermal conductivity (κ ), whereas Mg deficiency results in a\nL\npronounced reduction in κ . In comparison, Ag deficiency has a relatively minor\nL\ninfluence on κ . The increased κ observed in Sb-deficient films likely originates from\nL L\nthe formation of Mg-rich metallic secondary phases, as evidenced in Figures S9 and\nS12. In contrast, the presence of Mg vacancies and Ag-Mg antisite defects in Mg-\ndeficient films enhances phonon scattering, thereby reducing κ 49.”\nL\nFigure R1. Lattice thermal conductivity and electronic thermal conductivity of the\nflexible MgAgSb films.\nComment 4: Isotropy must be demonstrated by directional measurements or validated\nby calculations, rather than relying solely on grain size. The statement “nanoscale\ngrains suggest isotropic TE performance” is speculative and should be supported by\nappropriate references. The authors need to clarify the dual role of nanoscale grains,\nexplaining how they reduce κ via enhanced phonon scattering while potentially\ndegrading electrical transport through grain-boundary scattering. While the bending test\nis useful, it has its limitations. If possible, the strain should be estimated based on the\nbending radius and the thickness of the film/substrate. Additionally, post-bending SEM\nimages should be provided to confirm the absence of cracks, delamination, or failures\nin interconnects. The authors should also specify the temperature difference used for\ndevice performance normalization and discuss the associated uncertainties to ensure a\nfair comparison between devices.\nResponse: Thank you for this comment. We apologize for the confusion caused by\ndirectly linking nanoscale grains to isotropic thermoelectric performance. Our original\nintention was to indicate that the films are polycrystalline with randomly oriented grains,\nwhich generally leads to isotropic transport behavior. As shown by the SEM images,\nthe films consist of nanoscale grains, and the XRD patterns match those of powder\ndiffraction, indicating the absence of obvious preferred orientation. Based on these\ncharacteristics, the films are expected to exhibit isotropic thermoelectric properties. To\navoid misunderstanding, we have revised the related description on Pages 5 and 9\naccordingly: “Figure S1 shows the X-ray diffraction (XRD) patterns of the molecular-\nbeam-deposited films, which match well with the corresponding powder diffraction\npatterns of α-MgAgSb phase, confirming that flexible α-MgAgSb films were\nsuccessfully obtained on polyimide substrates (Figure 1c).” “The nanoscale grain\nstructure reveals the polycrystalline nature of the films. Together with the absence of\nobvious preferred orientation in the XRD patterns (Figure S1), the films are therefore\nexpected to exhibit nearly isotropic thermoelectric properties, even though S and σ were\nmeasured in-plane, while κ was measured cross-plane.”\nWe also appreciate your suggestion regarding the dual role of nanoscale grains.\nSpecifically, nanoscale grains enhance phonon scattering and thereby reduce the lattice\nthermal conductivity, while simultaneously introducing carrier scattering that lowers\ncarrier mobility compared with MgAgSb possessing larger grain sizes in bulk samples.\nAn explicit discussion has now been added on Page 10: “Notably, although all these\nfilms exhibit a reduced κ compared with bulk samples due to enhanced phonon\nL\nscattering from nanoscale grains, such nanoscale grains can also induce carrier\nscattering, leading to a relatively lower carrier mobility than that of bulk counterparts50\nand consequently relatively low zT values.”\nIn response to your suggestion regarding the strain experienced by the films during\nbending, we have estimated the sample strain (ε ) based on the bending radius (R)\nsample\nand the thicknesses of the film (d ) and substrate (d ), using ε = (d +\nsample substrate sample sample\nd ) / 2R, which is applicable when d << d . This calculation corresponds\nsubstrate sample substrate\nto an applied strain of approximately 0.75% in our case. Post-bending SEM images\nhave also been provided (Figure R2), where few cracks are observed after bending,\nindicating good mechanical flexibility of the film. Both results have been incorporated\ninto the revised manuscript on Pages 10-11 and Supporting Information: “We then\nassessed the flexibility of the α-MgAgSb film by subjecting it to repeated bending at a\nfixed bending radius of 10 mm, corresponding to an applied strain of approximately\n0.75% (Note S2 and Figure 3e).” “The surface morphology after 1000 bending cycles\n(Figure S14) shows few cracks.”\nFigure R2. The surface morphology of MgAgSb film after 1000 bending cycles.\nFinally, we thank you for the suggestion to clarify the temperature difference used for\ndevice performance normalization and its associated uncertainties. We apologize that\nthis information was not explicitly stated in the original manuscript, although it is\nprovided in the Supplementary Information. In this work, the temperature difference is\ncalculated based on the Seebeck coefficient at the hot-side temperature, following\nliterature methods (Science 2022, 377, 854-858), which could reflect the effective\ntemperature experienced by the device. The Seebeck coefficient at the cold side differs\nslightly, which introduces some uncertainty, but for the maximum temperature gradient\nof ~40 K, the difference is within 6%. Considering this factor together with the\ninstrumental uncertainty in Seebeck coefficient measurements, the overall uncertainty\nin the estimated temperature difference will be within 10%. Accordingly, the\nnormalized maximum power density calculated using this temperature difference\ncarries an uncertainty of approximately 12%. This has now been explicitly indicated in\nthe revised manuscript on Page 12 and Pages 17: “As shown in Figure 4b, when the\nhot-side temperature is 393 K (estimated ΔT = 16 K), the V reaches 40 mV. As the hot-\noc\nside temperature increases to 513 K (estimated ΔT = 40 K), the V rises to 66 mV.”\noc\n“Consequently, a maximum power output density (P /A) of 5.2 mW cm-2 is obtained\nmax\nat a hot-side temperature of 513 K, corresponding to a normalized power density\n(P /AΔT2) of 4.9 μW cm-2 K-2 using the ΔT.” “The Seebeck coefficient at the cold side\nmax\ndiffers from that at the hot side, which will introduce some uncertainty in ΔT. However,\nfor the maximum temperature gradient of ~40 K, this difference is within 6%.\nConsidering the instrumental uncertainty in Seebeck coefficient measurements, the\noverall uncertainty in the estimated ΔT will be within 10%.” “The normalized\nmaximum power density is calculated as P /AΔT2 with an estimated uncertainty of\nmax\napproximately 12%.”\nComment 5: The conclusion is somewhat repetitive and relies too heavily on phrases\nsuch as “for the first time”, “excellent”, and “unprecedented”. The statement that zT\nmay exceed 1 at higher temperatures is speculative, as no data beyond 523 K are\nprovided; the authors should clarify the basis for this expectation. While the discussion\nof device performance is clear, the term “unprecedented” should be avoided unless it is\nbacked by a direct numerical comparison with the best-performing flexible devices in\nthe literature. Instead of concluding with repeated praise, the conclusion would be\nstronger if it included a more forward-looking perspective on future studies.\nResponse: Thank you for the careful and constructive comments. We have revised the\nConclusion in accordance with your suggestions. Phrases such as “for the first time,”\n“excellent,” and “unprecedented” have been reworded, and the Conclusion has been\nreorganized to reduce repetition and improve clarity.\nRegarding the statement that zT may exceed 1, we have revised the text to state more\ncautiously that the zT may exceed the room-temperature value of 0.8 at elevated\ntemperatures. This expectation is based on the trends of decreasing thermal\nconductivity with increasing temperature due to enhanced phonon scattering, together\nwith the increased power factor measured in this work. An explicit discussion has now\nbeen added on Page 14: “This measured increase in PF with temperature, together with\nthe expected decrease in thermal conductivity at elevated temperatures due to enhanced\nphonon scattering, suggests that zT values exceeding 0.8 may be achievable at higher\ntemperatures.”\nWe also appreciate your suggestion to include a more forward-looking perspective. To\naddress this point, we have added a discussion outlining possible future research\ndirections such as grain enlargement and doping strategies to further enhance\nthermoelectric performance, as well as the integration of these films into flexible device\narchitectures for practical applications in Conclusion part: “In future studies, strategies\nsuch as grain enlargement and doping could be explored to further enhance\nthermoelectric performance, as the current films still underperform compared with\noptimized bulk materials. Moreover, developing scalable, large-area fabrication routes\nand integrating these films into flexible device architectures will be crucial for more\npractical applications.”\nComment 6: In the Film fabrication section, the temperature control needs to be\ndescribed more precisely. Since the stabilization of the α-MgAgSb phase is highly\nsensitive to temperature, it is important to specify the actual substrate temperature range\nrather than just the set temperature. The authors state that deposition time was adjusted\nto obtain ~180 nm films, but they do not provide information on the deposition rate or\nthickness uniformity. Small variations in Mg flux can lead to the formation of secondary\nphases, making these details crucial. Although QCM flux monitoring is mentioned, it\nremains unclear whether post-deposition compositional analysis, such as EDS or XPS\nquantification, was performed to confirm the stoichiometry of the films. Given the\nsensitivity of MgAgSb to the flux ratio, it is essential to state the nominal atomic flux\nratio (e.g., Mg: Ag: Sb = 1:1:1) and to explain how this ratio was adjusted for\nstoichiometric versus element-deficient films.\nResponse: Thank you very much for the valuable comments on film fabrication. We\nfully agree that accurate and detailed descriptions of the experimental parameters are\nessential for ensuring the reliability and reproducibility of the results. In fact, we have\nmeasured the actual substrate temperature at different set temperatures using an optical\npyrometer. It confirms that the substrate temperature closely matches the set\ntemperature when it is below 773 K. To address your concern, we have revised the\nmanuscript on Page 15 to supply this information: “The actual substrate temperature\nwas consistent with the set temperature when the temperature was below 773 K.”\nIn addition, we have added further details regarding the deposition conditions,\nincluding the deposition rate and thickness uniformity. Specifically, the films were\ndeposited at a rate of approximately 6 nm per minute for 30 minutes with the substrate\nrotating at 5 rpm, resulting in a uniform film thickness of about 180 nm. The revised\npart is highlighted on Page 16: “The films were deposited at a rate of 6 nm per minute\nfor 30 minutes with substrate rotating at 5 rpm, resulting in a thickness of approximately\n180 nm.”\nWe appreciate the insightful comments regarding the relationship between the\nelemental flux ratio and the resulting film composition. To verify that the film\ncomposition accurately reflects the intended deposition flux ratio, films were deposited\nsimultaneously on PI and Al O substrates under identical conditions. The films on\n2 3\nAl O substrates were used for compositional analysis, as EDS measurements on PI\n2 3\nsubstrates can introduce significant uncertainty in Mg quantification due to the overlap\nof low-energy X-ray lines from Mg, C, and O. As shown in Figure R3 and Table R2,\nthe composition of films deposited on Al O closely matches the intended Mg:Ag:Sb\n2 3\nratio of 1:1:1 when this flux ratio is maintained using QCM monitoring. Based on this,\noff-stoichiometric films were prepared by the flux of each element by 5% during\ndeposition, and the resulting decrease in Sb concentration in Sb-deficient film was also\nconfirmed by EDS analysis. The corresponding description has been revised and\nclarified on Page 15 of the manuscript: “The α-MgAgSb films were prepared by co-\ndepositing Mg, Ag, and Sb with a 1:1:1 flux ratio, monitored by a QCM, at a substrate\ntemperature of 523 K. Compositional analysis was performed by EDS on film deposited\non Al O substrate under the same conditions as those on polyimide. As shown in Figure\n2 3\nS18 and Table S4, the film composition closely matches the intended 1:1:1 ratio. Based\non this result, off-stoichiometric films were fabricated by individually reducing the flux\nof each element by 5% during deposition. EDS analysis further confirms a ~5% Sb\ndeficiency in the corresponding film (Figure S18 and Table S4).”\nFigure R3. EDS mapping result of Mg, Ag and Sb in the MgAgSb and Sb-deficient\nfilms on the Al O substrate.\n2 3\nTable R2. The element concentration of Mg, Ag and Sb in the MgAgSb and Sb-\ndeficient films on the Al O substrate.\n2 3\nSample Mg Ag Sb\n(atom %) (atom %) (atom %)\nMgAgSb 28.24 28.08 27.08\nSb deficient 28.53 28.37 26.51\nComment 7: In the Characterization section, the authors should specify whether XRD\nwas performed in grazing-incidence mode, which is more appropriate for ~180 nm\nfilms on polymer substrates. Regarding thickness measurement, the step-profile method\nis acceptable; however, the procedure for creating the step and the associated\nuncertainty should be clearly stated. The description of the Hall measurement is\nincomplete; it should include details about the magnetic field strength and the\nmeasurement geometry. Additionally, issues such as contact stability and the influence\nof the substrate should be briefly addressed. For the ZEM-3 measurements, the authors\nshould provide the sample dimensions used in the measurement fixture and include a\nconcise statement on data reproducibility across multiple samples to confirm the\nreliability of the reported results.\nResponse: Thank you for the careful and constructive suggestions. We would like to\nclarify that conventional XRD was initially used due to its experimental convenience.\nWe agree that grazing-incidence XRD (GIXRD) is a powerful technique for\ncharacterizing thin films, and in response to your comment, we have additionally\nperformed GIXRD measurements. As shown in Figure R4, the diffraction pattern\nobtained in grazing-incidence mode clearly reveals the characteristic peaks of α-\nMgAgSb, consistent with the results from conventional XRD. In our case, the film\nsurface is soft and not perfectly flat, which makes it difficult to fully suppress the\nsubstrate contribution even under grazing-incidence conditions. In addition, GIXRD\nmeasurements are more time-consuming, whereas conventional XRD provides reliable\nand efficient phase identification for our samples. We have added a brief explanation of\nthis point in the Characterization section of the revised manuscript on Page 15: “The\nphase composition and crystallinity of the stoichiometric MgAgSb film were examined\nusing XRD and grazing incidence XRD (GIXRD). XRD measurements were performed\non a Rigaku MiniFlex diffractometer with a Cu K source, while GIXRD was carried\nα+β\nout using a Rigaku TF-XRD system equipped with a Cu K source. Both techniques\nα\nreveal the characteristic diffraction peaks of the α-MgAgSb phase. Because GIXRD\nmeasurements are more time-consuming, conventional XRD, which provides reliable\nand efficient phase identification, was used for all element-deficient films.”\nFigure R4. Comparison of GIXRD and conventional XRD.\nRegarding the thickness measurement, the step used for surface profiling was naturally\nformed by the sample holder, creating a clear transition from the uncovered substrate\nto the film surface. The associated uncertainty in the thickness measurement is within\napproximately 5%. This information has been added to the revised manuscript on Page\n15. “The film thicknesses were measured using a surface profiler system (Bruker Dektak\n6M) by the step method. The step was created from an uncovered area of the substrate\nto the film surface. The measurement uncertainty was within 10 nm.”\nFor the Hall measurements, we apologize for the omission of experimental details in\nthe original manuscript. Hall carrier concentration and mobility at 300 K were measured\nusing a four-probe Hall system (Biorad Hall Effect Systems H5580) with the probes\nplaced at the corners of the film and a magnetic field of 0.45 T applied. The insulating\nsubstrate does not affect the measurement, and multiple measurements were performed\nto ensure stable electrical contacts, resulting in an uncertainty of approximately 1%.\nSuch information has been added on Page 15: “Hall carrier concentration and mobility\nat 300 K were measured using a four-probe Hall system (Biorad H5580) under a\nmagnetic field of 0.45 T using the van der Pauw method, which is suitable for samples\nof arbitrary geometry. The probes were placed at the corners of the film, and the\ninsulating substrate did not affect the measurements. Multiple measurements were\nperformed to ensure stable contacts, with an uncertainty of approximately 1%.”\nFinally, for the ZEM-3 measurements, the sample dimensions were 10 mm × 3 mm in\nlateral size with a thickness of 180 nm. Two additional samples were prepared to\nevaluate reproducibility, and their temperature-dependent electrical properties are\nshown in Figure R5. The results indicate good reproducibility of the film fabrication,\nwith variations within approximately 5%. We also added this information on Page 16:\n“The electric conductivity and Seebeck coefficient of thin films were measured using a\nZEM-3 (Advance Riko) apparatus in a He atmosphere, with samples having lateral\ndimensions of 10 mm × 3 mm. Multiple measurements confirmed good reproducibility\nof the film fabrication, with variations within approximately 5% (Figure S19).”\nWe appreciate these suggestions, which have helped improve the clarity and\ncompleteness of the manuscript.\nFigure R5. Reproducibility of the electrical performance (a) Resistivity, (b) Seebeck\ncoefficient, and (c) Power factor of phase pure MgAgSb films.\nReviewer #2 (Remarks to the Author):\nComment: In this manuscript, the authors present high-performance MgAgSb-based\nflexible thermoelectric film and device. By employing molecular beam deposition and\nfinely manipulating the composition, they successfully achieved a phase-pure α-\nMgAgSb film, leading to a high power factor. The as-fabricated device also\ndemonstrates a high normalized output power density. This work makes a great\ncontribution to the development of high-performance flexible thermoelectrics with an\nunusual way. The manuscript is well organized, and the experimental results\nconvincingly support the discussion and conclusions. I would like to recommend this\nwork after addressing the following comments:\nResponse: Thank you very much for your careful reading and thoughtful assessment\nof our work. We sincerely appreciate your constructive comments and helpful\nsuggestions. In response, we have addressed each point in detail and revised the\nmanuscript accordingly, as outlined below.\nComment 1: Besides molecular beam deposition, are there any other feasible methods\nto fabricate MgAgSb thin films? Since molecular beam epitaxy is a complex and\nexpensive equipment that may limit scalability.\nResponse: Thank you for this constructive suggestion and insightful question. The\nmain challenge in fabricating MgAgSb thin films lies in the precise control of\nstoichiometry and the complete reaction of all constituent elements. For this reason, we\nadopted molecular beam deposition using molecular beam epitaxy equipment, which\nenables accurate flux control and stable growth conditions. We agree that, in addition\nto molecular beam epitaxy, other thin-film fabrication techniques such as pulsed laser\ndeposition and sol-gel processing may in principle be applicable to MgAgSb films, as\nthey could also enable stoichiometry control and facilitate growth of the α phase. We\nalso acknowledge that molecular beam epitaxy systems are complex and costly, which\nmay limit scalability. However, by demonstrating the feasibility of growing high-\nperformance flexible MgAgSb thin films, future optimization using more scalable\ndeposition techniques can be expected. This forward-looking perspective has been\nadded to the revised manuscript on Page 14: “In future studies, strategies such as grain\nenlargement and doping could be explored to further enhance thermoelectric\nperformance, as the current films still underperform compared with optimized bulk\nmaterials. Moreover, developing scalable, large-area fabrication routes and integrating\nthese films into flexible device architectures will be crucial for more practical\napplications.”\nComment 2: Although a phase-pure film was obtained, the reported power factor is\nstill slightly lower than that of the corresponding bulk material. Please give some\nexplanations.\nResponse: Thank you very much for this valuable comment. In general, the\nthermoelectric performance of thin films is often lower than that of corresponding bulk\nmaterials, mainly due to reduced carrier mobility arising from defects, impurities, and\nstructural disorder. We appreciate your observation that, although our films are phase-\npure, their power factor remains slightly lower than that of bulk MgAgSb. We attribute\nthis difference primarily to the small grain size in the films, which enhances grain-\nboundary scattering and leads to lower carrier mobility compared with state-of-the-art\nbulk MgAgSb reported in the literature. Despite this reduction in carrier mobility, the\nnanoscale grain size, typically below 100 nm, effectively suppresses lattice thermal\nconductivity, thereby helping to maintain a relatively high zT in the thin films. This\ntrade-off between electrical and thermal transport has now been explicitly discussed in\nthe revised manuscript on Page 10: “Notably, although all these films exhibit a reduced\nκ compared with bulk samples due to enhanced phonon scattering from nanoscale\nL\ngrains, such nanoscale grains can also induce carrier scattering, leading to a relatively\nlower carrier mobility than that of bulk counterparts50 and consequently relatively low\nzT values.”\nComment 3: The authors report that a 5% elemental deficiency results in a noticeable\ndegradation of thermoelectric performance. Since this deficiency is relatively large, it\nwould be interesting to know whether smaller deviations in composition might have a\ndifferent impact on the film properties.\nResponse: Thank you very much for your insightful comments. In this work, we\nintentionally selected a relatively large elemental deficiency of 5% to clearly illustrate\nthe influence of non-stoichiometry on the thermoelectric properties of MgAgSb thin\nfilms. As observed, this level of deficiency leads to a noticeable reduction in electrical\ntransport properties, providing a boundary for how compositional deviation affects\nmaterial performance. We agree that a 5% deficiency may be relatively large for\npractical applications. For smaller deviations in composition, the impact on\nthermoelectric properties is expected to be less pronounced and unlikely to exceed the\ntrends observed here. Nevertheless, even small Sb deficiency should be avoided in\npractice, as it can significantly modify the band structure near the valence band\nmaximum and introduce impurity related scattering, which degrades carrier mobility\nand overall thermoelectric performance. A brief discussion addressing this point has\nnow been added to the revised manuscript: “Overall, stoichiometric films exhibit the\nbest TE performance among α-MgAgSb thin films, and even slight Sb deficiency should\nbe avoided whenever possible.”\nComment 4: In the device measurement, the hot-side temperature reached up to 513\nK. This temperature appears higher than what is typically expected for flexible\nelectronic device applications. Would that be harmful to the flexible device?\nResponse: Thank you very much for your insightful comment. We agree that 513 K is\nhigher than the typical operating temperature of most flexible devices, especially\nwearable devices intended for use on the human body. However, as noted in the\nmanuscript, flexible thermoelectric devices may also be relevant for higher temperature\napplication scenarios, such as aerospace surface monitoring and engine diagnostics,\nwhere elevated operating temperatures are required.\nIn this work, the electrical performance was measured up to 523 K using a polyimide\nsubstrate, which can generally withstand temperatures up to approximately 550 K.\nTherefore, operation at a hot side temperature of around 513 K is within the thermal\ntolerance of the substrate and the film system. In addition, we performed durability tests\nat 473 K, as shown in Figure 3d, demonstrating stable thermoelectric performance over\nextended periods. This suggests that operation at slightly lower temperatures than 513\nK would be even more reliable. To address this concern, we have added additional\ndiscussion in the revised manuscript to clarify the applicable temperature range and\npotential use scenarios on Page 12: “Notably, the device operates reliably at elevated\ntemperatures up to 513 K, making it suitable not only for wearable electronics but also\nfor practical applications such as aerospace surface monitoring, engine diagnostics,\nand smart factories, where moderate temperature gradients are available.”\nComment 5: In Fig. 4f, a finger touch generates an open-circuit voltage of about 3 mV.\nRecent studies have reported practical evaluations of power density for flexible\nthermoelectric generators under similar human-body heat conditions (e.g. Chem. Mater.\n31 2019, 5238-5244.). Could the authors estimate or calculate the corresponding output\npower density based on the device resistance?\nResponse: Thank you for this valuable suggestion and for bringing the relevant\nreference to our attention. We agree that estimating the output power under human body\nheat conditions provides a more practical assessment of device performance. Following\nthe method described in the referenced work, we estimated the output performance\nunder human body heat conditions. When a finger is placed in contact with the device,\nthe maximum output power is estimated to be 0.88 nW, corresponding to a power\ndensity of 12.2 µW cm-2. These results have now been added to the revised manuscript\non Page 13: “As shown in Figures. 4f-4g, the device generated an output voltage of\nabout 3.0 mV and a maximum output power of 0.88 nW when placed on the side or tip\nof a finger…”\nComment 6: There exist some typos, e.g. “A more promising route is to fabricate α-\nMgAgSb thin films via through bottom-up approaches.” The authors should carefully\nscrutinize the manuscript to avoid similar mistakes.\nResponse: Thank you for pointing out the typographical errors. We have carefully\nreviewed the entire manuscript and corrected the identified mistakes to improve\naccuracy and readability.\nReviewer #3 (Remarks to the Author):\nComment: MgAgSb bulk materials and films have been studied in some references. In\nthe manuscript, the authors were able to precisely control the chemical composition and\nphase composition of the prepared MgAgSb films and obtained the excellent\nthermoelectric properties. The flexibility of the prepared films and the output\ncharacteristics of thermoelectric devices assembled by studied films in the manuscript\nalso have been studied. This is a meaningful study. However, the manuscript lacks in-\ndepth characterization of the microstructure for the deposited films and in-depth\ntheoretical analysis for the experimental results. Some problems are following:\nResponse: Thank you very much for your careful reading, succinct overview of our\nwork, and constructive comments and suggestions. We truly appreciate your thoughtful\nfeedback. In response, we have carefully reviewed and revised our manuscript to\naddress your concerns. Below, you will find our point-by-point reply to each suggestion\nand revision.\nComment 1: The sample lacks an in-depth observation of its microstructure. Is there\nany method to characterize the vacancies of the atoms in the lattice? This is a difficult\nproblem. If possible, Try to do it.\nResponse: Thank you for this valuable comment. We agree that an in-depth\ncharacterization of atomic vacancies would provide important insight into the\nmicrostructure and its impact on thermoelectric performance. However, direct\nobservation of atomic vacancies is intrinsically challenging, as conventional\nmicroscopy techniques typically image columns of atoms rather than individual lattice\nvacancies. While advanced techniques may enable more direct characterization of\nvacancies, they are currently beyond the capabilities available in our laboratory.\nNevertheless, we recognize the critical role of atomic defects in determining film\nproperties. To address this indirectly, we have correlated the experimentally observed\nelemental deficiencies with thermoelectric performance through band structure\nconsiderations and SEM observations (Figure 2e and Figure S9), which provide\nqualitative insight into the effects of non-stoichiometry. In addition, our discussion is\nsupported by previous studies on atomic defects in bulk MgAgSb materials, which\nreport similar defect related influences on transport properties (Adv. Funct. Mater. 2025,\ne10200. doi.org/10.1002/adfm.202510200; J. Mater. Chem. A, 2016, 4, 16834-16840).\nWe regret that a more direct vacancy characterization could not be performed in this\nwork, but this will be an important objective for future studies.\nComment 2: Please elaborate in detail on the sources of the main charge carriers (holes)\nin the p-type MgAgSb films. Analyze the essence of the change in carrier concentration\nand mobility when the atomic vacancies in the MgAgSb lattice have appeared. At the\nsame time, discuss the fundamental reason for the variation of Seebeck coefficient and\nthermal conductivity with the occurrence of the atomic vacancies in the MgAgSb lattice.\nResponse: Thank you very much for your constructive suggestions. In α-MgAgSb\nfilms, Mg vacancies (V 2-) are recognized as the primary origin of p-type conduction\nMg\ndue to easy Mg loss during fabrication. Consequently, Mg deficiency introduces a\nhigher concentration of V 2-, leading to an increased hole concentration. In contrast,\nMg\nAg and Sb deficiencies may introduce Ag vacancies (V -) and Sb vacancies (V 3+),\nAg Sb\nwhich tend to increase and decrease the hole concentration, respectively.\nSimultaneously, elemental deficiency can promote the formation of impurity or\nsecondary phases, which may further modify the carrier concentration. Moreover, all\ntypes of vacancies accompanied by impurities act as scattering centers and therefore\nreduce carrier mobility. The variations in Seebeck coefficient are reflection of changes\nin carrier concentration. As shown in Figure 2b, the increased hole concentration\nassociated with V 2- corresponds to a reduced Seebeck coefficient, while Ag and Sb\nMg\ndeficiencies show a comparatively weaker influence, in agreement with the change of\ncarrier concentration. In particular, Sb vacancies also modify the valence band\nmaximum, further influencing the Seebeck coefficient.\nRegarding thermal transport, all films exhibit reduced total thermal conductivity.\nSeparation of the lattice contribution reveals that Mg-deficient films show a pronounced\nreduction in lattice thermal conductivity, which can be attributed to enhanced phonon\nscattering induced by Mg vacancies. Ag deficiency has a relatively minor effect on\nlattice thermal conductivity. In contrast, Sb-deficient films exhibit a slightly increased\nlattice thermal conductivity, which is likely related to the formation of Mg-rich metallic\nsecondary phases, as evidenced in Figures S9 and S12, since such phases generally\npossess higher lattice thermal conductivity.\nThese discussions on the role of atomic vacancies in determining carrier concentration,\nmobility, Seebeck coefficient, and thermal conductivity have now been incorporated\ninto the revised manuscript on Pages 7 and 11: “For the element-deficient films, Sb\ndeficiency is observed to reduce the room-temperature n , which may arise from the\nH\nformation of Sb vacancies (V 3+), These vacancies act as electron donors, leading to a\nSb\ndecreased n and consequently an increased S according to the Pisarenko relation. In\nH\nthe case of Ag deficiency, Ag vacancies (V -) may be induced, increasing n , as\nAg H\nreflected by the decreasing trend of S over a broad temperature range. In contrast, Mg\ndeficiency markedly increases n due to the formation of Mg vacancies (V 2-) and Ag-\nH Mg\nMg antistites defects (Ag -) 62,63, resulting in a much lower S. Notably, μ decreases\nMg H\nuniformly in all deficient films, primarily due to enhanced carrier scattering from point\ndefects and possible secondary phases associated with non-stoichiometry. The reduced\nμ intrinsically deteriorates electrical transport, resulting in all deficient films\nH\nexhibiting lower PFs than the non-deficient sample.”\n“To gain deeper insight into the impact of elemental deficiencies on thermal transport,\nwe have decomposed the total thermal conductivity into its electronic and lattice\ncomponents (Note S1 and Figure S13). It is evident that Sb deficiency leads to an\nincrease in lattice thermal conductivity (κ ), whereas Mg deficiency results in a\nL\npronounced reduction in κ . In comparison, Ag deficiency has a relatively minor\nL\ninfluence on κ . The increased κ observed in Sb-deficient films likely originates from\nL L\nthe formation of Mg-rich metallic secondary phases, as evidenced in Figures S9 and\nS12. In contrast, the presence of Mg vacancies and Ag-Mg antisite defects in Mg-\ndeficient films enhances phonon scattering, thereby reducing κ 49.”\nL\nComment 3: Fig.3 (d),(e) showed the excellent stability and flexibility of α-MgAgSb\nfilm. Please provide a reasonable theoretical explanation for this result.\nResponse: Thank you for this insightful comment. The excellent stability and\nflexibility of the α-MgAgSb films can be understood from both thermodynamic and\nmechanical perspectives. The good thermal and operational stability originate from the\nintrinsic phase stability of α-MgAgSb. Previous studies have shown that α-MgAgSb is\nthe only thermodynamically stable phase in the temperature range of approximately\n300 to 573 K, and therefore it does not undergo phase transitions or decomposition\nwithin the temperature window investigated in this work. This intrinsic phase stability\naccounts for the stable thermoelectric performance observed during long term testing.\nThe excellent flexibility arises from a combination of material properties, film thickness,\nand substrate support. The flexibility of thin films can be described by the inverse of\nthe critical bending radius before fracture, f = 1/r = 2σ /(hY), where h is the film\nb y\nthickness, σ is the yield stress, and Y is the Young’s modulus (Science 2019, 366, 690-\ny\n691). According to this relationship, thinner films can sustain much larger elastic\nbending deformations even if the intrinsic stiffness of the material is moderate. In our\ncase, the α-MgAgSb film thickness of approximately 180 nm is sufficiently small to\ntolerate large elastic bending strains. In addition, the use of an intrinsically flexible\npolyimide substrate provides mechanical support and redistributes bending induced\nstress, effectively reducing the strain experienced by the film during deformation. The\ncombination of intrinsic phase stability, nanoscale thickness, and flexible substrate\nsupport therefore explains the excellent stability and flexibility observed in Figures 3d\nand 3e. We have supplied this discussion on Pages 11: “This stability can be attributed\nto the intrinsic phase stability of α-MgAgSb, which is thermodynamically stable over a\nbroad temperature range and does not undergo phase transitions or decomposition\nwithin the temperature window investigated in this work64.” “This flexibility arises from\nthe small film thickness (about 180 nm), which allows large elastic bending strains25,\ntogether with the intrinsically flexible polyimide substrate that redistributes bending-\ninduced stress and reduces the effective strain in the film.”\nComment 4: In order to more clearly express the output characteristics of the\nthermoelectric device, please provide a figure showing the relationship between the\nopen-circuit voltage and the temperature difference.\nResponse: Thank you for this helpful suggestion. In response, we have added a new\nfigure illustrating the relationship between the open-circuit voltage and the temperature\ndifference, as shown in Figure R6. As expected, the open-circuit voltage increases with\nincreasing temperature difference, clearly revealing the output characteristics of the\nthermoelectric device. This figure has been included in the revised Supporting\nInformation, and the corresponding discussion has been added on Page 12: “As shown\nin Figure 4b, when the hot-side temperature is 393 K (estimated ΔT = 16 K), the V\noc\nreaches 40 mV. As the hot-side temperature increasing to 513 K (estimated ΔT = 40 K),\nthe V rise to 66 mV. The relationship between V and ΔT is shown in Figure S15,\noc oc\nclearly demonstrating that V of TE device increases with ΔT.”\noc\nFigure R6. The generated open-circuit voltage (V ) as a function of the temperature\noc\ndifference (ΔT) of the flexible MgAgSb thermoelectric device.\nComment 5: In page 11 line 278-279: “As shown in Fig. 4c and table S3, the\nperformance achieved in this work is unprecedented in terms of maximum power output\ndensity demonstrated,…” and Fig.4(c): Here, because the temperature difference affects\nthe maximum power output density of the thermoelectric device, using the maximum\npower output density in comparison with other references is meaningless. However, the\ncomparison of the normalized power density for different materials is meaningful. The\ncomparison of the maximum power output density shown in Fig. 4(c) needs to be deleted.\nResponse: Thank you very much for this valuable comment. We agree that the\ntemperature difference has a strong influence on the maximum power output density of\nthermoelectric devices, and that direct comparison of this quantity across different\nreports can be misleading. As you pointed out, only normalized power density provides\na meaningful basis for comparison. Accordingly, we have removed the comparison of\nthe maximum power output density in Figure 4c, together with the associated discussion\nin the manuscript, and retained only the comparison based on normalized power density.\nThis revision ensures a fairer and more physically meaningful comparison of device\nperformance.\nComment 6: To better understand the output characteristics of the thermoelectric\ndevice, please provide the external resistance and the internal resistance of the\nthermoelectric device corresponding to the maximum output power obtained under\ndifferent temperature differences in Fig.4(b) and in the manuscript.\nResponse: Thank you for this insightful suggestion. To better clarify the output\ncharacteristics of the thermoelectric device, we have determined both the internal and\nexternal resistances corresponding to the maximum output power under different\ntemperature differences. The internal resistance was obtained from the slope of the I-V\ncurves, defined as R = -dV/dI. The external resistance was calculated using R =\nin ext\nV /I − R , where V is the open-circuit voltage and I is the current at which the\noc opt in oc opt\nmaximum output power is achieved. As shown in Figure R7, the external resistance\nclosely matches the internal resistance at the point of maximum power output. This\nbehavior is consistent with the maximum power transfer theorem, which states that\nmaximum power is delivered to the load when the load resistance equals the internal\nresistance of the source. These results and the corresponding discussion have now been\nincluded in the revised manuscript: “Based on the measured output voltage and current,\nthe output power was calculated. The maximum output power (P ) is achieved when\nmax\nthe internal resistance of the device matches the external load resistance, as shown in\nFigure S16.”\nFigure R7. The external and internal resistance of the flexible MgAgSb device under\ndifferent temperature differences.\nComment 7: In order to clearly illustrate the influence of flexibility on the output\ncharacteristics of the thermoelectric device, please mark the bending conditions in\nFig.S15.\nResponse: Thank you for this helpful suggestion. We apologize for the omission of\nthese details in the original manuscript. In the revised version, we have enlarged the\noptical images in (original Figure S15) Figure S17 and clearly marked the bending\nconditions. Specifically, the device was bent while attached to a carbon pillar with a\nbending radius of 10 mm (Figure R8). This information has now been added to better\nillustrate the influence of flexibility on the output characteristics of the thermoelectric\ndevice.\nFigure R8. The performance of the flexible MgAgSb TE device under bending.\nComment 8: In page 12 line 284-285: “At a hot-side temperature of 513 K, the V is 60\nmV, and the P reaches 0.4 μW.” Here, from Fig.S15, the maximum power output density\ndoes not reach 0.4 μW. Please carefully check the data. Under this bending condition,\nwhat is the internal resistance of the thermoelectric device? What is the reason for the\ndifference between its internal resistance under this bending condition and without\nbending? Under the bending conditions, at the same temperature difference, both its\nopen-circuit voltage and maximum output power are lower than those of the\nthermoelectric device under no bending conditions? Why is this so? Please provide a\nreasonable explanation.\nResponse: Thank you very much for your careful reading and constructive comments.\nWe have rechecked the data related to the device performance under bending conditions\nand apologize for the oversight. The precise maximum output power under bending is\n0.36 μW rather than our rough estimated 0.4 μW. We have revised the manuscript on\nPage 12 to report these values explicitly to avoid any potential misunderstanding: “At\na hots stage temperature of 513 K, the V is 58 mV, and the P reaches 0.36 μW.”\noc max\nRegarding the internal resistance under bending conditions, it is calculated to be\napproximately 2300 Ω when hot plate temperature is 513 K, which is slightly higher\nthan that measured without bending, around 2200 Ω. We would like to clarify that this\ndifference does not originate from mechanical degradation of the device, but rather\nfrom differences in the measurement configuration. Specifically, to evaluate the output\nperformance under bending, the flexible thermoelectric device was wrapped around the\ntop surface of a cylindrical graphite rod with a radius of 10 mm, which was then placed\non a hot plate, as shown in Figure R8. Under this configuration, the effective hot-side\ntemperature experienced by the device is lower than that of a device placed flat directly\non the hot plate. As a result, the actual temperature difference across the device under\nbending is smaller, leading to a reduced open-circuit voltage and maximum output\npower compared with the unbent condition at the same nominal hot-plate temperature.\nBecause it is difficult to directly determine the exact temperature experienced by the\ndevice in the bent configuration, the hot-plate temperature was used as a reference. To\navoid confusion, we have added clarification to the manuscript accordingly to explain\nthe origin of the differences observed between the bent and unbent measurements on\nPage 12: “It should be noted that the flexible thermoelectric device was mounted on the\ncurved surface of a carbon pillar rather than directly on a flat heating stage, resulting\nin a different effective hot-side temperature on the device and, consequently, variations\nin the measured output voltage and power.”\nComment 9: On temperature difference evaluation of TE device, Why not use the\nthermocouple measurement but instead of calculation using the formula ΔT=V /S ∙ N ?\noc leg\nDoes it have any advantages over the measured values?\nResponse: Thank you for this valuable question. In principle, directly measuring the\ntemperature difference across a thermoelectric device using thermocouples is indeed\nthe most straightforward approach. However, in our experiments, an additional\npolyimide layer was used to cover and protect the ultrathin films. Placing\nthermocouples on this protective layer would not accurately reflect the actual\ntemperatures experienced by the thermoelectric legs, as the additional layer introduces\nextra thermal resistance and can lead to a discrepancy between the measured and the\ntrue temperature gradient across the device. For this reason, we evaluated the\ntemperature difference using the relation ΔT = V /SN , following approaches in the\noc leg\nliterature (Science 2022, 377, 854-858). This method reflects the effective temperature\ndifference experienced by the thermoelectric legs themselves rather than the\ntemperature at the outer surface. We acknowledge that this approach may also introduce\nsome uncertainty because the Seebeck coefficient at the cold side differs slightly from\nthat at the hot side. However, in our measurements the maximum temperature gradient\nwas approximately 40 K, for which the difference between the Seebeck coefficients at\nthe hot and cold sides is within 6%. Taking into account the experimental uncertainty\nin the Seebeck coefficient measurement, the overall uncertainty in the calculated\ntemperature difference is estimated to be within 10%. To address this, we have added\nsome discussion on Page 17: “The temperature difference across the flexible TE device\nduring heating is calculated by using ΔT = V /SN , following literature methods9,29,32.\noc leg\nThis approach could reflect the effective temperature difference experienced by the\ndevice…The Seebeck coefficient at the cold side differs from that at the hot side, which\nwill introduce some uncertainty in ΔT. However, for the maximum temperature gradient\nof ~40 K, this difference is within 6%. Considering the instrumental uncertainty in\nSeebeck coefficient measurements, the overall uncertainty in the estimated ΔT will be\nwithin 10%.”\nComment 10: In page 11 line 274-275: “As shown in Fig. 4b, when the hot-side\ntemperature is 393 K, the V reaches 40 mV, generating an output power of 0.17 μW…”\nHere, the “output power” should be “maximum output power”?\nResponse: Thank you for pointing this out. We apologize for the inaccurate wording.\nThe term “output power” has been revised to “maximum output power” to ensure rigor\nand clarity.\nComment 11: According to the custom, in order to clearly convey the meaning of the\ndata in the figure, the horizontal and vertical axes of Fig.4(b) should be labeled with\n\"output current\" and \"output voltage\" or \"output power\".\nResponse: Thank you for the helpful suggestion. We agree that explicit axis labels are\nimportant for clear data presentation. In the revised manuscript, the horizontal and\nvertical axes of Fig. 4(b) have been updated to clearly indicate “output current” and\n“output voltage” and “output power,” respectively.\nComment 12: In fact, the output voltage and output power of the thermoelectric device\ndepend on the temperature difference. In Fig.4(b) and S15, it is more appropriate to use\nthe temperature difference instead of the hot plate temperature to describe the data in\nfigures.\nResponse: Thank you for this valuable comment. We agree that thermoelectric device\nperformance is fundamentally determined by the temperature difference. Accordingly,\nFig. 4(b) has been revised to include the corresponding temperature difference in\naddition to the hot plate temperature. In our work, the hot side temperature is also\nhighlighted because the operating temperature range is an important consideration for\nflexible devices. For (original Figure S15) Figure S17, the actual temperature difference\nunder bending conditions is difficult to determine reliably, as discussed in our response\nto Comment 8. Therefore, we retained the hot plate temperature.\nComment 13: In the manuscript, to avoid any confusion, please use different symbols\nto represent the output voltage and the open-circuit voltage. And in the statements,\nplease replace \"V\" and \"P\" with \"output voltage\" and \"output power\" respectively.\nResponse: Thank you for this helpful suggestion. We apologize for the confusing\nnotation in the original manuscript. To avoid ambiguity, different symbols are now used\nto distinguish output voltage and open-circuit voltage, and the expressions “V” and “P”\nhave been replaced with “output voltage” and “output power” throughout the text and\nfigures.\nComment 14: In Fig. 4(e), what parameter does T represent?\nN\nResponse: Thank you for pointing this out. We apologize for the confusion. In Fig. 4(e),\nthe parameter actually represents the hot-side temperature T . The issue may be due to\nH\nthe resolution of the figure, which made T appear like T . To avoid misunderstanding,\nH N\nwe have updated the figure and replaced “T ” with “T ” for clearer presentation.\nH hot plate"}, {"round": 2, "reviewer_comments": {"reviewer_1": "The authors have satisfactorily addressed all of my comments, and the revisions have significantly improved the quality of the manuscript. I find the revised manuscript suitable for publication.", "reviewer_3": "The authors provided a good response to the reviewers' comments and have made appropriate revisions to the manuscript. My problem has now been resolved. The revised manuscript can be considered for acceptance."}, "author_response": "Dear reviewers,\nThank you very much for your positive response to our manuscript. We greatly\nappreciate the reviewers’ valuable and positive comments.\nSincerely yours,\nTakao Mori\nReviewer #1 (Remarks to the Author):\nComment: The authors have satisfactorily addressed all of my comments, and the\nrevisions have significantly improved the quality of the manuscript. I find the revised\nmanuscript suitable for publication.\nResponse: We sincerely thank the reviewer for the positive evaluation of our revised\nmanuscript.\nReviewer #3 (Remarks to the Author):\nComment: The authors provided a good response to the reviewers' comments and have\nmade appropriate revisions to the manuscript. My problem has now been resolved. The\nrevised manuscript can be considered for acceptance.\nResponse: We sincerely thank the reviewer for the positive comment and\nrecommendation."}]

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