Giant ZT enhancement in rhombohedral GeTe-based thermoelectric materials

Domain: biology
Published: 2026-03-15
Editorial outcome: minor_revision

Abstract
The peak figure of merit (ZT) of GeTe-based thermoelectric (TE) materials is typically attained in the high-temperature cubic phase, where the inevitable phase transition raises concerns over interfacial instability during operation. Therefore, developing high-performance rhombohedral GeTe below the phase transition temperature represents a more viable path toward practical applications. Herein, we propose a facile nanocomposite strategy to enhance the TE performance of rhombohedral GeTe by incorporating high-modulus TiB2 nanoparticles into Ge0.94Bi0.05Te matrix. We demonstrate that the nanoparticle-induced interfacial constraint effect contributes to increasing longitudinal elastic modulus and decreasing equivalent deformation potential, accounting for improved carrier mobility. Additionally, these TiB2 inclusions form heterogeneous interfaces that promote charge depletion and generate substantial thermal resistance, concurrently suppressing the heat transfer by carriers and phonons. Consequently, an extraordinary ZT of 2.66 at 613 K and a superior average ZT of 1.29 (300~613 K) are obtained in the rhombohedral GeTe-based composite. This work shows a paradigm for synergistically optimizing the electrical and thermal transports of emerging TE systems with nanoinclusions.

Introduction
By enabling direct solid-state conversion between heat and electricity, thermoelectric (TE) materials offer an alternative pathway for power generation and refrigeration, holding considerable promise for advancing waste heat recovery and thermal management solutions.1 The conversion efficiency of TE materials is typically characterized by the dimensionless figure of merit, ZT = S2σT / (κe + κL), where S is Seebeck coefficient, σ is electrical conductivity, T is absolute temperature, κe is electronic thermal conductivity and κL is lattice thermal conductivity.2 Therefore, the key to improving the thermoelectric performance lies in maximizing the power factor (PF = S2σ) or minimizing the thermal conductivity (κ = κe + κL) to endow the candidate materials with the characteristics of electron crystal-phonon glass.3

Despite being the most successful commercial TE material to date, Bi2Te3 operates primarily within a near-ambient temperature range,4 which limits its use for broader, more diverse applications. By contrast, GeTe presents itself as a promising TE material for sustained service within the mid- and high-temperature range.5 Not only does it offer an eco-friendly profile by being lead-free, a notable advantage over high-performance PbTe,6 but also delivers outstanding ZT values mainly due to its good electrical transport (e.g. PF can reach over 40 μWcm-1K-2 at 673 K7) in spite of intrinsically high thermal conductivity (e.g. κ exceeds 7 Wm-1K-1 at room temperature8).

Nevertheless, the practical application of GeTe thermoelectrics still faces several challenges. On one hand, the maximum ZT value is usually attained in cubic GeTe (over 615 K), the inherent phase transition from low temperature rhombohedral to high temperature cubic structure calls for the implementation of segmented architectures in TE devices,9,10 raising additional concerns over interfacial instability. On the other hand, the TE performance of GeTe within the temperature range of 300~615 K awaits further optimization, because the abundant intrinsic Ge vacancies not only deviate the hole concentration (p) from the optimal level, but also act as carrier scattering centers to restrict the carrier mobility (μH).11 Although the Ge vacancies can be efficiently suppressed by doping heavy elements such as Cd, Pb and Sb,12–14 which helps to optimize p, the PF only ranges from 16~37 μWcm-1K-2, primarily assigned to degraded μH due to increased alloying scattering. Such low μH inevitably delays the response speed of TE materials, presenting a significant obstacle to their commercial viability.15 While doping with Ge or Cu helps to enhance μH by discouraging carrier scattering via occupying Ge vacancies or providing additional carrier transport channels,16–19 yielding a high ZT value up to ~2.4 at 640 K, this approach is still heavily restricted by the solubility limit of dopants and the formation energy of point defects.

To address these concerns, a promising solution centers on developing rhombohedral GeTe with superior TE performance, particularly below the phase transition temperature, thereby establishing a groundwork for future development of efficient TE legs that eliminate the need for segmented architectures. Motivated by the exceptional efficacy of nanoparticles in optimizing electrical and thermal transport in typical TE systems, such as Bi2Te3, Mg3Sb2, Cu2Se, etc.,20–23 we seek to explore the specific interplay between heterogeneous interfaces and TE performance in rhombohedral GeTe from a nanocomposite perspective. Previously, we incorporated B inclusions into the GeTe matrix,24 with the aim of promoting the energy filtering effect to increase S and the formation of high-density dislocations to enhance phonon scattering. Unfortunately, this approach degraded the carrier mobility, which restricted further ZT enhancement. Herein, we find that direct incorporation of high-modulus nanoparticles into rhombohedral GeTe leads to a notable increase in μH despite increased interfacial potential barrier arising from a large grain boundary density as well as unfavorable energy band bending, with huge thermal resistance (Rx) at heterogeneous interfaces. This work aims to provide a deep insight into these exotic transport behaviors.

It is found that the TE performance of rhombohedral Ge0.94Bi0.05Te (the optimal composition identified by our previous study24) can be boosted by addition of TiB2 nanoparticles, and the underlying mechanism is shown in Fig. 1a. It is acknowledged that tuning deformation potential (Ξ) presents a powerful means to achieve high μH in TE materials.25 Notably, different from the classic Ξ modulation enabled by symmetry improvement via chemical bond engineering,25 the atomic displacement associated with elastic deformation is confined by the nanoparticle-induced interfacial constraint effect; this also reduces the sensitivity of the changes in band structure to elastic deformation, thereby lowering equivalent Ξ and enhancing μH. Additionally, the resulting heterogeneous interfaces contribute to facilitating charge transfer, and introducing high-frequency lattice vibration modes that enhance phonon-phonon scattering (Fig. 1a). The quality factor B, severing as an important indicator to reflect the degree of carrier-phonon decoupling,26 was calculated using Supplementary Equation (1), shown in Fig. 1b. The ZT value increases from 1.7 to 2.66 as B increases from 1.1 to 2.1 at 613 K, indicating that TiB2 addition helps to decouple the carrier-phonon interaction. To intuitively evaluate the thermoelectric properties without the interference of temperature, the figure of merit (Z) is presented in Fig. 1c. Clearly, the TiB2-added sample (x = 0.1) exhibits a high Z of 4.4  10-3 K-1 at 600 K, surpassing the values of most state-of-the-art works reported previously.11,24,27–34 In addition, our work also achieves an extraordinary average ZT of 1.29 in rhombohedral GeTe, comparable to the record-high value for the Ag/Sb/Pb/Bi alloyed GeTe (Fig. 1d),11,24,27–34 showing considerable potential of our strategy in TE property optimization.

Results
The crystal structure and microstructure of the as-prepared samples were examined to probe the structure-property relationship. The X-ray diffraction (XRD) patterns (Supplementary Fig. 1) reveal that all peaks can be indexed to the rhombohedral phase of GeTe, in good agreement with the standard PDF reference (JCPDS card: # 47-1079); no discernible TiB2 peaks were observed, due to the insufficient additive amount falling below the detection limit of the X-ray diffractor. The Rietveld refinement (Supplementary Fig. 2) was performed based on the XRD data (Supplementary Fig. 1) to obtain the average lattice parameters, and the results were summarized in Supplementary Table 1. It is apparent that the lattice parameters exhibit negligible variations with increasing x, indicating a limited impact of TiB2 addition on the lattice structure. Interestingly, Williamson-Hall analysis reveals similar micro-strain levels (~0.5%) for compositions with x between 0 and 0.1 within the margin of uncertainties, yet a pronounced increase to ~0.8% is observed in the x = 0.2 sample (Supplementary Fig. 3); these results imply that excessive TiB2 addition introduces severe local lattice distortions.35

The scanning electron microscopy (SEM) images of fracture surfaces show tightly packed grains with low porosity for all samples (Supplementary Fig. 4), in accordance with the calculated relative density data (~97%) in Supplementary Fig. 5. Compared to the pristine sample, the average grain size is nearly halved with the incorporation of TiB2 (Supplementary Fig. 4), which can be attributed to the pinning effect induced by secondary phases. However, it shows little dependence on the additive amount, remaining at a similar level across different compositions (x = 0.05~0.2). The chemical composition determined by the electronic probe mapping analysis (EPMA) is shown in Supplementary Fig. 6. The intensity of the Ti and B signals in the EMPA maps increases progressively with x, whereas the localized enrichment of Ti and B elements suggests a decrease in the dispersion homogeneity at higher addition levels. Concurrently, Ge precipitates are ubiquitously present for each sample, arising from the low Ge vacancy formation energy;36 this is a characteristic feature of GeTe-based thermoelectrics.

The scanning transmission electron microscopy (STEM) images provide a deeper understanding on nanostructures inside the as-prepared samples. In contrast to the pristine sample with micro-sized grains (Fig. 2a), Fig. 2b shows that the addition of TiB2 results in a nanocrystalline structure where the grain boundaries are decorated with identifiable nanoinclusions. Fig. 2c shows the detailed information about the nano feature in Fig. 2b. It is worth noting that, for the x = 0.1 sample, the nanoinclusion is half-surrounded by the matrix accompanied by the presence of nanopores. The corresponding energy dispersive X-ray spectroscopy (EDX) maps (Figs. 2d-h and Supplementary Fig. 7) reveal that these nanoinclusions are enriched with Ti and B, but depleted with Ge, Te and Bi, which implies that TiB2 appears as a secondary phase in the matrix, in accordance with the EMPA analysis result Supplementary Fig. 6). Atomically resolved high-angle annular dark-field (HAADF) STEM image (collected from the grain on the left side of Fig. 2c) of the matrix phase (Fig. 2i) displays an ordered atomic arrangement, which matches well with the crystal structure of rhombohedral GeTe along the [110] zone axis. The atomic columns with brighter and darker contrast are assigned to Te and Ge, respectively, evidenced by the overlaid results of atomic level STEM EDX maps (Supplementary Fig. 8); this is consistent with the site intensity of HAADF image in Fig. 2j (the contrast is proportional to the square of atomic number Z2). The separate elemental maps (Figs. 2i-l) show that the Bi atoms successfully enter the lattice of GeTe matrix. Fig. 2m shows the HAADF STEM images collected from the nanoinclusion, where two set of lattice fringes can be observed. The corresponding line intensity maps and calculated plane spacing values are in good agreement with the (110) and (100) crystal planes (Figs. 2n and 2o) for the hexagonal TiB2 with a space group of P 6/mmm (191), which is consistent with the crystal structure of the crystallographic information file (CIF) (number: ICSD190893). The presence of nano regions with distinct orientations demonstrates this nanoinclusion constitutes a polycrystalline aggregate.

Fig. 2p reveals the atomic structure of the interface between matrix phase and TiB2 inclusions, highlighted by the red box in Fig. 2c. An incoherent phase boundary is observed, where the upper domain is GeTe phase along the [110] zone axis (confirmed by the top right inserted fast Fourier transform (FFT) pattern), and the bottom domain is TiB2 secondary phase (confirmed by the bottom left inserted FFT pattern and plane spacing). Nevertheless, Fig. 2q shows one of the EDX line scan profiles in Supplementary Fig. 9 (line 1) across the interface; a sharp interface is observed in absence of reaction layers, indicating that these two phases are in immediate adjacent to each other. The quality of the interfacial contact seems sensitive to the additive content. Notably, the interfacial adhesion deteriorates in the x = 0.2 sample, where some inclusions even exhibit minimal contact with pore edges (Supplementary Fig. 10). The strain analysis shows that the matrix near the interface accommodates strains through localized lattice distortions (Supplementary Fig. 11), in line with the Williamson-Hall analysis result (Supplementary Fig. 3). Furthermore, Supplementary Fig. 12 shows the elemental distribution of Ti and Te shows an overlap, which does not align with the natural interface morphology. When the electron beam is focused on the TiB2 side (top right region in Supplementary Fig. 12i), two distinct sets of diffraction spots (blue circle: TiB2; red circle: GeTe) appear in the FFT pattern (Supplementary Fig. 12j) corresponding to the region j in Supplementary Fig. 12i. Therefore, the thin edge of the TiB2 grain is likely to extend over the GeTe grain, giving rise to a discontinuous interface.

The effects of TiB2 addition on the electrical transport properties of Ge0.94Bi0.05Te were systematically investigated. As Fig. 3a shows, all samples exhibit a degenerate conduction behavior, as evidenced by the decrease in σ with increasing T. It is clear that σ can be efficiently reduced by addition of TiB2. Particularly, the room-temperature σ shows a gradual decrease from 3329.3 Scm-1 to 2765.7 Scm-1 as the additive content increases from 0 to 0.2 wt%. Meanwhile, the positive S values in Fig. 3b indicate that the electrical transport is dominated by holes. At 613 K, S increases from 216.0 μVK-1 to 261.6 μVK-1 with the TiB2 content rising from 0 to 0.1 wt%, and almost keeps constant when the additive content further increases up to 0.2 wt%. Consequently, a maximum PF of 50.1 μWcm-1K-2 is achieved in the x = 0.1 sample at 573 K (Fig. 3c), representing 19% enhancement compared to the pristine sample (40.5 μWcm-1K-2 at 573 K). Similar to the variations of σ, the changes in κ follow a downward trend with increasing additive content (Fig. 3d); the value decreases from 3.2 Wm-1K-1 for the x = 0 sample to 2.3 Wm-1K-1 for the x = 0.2 sample at 300 K, showing a reduction of 28%. As a result, the enhanced PF together with reduced κ yields a maximum ZT of ~2.5 in both the x = 0.1 and x = 0.2 samples at 613 K (Fig. 3e), showing about 32% increase in comparison with the pristine sample (ZT = 1.7 at 613 K). The good reproducibility and repeatability of our experimental results are illustrated in Supplementary Figs. 13 and 14, respectively. Notably, a maximum ZT of 2.66 can be even obtained at 613 K (Fig. 3e) when the specific heat capacity (Cp) determined by the differential scanning calorimetry (DSC) (0.225 Jg-1K-1; Supplementary Fig. 15) is used instead of the theoretical value derived from Dulong-Petit law (0.241 Jg-1K-1), very close to the record-high ZT reported by Jiang et al. for cubic GeTe-based thermoelectrics calculated using the same method (ZT = 2.7 at 750 K).34 Such giant enhancement in ZT below the phase transition temperature is of great significance for practical applications. Furthermore, a maximum quality factor B of 2.4 can be achieved at 600 K when the additive content increases up to 0.1 wt% (Fig. 3f), which is quite competitive among the GeTe-based materials reported in previous studies (B = 0.4~2.5).37

In order to better understand the electrical transport behavior of the as-prepared samples, carrier concentration (p) and mobility (μH) were measured at 300 K. As Fig. 4a shows, p decreases from 2.71020 cm-3 to 2.11020 cm-3 as x increases from 0 to 0.05, and then drop gradually to 1.91020 cm-3 with x further increasing to 0.2; the corresponding μH exhibits an initial increase followed by a slight decline, reaching a maximum value of 96.9 cm2V-1s-1 at x = 0.1. Fig. 4b illustrates that the μH of this optimal composition exceeds the theoretical limit value calculated using the single parabolic band (SPB) model, which outperforms most GeTe-based thermoelectrics.11,16,17,24,28,30,32,33,42 Supplementary Fig. 16 presents the weighted mobility (μw) within the entire temperature range, calculated from Supplementary Equation (2). The variation trend of μw with additive content (Supplementary Fig. 16) agrees well with that observed for μH at room temperature. Basically, the reduction in p should be ascribed to charge depletion at the heterogeneous interface; the electron transfer from TiB2 into GeTe is encouraged, because the work function of GeTe matrix (~5.09 eV) is higher than that of TiB2 inclusions (~4.72 eV),9,38,39 as shown in Fig. 4c. The concept of electron donation from TiB2 can also be supported by Ge 2p X-ray photoelectron spectrometer (XPS) spectra, where a peak shift toward lower binding energy can be observed after TiB2 addition (Supplementary Fig. 17).40 Typically, an increase in the potential barrier would be anticipated, due to the band bending at the heterogeneous interface (Fig. 4c) along with increased grain boundary density (Supplementary Fig. 4), which is likely to deteriorate μH. The strains were also reported to make negligible contributions to modifying the band shape and hence the effective mass in rhombohedral GeTe.41 Interestingly, the TiB2-added samples still show enhanced μH compared to the pristine sample, suggesting that additional regulatory factors are involved.

By plotting μw against T-1, a linear relationship is presented below 473 K for all samples (Supplementary Fig. 18), indicative of acoustic phonon scattering as the dominating mechanism in degenerate semiconductors. Therefore, a scattering factor (r) of -0.5 was adopted to calculate the Pisarenko curve based on the SPB model using Supplementary Equations (3-9) (Fig. 4d). It is found that all data points exactly fall onto the calculated curve, implying that the S values are primarily governed by p, with a fixed electronic density of state effective mass (md*) of 1.72 me. The carrier mobility can be evaluated using Equation (1):43

μH = 8𝜋0.5ħ4𝑒𝐶𝐿 / (3𝑚𝑑 *2.5(𝑘𝐵𝑇)1.5𝛯2) (1)

where ħ is the reduced Planck constant, CL is the longitudinal elastic modulus, kB is the Boltzmann constant and Ξ is the deformation potential. Here, considering a fixed md* for all samples, μH should be mainly determined by CL and Ξ.

Fig. 4e shows the CL data of the as-prepared samples. Minimal TiB2 addition (0.05~0.2 wt%) has already proven effective in enhancing CL (red points). This enhancement results from both the phase mixing effect and load transfer effect, as reported by Liu et al. for composite materials.44 In view that the theoretical CL, calculated using the volume mixture rule (blue points),45 shows a slight increase from 70.3 GPa to 71.7 GPa with increasing x, the phase mixing effect does not take a dominating role. Thus, the difference between the experimental data and mixture rule data (pink region) should represent the contribution from the load transfer effect, which could be understood through the inset in Fig. 4e and Equation (2):46

σ = εCL (2)

where σ and ε represent the longitudinal stress and strain, respectively. It is noted that the CL of TiB2 is ~582 GPa,47 about eight times the value of GeTe (70.3 GPa),48 demonstrating superior resistance to elastic deformation. Given an intimate contact between the inclusions and matrix material, the ε of GeTe matrix would be constrained by TiB2 particles (Δε) when a tensile stress (σ) is loaded, giving rise to a smaller elastic strain compared to the pristine GeTe. Similarly, TiB2 can also act as a restraint against matrix contraction under compression. Consequently, effective load transfer from the matrix to the reinforcing phases is finalized when the coordinated elastic deformation is established at the interface, enabling the inclusions to bear a larger stress.49 The enhanced stiffness induced by TiB2 particles is also echoed by the Young’s modulus data measured by a nano indenter (Supplementary Fig. 19).

Fig. 4f displays the mean free path of carriers (lcar) and relative deformation potential (Ξ/Ξ0) calculated using Supplementary Equations (10-12). It is evident that lcar shows an increase followed by a decline, peaking at x = 0.1; this variation trend matches well with changes in μH, but is opposite to that of Ξ/Ξ0. According to the Bardeen-Shockley theory,50 the thermal vibrations can lead to the dilation or shrinkage of crystal lattices and hence the changes in electronic band energy. The shifts of energy band boundaries with elastic deformation are therefore defined as Ξ, acting as an indicator to reflect the intensity of carrier-phonon coupling.51 Previous investigations mainly focus on minimizing intrinsic Ξ by improving the symmetry structure via proper elemental doping.43 Herein, our work, despite methodological differences, converges on a similar advantage. Although the XRD Rietveld refinement results (Supplementary Fig. 2 and Supplementary Table 1) show that the atomic positions and angles are not significantly altered after TiB2 addition, indicative of unchanged intrinsic Ξ, the thermal vibration-induced elastic deformation can be efficiently weakened by the interfacial constraint effect, thereby limiting the actual shifts of energy band boundaries of the matrix material. In essence, this result can be alternatively understood as a reduction in the equivalent Ξ that leads to enhanced μH.

Owing to the difference in thermal expansion coefficients (TEC) between GeTe (5.60×10-5 K-1 between 296~648 K) and TiB2 (2.37×10-5 K-1 between 250~900 K),24,52 the misfit strains (εm) can be generated according to the Eshelby’s inclusion model (Equation (3)):53

εm = (αm – αi)ΔT (3)

where αm and αi denote the TEC of the matrix and inclusions, respectively, and ΔT is the temperature difference. Because the TEC of GeTe is greater than that of TiB2, GeTe is subjected to a large tensile stress during the cooling stage. A simplified two-phase model was employed to perform a preliminary finite element analysis of the stress distribution in the sintered composite, serving as theoretical evidence for stress at the interfaces (Supplementary Fig. 20 and Supplementary Table 2). It is inferred that the ‘void-particle’ structure in Fig. 2c may be a natural consequence of differential contraction between the matrix and the secondary phases. To offset the increased surface energy caused by pore formation, the secondary phase tends to resist separation from the matrix on one facet to keep a low-energy state.54 As x further increases up to 0.2, obvious aggregation of TiB2 nanoparticles can be formed, which is likely to induce severe stress concentrations.55 The interfacial debonding (Supplementary Fig. 10) may occur with the stress exceeding the elastic limit to trigger lattice distortions (Supplementary Fig. 11). The complex interface presented in Supplementary Fig. 12 is likely a direct manifestation of stress levels exceeding the critical threshold. Because the severe lattice distortions and deteriorated interfacial contacts can lead to partial failure of load transfer effect, a small decline in CL and a recovery in Ξ/Ξ0 are revealed.

In order to unveil the origin of reduced κL in the TiB2-added samples, the electronic (κe) and lattice (κL) contributions were clarified. As expected, κe exhibits a trend which mirrors that of σ (Fig. 5a), as it is strongly influenced by the latter. Notably, TiB2 addition proves effective in lowering κL. By incorporating 0.2 wt% TiB2 into the matrix, κL is reduced from 1.15 Wm-1K-1 to 0.71 Wm-1K-1 at 300 K, showing a reduction of 38% (Fig. 5b). The significantly reduced κL in combination with the enhanced μw yields a maximum μw/κL ratio of ~600 for both the x = 0.1 and x = 0.2 samples (Supplementary Fig. 21), reflecting a dramatic net gain between electrical and thermal transport. Such high μw/κL ratios indicate that proper TiB2 addition can enhance phonon scattering without degrading carrier transport; this effective carrier-phonon decoupling is mainly responsible for the increased B in Fig. 3f.

To further identify the primary factors influencing κL, the average sound velocity (νave) was derived from the data in Supplementary Table 3 based on Supplementary Equation (13), and the mean phonon free path (lp) at room temperature was calculated using Supplementary Equation (14). As shown in Fig. 5c, despite a nearly constant νave across all samples, a gradual reduction in lp occurs with increasing x, indicating that the intensity of phonon scattering is positively correlated with TiB2 content. The κL data were fitted by the Debye-Callaway model using Supplementary Equations (15-20) to examine the differences between experimental and simulation results (Fig. 5d),56 based on the physical parameters listed in Supplementary Table 4. For the x = 0 sample, the simulated κL basically match with the experimental κL, with the contributions from Umklapp process scattering, grain boundary scattering and point defect scattering taken into account. In contrast, a marked discrepancy persists between the experimental and simulated values for the x = 0.1 sample, even after incorporating the additional contributions from nanoparticle scattering. Given that lp ranges from 0.7 to 1.1 nm, much shorter than the size of TiB2 nanoinclusions (300~500 nm), the scattering effect induced by heterogeneous interfaces should prevail over the size effect, which is overlooked in the theoretical model. On one hand, the atomic displacement is confined due to the interfacial constraint effect, leading to an increased effective force constant F and hence a higher frequency ω, according to Equation (4):57

𝜔 = 2√(F/M) sin(πk / 2kc) (4)

where F is the force constant, M is the atomic mass, k is the wave vector magnitude, and kc is the cut-off wave vector magnitude. On the other hand, the phonon density of states (PhDoS) of GeTe and TiB2 are mainly distributed within the frequency range of 0~5.5 THz and 3.8~20 THz, respectively, showing a limited overlap region (Fig. 5e).58,59 Therefore, the addition of TiB2 nanoparticles can induce high-frequency vibration modes near the interface; the resulting high-energy phonons can effectively scatter low-energy phonons, thereby generating huge interfacial thermal resistance (Rx).60 The Rx of the as-prepared composites can be roughly estimated using Supplementary Equation (21), and the calculation results were summarized in Fig. 5f. As expected, a large Rx of 3.2ⅹ10-7 m2KW-1 is generated after addition of 0.1 wt% TiB2. Despite a doubling in TiB2 content (0.2 wt%), the Rx increases by a smaller margin, which could be attributed to the limited effective contact area of TiB2 nanoinclusions due to severe aggregations.

Methods
Synthesis
Raw materials of Ge (powders, 99.999%), Te (powders, 99.999%) and Bi (powders, 99.99%) weighted according to the optimal matrix composition (Ge0.94Bi0.05Te) were first sealed in tungsten carbide jars under Ar atmosphere, followed by high-energy planetary milling at 450 rpm for 12 h. Subsequently, different mass ratios of TiB2 (powders, 99.9%) were added into the mixture based on the nominal compositions (Ge0.94Bi0.05Te + x wt%, x = 0, 0.05, 0.1 and 0.2), after which the combined powders are subjected to planetary milling at 300 rpm for 3h. Finally, different batches of resulting powders were sintered at 873 K for 5 min under an axial pressure of 60 MPa in a vacuum of 5 Pascal, using a spark plasma sintering furnace (SPS 211Lx, Fuji Electronic, Japan).

Characterization
The phase identification was carried out by an X-ray diffractometer with a Cu Kα source (D8 ADVANCE, Bruker, Germany; λ =1.5418 Å). The Rietveld refinement was performed using the Topas software. The internal lattice strain was estimated by the Williamson-Hall method. The morphology and microstructure of fracture surfaces were determined by a field-emission scanning electron microscope (FESEM, Zeiss Merlin, Germany). The average grain size was evaluated using the linear intercept method. The chemical composition was examined by an electron probe micro analyzer (EPMA, JXA-8230, JEOL, Japan). STEM characterization was conducted by a JEOL JEM-ARM300F2 GRAND ARMTM2 aberration-corrected STEM, operated at 300 kV.

Transport property measurement
The electrical conductivity (σ) and Seebeck coefficient (S) were recorded by a transport property measurement system (ZEM-3, ADVANCE RIKO, Japan) under low-pressure He atmosphere. The total thermal conductivity (κ) was calculated from the equation κ = ρDCp, where ρ is the bulk density obtained by the Archimedes’ method, D is the diffusivity measured by a laser flash instrument (LFA457, Netzsch, Germany), and Cp is the specific heat capacity determined by both the Dulong-Petit law and DSC (STA 449 F3, Jupiter, Netzsch, Germany). The electronic thermal conductivity (κe) was calculated from the equation κe = LσT, where L represents the Lorenz factor estimated by the single parabolic band model, σ is the measured electrical conductivity, and T is the absolute temperature. The lattice thermal conductivity (κL) was derived from the equation κL = κ- κe. Both the electrical and thermal transport data were collected perpendicular to the axial SPS pressure. The longitudinal and transversal sound velocities were determined by the ultrasonic probing method. The carrier concentration and mobility were determined by a Hall measurement system (ResiTest 8340DC, Toyo, Japan).

Mechanical property measurement
The longitudinal elasticity modulus (CL) was calculated from the equation CL = ρvL2, where ρ is the bulk density and vL is the longitudinal sound velocity. The Young’s modulus and microhardness were determined by a nano indenter (Nano identer G200, China) at room temperature in air.

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "The paper titled “Giant ZT enhancement in rhombohedral GeTe-based thermoelectric materials” reports a significant\nenhancement in the thermoelectric figure of merit (zT) for p-type Ge0.94Bi0.05Te + x% TiB2 (x = 0, 0.5, 1.0, 2.0). The authors\ndemonstrate that the zT value increases from 1.7 for pristine Ge0.94Bi0.05Te to 2.5 for the Ge0.94Bi0.05Te + 1% TiB2\nsample at 613 K. A detailed discussion is provided on the enhancement of carrier mobility, despite the presence of\nincreased potential barriers at the composite interfaces and band bending effects. This mobility improvement is\nattributed to a reduction in the deformation potential. While the intrinsic deformation potential remains nearly unchanged compared to\npristine Ge0.94Bi0.05Te, the equivalent deformation potential decreases due to misfit strain and an increase in the\nlongitudinal Young’s modulus. The understanding of the paper can be improved by incorporating the following points\n(revisions):\n1. According to Figure S3 in the Supplementary Information, the internal strain decreases for Ge0.94Bi0.05Te + x% TiB2 (x =\n0.5 and 1) compared to the pristine sample. However, this trend appears contradictory, since the incorporation of TiB2 is\ngenerally expected to introduce additional strain. The observed reduction in internal strain at lower TiB2 contents requires\nfurther clarification. Whereas the internal strain increases for the Ge0.94Bi0.05Te + 2% TiB2 relative to the pristine sample.\n2. The authors attribute the reduction in the equivalent deformation potential in the TiB2 containing samples, to the misfit\nstrain arising from the difference in the coefficients of thermal expansion (CTE) between GeTe and TiB2, which is tensile in\nnature. However, as shown in Figure S3, the internal strain in Ge0.94Bi0.05Te + x% TiB2 (x = 0.5 and 1) samples is lower\nthan that of the pristine sample. Under these conditions, a decrease in internal strain would be expected to increase the\ndeformation potential, whereas a reduction in deformation potential is observed.\n3. Based on the authors’ argument, the Ge0.94Bi0.05Te + 2% TiB2 sample should exhibit the highest tensile misfit strain,\nwhich is consistent with the internal strain values shown in Figure S3, where this composition displays the largest strain.\nHowever, despite this increased strain, the sample does not exhibit the lowest deformation potential.\n4. Why does the Ge0.94Bi0.05Te + 2% TiB2 sample exhibit the lowest load-transfer effect among the TiB2-added samples,\nwhere it would be expected to show the highest load transfer effect?\n5. The incorporation of TiB2 into Ge0.94Bi0.05Te is expected to increase the potential barrier and induce band bending at\nthe heterogeneous interfaces, which should enhance charge-carrier scattering. Accordingly, the charge-carrier mean free\npath would be expected to decrease. However, as shown in Figure 4f, the mean free path in the TiB2-containing samples\nincreases instead.\n6. There is a significant difference in the lattice thermal conductivity between the experimentally observed and theoretically\ncalculated for the Ge0.94Bi0.05Te + 1% TiB2 sample. This could be explained elaborately.", "reviewer_2": "This study is experimentally comprehensive as it combining transport measurements, advanced characterization,\nmechanical analysis. Concept of interfacial constraint induced reduction of equivalent deformation potential is interesting.\nOverall, the manuscript is strong and suitable for publication after addressing the concerns below.\nYour previous similar study, which is published in same journal (Ref 24), reduce the degree of novelty. Both studies employ\na nanocomposite approach in rhombohedral GeTe-based systems with secondary-phase inclusions. You have already\ndemonstrated exceptional ZT enhancement below the phase transition temperature, emphasizing heterogeneous interfaces,\ncarrier concentration modulation, and reduced thermal conductivity in previous study. The current work replaces B-based\ninclusions with TiB₂, but the overall materials design philosophy and performance target remain largely unchanged. The\nreported ZT (2.66 at 613 K) and average ZT (1.29) are comparable to those already reported in previous one.\nAlthough the authors introduce the new concept of interfacial constraint–induced reduction of equivalent deformation\npotential, it is not decisively demonstrated that this effect could not also be operative in previous material.\nRecommendations\nClearly state what is new in this manuscript compared to previous study, beyond changing the type of nano inclusion.\nExplain why TiB₂ is fundamentally different from the inclusions used in Previous study, and what new understanding it\nprovides.", "reviewer_3": "Yu, J.C et al., demonstrated that incorporating TiB₂ into GeTe enhances carrier mobility while suppressing heat conduction,\nachieving a high ZT of 2.66 below the phase transition. This paper provides deep insights into the enhancement of carrier\nmobility resulting from a reduced deformation potential. These findings and conclusions are supported by extensive\nexperimental data, including XRD, SEM, STEM, XPS, thermoelectric measurements, elastic modulus data, sound velocity\nmeasurements, and more. Therefore, this work should be of broad interest to researchers in the fields of inorganic chemistry\nand thermoelectrics. However, a minor revision of manuscript is needed before it can be accepted for publication.\n1. The addition of TiB₂ reduces the grain size of sintered GeTe samples. How does this grain size reduction affect the\nincrease in longitudinal elastic modulus and the decrease in deformation potential?\n2. The authors should provide information on the crystal structure of TiB₂.\n3. Does the effective mass of carriers observed in this experiment agree with the values reported in other literature?"}, "author_response": "Feb. 12, 2026\nDear reviewers,\nThank you for your reports on our manuscript entitled “Giant ZT enhancement in\nrhombohedral GeTe-based thermoelectric materials” (Manuscript number:\nNCOMMS-25-104821A). We are very grateful for your insightful comments and the\nopportunity to revise our work. We have carefully addressed your concerns, and we\nbelieve the quality of our manuscript has been significantly improved for publications\nat Nature Communications. All modifications are highlighted in yellow in the main\ntext, and our detailed point-by-point responses are provided below.\nReviewer #1：\nComments:\nThe paper titled “Giant ZT enhancement in rhombohedral GeTe-based thermoelectric\nmaterials” reports a significant enhancement in the thermoelectric figure of merit (zT)\nfor p-type Ge Bi Te + x wt % TiB (x = 0, 0.05, 0.1, 0.2). The authors demonstrate\n0.94 0.05 2\nthat the zT value increases from 1.7 for pristine Ge Bi Te to 2.5 for the\n0.94 0.05\nGe Bi Te + 0.1 wt % TiB sample at 613 K. A detailed discussion is provided on\n0.94 0.05 2\nthe enhancement of carrier mobility, despite the presence of increased potential barriers\nat the composite interfaces and band bending effects. This mobility improvement is\nattributed to a reduction in the deformation potential. While the intrinsic deformation\npotential remains nearly unchanged compared to pristine Ge Bi Te, the equivalent\n0.94 0.05\ndeformation potential decreases due to misfit strain and an increase in the longitudinal\nYoung’s modulus. The understanding of the paper can be improved by incorporating\nthe following points (revisions).\nResponse: Thank you for your accurate description of our work. We have tried our best\nto address the concerns you raised, and we hope the revision can satisfy your\nrequirements.\n1. According to Figure S3 in the Supplementary Information, the internal strain\ndecreases for Ge Bi Te + x wt % TiB (x = 0.05 and 0.1) compared to the\n0.94 0.05 2\npristine sample. However, this trend appears contradictory, since the incorporation\nof TiB is generally expected to introduce additional strain. The observed reduction\n2\nin internal strain at lower TiB contents requires further clarification. Whereas the\n2\ninternal strain increases for the Ge Bi Te + 0.2 wt % TiB relative to the pristine\n0.94 0.05 2\nsample.\nResponse 1.1: We appreciate your valuable comments. Please note that the strains for\nthe x = 0.05 and 0.1 samples compared to the pristine sample are nearly unchanged by\nconsidering error bars, and the strain increases in the x = 0.2 sample. We are very sorry\nfor causing such confusions. We would like to clarify that the Williamson-Hall strain\nanalysis is used to calculate the micro-strains induced by lattice distortions (Adv. Mater.\n2019, 31, 1900108), rather than the thermal strains resulting from the thermal expansion\nmismatch. Below is the detailed analysis.\nHerein, the micro-strains were calculated using the following Equation: βcosθ = Kλ/D\n+ Cε sinθ, where β is the full width at half maximum (FWHM), θ denotes the\nXRD\ndiffraction angle, K is the Scherrer constant, λ represents the X-ray wavelength, D\ncorresponds to the average grain size, C is a constant related to the nature of the strain\nand details of the analysis method, and ε is the lattice strain. By plotting βcosθ\nXRD\nagainst sinθ, Cε can be derived from the slope based on the least squares method,\nXRD\nwhich inherently introduces calculation errors. In fact, the slight variations (0.04% ~\n0.07%) in Cε for the x = 0.05 and 0.1 samples compared to the pristine sample are\nXRD\nexactly within the margin of uncertainties. We have added error bars into the calculated\ndata, shown in Figure S3b. The overall trend shows that the value remains relatively\nconstant across the range of x = 0 ~ 0.1, but exhibits an obvious increase at x = 0.2.\nIn theory, if the thermal stress remains entirely within the elastic limit of the material,\nit only induces uniform elastic lattice strain without causing permanent lattice\ndistortions; such elastic strain is fully recoverable once the stress is released.\nConversely, only when the local stress exceeds the elastic limit will the crystal structure\nundergo permanent lattice distortions. For example, it was reported that huge tensile\nstress stemming from the mismatch in thermal expansion coefficient between the matrix\nand inclusions during the cooling stage could induce lattice distortions and defect\nevolution (Nat. Commun. 2024, 15, 5915). The negligible changes in Cε for the x\nXRD\n= 0.05 and 0.1 samples indicate that the stress level is still below the elastic limit, which\nis hard to trigger lattice distortions.\nHowever, the case is different for the x = 0.2 sample, where the local stress\nconcentration can be produced by obvious particle aggregations (Compos. Struct. 2015,\n133, 246-256), supported by the EPMA maps (Figure S6). At this time, the tensile\nstress is likely to exceed the elastic limit, and thus distinct lattice distortions are\nobserved, supported by the GPA analysis in Figure S11e.\nThe relevant figures and texts have been modified accordingly.\nFigure S3b Calculated Cε data for the Ge Bi Te + x wt% TiB samples with error bars\nXRD 0.94 0.05 2\nFigure S6 EMPA analysis results for the as-prepared Ge Bi Te + x wt%TiB samples\n0.94 0.05 2\nFigure S11 d The STEM image of the interface in the Ge Bi Te + 0.2 wt% TiB sample; e\n0.94 0.05 2\nThe GPA analysis corresponding to the region in d marked with the white box\nFigure changes in the Supplementary Materials:\nFigure S3 a Williamson-Hall strain analysis for the as-prepared Ge Bi Te + x wt%TiB samples;\n0.94 0.05 2\nb Calculated micro-strain values with error bars\nText changes in the Manuscript:\nInterestingly, Williamson-Hall analysis reveals similar micro-strain levels (~0.5%) for\ncompositions with x between 0 and 0.1 within the margin of uncertainties, yet a\npronounced increase to ~0.8% is observed in the x = 0.2 sample (Figure S3); these\nresults imply that excessive TiB addition introduces severe local lattice distortions.\n2\n(Page 5)\n2. The authors attribute the reduction in the equivalent deformation potential in the\nTiB containing samples, to the misfit strain arising from the difference in the\n2\ncoefficients of thermal expansion (CTE) between GeTe and TiB , which is tensile\n2\nin nature. However, as shown in Figure S3, the internal strain in Ge Bi Te + x%\n0.94 0.05\nTiB (x = 0.05 and 0.1) samples is lower than that of the pristine sample. Under\n2\nthese conditions, a decrease in internal strain would be expected to increase the\ndeformation potential, whereas a reduction in deformation potential is observed.\nResponse 1.2: Thanks for your comment. We would like to clarify that the reduction\nin the equivalent deformation potential should be ascribed to reduced sensitivity of the\nchanges in band structure to elastic deformation as a result of the interfacial constraint\neffect, instead of the misfit strain arising from the difference in the coefficients of\nthermal expansion (CTE) between GeTe and TiB as denoted by the reviewer. We have\n2\nhighlighted this point in the Introduction section.\nAs mentioned in response 1.1, our experimental results show that the micro-strain level\nis similar for the x = 0.05 and 0.1 samples, and such low additive content is inadequate\nto trigger permanent lattice distortions. As the TiB content increases from 0 to 0.1, the\n2\ndistribution of nanoparticle-induced elastic strains is expected to be broadened. Due to\nthe higher elastic modulus of TiB (~582 GPa) compared to GeTe (70.3 GPa), the TiB\n2 2\ninclusions bear larger stress because of the load transfer effect resulting from the\ncoordinated elastic deformation at the interface (J. Mater. Res. 2025, 40, 250-264),\nwhich is commonly reported for composite materials. This helps the matrix material to\nincrease the resistance to elastic deformation. Consequently, the sensitivity of the\nchanges in band structure to elastic deformation is reduced in GeTe and the equivalent\nΞ is lowered.\nText changes in the Manuscript:\nNotably, different from the classic Ξ modulation enabled by symmetry improvement\nvia chemical bond engineering,25 the atomic displacement associated with elastic\ndeformation is confined by the nanoparticle-induced interfacial constraint effect; this\nalso reduces the sensitivity of the changes in band structure to elastic deformation,\nthereby lowering equivalent Ξ and enhancing μ . (Page 4)\nH\n3. Based on the authors’ argument, the Ge 0.94 Bi 0.05 Te + 0.2 wt% TiB 2 sample should\nexhibit the highest tensile misfit strain, which is consistent with the internal strain\nvalues shown in Figure S3, where this composition displays the largest strain.\nHowever, despite this increased strain, the sample does not exhibit the lowest\ndeformation potential.\nResponse 1.3: Thanks for your comment. This is also related to the above comments,\nto which we should make a clear clarification of the relationship between the equivalent\nΞ and elastic strains. Herein, the high modulus of TiB enables it to bear a lager stress\n2\nin presence of elastic strains, thereby increasing the resistance to elastic deformation in\nGeTe matrix. This helps to lower the sensitivity of the changes in band structure to\nelastic deformation and hence the equivalent Ξ.\nIn fact, according to the Williamson-Hall strain analysis results, the x = 0.2 sample\nshould exhibit the highest micro-stain, reflecting severe permanent lattice distortions.\nOn one hand, the crystal lattice with inelastic deformation cannot participate into the\ncoordinated elastic deformation at the interface. On the other hand, the differential\ncontraction between the matrix and the secondary phases due to the mismatched\nthermal expansion coefficient during the cooling stage even leads to interfacial\nadhesion deterioration and interfacial debonding. Figure S10 shows that some\ninclusions even exhibit minimal contact with pore edges in the x = 0.2 sample.\nFigure S10 STEM-EDX images of the Ge Bi Te + 0.2 wt%TiB sample\n0.94 0.05 2\nFigure S12 shows that the elemental distribution of Ti and Te shows an overlap, which\ndoes not align with the natural interface morphology. When the electron beam is\nfocused on the TiB side (top right region in Figure S12i), two distinct sets of\n2\ndiffraction spots (blue circle: TiB ; red circle: GeTe) appear in the FFT pattern (Figure\n2\ngrain is likely to extend over the GeTe grain, giving rise to a discontinuous interface.\nThis complex interface is likely a direct manifestation of stress levels exceeding the\ncritical threshold. Because the deteriorated interfacial contact and inelastic deformation\ncan lead to partial failure of effective load transfer effect, the equivalent Ξ of the x =\n0.2 sample is not the lowest.\nFigure S12 The detailed information about the interface between the secondary phase and matrix\nphase in the Ge Bi Te + 0.2 wt%TiB sample\n0.94 0.05 2\n4. Why does the Ge Bi Te + 0.2 wt% TiB sample exhibit the lowest load-transfer\n0.94 0.05 2\neffect among the TiB -added samples, where it would be expected to show the\n2\nhighest load transfer effect?\nResponse 1.4: Thanks for your comment. The load transfer effect works on the basis\nof coordinated elastic deformation with intimate interfacial contact. In the x = 0.2\nsample, partial particle aggregations lead to stress concentration that gives rise to lattice\ndistortions and deteriorated interfacial contact, and thus the lowest load transfer effect\nis not yielded. We have provided detailed explanations in responses 1.1, 1.2 and 1.3.\nThe main text has been modified to highlight the reasons.\nText changes in the Manuscript:\nAs x further increases up to 0.2, obvious aggregation of TiB nanoparticles can be\n2\nformed, which is likely to induce severe stress concentrations.55 The interfacial\ndebonding (Figure S10) may occur with the stress exceeding the elastic limit to trigger\nlattice distortions (Figure S11). The complex interface presented in Figure S12 is likely\na direct manifestation of stress levels exceeding the critical threshold. Because the\nsevere lattice distortions and deteriorated interfacial contacts can lead to partial failure\nof load transfer effect, a small decline in C and a recovery in Ξ/Ξ are revealed. (Page\nL 0\n12)\n5. The incorporation of TiB into Ge Bi Te is expected to increase the potential\n2 0.94 0.05\nbarrier and induce band bending at the heterogeneous interfaces, which should\nenhance charge-carrier scattering. Accordingly, the charge-carrier mean free path\nwould be expected to decrease. However, as shown in Figure 4f, the mean free path\nin the TiB -containing samples increases instead.\ncarrier scattering will be enhanced by the heterogeneous interfaces in theory. However,\nthe observed mobility is influenced by multiple aspects beyond the interface scattering.\nTo analyze the scattering mechanisms, we first determined the dominating scattering\nmechanism using the Pisarenko curve based on the SPB model (Figure 4d), and found\nthat all data points exactly fall onto the calculated curve with a scattering factor of -0.5;\nthis implies that the electronic density of state effective mass is almost unchanged (1.72\nm ), and the acoustic phonon scattering is the dominating mechanism.\ne\nFigure 4d Seebeck coefficient plot against carrier concentration based on the SPB model at\nIn addition to the interface scattering, please note that the TiB inclusions also change\n2\nthe deformation potential that can affect the mobility. As the deformation potential (Ξ)\nis defined as the shifts of energy band boundaries with elastic deformation, it can act as\nan indicator to reflect the intensity of carrier-phonon coupling (Proc. Natl. Acad. Sci.\n2012, 109, 9705-9709). Although the addition of TiB nanoparticles brings about\n2\nheterogeneous interfaces, the interface scattering is not the dominating mechanism here.\nThe benefits of Ξ reduction that weakens acoustic phonon scattering overweigh the\ndetrimental effects of interface scattering, thereby enhancing the carrier mobility and\nincreasing the mean free path of carriers.\n6. There is a significant difference in the lattice thermal conductivity between the\nexperimentally observed and theoretically calculated for the Ge Bi Te + 0.1 wt%\n0.94 0.05\nTiB sample. This could be explained elaborately.\nthe lattice thermal conductivity between the experimentally observed and theoretically\ncalculated for the Ge Bi Te + 0.1 wt% TiB sample should originate from the\n0.94 0.05 2\ninterfacial constraint effect and the mismatch of phonon density of state between matrix\nand inclusions. It is reported that the dynamic (elastic) strains due to thermal vibrations\nare also responsible for broadening the angular frequency (Joule 2019, 3, 1276-1288).\nHerein, the atomic displacement is confined due to the interfacial constraint effect,\nleading to an increased effective force constant F and hence a higher frequency,\naccording to the following Equation: , where F is the force constant,\n𝐹 𝜋 𝑘\nM is the atomic mass, k is the wave vec𝜔to=r a2n√d 𝑀k\nc\nsiisn t h(e2 c𝑘u𝑐)t-off wave vector. Meanwhile,\nthe phonon density of states of GeTe and TiB are mainly distributed within the\n2\nfrequency range of 0~5.5 THz and 3.8~20 THz, respectively, showing a limited overlap\nregion. Therefore, the addition of TiB nanoparticles can induce high-frequency\n2\nvibration modes near the interface; the resulting high-energy phonons can effectively\nscatter low-energy phonons, thereby generating huge interfacial thermal resistance.\nWe have modified the main text to explain this phenomenon elaborately.\nText changes in the Manuscript:\nGiven that l ranges from 0.7 to 1.1 nm, much shorter than the size of TiB\np 2\nnanoinclusions (300~500 nm), the scattering effect induced by heterogeneous\ninterfaces should prevail over the size effect, which is overlooked in the theoretical\nmodel. On one hand, the atomic displacement is confined due to the interfacial\nconstraint effect, leading to an increased effective force constant F and hence a higher\nfrequency ω, according to Equation 4:57\n(4)\n𝐹 𝜋 𝑘\n𝜔 = 2√𝑀sin (2𝑘𝑐)\nwhere F is the force constant, M is the atomic mass, k is the wave vector, and k is the\nc\ncut-off wave vector. On the other hand, the phonon density of states (PhDoS) of GeTe\nand TiB are mainly distributed within the frequency range of 0~5.5 THz and 3.8~20\naddition of TiB nanoparticles can induce high-frequency vibration modes near the\n2\ninterface; the resulting high-energy phonons can effectively scatter low-energy phonons,\nthereby generating huge interfacial thermal resistance (R ).60 (Pages 13-14)\nx\nReviewer #2：\nComments:\nThis study is experimentally comprehensive as it combining transport measurements,\nadvanced characterization, mechanical analysis. Concept of interfacial constraint\ninduced reduction of equivalent deformation potential is interesting. Overall, the\nmanuscript is strong and suitable for publication after addressing the concerns below.\nResponse: Thank you for your recognition of our work.\n1. Your previous similar study, which is published in same journal (Ref 24), reduce\nthe degree of novelty. Both studies employ a nanocomposite approach in\nrhombohedral GeTe-based systems with secondary-phase inclusions. You have\nalready demonstrated exceptional ZT enhancement below the phase transition\ntemperature, emphasizing heterogeneous interfaces, carrier concentration\nmodulation, and reduced thermal conductivity in previous study. The current work\nreplaces B-based inclusions with TiB , but the overall materials design philosophy\n2\nand performance target remain largely unchanged. The reported ZT (2.66 at 613 K)\nand average ZT (1.29) are comparable to those already reported in previous one.\nAlthough the authors introduce the new concept of interfacial constraint-induced\nreduction of equivalent deformation potential, it is not decisively demonstrated that\nthis effect could not also be operative in previous material.\nResponse 2.1: Thank you for your valuable comments by comparing our current and\nprevious works. We agree that our previous work is indeed relevant to composite\nstrategy. However, beyond the composite approach, the present work demonstrates its\nnovelty in terms of new concept, high performance and deep analysis. Below we have\nmade a clear clarification.\nFirst, we highlight that the new concept of interfacial constraint-induced reduction of\nequivalent deformation potential is not applicable to the previous material.\nThe deformation potential (Ξ) is defined as the shifts of energy band boundaries with\nelastic deformation, acting as an indicator to reflect the intensity of carrier-phonon\ncoupling (Proc. Natl. Acad. Sci. 2012, 109, 9705-9709). Therefore, the reduction in Ξ\nreflects the weakened scattering effect of acoustic phonons on carriers, which helps to\nincrease carrier mobility. This effect becomes pronounced when the acoustic phonon\nscattering is the dominating mechanism.\nBy comparing the Pisarenko curves of these two samples, it is clear that the scattering\nfactor (r) of the Ge Bi Te/TiB sample is -0.5, confirming the acoustic phonon\n0.94 0.05 2\nscattering as the dominating mechanism (Figure R1a), whilst the r value of the\nGe Bi Te/B sample deviates upward from -0.5, indicating that interface scattering\n0.94 0.05\nmechanism is involved (Figure R1b). Moreover, the carrier mobility is expected to\nshow an increase if the interfacial constraint effect works, as demonstrated in Figure\nR1c for the Ge Bi Te/TiB sample. However, it is found that the carrier mobility\n0.94 0.05 2\nsuffers from degradation for the Ge Bi Te/B sample, shown in Figure R1d.\n0.94 0.05\nFigure R1 The Pisarenko curves for (a) TiB -added samples and (b) B-added samples; carrier\n2\nconcentration and mobility for (c) TiB -added samples and (d) B-added samples\ncalculated the figure of merit (Z) to intuitively evaluate the thermoelectric properties\nwithout the interference of temperature. By comparing the Z value and average ZT in\ndifferent works, we find that the Z value of the Ge Bi Te/TiB sample (Z = 4.4 \n0.94 0.05 2\n10-3 K-1 @600 K) is consistently higher than that of the Ge Bi Te/B sample (Z =\n0.94 0.05\n4.0  10-3 K-1 @613 K) across the entire temperature range, resulting in a higher average\nZT for the Ge Bi Te/TiB sample (ZT = 1.29) compared to the Ge Bi Te/B\n0.94 0.05 2 ave 0.94 0.05\nsample (ZT = 1.1). In fact, the average ZT of rhombohedral GeTe (between 300 and\nave\n2022, 377, 208-213.\nFigure 1 Nanocomposite strategy and enhanced thermoelectric figure of merits of GeTe-based\nmaterials. c Comparison of Z values in this work with different GeTe-based thermoelectrics.11,24,27–\n34 (T denotes the phase transition temperature) d Average ZT value contrast of various GeTe-based\npt\nthermoelectrics.11,24,27–34\n2. Clearly state what is new in this manuscript compared to previous study, beyond\nchanging the type of nano inclusion. Explain why TiB is fundamentally different\n2\nfrom the inclusions used in Previous study, and what new understanding it provides.\nResponse 2.2: Thank you for your suggestion. We have made a clearer clarification to\nhighlight the new findings in the present work. We believe that TiB inclusions is\n2\nfundamentally different from B inclusions used in previous study, and the reasons are\nlisted as below.\n1) The underlying mechanism of electrical transport is different. The B addition aims\nto increase Seebeck coefficient by inducing the energy filtering effect through\nelevating interfacial potential barrier, whilst the TiB addition contributes to\n2\nenhancing carrier mobility by reducing the equivalent deformation potential via the\nnanoparticle-induced interfacial constraint effect.\n2) The underlying mechanism of thermal transport is different. The B inclusions\nfacilitate the formation of high-density dislocations, which helps to enhance defect\nscattering on phonons. In contrast, the TiB inclusions induce high-frequency\n2\nvibration mode near the interface, contributing to enhancing phonon-phonon\nscattering.\n3) The thermoelectric performance enhancement is distinct. Both the Z value and\naverage ZT value of the Ge Bi Te/TiB sample are higher than those of the\n0.94 0.05 2\nGe Bi Te/B sample. The average ZT of rhombohedral GeTe (between 300 and\n0.94 0.05\nin Science 2022, 377, 208-213.\n4) The elastic modulus of TiB (~582 GPa; Acta Mater. 2011, 59, 4886-4894) nearly\n2\ndoubles the value of B (~306 GPa; ACS Nano, 2013, 7, 10112-10120), showing\ngreater potential in generating load transfer effects. This provides more\nopportunities to introduce a new mechanism, i.e., decreased equivalent deformation\npotential, in the GeTe/TiB composite, which has never been found in previous\n2\nstudies.\nImportantly, we emphasize that our work provides new understanding on deformation\npotential modulation. Unlike the classical deformation potential modulation method\nenabled by crystal symmetry improvement (Science 2025, 390, 1266-1271), we\ndemonstrate for the first time that incorporating high-modulus nanoparticles can\neffectively reduce the equivalent deformation potential, offering a novel perspective on\ncarrier-phonon decoupling.\nWe have included the above clarifications in the revised manuscript to highlight the\nnew findings of our present work.\nText changes in the Manuscript:\n1. Previously, we incorporated B inclusions into the GeTe matrix,24 with the aim of\npromoting the energy filtering effect to increase S and the formation of high-density\ndislocations to enhance phonon scattering. Unfortunately, this approach degraded the\ncarrier mobility, which restricted further ZT enhancement. Herein, we find that direct\nincorporation of high-modulus nanoparticles into rhombohedral GeTe leads to a notable\nincrease in μ despite increased interfacial potential barrier arising from a large grain\nH\nboundary density as well as unfavorable energy band bending, with huge thermal\nresistance (R ) at heterogeneous interfaces. This work aims to provide a deep insight\nx\ninto these exotic transport behaviors. (Page 3)\n2. Notably, different from the classic Ξ modulation enabled by symmetry improvement\nvia chemical bond engineering,25 the atomic displacement associated with elastic\ndeformation is confined by the nanoparticle-induced interfacial constraint effect; this\nalso reduces the sensitivity of the changes in band structure to elastic deformation,\nthereby lowering equivalent Ξ and enhancing μ . We reveal this mechanism for the first\nH\ntime, offering a novel perspective on electrical transport modulation. Additionally, the\nresulting heterogeneous interfaces contribute to facilitating charge transfer, and\nintroducing high-frequency lattice vibration modes that enhance phonon-phonon\nscattering. (Page 4)\n3. In addition, our work also achieves an extraordinary average ZT of 1.29 in\nrhombohedral GeTe, comparable to the record-high value for the Ag/Sb/Pb/Bi alloyed\nGeTe (Figure 1d),11,24,27-34 showing considerable potential of our strategy in TE\nproperty optimization. (Page 4)\nReviewer #3：\nComments:\nYu, J.C et al., demonstrated that incorporating TiB₂ into GeTe enhances carrier mobility\nwhile suppressing heat conduction, achieving a high ZT of 2.66 below the phase\ntransition. This paper provides deep insights into the enhancement of carrier mobility\nresulting from a reduced deformation potential. These findings and conclusions are\nsupported by extensive experimental data, including XRD, SEM, STEM, XPS,\nthermoelectric measurements, elastic modulus data, sound velocity measurements,\nand more. Therefore, this work should be of broad interest to researchers in the fields of\ninorganic chemistry and thermoelectrics. However, a minor revision of manuscript is\nneeded before it can be accepted for publication.\nResponse: Thank you very much for your recognition of our work. Below please find\nour responses.\n1. The addition of TiB reduces the grain size of sintered GeTe samples. How does\n2\nthis grain size reduction affect the increase in longitudinal elastic modulus and the\ndecrease in deformation potential?\nResponse 3.1: Thank you for your valuable comments. The elastic modulus is\ndetermined mainly by interatomic bonding forces and interatomic distance. Since grain\nrefinement contributes only minimally to altering chemical bonding or atomic\ndisplacement, the longitudinal elastic modulus should remain relatively insensitive to\ngrain size.\nThe deformation potential (Ξ) is defined as the shifts of energy band boundaries with\nelastic deformation (Proc. Natl. Acad. Sci. 2012, 109, 9705-9709). For bulk materials,\nit is less likely to modulate band structures and elastic deformation by reducing grain\nsize. It is therefore inferred that the grain refinement does not take a vital role in\nreduction of equivalent deformation potential.\n2. The authors should provide information on the crystal structure of TiB .\ncrystal structure of TiB is provided. In this work, the crystal structure of TiB is\n2 2\nsuccessfully indexed using the CIF file (ICSD: 190893). It exhibits a hexagonal\nstructure with a space group of P 6/mmm (191), the unit cell parameters of which are a\n= 3.031Å, b = 3.031Å and c = 3.237Å, with cell volume of 25.75 Å3.\nText changes in the Manuscript:\nThe corresponding line intensity maps and calculated plane spacing values are in good\nagreement with the (110) and (100) crystal planes (Figures 2n and 2o) for the\nhexagonal TiB with a space group of P 6/mmm (191), which is consistent with the\n2\ncrystal structure of the CIF file (ICSD: 190893). (Page 6)\n3. Does the effective mass of carriers observed in this experiment agree with the values\nreported in other literature?\nResponse 3.3: Thank you for your question. Accordingly, we have checked the\ncalculated effective mass in previous studies. As the matrix composition in our work is\nGe Bi Te, we mainly focused on the Bi-doped GeTe samples. It was reported that\n0.94 0.05\nthe effective mass for Bi-doped GeTe is within the range of 1.6~2.1 m (Proc. Natl.\ne\nAcad. Sci. 2018, 115, 5332-5337; J. Mater. Chem. A, 2020, 8 21642-21648; Chemical\nEng. J. 2023, 474, 145820). Therefore, our effective mass data (1.72 m ) is in broad\ne\nagreement with previous investigations.\nWe hope you will be satisfied with the revised version. Of course, we will be happy to\nprovide further clarification or response to any other queries.\nYours sincerely,\nJing-Feng Li, Xiaoyuan Zhou, Yu Pan and Yilin Jiang (on behalf of all authors)."}, {"round": 2, "reviewer_comments": {"reviewer_1": "Revisions are satisfactory", "reviewer_2": "I accept the authors response to my comments and changes in manuscript. In my opinion, manuscript is acceptable for publication.", "reviewer_3": "The revisions are satisfied with reviewers' comments. I would recommend it for acceptance in its current form."}, "author_response": "Feb. 26, 2026\nDear reviewers,\nThank you for your reports on our manuscript entitled “Giant ZT enhancement in\nrhombohedral GeTe-based thermoelectric materials” (Manuscript number:\nNCOMMS-25-104821B). We are very grateful for your comments, and our detailed\npoint-by-point responses are provided below.\nReviewer 1\nRevisions are satisfactory.\nResponse: Thanks for your comment, and we are happy that you are satisfied with our\nwork.\nReviewer 2\nI accept the authors response to my comments and changes in manuscript. In my\nopinion, manuscript is acceptable for publication.\nResponse: Thanks for your recognition of our work and your recommendation.\nReviewer 3\nThe revisions are satisfied with reviewers' comments. I would recommend it for\nacceptance in its current form.\nResponse: Thanks for your comment, and we are happy that you are satisfied with our\nwork.\nAgain, thank you for your efforts devoted into improving the quality of our paper.\nKind regards,\nJing-Feng Li, Xiaoyuan Zhou, Yu Pan and Yilin Jiang."}]

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