Atomic-scale mechanism unlocks thermal-stable high-κ performance in HfO_2 via coherent interfaces

Domain: chemistry
Published: 2026-01-16
Editorial outcome: major_revision

Abstract
Complementary-metal-oxide-semiconductor-compatible HfO2-based high-κ dielectrics are pivotal for next-generation electronics in the post-Moore’s Law era. However, establishing coherent interfaces via morphotropic phase boundaries across the tetragonal and orthorhombic (ferroelectric or antiferroelectric) phases—a key strategy for enhancing dielectric properties—remains challenging due to unclear atomic-scale mechanisms and inherent thermal instability, which compromises long-term stability and reliability. To address this, we leverage metallurgical quenching principles to stabilize tetragonal/orthorhombic-antiferroelectric morphotropic phase boundaries in HfO2-based (Lu:Hf0.6Zr0.4O2) bulk crystals. Through precise composition tuning and growth optimization, we stabilize these metastable morphotropic phase boundaries at the tetragonal/orthorhombic-antiferroelectric interface at room temperature, achieving a comparable κ-value (57) to actively studied tetragonal/orthorhombic-ferroelectric counterparts. Microstructural characterization reveals how tensile strain within the t-phase drives dielectric enhancement through softening of the low-frequency Eu phonon mode. Critically, the tetragonal/orthorhombic-antiferroelectric morphotropic phase boundary demonstrates a ~58% reduction in κ variation rate over 30–200 °C relative to tetragonal/orthorhombic-ferroelectric counterparts, signifying superior thermal stability. Our study establishes a generalizable design paradigm for developing high-κ dielectrics in fluorite-structured materials, advancing next-generation complementary-metal-oxide-semiconductor-compatible-integrated functional devices for data storage, energy harvesting, sensing, and integrated photonics.

Introduction
As the demand for reducing equivalent oxide thickness continues to grow in the ongoing miniaturization of microelectronic devices, such as dynamic random-access memory (DRAM) and field-effect transistors (FET), modern downscaling efforts increasingly rely on the transformative utilization of gate materials that combine a high dielectric constant (κ), wide band gap, and excellent compatibility with silicon-based integrated circuit technology1–6. Over the past decades, HfO2-based fluorite-structure materials have demonstrated remarkable compatibility with mature complementary metal-oxide-semiconductor (CMOS) technology and superior dielectric performance in contrast to traditional SiO2-based dielectrics. Among HfO2 polymorphs, including Fm−3m (c), P42/nmc (t), ferroelectric Pbc21 (o-FE), antiferroelectric Pbca (o-AFE), and monoclinic P2/c (m) phases7,8, the t-phase is widely regarded as the primary high-κ candidate due to its high theoretical κ (~70), which far exceeds those of other polymorphs with κ-values typically below 409. However, the experimentally achievable κ in t-phase HfO2-based materials rarely exceeds ~40, even with optimized manufacturing processes and compositional engineering10, falling short of the stringent demands for next-generation high-density/high-speed electronic and memory devices in the post-Moore’s Law era1,11. Beyond high κ, robust dielectric thermal stability has become equally critical for ensuring the operational reliability of these CMOS-integrated systems12, necessitating innovative approaches to simultaneously enhance both κ and dielectric thermal stability in HfO2-based materials.

Constructing coherent phase interfaces represents an established strategy for tailoring material properties in metals and ceramics13–16. For HfO2-based materials, engineering morphotropic phase boundaries (MPBs) between the t and o (o-FE or o-AFE) phases has emerged as an effective strategy for enhancing dielectric properties17. However, despite their promising dielectric improvements, the lack of microstructural characterization obscures the origin of this enhancement, leading to an inconsistent κ variation range (38–68)18–30. Furthermore, the inherently low energy barrier (~46.0 meV per f.u.) between the t and o-FE phases readily facilitates a phase transition under thermal or electric field stimuli, severely compromising dielectric stability and degrading device endurance17,31,32. In contrast, the energy barrier for the t-to-o-AFE transition is significantly higher (~68.8 meV per f.u.), ~1.5 times that of the t/o-FE interface (Fig. 1a)32, suggesting t/o-AFE MPBs could deliver superior dielectric stability. Current t/o MPB research in HfO2-based dielectrics focuses primarily on thin films, where the intermediate free energy of the o-FE phase between the t and o-AFE phases often leads to mixed o-FE and o-AFE phases (Fig. 1)33,34. Critically, this higher energy barrier for the t-to-o-AFE transition, as opposed to the t-to-o-FE transition, makes t/o-AFE MPB formation more challenging than t/o-FE MPBs, leaving the interplay between t/o-AFE MPB configurations and their dielectric properties poorly understood. This gap highlights the need for systematic exploration into t/o-AFE MPBs to unlock their full potential.

Recent advances in HfO2-based bulk crystals, prepared via the optical floating zone (OFZ) technique, have demonstrated successful stabilization of both t and o (o-AFE or o-FE) phases32,35. Significantly, precise control over t-to-o phase transition pathways can be realized by strategic composition engineering combined with controlled temperature gradient distribution35, providing a feasible avenue for stabilizing HfO2-based t/o-AFE MPBs. In this study, inspired by the metallurgical quenching principles, we successfully grow HfO2-based (Lu:Hf0.6Zr0.4O2, Lu:HZO) bulk crystals featuring a well-defined t-o phase boundary. Our structural analyses reveal that the t-o phase boundary primarily represents the interface between the non-polar t and antiferroelectric o-AFE phases. Subsequent dielectric characterization reveals that our t/o-AFE MPBs achieve a comparable κ-value (57) to actively studied t/o-FE MPBs. Through detailed microstructural observations and strain analyses, we identify the mechanism behind the dielectric enhancement near the t/o-AFE MPBs, which is primarily attributed to the frequency shift in the infrared-active low-frequency Eu phonon mode of the t-phase driven by local structural modifications at the phase boundary. Moreover, t/o-AFE MPBs exhibit significantly enhanced thermal stability, demonstrating less than half the κ variation rate observed in the t/o-FE MPBs across the temperature range from 30 to 200 °C. Our findings establish a clear structure-property relationship in HfO2-based t/o-AFE MPBs, and provide a versatile design framework for fluorite-structured functional devices with applications in CMOS-integrated data storage, energy harvesting, sensing, and photonic technologies36,37.

Results
Design strategy and growth of Lu:HZO bulk crystals
As illustrated in Fig. 1c, our approach for achieving t/o-AFE MPBs in HfO2-based bulk crystals involves three sequential steps, corresponding to the formation of the t-phase (Step 1), controlled t-to-o phase transition (Step 2), and preserving t/o-AFE MPBs to room temperature (Step 3). The t-phase is metastable at room temperature due to its higher formation energy relative to orthorhombic phases (o-AFE or o-FE). Its critical nucleation dimension typically falls within a few nanometers, rendering its stabilization challenging even in thin films or nanoparticles38,39. To address this challenge, in Step 1, we employed the OFZ growth method for preserving high-temperature metastable phases down to room temperature via ultrahigh heating temperatures (Supplementary Fig. 1, up to 3000 °C), steep thermal gradients, and controllable growth rates40. Codoping with rare-earth (RE3+) and Zr4+ ions offers a direct solution to stabilize t-phase HfO2-based bulk crystals at room temperature by effectively suppressing m-phase interference and modulating the t-to-o phase transition temperature32,35. Lu3+ offers a distinct advantage for o-phase stabilization: the doping concentration needed to suppress the detrimental m-phase formation (via the t→c+m eutectoid reaction) is lower than that required for larger RE3+ ions and falls within the typical range for o-phase stabilization in HfO2 systems6. Here we used the Hf0.6Zr0.4O2 (HZO) doped with Lu (Lu:HZO)—a composition optimized for t-phase stability—to systematically explore dopant concentrations35.

Regarding Step 2, controlled temperature-driven t-to-o phase transition enables the formation of o phases (o-AFE or o-FE) from the high-temperature metastable t-phase6. The steep temperature gradient and fast growth rate intrinsic to the OFZ growth strategy offer a feasible control over the t-phase conversion, benefiting the formation of well-defined t/o phase boundaries within Lu:HZO bulk crystals. As the as-grown crystal traverses its Curie temperature (TC) during cooling, the o-phase precipitation initiates31. The cooling pathway from the high-temperature supplies sufficient transformation energy to overcome the activation barriers for both t→o-AFE and t→o-FE conversions. The o-AFE phase possesses a lower formation energy than the o-FE phase, thus favoring its preferential nucleation during the t-to-o conversion32. Consequently, combining with the pure t-phase region, t/o-AFE MPBs will form at the t/t+o-AFE phase interface within Lu:HZO bulk crystals.

Step 3 aims to stabilize the t/o-AFE MPBs in Lu:HZO bulk crystals to room temperature utilizing a non-equilibrium processing strategy. Post-growth rapid quenching (cooling within ~2 s) quickly removes the as-grown crystal from the high-temperature regime, effectively suppressing further t-to-o phase transition. This non-equilibrium process preserves the formed t/o-AFE MPBs to room temperature by minimizing high-temperature exposure. Leveraging this OFZ strategy, we grew a series of Lu:HZO bulk crystals. To identify the optimal dopant concentration, three distinct Lu doping levels were chosen: 9.25 at%, 9.75 at%, and 10 at%, all exhibit crack-free, high crystallinity (Supplementary Fig. 2), validating the efficacy and feasibility of the OFZ growth strategy for scalable production.

The different bond vibrational properties among HfO2 polymorphic phases serve as effective markers for phase identification within Lu:HZO bulk crystals. Specifically, the t-phase exhibits robust A1g and B1g Raman modes around 270 cm−1, while the o phases manifest strong bond vibrations in the vicinity of 370 cm−1, including the Ag mode for o-AFE and A1 mode for o-FE41. We employed Raman spectroscopy to analyze the phase distribution along the crystal growth direction. The Lu:HZO (9.25 at%) crystal simultaneously presents the t- and o-phase phonon vibrational modes, suggesting that the Lu doping level is insufficient to achieve the pure t-phase. With a rise of Lu doping concentration to 9.75 at%, apart from the mixture region of t and o phases, the pure t-phase is observed in the top region, yielding an unequivocal t/t+o phase interface within the as-grown bulk crystal. As the Lu doping level is further raised to 10 at%, the pure t-phase existing range is expanded by reducing the t+o phase region, underscoring the critical role of composition optimization in manipulating the t/o MPB interface within Lu:HZO bulk crystals.

Focusing on the optimized Lu:HZO (10 at%) phase component, we further refined the OFZ growth parameters to verify the controllability of the t/t+o phase boundary formation. Three different movement distances (d) after the growth process, before quenching, were tested, corresponding to 0 mm (Crystal 1), 5 mm (Crystal 2), and 10 mm (Crystal 3), with results shown in Fig. 1d. With increasing the d value, the t/t+o phase boundary moves towards the top of the as-grown crystal, accompanied by a shrinking t-phase region and an expanding t+o mixed phase region. The observed o-phase Raman signature at 370 cm−1 closely matches the characteristic vibrational mode of the o-AFE phase, providing compelling support for the structurally stabilized o-AFE phase formation. This aligns with expectations since the o-AFE phase has a lower formation energy than the o-FE phase32. Upon enlarging the d value to 10 mm, the t-phase region completely disappears, leaving only the t+o mixed phase region in the as-fabricated bulk crystal. The differing t/t+o phase interface positions observed in three Lu:HZO crystals (10 at%), measured at varying distances d, explicitly demonstrate the critical role of quenching. This result underscores that precise dimensional control of as-grown crystals is essential, and the quenching step itself must be executed with minimal delay under conditions of steep thermal gradients and rapid growth rates. These findings highlight the versatility of the OFZ growth method in precisely tuning phase distribution within the bulk crystal, even without altering the raw material component. Additionally, to substantiate the phonon-related evidence of the t/o-AFE MPBs on the adjacent t-phase, we compared the position-dependent Raman spectra collected from Lu:HZO bulk crystals with varying d values. In t-phase HfO2 or ZrO2, the vibrational Raman peak near 270 cm−1 arises from Zr/Hf-O stretching modes, serving as a direct indicator of local structural variations42. As demonstrated in Supplementary Fig. 3, the Raman mode (around 270 cm−1) of all three bulk crystals exhibits a similar trend near the phase interface between the t and t+o-AFE regions. From left to right within the crystal, this Raman mode shows a declining trend followed by an increase. The inversion point reflects the critical boundary for o-AFE phase formation, demonstrating that t/o-AFE MPBs drastically reconfigure the vibrational behavior of the t-phase. Due to the emergence of the o-AFE phase, the leftmost t+o phase region exerts an influence comparable to that of the rightmost t-phase (Supplementary Fig. 3a, b), even though its location before quenching is at a significantly lower temperature. This variation in Raman spectra confirms that the introduction of t/o-AFE MPBs can modulate the strain state of the adjacent t-phase.

As exhibited in Fig. 2a, multiple polymorphs can coexist in fabricating HfO2-based materials. With regard to HfO2-based thin films, the frequent presence of the m phase complicates the phase component and hampers the relevant MPB analysis17. In contrast, for bulk-crystal growth, combining ion adjustment and growth control effectively disentangles the m-phase interference and allows straightforward adjustment of the t/t+o-AFE interface35,43, facilitating deeper insight into how the phase boundary influences dielectric property. The Lu:HZO bulk crystals experience a series of phase transitions during the crystal growth process. The crystallization from the melt will form the c phase first. Then, following the downward movement across the transition temperature (above 2500 °C)6, the c phase rapidly transforms into the t-phase by expanding its (220) interplanar spacing and contraction of its (004) interplanar spacing (Supplementary Fig. 4). Subsequently, the steep temperature gradient along the growth direction further brings a partial t-phase section into the o-AFE phase once the location temperature falls below the t-o transition threshold. The rapid quenching process following growth benefits the stabilization of different phase distributions within the bulk crystal, providing an opportunity to obtain a well-defined t/t+o-AFE interface and permitting exploration of its MPB influence.

To further analyze the phase difference between the pure t and mixed t+o-AFE regions within as-grown Lu:HZO crystals, we took Crystal 2 as a representative case and collected XRPD data from the t-phase (St) and t+o-AFE (St+o) regions. As shown in Fig. 2b and Supplementary Fig. 5, the two orthorhombic phases exhibit clear diffraction signals at ~53° and 56°, whereas the t-phase theoretically lacks diffraction peaks at these positions due to its high structural symmetry. The XRPD pattern from St region matches well with the standard t-phase reference, showing no evidence of o-phase diffraction peaks. By comparison, the o-phase diffraction peaks around 53° and 56° are observed in St+o region. This result coincides with the above-mentioned Raman analysis that t and o-AFE phases coexist in the t+o-AFE region. On that basis, we surveyed the element distribution of Crystal 2 using electron probe microanalysis (EPMA) from the t-phase to t+o-AFE regions. As exhibited in Fig. 2c, the selected zone with different phases demonstrates uniform element distribution, indicating that the phase variation mainly stems from the modulation role of the OFZ growth strategy rather than compositional gradients. The detailed structural difference between St and St+o was analyzed by performing Rietveld refinement characterization (Supplementary Figs. 4 and 6). As shown in Supplementary Table 1, the t-phase c/(√2a) of St is determined to be 1.010, a value smaller than that of the theoretically standard t-phase (1.028) but larger than that within St+o (1.007)44. This phenomenon reveals that the as-obtained t-phase in Lu:HZO bulk crystals shows a weak structural anisotropy in contrast to the ideal t-phase, with position located at a lower-temperature region prior to quenching, displaying further reduced lattice distortion.

Dielectric characterization and t/o-AFE MPBs in Lu:HZO bulk crystals
In the subsequent context, we prepared the samples (Supplementary Fig. 7) and conducted the frequency-dependent dielectric characterization of as-grown Lu:HZO crystals and compared the dielectric properties across various phase components, involving m, o, t, c, and different MPB-engineered configurations (Supplementary Figs. 8 and 9). All bulk crystalline samples exhibit low dielectric loss (<0.02), comparable to those reported in thin films45–47. Nevertheless, their κ-values show notable variation. As elucidated in Fig. 2d, m-phase HfO2 (~14) and HZO (~15) show low room-temperature dielectric constant (κr) values in contrast to other polymorphs, being in good agreement with the theoretical calculations9. The o-AFE sample exhibits an κr value of 33, which is slightly higher than those of c-HfO2 (~28) and c-ZrO2 (~29)8,48. By contrast, the t-phase sample exhibits a clear dielectric advantage with a value on the order of 40, aligning well with the experimental results achieved in HfO2-based films10. Next, we compared the dielectric performances of three different MPB configurations, corresponding to t+o-AFE, t/o-FE, and t/o-AFE interfaces. The t+o-AFE and t/o-FE samples present a slight reduction in κ compared to the pure t-phase, indicating that the simple phase mixing within the MPB structure does not inherently enhance the dielectric property. It is worth noting that the sample around the t/t+o-AFE interface demonstrates an κr value of 57, comparable to those of the t/o-FE MPB films (Supplementary Fig. 10, Supplementary Table 2), representing a 43% increase over the pure t-phase sample. Additionally, the temperature-dependent dielectric measurements (Fig. 2e, f and Supplementary Fig. 11) reveal a significantly higher TC (~670 °C) in the t/o-AFE MPBs compared to their t/o-FE counterparts (~425 °C). Our thermal stability analysis compared the t/o-AFE and t/o-FE samples across the temperature range of 30–200 °C, which aligns with the practical operating window of modern DRAM and FET devices49,50. The t/o-AFE MPBs exhibit superior dielectric thermal stability compared to t/o-FE MPBs, as demonstrated by significantly reduced dielectric variation (7% for t/o-AFE MPBs versus 17% for t/o-FE MPBs). Critically, these structures maintain κr = 55.1 after thermal cycling, nearly identical to the pre-test value of 57, and retain κr = 55.4 even after 2 months of aging (Supplementary Fig. 12). This exceptional thermal and temporal stability originates from the intrinsically larger energy barrier for the t-to-o phase transition in the o-AFE phase32, confirming their viability for practical high-κ device implementation. This finding highlights the universality of the MPB role in modulating the dielectric properties of HfO2-based materials, ranging from thin films to bulk crystals. The manipulation of MPB distribution of HfO2-based materials remains challenging owing to various influencing variables, such as ion doping, interface engineering, and post-processing17. Thus, an in-depth understanding of the interplay between the crystal structure of MPB and dielectric response becomes crucial. The robust κ observed at the t/t+o-AFE interface in the Lu:HZO crystal provides a valuable paradigm to clarify the MPB effects, benefiting from the absence of m-phase interference and the larger grain size in contrast to film counterparts32,35.

The enhanced dielectric properties observed at the t/t+o-AFE phase boundary in Lu:HZO bulk crystals are intricately linked to the microstructural characteristics of the t/o-AFE phase boundaries. This underscores the critical role of analyzing the coherent interfaces at the t/o-AFE MPBs and their associated strain distribution to elucidate the underlying enhancement mechanisms. As summarized in Supplementary Table 1, the refined lattice parameters of the o-AFE phase (a=10.1365 Å, b=5.2135 Å, and c=5.0833 Å) exhibit apparent differences compared to those of the t-phase (a=b=3.6015 Å, and c=5.1431 Å), indicating the presence of strain near the t/o MPB caused by the martensitic transformation characteristic in the t-o transition6,51. To assess the potential strain effect on the t-phase induced by the adjacent o-AFE phase near the t/o MPB, we theoretically modeled the strain variations across various coherent interfaces between the t and o-AFE phases. Combined with the reported t-o transformation routes, the possible coherent interfaces at the t/o MPB were identified and are presented in Fig. 3, focusing on the {001} and {110} planes of the t-phase. Among the investigated strain configurations on the t-phase, Case-(1) and Case-(2) induce tensile strain, whereas the other four cases result in compressive strain. Types I, III, VII, and VIII coherent interfaces exhibit the maximum tensile strain, reaching 2.36% (Case-(1)). In contrast, the largest compressive strain is observed in Types VII and VIII coherent interfaces, with a value of −1.45% (Case-(6)). Type VII demonstrates the most pronounced horizontal and vertical in-plane strain difference at the coherent interface (Case-(1) and Case-(6)), while Type II displays the minimal in-plane strain disparity (Case-(3) and Case-(4)).

Microstructural survey and local strain analysis in Lu:HZO bulk crystals
Accurate identification of MPB configurations and their associated local strain fields in Lu:HZO bulk crystals necessitates atomic-scale structural characterization, particularly focusing on the interfacial strain mechanism by precise mapping of anion or cation distributions near the phase boundaries. To investigate these atomic-scale structural characteristics, we utilized integrated differential phase contrast scanning transmission electron microscopy (iDPC-STEM). This advanced technique was selected for its exceptional ability to simultaneously resolve both light (e.g., oxygen) and heavy (e.g., Hf/Zr/Lu) elements with high contrast (Fig. 4)48,52. As shown in Fig. 4a and Supplementary Fig. 13, the b-axis serves as the optimal observation direction for identifying the o-phase, as it clearly reveals the characteristic oxygen displacement patterns within polarization layers33,34. Specifically, the o-AFE and o-FE phases can be distinguished by their antiparallel and parallel polarization vector alignments, respectively. In Crystal 2 (Fig. 4e), the o phase exhibits o-AFE behavior, with antiparallel polarization along the c-axis, in full agreement with the prior structural and optical characterization results. As shown in Fig. 4b and Supplementary Fig. 13, the atomic arrangements along the c-axis exhibit no major structural differences between o-FE and o-AFE phases. Key identifiers of the o-phase include periodic variations in vertical Hf-Hf projected distances and horizontal displacements of O atoms, facilitating the o-phase identification within the t/o MPB regions. Our observation reveals a trapezoidal arrangement of Hf atoms (Fig. 4f), which shows excellent agreement with the predicted c-axis atomic distribution of the o phase. Given the predominance of the t-phase at the t/o MPBs, we aligned the imaging orientation with the t-phase crystal structure. As exhibited in Fig. 4c, d, observations along the c-axis or <110> directions of the t-phase are vital for defining subsequent t/o phase coherent interfaces. The atomic arrangements of the t-phase appear similar along both observation directions, making them difficult to distinguish in STEM characterization. To quantitatively characterize the t-phase observation direction, we introduced the R-value, defined as (h1+h2)/(v1+v2), which directly reflects tetragonality in the Hf atomic sublattice, as shown in Fig. 4g. Theoretically, R=1 represents the c-axis orientation, while R≠1 signifies the <110> orientation due to the anisotropic lattice parameter (c≠√2a) in the t-phase structure41. R>1 and R<1 reflect the c-axis alignment of the associated t-phase crystalline grains along the horizontal and vertical directions, respectively. To verify the t-phase observation direction, we analyzed the observed t-phase R-value distribution corresponding to the original image (Supplementary Fig. 14a, c). In Fig. 4h and Supplementary Fig. 14a, b, the R-value peaks at 1 with a range of 0.96–1.05, confirming observation along the c-axis direction of the t-phase. Conversely, statistical analysis in Fig. 4i and Supplementary Fig. 14c, d reveals R values spanning from 0.95 to 1.045, with dominant peaks at 1.005 and 0.985, strongly indicating the <110> observation direction of the t-phase.

After confirming the coexistence of crystalline phases within Crystal 2, we systematically investigated the local structural evolution at the t/o MPBs. Our analysis focused on MPBs aligned with either the b- or c-axis of the o-AFE phase, corresponding to the c-axis or <110> direction of the t-phase, respectively. The a-axis orientation of the o-AFE phase was excluded due to the dense arrangement of O atoms, which obscures a clear structural interpretation48. As demonstrated in Fig. 5a, b, Fig. 6a, c, and Supplementary Figs. 15–25, several different coherent interfaces between the t-phase and o-AFE phases were observed, suggesting the different t-to-o transformation pathways. These findings from coherent t/o-AFE interfaces experimentally validate the prevalence of t/o-AFE MPBs in Lu:HZO bulk crystals. This system establishes a unique platform to investigate local structural variations across differing MPB configurations at atomic resolution. As shown in Fig. 5a, we systematically analyzed the local structural characteristics of a representative t/o coherent interface within the Lu:HZO bulk crystal. The upper-right region displays characteristic c-axis-oriented o-phase features, whereas the lower-left region exhibits distinct t-phase structural signatures48. To determine the crystallographic orientation of the t-phase, we performed a statistical analysis of the R values within the t-phase region based on the iDPC-STEM data presented in Fig. 5a, as summarized in Supplementary Fig. 20. The dominant R values peak at 0.985 and 1.01, providing compelling evidence for the <110> zone-axis alignment in the observed t-phase region41. We then established the projected Hf-Hf distance variation as a quantitative metric to track the structural phase evolution from the t-phase to the o-AFE phase (Supplementary Fig. 21). In the t-phase region, the Hf-Hf distances remain nearly constant, while in the o-AFE phase region, they exhibit periodic fluctuations between odd and even columns. This variation allowed us to identify three distinct phase regions during the structural evolution, corresponding to the t, transitional (tt), and o-AFE phases. As shown in Fig. 5c, Row 8 predominantly exhibits t-phase characteristics, with only a localized right-side region developing the disparities of odd-even-column Hf-Hf distances indicative of the onset of the tt-phase. Row 22 captures a complete phase evolution sequence from the t-phase to the o-AFE phase, where the Hf-Hf distances progressively diverge in the tt-phase region before settling into characteristic values of ~319 pm (odd columns) and ~221 pm (even columns) in the o-AFE phase. In contrast, Row 38 presents a simple two-region distribution, where the o-AFE phase dominates with minimal tt-phase presence. Within the tt-phase region, distinct Hf-Hf column configurations—evident through adjacent vertical column differences—reveal fundamental structural deviations from both t and o-AFE phases. This contrast originates from differential ordering behaviors between odd and even atomic columns during phase formation. Overall, Fig. 5b summarizes the systematic variation in Hf-Hf distances across different Rows, clearly delineating the spatial distributions of the t, tt, and o-AFE phases.

Building on these structural observations, we quantitatively analyzed strain evolution at the t/o-AFE MPBs. For this analysis, we first selected the coherent t/o interface configuration shown in Fig. 5a, b to track strain variations through the complete t-to-o phase transition pathway. For strain calculations, we defined the reference state using the average Hf-Hf distance across the entire t-phase region. As shown in Fig. 5b, d, we selected three different regions to systematically evaluate the local vertical strain variations throughout the t-to-o phase transition, corresponding to Rows 2–9, Rows 16–23, and Rows 34–41. To quantify strain evolution, we analyzed eight rows in each selected region, computing their average Hf-Hf distances relative to the reference t-phase state. During the phase transition process in Rows 2–9, the t-phase region exhibits minor vertical strain fluctuations (−0.7% to 0.3%) attributed to different grain orientations caused by the rapid quenching process. As the transformation progresses into the tt-phase region, a pronounced vertical tensile strain becomes evident. In Rows 16–23, the vertical strain remains near zero (−0.8% to 0.6%) in the t-phase region, then undergoes a substantial increase when transitioning to the tt-phase region. Upon complete transformation into the o-AFE phase, the vertical strain stabilizes at ~2%, as determined by averaging the strain values across the o-AFE phases in the selected eight Rows. A similar strain evolution is observed in Rows 34–41, where vertical strain increases from ~1.05% (tt-phase) to ~2.3% (o-AFE phase). Additionally, we selected the t-phase and o-AFE phase regions in Fig. 5b to quantify the average vertical strain across the t-to-o phase transition, obtaining a value of 2.53%. The measured vertical strain shows excellent agreement with the theoretical prediction for Case-(1) in Fig. 3j (2.36%). The complementary horizontal strain analysis of the iDPC-STEM data (Fig. 5a, b) reveals distinct behavior. The observed average compressive strain of −0.83% occupies an intermediate position between the theoretical values for Case-(4) (−0.5%) and Case-(6) (−1.45%). This critical comparison of experimental and theoretical strain values provides compelling evidence for the non-uniform spatial distribution of t-phase grains along both <110> and c-axis orientations, strongly supporting the proposed nanoscale disorder in t-phase grain arrangement53.

Using the coherent interface featuring Case-(1) as a model system, we analyzed strain generation during the t-to-o phase transition. As illustrated in Fig. 5e, the transition involves antiparallel displacement of Hf atoms within each row, contrasting with adjacent columns. Moreover, the Hf columns present periodic expansion and contraction of horizontal Hf-Hf distances along the c-axis of the t-phase. Simultaneously, the sublattice of O atoms reorganizes, exhibiting antiparallel displacements between neighboring rows. Specifically, O atoms in the spacer layers progressively overlap along the observation direction, while those in the polarization layers separate vertically, reflecting the structural differences between these two distinct atomic configurations. The atomic rearrangement during the t-to-o phase transition leads to distinct lattice configurations between the two phases. While the t-phase exhibits its maximum lattice parameter along the c-axis, the o-AFE phase maximizes along the b-axis instead. This structural reorganization generates substantial tensile strain along the <110> direction of the original t-phase lattice.

Furthermore, our atomic-resolution STEM analysis revealed another coherent t/o-AFE interface viewed along the o-AFE c-axis direction (Supplementary Figs. 15 and 16). As exemplified in Supplementary Fig. 15, for the t-phase, this interfacial configuration generates tensile strain along its c-axis (1.56%) and compressive strain along its <110> (−0.42%) direction, consistent with the strain states described for Case-(2) (ct // bo-AFE) and Case-(4) (<110>t // ao-AFE) in Fig. 3j. Regarding the c-axis observation direction of the o-AFE phase, another t/o coherent interface is also observed (Supplementary Fig. 17). The R-value comparative analysis highlights a distribution anisotropy of the t-phase, with a predominance of c-axis-aligned regions over those oriented along the <110> direction. Building on the previously described phase identification methodology, the t/o phase boundary can be unambiguously resolved through atomic-scale analysis of Hf atom arrangements34. STEM imaging confirms the c-axis orientation of the t-phase in the right region, as evidenced by its R value centered near 1, while the left region aligns with the c-axis orientation of the o-AFE phase. The average strain calculation reveals a vertical tensile strain of 2.34% in the t-phase relative to the o-AFE region, closely matching the theoretical prediction for Case-(1) in Fig. 3j (2.36%). In contrast, the horizontal strain analysis yields an average compressive strain of −0.72%, located in the theoretical range between Case-(4) (−0.5%) and Case-(6) (−1.45%). Furthermore, coherent t/o-AFE interfaces viewed along the c-axis direction of the o-AFE phase exhibit mixed configurations of Case-(1) and Case-(2) (Supplementary Figs. 18 and 19). This phase coexistence generates an average vertical tensile strain of ~2%, slightly lower than the interfacial strains observed at single-orientation t/o-AFE boundaries (Fig. 5 and supplementary Fig. 17). The reduced strain magnitude directly results from the competitive coexistence of t-phase with different orientations (<110> and c-axis).

Figure 6a, b reveals a t/o-AFE coherent interface, with structural analysis confirming the b-axis alignment of the o-AFE phase through antiparallel polarization vector arrangements34. R-factor quantification (Supplementary Fig. 22) identifies the c-axis orientation in the t-phase region, while horizontal Hf-Hf bond length analysis decipher the clear t-to-o transformation pathways. This interfacial configuration drives weak average compressive strain (−0.17%) in the t-phase along the vertical direction, aligning with the theoretical Case-(3) value (−0.2%) given in Fig. 3j. Besides, as shown in Fig. 6c, d and Supplementary Figs. 23 and 24, another t/o coherent interfacial configuration viewed along the o-AFE b-axis direction produces weak horizontal strains within the t-phase. The t-phase exhibits negligible average in-plane strain (~0%) while sustaining vertical compressive strain of −1.27% (Fig. 6c, d). The weak horizontal strain matches Case-(3) (−0.2%) in Fig. 3j, while the stronger vertical strain lies between Case-(4) (−0.5%) and Case-(6) (−1.45%). This observation suggests a potential crystallographic match between the b-axis of the o-AFE phase and either the c-axis or <110> direction of the t-phase. As shown in Supplementary Fig. 25, the interfacial connection between the b-axis o-AFE phase and <110>- or c-axis oriented t-phase yields the Case-(5) configuration. The obtained vertical average strain in the t phase is determined to be −0.81%, lying between Case-(3) and Case-(5).

Enhancement mechanism of dielectric constant at t/o-AFE MPBs
Systematic nanoscale strain mapping at the t/o MPBs in Lu-doped HZO bulk crystals reveals the strain-driven mechanisms governing t-to-o phase transitions. Through microscopic characterization, all six distinct strain configurations (from Case-(1) to Case-(6)) have been identified. By correlating these configurations with strain distribution statistics, we propose detailed interfacial connectivity models (Supplementary Fig. 26 and Supplementary Table 3). Our analysis shows that variations in the coordinate matching relationships between the t and o-AFE phases lead to differential strain states in the t-phase. Notably, STEM measurements reveal a maximum tensile strain of 2.53%, approximately twice the magnitude of the maximum compressive strain (−1.27%). Furthermore, averaging strain data from coherent t/o-AFE interfaces (Supplementary Table 3) shows the mean tensile strain (1.67%) is roughly triple the magnitude of the mean compressive strain (−0.54%), confirming tensile strain predominance at t/o MPBs within as-grown Lu:HZO bulk crystals. These structural insights provide a solid foundation for understanding how strain mediates dielectric response modulation within Lu-doped HZO bulk crystals.

The static dielectric constant (κs) mainly contains the electronic contribution (κ∞) and the ion contribution (κion). Although different HfO2-based polymorphs exhibit a similar κ∞ value (~5), they show an evident discrepancy in κion originating from distinct infrared-active phonon vibrational modes54,55. The calculation of κs can be expressed as,

κs = κ∞ + κion = κ∞ + 4πe2 Z*2 / (M V ωTO2) (1)

where e, M, and V correspond to the electronic charge, a reference mass, and the lattice volume, respectively. ωTO represents the vibration frequency of infrared-active transverse optical (TO) phonons, and Z* denotes the relevant mode Born effective charge. Note that the κion contribution is positively proportional to the Z*/ωTO2, implying that the variation of ωTO can seriously affect the associated dielectric property.

The vibrational modes of HfO2-based materials are inherently connected to the alteration of their crystal structures. Strain serves as an effective modulation strategy for controlling crystal phases in HfO2-based materials56,57, enabling precise modulation of lattice vibration frequencies across different phonon modes and potentially inducing phase transitions between polymorphs. In the t-phase HfO2, the three infrared-active TO vibrational modes consist of two distinct Eu modes (~129 cm−1 and ~460 cm−1) and an A2u mode (~321 cm−1)41. Notably, the low-frequency Eu mode exhibits exceptional strain sensitivity compared to the other two vibrational modes, demonstrating a negative correlation with applied strain43. Experimental characterization at the t/o-AFE MPBs in Lu:HZO bulk crystals reveals substantially enhanced tensile lattice strain in the t-phase compared to compressive strain, establishing tensile strain dominance in the underlying mechanism. Theoretical analysis of strain-mediated variations in the infrared-active low-frequency Eu mode was performed to elucidate the mechanism by which strain modulates the dielectric properties of the tetragonal phase, with the result shown in Supplementary Fig. 27. These frequency shifts correlate strongly with anisotropic strain distributions along the c-axis and <110> crystallographic directions of the t-phase (Fig. 3). As shown in Supplementary Fig. 27, compressive strain along either direction increases the low-frequency Eu mode frequency, while tensile strain reduces it—a trend consistent with prior theoretical predictions in HfO2-based systems43. Within Lu:HZO bulk crystals, substantial tensile strain at t/o-AFE MPBs induces significant low-frequency Eu mode softening58,59. This phonon softening directly drives the enhanced dielectric response observed in Lu:HZO systems via the strain-polarization coupling mechanism described by Eq. (1). The comparable magnitudes of Z* among the three infrared-active TO vibrational modes suggest that the frequency blueshift of the t-phase low-frequency Eu phonon mode will significantly enhance the κion41. This enhancement originates from the dominant contribution of the low-frequency Eu mode to κion, which is typically two-fold greater than that of the A2u mode and five-fold larger than the high-frequency Eu mode43,47. This strain-mediated mechanism underpins the dielectric enhancement at t/o-MPBs and establishes a pathway for property optimization through engineered coherent t/o-AFE interfaces. Our findings demonstrate that interface engineering enables selective tuning of mode-specific phonon contributions, providing a universal strain-mediated framework for controlling dielectric responses.

Methods
Crystalgrowth
The polycrystalline Lu:Hf0.6Zr0.4O2 (Lu:HZO) powder was synthesized via high-temperature solid-state sintering. High-purity precursors, including Lu2O3 (99.99%), HfO2 (99.99%), and ZrO2 (99.99%), were stoichiometrically weighed with a fixed Zr:Hf molar ratio (4:6) and varying Lu doping concentrations (9.25 at%, 9.75 at%, and 10 at%). The precursor mixture underwent ethanol-assisted homogenization followed by drying and mechanical grinding. Calcination was performed in a muffle furnace at 1100 °C for 5 h under ambient atmosphere. The resultant powder was re-ground and subsequently consolidated into feed/seed rods through uniaxial pressing (60 MPa, 10 min). Stoichiometrically mixed Lu:HZO rods were directly sintered at 1400 °C for 5 h in air for bulk crystal preparation.

Single crystal growth was achieved using an OFZ furnace (Crystal Systems Inc., FZ-T-123000-X-I-S-SU) equipped with four ellipsoidal mirrors capable of reaching 3000 °C. Optimized growth parameters included counter-rotation of feed (5 rpm) and seed rods (10 rpm) under oxygen flow (150 mL min−1). Supplementary Fig. 1 illustrates the OFZ crystal growth process: the feed and seed rods were connected by a molten zone sustained via surface tension. As growth proceeded, both rods moved downward at a coordinated rate, enabling continuous crystal growth onto the seed rod. Upon completion of crystal growth, seed rotation ceased. The as-grown crystal was lowered a specific distance d from its uppermost position to the highest heating point. The quenching process then began: the pull-down rod, attached to the seed rod, rapidly descended ~50 cm (within ~2 s), transferring the crystal into the ambient room-temperature environment to achieve quenching. Following this rapid transfer, the system power was linearly ramped down to zero over 2.5 h. The xenon lamps were then switched off, and the crystal was retrieved after the equipment cools and powers down.

Raman, XRPD, and EPMA measurements
The as-grown crystals were subjected to comprehensive structural and functional characterization without post-processing. Phase identification was conducted using a Horiba iHR550 Raman spectrometer equipped with a 633 nm He-Ne excitation laser (5 mW output power), with spatial mapping performed at 2 mm intervals across selected crystal regions. High-resolution X-ray powder diffraction analysis was performed on a Rigaku SmartLab diffractometer with Cu Kα radiation (1.5406 Å), employing two scanning protocols: phase identification scans (10°–90° 2θ range, 3° min−1 step rate) and structural refinement scans (10°–120° 2θ range, 1° min−1 step rate). Each sample was ground into micrometer-scale powder using an agate mortar to ensure random crystallite orientation—a prerequisite for representative polycrystalline XRPD patterns. Rietveld refinement of crystal structures was implemented using TOPAS software. Chemical composition analysis was performed via electron probe microanalysis (EPMA, Shimadzu EPMA-1720H) with a 200 μm step resolution across designated crystal zones.

Dielectric measurement
For the dielectric properties, the m-HfO2 (Pure HfO2) and m-HZO (Hf0.6Zr0.4O2) ceramics were sintered using the method mentioned above. The o-AFE phase (Lu:HfO2 (10 at%)) and the c-HfO2 (Lu:HfO2 (16 at%)) samples were grown by the OFZ method without the rapid quenching. The t/o-FE (Lu:Hf0.6Zr0.4O2 (10 at%)) sample was prepared by annealing for the t-phase part of the Crystal 235. The c-ZrO2 sample is from the commercially available YSZ crystal. We utilized a measurement approach commonly employed for bulk crystals and ceramics61. To ensure comparability across different regions within the same crystal, samples were sectioned perpendicular to the growth direction into circular slices ~3 mm in diameter and 0.3 mm thick. A similar procedure was applied to prepare m-HfO2 and m-HZO ceramic reference samples. For measurements at specific regions (e.g., the t+o-AFE, t/o-AFE, and t-HZO dielectric samples within Crystal 2), we primarily verified the position based on position-dependent Raman characterization. All slice surfaces were carefully polished and cleaned prior to depositing platinum electrodes using magnetron sputtering (KT-Z1650PVD) for 1 min. Dielectric spectroscopy was acquired using a Wayne Kerr 6500B precision impedance analyzer. The temperature-dependent dielectric constant κr was surveyed with a heating rate of 5 °C min−1.

STEM characterization
The crystal orientation identification and scanning transmission electron microscopy (STEM) sample preparation of Lu:HZO samples were carried out using the Crossbeam 550L dual-beam system from Carl Zeiss, which integrates both electron beam and focused ion beam (FIB) systems, and is equipped with an Oxford Instruments electron backscatter detector. The sample preparation process involved electron beam imaging and Ga ion milling to obtain thin film samples suitable for STEM analysis. Advanced microstructural characterization was performed using a double-probe-corrected ThermoFisher Scientific Themis Z microscope operating at 300 kV. The four-segment DF4 detector was employed to acquire 2048×2048 pixel images of integrated differential phase contrast iDPC-STEM images, with a pixel dwell time of 2 μs. The convergence semi-angle and collection semi-angle were 25 mrad and 6–24 mrad, respectively. All iDPC-STEM images are Fourier-filtered in Gatan Microscopy Suite (GMS, v3.22.1461.0) to reduce contrast noise, which does not affect the results of our measurements. The multiple-ellipse fitting algorithm in CalAtom Software was used to accurately determine the Hf/Zr cation positions.

Theoretical calculation
All first-principles density functional theory calculations were performed using Vienna Abinitio Simulation Package (VASP) within the projector–augmented-wave formalism and the PBEsol generalized-gradient approximation62. A plane-wave cutoff energy of 600 eV was employed. Electronic convergence was set to 10−7 eV, and ionic relaxations proceeded until the residual forces were below 10−3 eV Å−1. A 12×12×8 Monkhorst–Pack k-point mesh was used for the t phase4. Phonon properties were computed using the finite-displacement method as implemented in the PHONOPY package. A 4×4×2 supercell was used to generate symmetry-inequivalent displacements, and Hellmann–Feynman forces from VASP static calculations were used to construct the force-constant matrices. Phonon-mode symmetries and irreducible representations were obtained using the PHONOPY package.

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "In this manuscript, the synthesis and characterization of morphotropic phase boundaries between the tetragonal and antiferroelectric orthorhombic phases in Lu-doped HZO bulk crystals is presented. The authors use optical floating zone growth combined with quenching to stabilize the t/o-AFE interface. A dielectric constant of 57 is obtained. The authors attribute dielectric enhancement to tensile strain in the tetragonal phase that results in softening of the low-frequency Eu phonon mode. After additional analysis, clarification of some of the experimental techniques, and elaboration on the relevance to CMOS-compatible thin films, I would recommend publication. My comments are as follows:\n1. Can the authors explain why they have chosen the title “Beyond morphotropic phase boundaries,” since the work focuses on MPBs?\n2. Further details should be provided about the quenching technique, since it is central to the results. The authors claim that the crystals were quenched within ~2 seconds. How sensitive to variations in the quenching process is the stabilization of the desired MPB?\n3. How were the XRD scans performed to identify different phases in different regions of the crystal? Was this a microdiffraction experiment?\n4. The differences in the XRD data in Fig. 2b are hard to see due to the chosen scale. This figure should be adjusted so that the reader can more easily see the highlighted regions. Additionally, the authors claim that the pattern from the St region matches the t-phase reference and has no evidence of o-phase diffraction. This seems like a challenging claim to make due to the many similar reflections of these phases. Can the authors clarify this statement?\n5. How were the crystals prepared for the dielectric measurements, and how were specific regions measured?\n6. The STEM analysis is very rigorous; however, only a few selected interfaces are shown. One issue with TEM analysis is that it only represents a small sample of the crystal. Have the authors verified these conclusions in other locations?\n7. Is the transitional phase a distinct crystallographic structure, or a highly strained tetragonal region? This should be clarified.\n8. The argument that the tensile strain induces softening of the Eu phonon mode is not supported by experimental evidence. Is it possible to provide evidence of this via Raman spectroscopy with a measurement in the tetragonal region taken adjacent to the interface vs. a region far from the interface? As it stands, this argument is supported only by theoretical work and the link between tensile strain and dielectric enhancement is primarily correlative.\n9. The manuscript would benefit from discussion about how the findings here can be applied to HfO2-based thin films for CMOS applications, especially since the authors state that their work, “establishes a generalizable design paradigm for developing high-κ dielectrics in fluorite-structured materials, advancing next-generation CMOS integrated functional devices.”", "reviewer_2": "This paper reports that a high dielectric constant could be achieved by synthesizing HfZrO bulk crystals using high-temperature rapid thermal processing and forming a t/o-AFE interface. Using XRPD, Raman analysis, electrical measurements, and TEM analysis, the details of the t/o-AFE MPB are carefully analyzed. This is a very interesting study from the perspective of crystallography.\nHowever, the authors' claims that this study will contribute to applications in CMOS and DRAM are not supported by any experimental evidence, making them completely unconvincing. Semiconductor devices require uniform and homogeneous material properties on the nanometer scale. In contrast, the XRPD, Raman, and electrical properties observed in the bulk crystals in this study are presumably averaged properties analyzed over a scale several orders of magnitude larger. The paper does not disclose the electrode dimensions or arrangement used to measure the dielectric properties. On the other hand, TEM analysis also confirmed that tensile strain and compressive strain compete locally, raising concerns that performance variations may occur when applied to semiconductor devices. The temperature used in this crystal synthesis was too high compared to semiconductor manufacturing processes, and the practical feasibility has not been demonstrated. Submission to a ceramics journal is encouraged.", "reviewer_3": "This study utilizes the quenching technique and Lu-doped Hf₀.₆Zr₀.₄O₂ (Lu:HZO) composition previously reported in prior works to realize a thermally stable HfO₂-based morphotropic phase boundary (t/o-AFE MPB). The paper provides comprehensive analyses on the structural evolution, interfacial characteristics, and dielectric performance of this system. However, several major revisions are required before this study can be considered for publication.\n1. The main problem statement of this study originates from the insufficient thermal stability of HfO₂-based MPB thin films. However, as also mentioned by the authors, the main application fields of MPB thin films are DRAM capacitors and advanced FET devices. In this context, the thermal stability analysis in the manuscript focuses on rather extreme temperature ranges (typically from 400 °C up to 600 °C). It remains unclear what type of application requires such high-temperature stability and how this range correlates with realistic device operation or processing conditions. The authors should provide a more detailed explanation of the technological relevance of this temperature window and clarify whether the observed improvement in stability is meaningful for semiconductor integration.\n2. The room-temperature dielectric constant reported in this study is noticeably lower than the values reported in several previous studies on HfO₂-based MPB systems (often exceeding 65–70). It would strengthen the manuscript if the authors could clarify the origin of this reduction. In particular, the relationship between the reduced dielectric constant and the improved thermal stability should be discussed quantitatively. The authors are encouraged to justify why the enhancement of thermal stability, rather than dielectric performance, represents the more critical metric for practical device applications.\n3. The manuscript discusses temperature-dependent dielectric constant κ(T) measured during heating, but for MPB-based applications in DRAM/FET stacks the more critical question is reversibility after process thermal budgets. In other words, do the dielectric/structural properties fully (or acceptably) recover at room temperature after high-T steps typical of BEOL integration? I recommend adding a post-anneal recovery study that mimics realistic process conditions and reports pre/post room-temperature metrics.\n4. The authors focus on the thermal stability of the t/o-AFE morphotropic phase boundary (MPB), but the stability of HfO₂-based phases is known to be strongly affected not only by temperature but also by electrical cycling. Recent studies on HfO₂- and HZO-based ferroelectric thin films have demonstrated that repetitive polarization switching or bias cycling can induce stress comparable to that generated by thermal annealing, significantly altering the phase distribution and energy landscape between the t, o-FE, and o-AFE states. If the main purpose of this study is to clarify phase stability and the associated energy differences among MPB states, it would further strengthen the work to discuss or experimentally address the effect of electrical cycling.\n5. There are several different interpretations regarding the origin of the dielectric constant boosting effect observed near the morphotropic phase boundary (MPB). Among these, the most widely accepted mechanism for HfOₓ-based MPB thin films attributes the enhanced dielectric response to a reversible, field-induced phase transition—in which a portion of the antiferroelectric phase is converted into the ferroelectric phase under an applied bias, due to the relatively low energy barrier between these states (see Kai Ni et al., IEDM 2019, DOI: 10.1109/IEDM19573.2019.8993495).\nFrom this perspective, the proposed t/o-AFE MPB in this work represents an AFE-to-AFE boundary, which makes it difficult to rationalize the observed dielectric constant boosting using the conventional field-induced phase transition model. In most previous MPB systems, the enhancement arises precisely because of the low energy barrier between the coexisting FE and AFE phases that facilitates field-induced switching.\nIn this manuscript, the authors briefly mention a different origin for the dielectric enhancement, referring to strain–phonon coupling at the coherent t/o interface. However, the current explanation and literature discussion appear too brief to fully convince readers of the validity of this alternative mechanism. The manuscript would benefit from a more detailed and quantitative discussion comparing the proposed strain–phonon mechanism with the established field-induced transition model, supported by experimental or theoretical evidence (e.g., phonon mode softening vs polarization switching data).\n6. While the authors cite prior work from their group, lutetium (Lu) still remains a relatively unfamiliar dopant in the HfO₂/HZO community compared with more established options. To make the manuscript more convincing and broadly useful, please clarify the specific role of Lu in this study and substantiate its CMOS compatibility and competitiveness relative to conventional dopants.\nProvided that the clarifications and additional analyses outlined above are satisfactorily addressed, I believe this work would be suitable for publication in Nature Communications."}, "author_response": "Responses to Reviewers’ comments\n“Atomic-scale mechanism unlocks thermal-stable high-κ performance in HfO via coherent\n2\ninterfaces” (NCOMMS-25-76784-T)\nBy Y. H. Shen, et al.\nWe greatly appreciate the constructive comments and suggestions from all Reviewers,\nwhich have significantly helped us improve our manuscript. Based on the Reviewers’ feedback,\nwe have made suitable revisions. The following are our point-by-point responses to the\nReviewers’ comments; the corresponding changes have also been highlighted in red in the\nrevised manuscript.\nReviewer #1 (Remarks to the Author):\nIn this manuscript, the synthesis and characterization of morphotropic phase boundaries\nbetween the tetragonal and antiferroelectric orthorhombic phases in Lu-doped HZO bulk\ncrystals is presented. The authors use optical floating zone growth combined with quenching\nto stabilize the t/o-AFE interface. A dielectric constant of 57 is obtained. The authors\nattribute dielectric enhancement to tensile strain in the tetragonal phase that results in softening of the\nlow-frequency E phonon mode. After additional analysis, clarification of some of the\nu\nexperimental techniques, and elaboration on the relevance to CMOS-compatible thin films, I\nwould recommend publication. My comments are as follows:\nResponse: Thanks for the Reviewer’s positive feedback. We sincerely appreciate their\nmeticulous evaluation and are encouraged by the recognition of the significance and technical\ninnovations of our work on the morphotropic phase boundary (MPB) design strategy between\nthe tetragonal (t) and orthorhombic antiferroelectric (o-AFE) in Lu:HZO bulk crystals. The\nReviewer’s constructive comments are invaluable in identifying areas for improvement in the\nmanuscript. We have carefully addressed each of the points raised and hope that the revised\nmanuscript now meets the high standards of this journal.\n1. Can the authors explain why they have chosen the title “Beyond morphotropic phase\nboundaries,” since the work focuses on MPBs?\nResponse: Thanks for raising this important point regarding the title. We appreciate the\nopportunity to clarify our rationale. Our work indeed focuses on a specific type of morphotropic\nphase boundary (MPB), and the revised title (removing this “beyond morphotropic phase\nboundaries”) aims to precisely capture the paradigm shift our study introduces within the\nMPB framework for HfO -based dielectrics.\n2\ntetragonal (t) and orthorhombic ferroelectric (o-FE) phases. While effective for boosting the\ndielectric constant (κ), such t/o-FE MPBs often suffer from intrinsic instability, leading to\nsignificant κ degradation with temperature.\nOur work introduces and validates a novel MPB design strategy: the t/o-AFE phase\nboundary. Guided by energy barrier analysis, we identified that the t/o-AFE transition has a\nsignificantly higher barrier (~68.8 meV per f.u.) than the t/o-FE transition (~46.0 meV per f.u.),\nsuggesting a path toward greater stability. Inspired by metallurgical quenching, we successfully\nfabricated t/o-AFE MPBs in bulk HfO crystals, achieving a high κ (~57) comparable to state-\n2\nof-the-art t/o-FE MPBs. Crucially, these t/o-AFE MPBs exhibit superior thermal stability,\nwith less than half the κ variation rate of their t/o-FE counterparts over 30–200°C.\nFurthermore, we go beyond simply reporting a new MPB composition by elucidating its\natomic-scale enhancement mechanism. Through microstructural strain analysis and theoretical\ncalculations, we demonstrated that pronounced tensile strain at the coherent t/o-AFE interface\nsoftens a key phonon mode in the t-phase, directly driving the dielectric enhancement. We also\nidentified the optimal crystallographic orientation between the phases for maximum\nperformance.\nTherefore, the title “Atomic-scale mechanism unlocks thermal-stable high-κ performance\nin HfO via coherent interfaces” accurately reflects our core contributions:\n2\n1. Shift in MPB paradigm: It highlights our move from the conventional, thermally unstable\nt/o-FE MPB to a new, stable t/o-AFE MPB system.\n2. Mechanistic insight: It emphasizes our foundational discovery of the atomic-scale (strain-\nphonon) mechanism responsible for the enhanced performance.\n3. Key outcome: It clearly states the achieved goal: thermal-stable high-κ performance, which\naddresses a critical limitation in the field.\nWe believe this title succinctly conveys that our work redefines the approach to designing\nhigh-performance MPBs in fluorite-structure dielectrics by providing both a new structural\nstrategy and a fundamental mechanistic understanding.\n2. Further details should be provided about the quenching technique, since it is central to the\nresults. The authors claim that the crystals were quenched within ~2 seconds. How sensitive to\nvariations in the quenching process is the stabilization of the desired MPB?\nFig. R1. (Supplementary Fig. 1a). Schematic diagram of the optical floating zone method.\nResponse: Thanks for these constructive comments. The quenching process was primarily\nemployed to stabilize the t-phase in as-grown bulk crystals, as the presence of the t-phase is\nvital for preparing t/o-AFE MPBs. Following the formation of t/o-AFE MPBs, rapid quenching\neffectively suppresses the subsequent t-to-o phase transition. Due to the sharp vertical\ntemperature gradient near the peak temperature point (>1000 °C/cm) during crystal growth\n[Cryst. Growth Des. 23, 2609-2618, (2023)], careful consideration of the quenching initiation\npoint was required.\nRegarding the quenching procedure details, Figure R1 illustrates the optical floating zone\n(OFZ) crystal growth process: the feed and seed rods are connected by a molten zone sustained\nvia surface tension. As growth proceeds, both rods move downward at a coordinated rate,\nenabling continuous crystal growth onto the seed rod. Upon completion of crystal growth, seed\nrotation ceases. The as-grown crystal is lowered a specific distance d from its uppermost\nposition to the highest heating point. The quenching process then begins: the pull-down rod,\nattached to the seed rod, rapidly descends approximately 50 cm (within ~2 seconds),\ntransferring the crystal into the ambient room-temperature environment to achieve quenching.\nFollowing this rapid transfer, the system power is linearly ramped down to zero over 2.5 hours.\nThe xenon lamps are then switched off, and the crystal is retrieved after the equipment cools\nand powers down.\nConcerning the influence of quenching, the significance of this process is directly\ndemonstrated by our position-dependent growth of Lu:HZO bulk crystals (10 at.% Lu doping),\nas evidenced by Fig. 1d. The as-grown crystals at three different distances d prior to quenching\nexhibit distinct t/(t+o) phase interface positions, corresponding to a time interval of 15 minutes\n(at a growth rate of 20 mm/h). This indicates that quenching must be executed rapidly under\nsuch significant temperature gradients and high growth rates. Consequently, we strictly\ncontrolled the dimensions of the as-grown crystals. Upon completion of growth, the as-grown\nbulk crystals were transferred to room temperature within approximately 2 seconds.\nRevision: To express the importance of the quenching process, we supplemented the sentences\nin the main text on Page 8 “The differing t/t+o phase interface positions observed in three\nLu:HZO crystals (10 at.%), measured at varying distances d, explicitly demonstrate the critical\nrole of quenching. This result underscores that precise dimensional control of as-grown crystals\nis essential, and the quenching step itself must be executed with minimal delay under conditions\nof steep thermal gradients and rapid growth rates.”\nMoreover, we modified the sentences in the experimental section of Supplementary\nInformation “The OFZ process leveraged surface tension effects in the molten zone for crystal\ngrowth. When the growth of crystals was finished, we directly pulled the crystals down to room\ntemperature from the high-temperature center within a very short time (typically within 2 s).”\nas “Supplementary Fig. 1a illustrates the optical floating zone (OFZ) crystal growth process: a\nmolten zone, sustained via surface tension, connects the feed rod and seed rod. As growth\nproceeds, both rods move downward at a coordinated rate, enabling continuous crystal growth\nonto the seed rod. Upon completion, the seed rotation was stopped. The as-grown crystal was\nthen lowered a specific distance d from its uppermost position to the highest heating point. To\nquench the crystal, the pull-down rod, attached to the seed rod, rapidly descended\napproximately 50 cm (within ~2 seconds), transferring the crystal directly into the ambient\nroom-temperature environment. Following this rapid transfer, the system power was linearly\nramped down to zero over 2.5 hours. The xenon lamps were then switched off, and the crystal\nwas retrieved after the equipment had cooled and powered down.”\n3. How were the XRD scans performed to identify different phases in different regions of the\ncrystal? Was this a microdiffraction experiment?\nResponse: Thanks for these valuable comments. To accurately identify the phase compositions\nin distinct regions of Lu:HZO bulk crystals—specifically the t-phase region (S) and the t+o-\nt\nAFE mixed-phase region (S )—we employed polycrystalline X-ray powder diffraction\nt+o\n(XRPD) rather than microdiffraction. Crystal 2 was prioritized for XRPD testing since its\nRaman spectra (Fig. 1d) confirmed a well-defined t/t+o-AFE interface, with the top region\nbeing pure t-phase and the lower region a mixed t+o-AFE phase. To resolve phase compositions\nin these regions, we extracted two samples (S and S ) from the t-phase and t+o-AFE zones,\nt t+o\nrespectively (Fig. 2b). Each sample was ground into micrometer-scale powder using an agate\nmortar to ensure random crystallite orientation—a prerequisite for representative\npolycrystalline XRPD patterns. Results (Fig. 2b) show that the S sample perfectly matches the\nt\nstandard t-phase (ICSD No. 173966) without detectable o-phase peaks, while the S sample\nt+o\nexhibits t-phase peaks alongside additional o-AFE reflections at 2θ around 53° and 56° (ICSD\nNo. 79913).\nRevision: To express the clear XRPD characterization, we updated the full description of\nXRPD within Fig. 2b with “X-ray powder diffraction (XRPD)”. Moreover, we supplemented\nthe elucidation “Each sample was ground into micrometer-scale powder using an agate mortar\nto ensure random crystallite orientation—a prerequisite for representative polycrystalline\nXRPD patterns.” to the Experimental section of Supplementary Information.\n4. The differences in the XRD data in Fig. 2b are hard to see due to the chosen scale. This figure\nshould be adjusted so that the reader can more easily see the highlighted regions. Additionally,\nthe authors claim that the pattern from the S region matches the t-phase reference and has no\nt\nevidence of o-phase diffraction. This seems like a challenging claim to make due to the many\nsimilar reflections of these phases. Can the authors clarify this statement?\nFig. R2 (updated in Fig. 2b). Enlarged view of room-temperature X-ray powder diffraction\n(XRPD) data of the top (S) and bottom (S ) part of Crystal 2. The blue regions correspond\nt t+o\nto the diffraction signals at approximately 53° and 56°.\nResponse: Thanks for the valuable feedback. In the revised manuscript, to clarify the XRPD\ncomparison, we enlarged the presented data region to a 2θ range of 45o to 65o and moved the\noriginal XRPD spectra to the Supplementary Information. We believe this revision better\ndemonstrates the phases present at different growth regions.\nAs illustrated in Fig. R2, the t-phase exhibits a distinct diffraction pattern compared to the\ntwo orthorhombic phases (o-FE or o-AFE). Specifically, the two orthorhombic phases exhibit\nclear diffraction signals at approximately 53° and 56°, whereas the t-phase theoretically lacks\ndiffraction peaks at these positions due to its high structural symmetry. This indicates that the\ndiffraction signals near 53° and 56° can be used to determine whether o-phase components are\npresent within the as-grown bulk crystals. Unlike the S section, the S section displays no\nt+o t\ndiffraction signals around these angles, suggesting typical t-phase characteristics. This\nobservation aligns with prior Raman data (Fig. 1d), where no o-phase signal was detected in\nthe S region. Therefore, we conclude that the S region corresponds to the t-phase based on\nt t\nboth the measured XRPD and Raman results.\nRevision: We replaced Fig. 2b by Fig. R2, while placing the full scan-range XRPD data as\nSupplementary Fig. 4. Moreover, we modified the sentences on Page 12 “As shown in Fig. 2b,\nthe XRPD pattern from S region matches well with the standard t-phase reference, showing no\nt\nevidence of o-phase diffraction peaks.”as “As shown in Fig. 2b, the two orthorhombic phases\nexhibit clear diffraction signals at approximately 53° and 56°, whereas the t-phase theoretically\nlacks diffraction peaks at these positions due to its higher structural symmetry. The XRPD\npattern from S region matches well with the standard t-phase reference, showing no evidence\nt\nof o-phase diffraction peaks.”(Page 11)\n5. How were the crystals prepared for the dielectric measurements, and how were specific\nregions measured?\nFig. R3. (Supplementary Fig. 7). Schematic diagram of the bulk-crystal samples for the\ndielectric characterization.\nResponse: Thanks for this valuable comment. In the revised manuscript, we have provided a\ndetailed description of the sample preparation and measurement process for dielectric\ncharacterization.\nAs shown in Fig. R3, we utilized a measurement approach commonly employed for bulk\ncrystals and ceramics [J. Am. Ceram. Soc. 105, 1265–1275 (2022)]. To ensure comparability\nacross different regions within the same crystal, samples were sectioned perpendicular to the\ngrowth direction into circular slices approximately 3 mm in diameter and 0.3 mm in thickness.\nA similar procedure was applied to prepare m-HfO₂ and m-HZO ceramic reference samples.\nFor measurements at specific regions (e.g., the t+o-AFE, t/o-AFE, and t-HZO dielectric\nsamples within Crystal 2), we primarily verified the position based on position-dependent\nRaman characterization. All slice surfaces were carefully polished and cleaned prior to\ndepositing platinum electrodes using magnetron sputtering (KT-Z1650PVD) for 1 minute. To\nvalidate the reliability of our dielectric characterization, we compared our measured room-\ntemperature κ-values with reported literature values for m-HfO₂, c-HfO₂, c-ZrO₂, and t-HZO\n[Phys. Rev. B 63, 174108 (2001); Phys. Rev. B 65, 233106 (2002); ACS Appl. Mater. Interfaces\n16, 60811–60818 (2024)]. The measured values agreed well with those previously reported,\nfurther confirming the reliability of our dielectric measurements. We hope the above\ninterpretation clarifies the dielectric characterization, benefiting the understanding of the\ndetailed measurement process.\nRevision: Following the Reviewer’s suggestion, we have supplemented the following details\n“We utilized a measurement approach commonly employed for bulk crystals and ceramics2. To\nensure comparability across different regions within the same crystal, samples were sectioned\nperpendicular to the growth direction into circular slices approximately 3 mm in diameter and\n0.3 mm in thickness. A similar procedure was applied to prepare m-HfO₂ and m-HZO ceramic\nreference samples. For measurements at specific regions (e.g., the t+o-AFE, t/o-AFE, and t-\nHZO samples within Crystal 2), we primarily verified the position based on position-dependent\nRaman characterization. All slice surfaces were carefully polished and cleaned prior to\ndepositing platinum electrodes using magnetron sputtering (KT-Z1650PVD) for 1 minute.” to\nthe Experimental section of Supplementary Information.\n6. The STEM analysis is very rigorous; however, only a few selected interfaces are shown. One\nissue with TEM analysis is that it only represents a small sample of the crystal. Have the authors\nverified these conclusions in other locations?\nResponse: Thanks for these constructive comments. We agree with the Reviewer’s comments\nthat STEM characterization requires meticulous analysis due to the nanoscale dimensions of\nthe regions examined. Our STEM investigations primarily focus on the local structural\nevolution at the t/o-AFE MPBs to build a relationship between the dielectric property and local\nMPB configurations. By combining EBSD orientation and FIB processing, we fabricated\ndistinct micro-slices to elucidate potential crystallographic correlations between the t and o-\nAFE phases. The obtained results in Figs. 5, 6, and Supplementary Figs. 15–25 corroborated\nthe relationships demonstrated in Fig. 3, further underscoring the significance of local strain\nanalysis for the t-phase.\nFig. R4. (Supplementary Fig. 16). Observed iDPC-STEM imaging of the t/o coherent\ninterfaces similar to Supplementary Fig. 15, within Crystal 2. a, Raw iDPC-STEM imaging,\nwith the t and o-AFE phase identification. b, iDPC-STEM imaging with the corresponding Hf-\nHf distance. c, iDPC-STEM imaging with the corresponding R-value distribution. Scale bar: 1\nnm. d, Statistical histogram of the R-value for the t phase enclosed by the dashed line in\nSupplementary Fig. 16a. The strains are calculated based on the average Hf-Hf bond length of\nthe t and o-AFE phase regions enclosed by the dashed line in Supplementary Fig. 16. The\naverage vertical strains in the t phase are ~1.2%, corresponding to Case-(2) (c // b ).\nt o-AFE\nFig. R5. (Supplementary Fig. 18). Observed t/o coherent interfaces within Crystal 2, with\nthe c-axis observation direction of the o-AFE phase. a, Raw iDPC-STEM imaging. b, iDPC-\nSTEM imaging with the corresponding Hf-Hf distance. c, iDPC-STEM imaging with the\ncorresponding R-value distribution. Scale bar: 1 nm. d, Statistical histogram of the R-value for\nthe t phase enclosed by the dashed line in Supplementary Fig. 18a. e-h, Structural schematic\ndiagrams of the strain relationship on the t phase induced by the o-AFE phase corresponding\nto the strain state. For (e), Case-(2) (c // b ); For (f), Case-(1) (<110> // b ); For (g),\nt o-AFE t o-AFE\nCase-(4) (<110> // a ); For (h), Case-(4) (<110> // a ). The strains are calculated based\nt o-AFE t o-AFE\non the average Hf-Hf bond length of the t and o-AFE phase regions enclosed by the dashed\nline in Supplementary Fig. 18a. The average vertical strains in the t phase are ~2%, lying\nbetween Case-(1) (<110> // b ) and Case-(2) (c // b ).\nt o-AFE t o-AFE\nFig. R6. (Supplementary Fig. 19). Observed iDPC-STEM imaging of the t/o coherent\ninterfaces similar to Supplementary Fig. 18, within Crystal 2. a, Raw iDPC-STEM imaging,\nwith the t and o-AFE phase identification. b, iDPC-STEM imaging with the corresponding Hf-\nHf distance. c, iDPC-STEM imaging with the corresponding R-value distribution. Scale bar: 1\nnm. d, Statistical histogram of the R-value for the t phase enclosed by the dashed line in\nSupplementary Fig. 19a. The strains are calculated based on the average Hf-Hf bond length of\nthe t and o-AFE phase regions enclosed by the dashed line in Supplementary Fig. 19a. The\naverage vertical strains in the t phase are ~1.94%, lying between Case-(1) (<110> // b )\nt o-AFE\nand Case-(2) (c // b ).\nt o-AFE\nFig. R7. (Supplementary Fig. 24). Observed t/o coherent interfaces similar to\nSupplementary Fig. 23, within Crystal 2, with the c-axis observation direction of the o-\nAFE phase. a, Raw iDPC-STEM imaging. b, iDPC-STEM imaging with the corresponding\nHf-Hf distance. c, iDPC-STEM imaging with the corresponding R-value distribution. Scale bar:\n1 nm. d, Statistical histogram of the R-value for the t phase enclosed by the dashed line in\nSupplementary Fig. 24a. The strains are calculated based on the average Hf-Hf bond length of\nthe t and o-AFE phase regions enclosed by the dashed line in Supplementary Fig. 24a. The\naverage horizontal strains in the t phase are ~-0.1%, corresponding to Case-(3) (<110> // c\nt o-\n).\nAFE\nFig. R8. (Supplementary Fig. 25). Observed t/o coherent interfaces within Crystal 2, with\nthe c-axis observation direction of the o-AFE phase. a, Raw iDPC-STEM imaging. b, iDPC-\nSTEM imaging with the corresponding Hf-Hf distance. c, iDPC-STEM imaging with the\ncorresponding R-value distribution. Scale bar: 1 nm. d, Statistical histogram of the R-value for\nthe t phase enclosed by the dashed line in Supplementary Fig. 25a. e-h, Structural schematic\ndiagrams of the strain relationship on the t phase induced by the o-AFE phase corresponding\nto the strain state. For (e), Case-(4) (<110> // a ); For (f), Case-(6) (c // a ); For (g),\nt o-AFE t o-AFE\nCase-(5) (c // c ); For (h), Case-(3) (<110> // c ). The strains are calculated based on\nt o-AFE t o-AFE\nthe average Hf-Hf bond length of the t and o-AFE phase regions enclosed by the dashed line\nin Supplementary Fig. 25a. The average vertical strains in the t phase are ~-0.81%, lying\nbetween Case-(3) (<110> // c ) and Case-(5) (c // c ).\nt o-AFE t o-AFE\nTo verify the universality of t/o-AFE MPBs within Lu:HZO bulk crystals, we regrew a\ncrystal using the same preparation protocol as Crystal 2 and fabricated five new STEM\nspecimens around the t/t+o phase boundary for iDPC-STEM characterization, with the results\npresented in Figs. R4-R8. These samples exhibit well-defined t/o phase interfaces. Through\nstructural analysis, we quantified the average t-phase strains originating from adjacent o-AFE\nphases. These findings align with the results reported in the main text, further validating the\nprevalent occurrence of t/o-AFE MPBs in Lu:HZO bulk crystals.\nFor STEM characterization, the densely arranged O atoms align with the a-axis orientation\nof the o-AFE phase, restricting our analysis to alignments along either the b- or c-axis.\nConsequently, observations are limited to the specific coherent t/o-AFE interfaces illustrated\nin Fig. 3a-i. The original STEM results of t/o-AFE MPBs revealed the crystallographic\ncorrelations between t and o-AFE phases, as shown in Fig. 3j (encompassing Cases-(1) to (4)\nand (6)). Subsequent updated analysis has now identified the previously unobserved Case-(5)\ninterface (Fig. R8), enabling comprehensive analysis of strain generation at all t/o-AFE phase\nconnections. The systematic observation of all interfaces within the crystal further substantiates\nour conclusion that tensile strain dominates within as-grown Lu:HZO bulk crystals\n(Supplementary Table 3). Exploration of additional coherent t/o-AFE interfaces may require\nconsideration of specific observation orientations.\nRevision: Based on this feedback, we have added Figs. R4, R5, R6, R7, and R8 as\nSupplementary Figs. 16 (Page 14), 18 (Page 16), 19 (Page 17), 24 (Page 21), and 25 (Page 22),\nrespectively, and incorporated the strain cases to Supplementary Table 3 in Supplementary\nInformation.\nWe have supplemented the main text with the following discussion: “These findings from\ncoherent t/o-AFE interfaces experimentally validate the prevalence of t/o-AFE MPBs in\nLu:HZO bulk crystals. This system establishes a unique platform to investigate local structural\nvariations across differing MPB configurations at atomic resolution.” (Page 19)\nWe have modified the sentences “Additionally, as illustrated in Supplementary Fig. 11,\nwe observed another t/o-AFE coherent interface …... described for Case-(2) (c // b ) and\nt o-AFE\nCase-(4) (<110> // a ) in Fig. 3j.” as “Furthermore, our atomic-resolution STEM analysis\nt o-AFE\nrevealed another coherent t/o-AFE interface viewed along the o-AFE c-axis direction\n(Supplementary Figs. 15 and 16). As exemplified in Supplementary Fig. 15, for the t-phase,\nthis interfacial configuration generates tensile strain along its c-axis (1.56%) and compressive\nstrain along its <110> (-0.42%) direction, consistent with the strain states described for Case-\n(2) (c // b ) and Case-(4) (<110> // a ) in Fig. 3j.” (Page 21)\nt o-AFE t o-AFE\nWe have added the sentences in the main text: “Furthermore, coherent t/o-AFE interfaces\nviewed along the c-axis direction of the o-AFE phase exhibit mixed configurations of Case-(1)\nand Case-(2) (Supplementary Figs. 18 and 19). This phase coexistence generates an average\nvertical tensile strain of ~2%, slightly lower than the interfacial strains observed at single-\norientation t/o-AFE boundaries (Fig. 5 and supplementary Fig. 17). The reduced strain\nmagnitude directly results from the competitive coexistence of t-phase with different\norientations ( 110 and c-axis).” (Page 22)\n< >\nWe have also updated the sentences “Besides, as shown in Fig. 6c,d, another t/o coherent\ninterfacial configuration viewed …… between the b-axis of the o-AFE phase and either the c-\naxis or <110> direction of the t-phase.” as “Besides, as shown in Fig. 6c,d and Supplementary\nFigs. 23 and 24, another t/o coherent interfacial configuration viewed along the o-AFE b-axis\ndirection produces weak horizontal strains within the t-phase. The t-phase exhibits negligible\naverage in-plane strain (~0%) while sustaining vertical compressive strain of -1.27% (Fig. 6c,d).\nThe weak horizontal strain matches Case-(3) (-0.2%) in Fig. 3j, while the stronger vertical\nstrain lies between Case-(4) (-0.5%) and Case-(6) (-1.45%). This observation suggests a\npotential crystallographic match between the b-axis of the o-AFE phase and either the c-axis\nor <110> direction of the t-phase. As shown in Supplementary Fig. 25, the interfacial\nconnection between the b-axis o-AFE phase and <110>- or c-axis oriented t-phase yields the\nCase-(5) configuration. The obtained vertical average strain in the t phase is determined to be\n-0.81%, lying between Case-(3) and Case-(5).” (Page 23)\nAdditionally, we have updated the sentence “Through microscopic characterization, five\ndistinct strain configurations (Case-(1), Case-(2), Case-(3), Case-(4), and Case-(6)) have been\nidentified.” as “Through microscopic characterization, all six distinct strain configurations\nfrom Case-(1) to Case-(6) have been identified.” (Page 24)\n7. Is the transitional phase a distinct crystallographic structure, or a highly strained tetragonal\nregion? This should be clarified.\nResponse: Thanks for this valuable comment. As discussed in this study, an obvious difference\nin lattice parameters exists between the t and o-AFE phases (shown in Supplementary Table\nS1), yielding the key strain source around the t/o-AFE MPBs. Regarding the transitional phase\n(t) in Fig. 5b, we employed this region to indicate the transitional region between the t and o-\nt\nAFE phases. Strictly speaking, this region cannot be defined as the highly strained t-phase\nbecause the adjacent vertical Hf-Hf columns demonstrate an obvious difference, resulting in\nan apparent strain variation across the area (Fig. 5d). This contrast originates from differential\nordering behaviors between odd and even atomic columns during phase formation. Therefore,\nto describe this region accurately, we defined it as a transitional region between the t-phase and\nthe adjacent o-AFE phase.\nRevision: According to this feedback, we have supplemented the main text with the following\ndiscussion: “Within the t-phase region, distinct Hf-Hf column configurations—evident\nt\nthrough adjacent vertical column differences—reveal fundamental structural deviations from\nboth t and o-AFE phases. This contrast originates from differential ordering behaviors between\nodd and even atomic columns during phase formation.” (Page 20)\n8. The argument that the tensile strain induces softening of the E phonon mode is not supported\nu\nby experimental evidence. Is it possible to provide evidence of this via Raman spectroscopy\nwith a measurement in the tetragonal region taken adjacent to the interface vs. a region far from\nthe interface? As it stands, this argument is supported only by theoretical work and the link\nbetween tensile strain and dielectric enhancement is primarily correlative.\nFig. R9. (Supplementary Fig. 3). Position-dependent shift behavior of the Raman peak of\nt-phase around ~270 cm-1 with different d values. The black dashed line denotes the t/t+o\nphase interface within as-grown bulk crystals, as determined by Raman characterization. a. For\nd = 0 mm, b. For d = 5 mm, c. For d = 10 mm.\nResponse: Thanks for these helpful comments. In this study, we aimed to verify the dielectric\nenhancement around the t/o-AFE MPBs by analyzing local strain modulation between the two\nphases. To substantiate the phonon-related evidence of the t/o-AFE MPBs on the adjacent t-\nphase, we compared the position-dependent Raman spectra collected from Lu:HZO bulk\ncrystals with varying d values (defined in Fig. 1d). In t-phase HfO or ZrO , the vibrational\n2 2\nRaman peak near 270 cm-1 arises from Zr/Hf-O stretching modes, serving as a direct indicator\nof local structural variations [J. Am. Ceram. Soc. 80, 1453–1460 (1997)]. As illustrated in Fig.\nR9, all three bulk crystals exhibit a similar trend near the phase interface between the t and t+o-\nAFE regions. From left to right within the crystal, this Raman mode shows a declining trend\nfollowed by an increase. The inversion point reflects the critical boundary for o-AFE phase\nformation, demonstrating that t/o-AFE MPBs drastically reconfigure the vibrational behavior\nof the t-phase.\nAs shown Fig. R9a,b, due to the emergence of the o-AFE phase, the leftmost t+o phase\nregion exerts an influence comparable to that of the rightmost t-phase, even though its location\nbefore quenching was at a significantly lower temperature. This variation in Raman spectra\nconfirms that the introduction of t/o-AFE MPBs can modulate the strain state of the adjacent t-\nphase, which is strongly correlated with changes in dielectric properties. Subsequent dielectric\ncharacterization further confirms the critical role of t/o-AFE MPBs, and local strain analysis\nprovides additional insight into how configuring coherent t/o-AFE interfaces can effectively\nenhance the dielectric performance. We hope this clarification offers a clearer understanding\nof the role of t/o-AFE MPBs and supports further investigation into the underlying mechanisms\nof MPB-based device design in HfO systems.\ndiscussion: “Additionally, to substantiate the phonon-related evidence of the t/o-AFE MPBs\non the adjacent t-phase, we compared the position-dependent Raman spectra collected from\nLu:HZO bulk crystals with varying d values. In t-phase HfO or ZrO , the vibrational Raman\n2 2\npeak near 270 cm-1 arises from Zr/Hf-O stretching modes, serving as a direct indicator of local\nstructural variations42. As demonstrated in Supplementary Fig. 3, the Raman mode (around 270\ncm-1) of all three bulk crystals exhibits a similar trend near the phase interface between the t\nand t+o-AFE regions. From left to right within the crystal, this Raman mode shows a declining\ntrend followed by an increase. The inversion point reflects the critical boundary for o-AFE\nphase formation, demonstrating that t/o-AFE MPBs drastically reconfigure the vibrational\nbehavior of the t-phase. Due to the emergence of the o-AFE phase, the leftmost t+o phase\nregion exerts an influence comparable to that of the rightmost t-phase (Supplementary Fig.\n3a,b), even though its location before quenching is at a significantly lower temperature. This\nvariation in Raman spectra confirms that the introduction of t/o-AFE MPBs can modulate the\nstrain state of the adjacent t-phase.” (Page 8)\n9. The manuscript would benefit from discussion about how the findings here can be applied\nto HfO -based thin films for CMOS applications, especially since the authors state that their\n2\nwork, “establishes a generalizable design paradigm for developing high-κ dielectrics in\nfluorite-structured materials, advancing next-generation CMOS integrated functional\ndevices.”\nResponse: We appreciate these constructive comments. Dielectric optimization is crucial for\nHfO -based dielectrics, particularly in thin-film applications, owing to their excellent\n2\ncompatibility with CMOS integrated technology. The findings of this study underscore the role\nof t/o-AFE MPBs in simultaneously enhancing the dielectric constant and thermal stability. To\nfurther elaborate on how these key findings can guide the design and fabrication of high-\nperformance HfO -based thin films, we provide a detailed discussion in the corresponding\n2\nsection.\nFor HfO -based thin films, given their typical textured orientation on an atomic scale\n2\n[Nature 580, 478–482 (2020)], the configuration of t/o-AFE MPBs can be achieved through\nlayered architecture designs, such as nanolaminates and superlattices. Along with optimal\ncoherent t/o-AFE interface design, each t-phase or o-AFE layer can be tailored according to its\nspecific compositional requirements. For the t-phase segment, codoping with Zr4+ ions\nrepresents a promising strategy, which has been widely adopted in most thin-film applications\n[ACS Appl. Mater. Interfaces 16, 60811–60818 (2024)]. In contrast, optimizing the o-AFE\nlayer remains challenging due to the large formation energy difference between the t and o-\nAFE phases. Stabilization of the o-AFE phase can be approached through a combination of ion\ndoping and local strain control. RE doping has proven effective in adjusting the o-phase\nformation within both bulk and thin-film materials [Nat. Rev. Mater. 7, 653–669 (2022);\nNat. Mater. 20, 826–832 (2021)]. In terms of strain engineering, a comprehensive approach\nconsidering adjacent layers and intrinsic modulation induced by ions offers a viable pathway\nfor achieving the desired o-phase formation [Adv. Mater. Technol. 10, 2401041 (2024)].\nMoreover, precise control of grain growth is also essential, as the size effect represents a critical\nfactor mediating the t-to-o phase transition, which is directly correlated with the tailoring of\nt/o-AFE MPB configurations [Nat. Rev. Mater. 7, 653–669 (2022)].\nRevision: To clarify the potential applications in HfO -based thin films, We have modified the\n2\nsentences “While Zr⁴⁺ doping readily stabilizes the t-phase in such films… enabling the tailored\ndesign of t/o-AFE MPB in thin-film systems.” as “For HfO -based thin films, given their\n2\ntypical textured orientation on an atomic scale40, the configuration of t/o-AFE MPBs can be\nachieved through layered architecture designs, such as nanolaminates and superlattices. Along\nwith optimal coherent t/o-AFE interface design, individual t-phase or o-AFE layer can be\ntailored according to its specific compositional requirements. For the t-phase segment,\ncodoping with Zr4+ ions represents a promising strategy, which has been widely adopted in\nthin-film applications10. In contrast, optimizing the o-AFE layer remains challenging due to the\nlarge formation energy difference between the t and o-AFE phases. Stabilization of the o-AFE\nphase can be approached through a combination of ion doping and local strain control. RE\ndoping has proven effective in adjusting the o-phase formation within both bulk and thin-film\nmaterials6,32. Strain engineering, which incorporates the influence of adjacent layers and\nintrinsic ion-induced modulation, offers a viable pathway for stabilizing the desired o-phase17.\nConcurrently, achieving precise control over grain growth is also essential, given the mediating\nrole of the size effect in the t-to-o phase transition. This effect is directly correlated with the\nstrategic tailoring of t/o-AFE MPB configurations6.” (Page 28).\nReviewer #2 (Remarks to the Author):\nThis paper reports that a high dielectric constant could be achieved by synthesizing HfZrO bulk\ncrystals using high-temperature rapid thermal processing and forming a t/o-AFE interface.\nUsing XRPD, Raman analysis, electrical measurements, and TEM analysis, the details of the\nt/o-AFE MPB are carefully analyzed. This is a very interesting study from the perspective of\ncrystallography.\nResponse: We sincerely thank the Reviewer’s comprehensive comments, which have\nsignificantly improved the rigor and clarity of our manuscript. We have carefully considered\nall comments and revised the paper accordingly. Below, we provide detailed point-by-point\nresponses to the comments.\nHowever, the authors' claims that this study will contribute to applications in CMOS and\nDRAM are not supported by any experimental evidence, making them completely\nunconvincing. Semiconductor devices require uniform and homogeneous material properties\non the nanometer scale. In contrast, the XRPD, Raman, and electrical properties observed in\nthe bulk crystals in this study are presumably averaged properties analyzed over a scale several\norders of magnitude larger. The paper does not disclose the electrode dimensions or\narrangement used to measure the dielectric properties. On the other hand, TEM analysis also\nconfirmed that tensile strain and compressive strain compete locally, raising concerns that\nperformance variations may occur when applied to semiconductor devices. The temperature\nused in this crystal synthesis was too high compared to semiconductor manufacturing processes,\nand the practical feasibility has not been demonstrated.\nSubmission to a ceramics journal is encouraged.\nResponse: We sincerely thank the Reviewer for the insightful evaluation of our work and for\nhighlighting the critical importance of connecting fundamental mechanisms to practical\napplications. We have carefully revised the manuscript to address the Reviewer’s constructive\npoints. Our key clarification and revisions are summarized below.\nClarification of the study’s aim and its relevance: We fully agree with the Reviewer that\nbulk crystals cannot be directly integrated into CMOS or DRAM fabrication processes. We\napologize for any unclear statement in our original manuscript that may have implied otherwise.\nThe primary aim of this study is not to propose the direct use of these bulk crystals in\ndevices, but rather to uncover the fundamental dielectric enhancement mechanism in\nHfO\n2\n-based systems by leveraging a uniquely clean model system.\nThis is because the fundamental dielectric enhancement mechanism in HfO -based t/o\nfilm configurations. Our study systematically uncovers this enhancement mechanism through\na combination of experimental characterizations and theoretical calculations from a strain-\nmediated perspective, as elaborated in the following sections. Dielectric performance\nmeasurements confirm that the t/o-AFE MPBs achieve a dielectric constant comparable to that\nof widely studied t/o-FE MPBs, while significantly surpassing single-phase systems. Moreover,\nthe t/o-AFE MPBs exhibit a ~58% reduction in the κ variation rate across the temperature range\nof 30–200°C compared to t/o-FE MPBs, underscoring their superior thermal stability.\nAs the Reviewer keenly noted, nanoscale uniformity is paramount for semiconductor\ndevices. However, the inherent polycrystallinity, interfacial defects, and complex strain states\nin thin films often complicate the isolation of a single contributing mechanism [Adv. Mater.\nTechnol. 10, 2401041 (2024)]. By studying high-quality, m-phase-free bulk crystals with\nlarge grains, we can precisely engineer and analyze coherent t/o interfaces without these\nconfounding factors. This allows us to unambiguously establish a causal link between\ninterface-driven tensile strain, phonon softening, and the resultant high dielectric\nconstant (κ). We believe this fundamental understanding is universal and provides a critical\ndesign principle for optimizing thin-film counterparts, where replicating such ideal interfaces\nat the nanoscale becomes the engineering goal.\nFig. R3. (Supplementary Fig. 7). Schematic diagram of the bulk-crystal samples for the\ndielectric characterization.\nDirect responses to specific concerns\n Electrode dimensions & measurement representativeness: We have added details\nof the dielectric measurement geometry to the Methods section (Fig. R3,\nSupplementary Fig. 7). Samples were sectioned into disks (~3 mm diameter, ~0.3 mm\nthickness) with sputtered Pt electrodes. While this measures a macroscopic average, the\nkey comparison is between different regions (t-phase vs. t/o-MPB) of the same crystal\nunder identical measurement conditions. The significant κ enhancement at the MPB is\ntherefore a robust relative effect attributable to the local interface structure, which we\nthen probe locally via STEM.\n Local strain competition & performance variation: The Reviewer is correct that we\nobserve competing tensile and compressive strains at the atomic scale. Our extensive\niDPC-STEM analysis on newly fabricated five additional specimens around the t/t+o\nphase boundary (Figs. R4-R8) and statistical assessment confirm that tensile strain\ndominates on average (mean tensile strain ~1.67% vs. mean compressive strain\n~0.54%). This net tensile state is the key mechanistic driver, as supported by our new\ntheoretical calculations, showing it softens the low-frequency polar phonon mode (Fig.\nR10, Supplementary Fig. S27, and Supplementary Discussion). In thin films, this\ninsight directs efforts toward achieving a net tensile strain state at engineered t/o\ninterfaces.\n High synthesis temperature: We acknowledge the temperature disparity. The high-\ntemperature OFZ method is used here as a synthesis tool to access the metastable t and\no phases and form the model MPB system for fundamental study. The derived design\nrule—creating coherent t/o interfaces under tensile strain—is process-\nindependent.\nFig. R4. (Supplementary Fig. 16). Observed iDPC-STEM imaging of the t/o coherent\ninterfaces similar to Supplementary Fig. 15, within Crystal 2. a, Raw iDPC-STEM imaging,\nwith the t and o-AFE phase identification. b, iDPC-STEM imaging with the corresponding Hf-\nHf distance. c, iDPC-STEM imaging with the corresponding R-value distribution. Scale bar: 1\nnm. d, Statistical histogram of the R-value for the t phase enclosed by the dashed line in\nSupplementary Fig. 16a. The strains are calculated based on the average Hf-Hf bond length of\nthe t and o-AFE phase regions enclosed by the dashed line in Supplementary Fig. 16a. The\naverage vertical strains in the t phase are ~1.2%, corresponding to the Case-(2) (c // b ).\nt o-AFE\nFig. R5. (Supplementary Fig. 18). Observed t/o coherent interfaces within Crystal 2, with\nthe c-axis observation direction of the o-AFE phase. a, Raw iDPC-STEM imaging. b, iDPC-\nSTEM imaging with the corresponding Hf-Hf distance. c, iDPC-STEM imaging with the\ncorresponding R-value distribution. Scale bar: 1 nm. d, Statistical histogram of the R-value for\nthe t phase enclosed by the dashed line in Supplementary Fig. 18a. e-h, Structural schematic\ndiagrams of the strain relationship on the t phase induced by the o-AFE phase corresponding\nto the strain state. For (e), Case-(2) (c // b ); For (f), Case-(1) (<110> // b ); For (g),\nt o-AFE t o-AFE\nCase-(4) (<110> // a ); For (h), Case-(4) (<110> // a ). The strains are calculated based\nt o-AFE t o-AFE\non the average Hf-Hf bond length of the t and o-AFE phase regions enclosed by the dashed\nline in Supplementary Fig. 18a. The average vertical strains in the t phase are ~2%, lying\nbetween Case-(1) (<110> // b ) and Case-(2) (c // b ).\nt o-AFE t o-AFE\nFig. R6. (Supplementary Fig. 19). Observed iDPC-STEM imaging of the t/o coherent\ninterfaces similar to Supplementary Fig. 18, within Crystal 2. a, Raw iDPC-STEM imaging,\nwith the t and o-AFE phase identification. b, iDPC-STEM imaging with the corresponding Hf-\nHf distance. c, iDPC-STEM imaging with the corresponding R-value distribution. Scale bar: 1\nnm. d, Statistical histogram of the R-value for the t phase enclosed by the dashed line in\nSupplementary Fig. 19a. The strains are calculated based on the average Hf-Hf bond length of\nthe t and o-AFE phase regions enclosed by the dashed line in Supplementary Fig. 19a. The\naverage vertical strains in the t phase are ~1.94%, lying between Case-(1) (<110> // b )\nt o-AFE\nand Case-(2) (c // b ).\nt o-AFE\nFig. R7. (Supplementary Fig. 24). Observed t/o coherent interfaces similar to\nSupplementary Fig. 23, within Crystal 2, with the c-axis observation direction of the o-\nAFE phase. a, Raw iDPC-STEM imaging. b, iDPC-STEM imaging with the corresponding\nHf-Hf distance. c, iDPC-STEM imaging with the corresponding R-value distribution. Scale bar:\n1 nm. d, Statistical histogram of the R-value for the t phase enclosed by the dashed line in\nSupplementary Fig. 24a. The strains are calculated based on the average Hf-Hf bond length of\nthe t and o-AFE phase regions enclosed by the dashed line in Supplementary Fig. 24a. The\naverage horizontal strains in the t phase are ~-0.1%, corresponding to Case-(3) (<110> // c\nt o-\n).\nAFE\nFig. R8. (Supplementary Fig. 25). Observed t/o coherent interfaces within Crystal 2, with\nthe c-axis observation direction of the o-AFE phase. a, Raw iDPC-STEM imaging. b, iDPC-\nSTEM imaging with the corresponding Hf-Hf distance. c, iDPC-STEM imaging with the\ncorresponding R-value distribution. Scale bar: 1 nm. d, Statistical histogram of the R-value for\nthe t phase enclosed by the dashed line in Supplementary Fig. 25a. e-h, Structural schematic\ndiagrams of the strain relationship on the t phase induced by the o-AFE phase corresponding\nto the strain state. For (e), Case-(4) (<110> // a ); For (f), Case-(6) (c // a ); For (g),\nt o-AFE t o-AFE\nCase-(5) (c // c ); For (h), Case-(3) (<110> // c ). The strains are calculated based on\nt o-AFE t o-AFE\nthe average Hf-Hf bond length of the t and o-AFE phase regions enclosed by the dashed line\nin Supplementary Fig. 25a. The average vertical strains in the t phase are ~-0.81%, lying\nbetween Case-(3) (<110> // c ) and Case-(5) (c // c ).\nt o-AFE t o-AFE\nFig. R10. (Supplementary Fig. 27). Strain-induced frequency variation of the infrared-\nactive low-frequency E mode of the t-phase. a, Applied strain along the <110> direction. b,\nu\nApplied strain along the c-axis direction.\nTo further elaborate on how these key findings can guide the design and fabrication\nof high-performance HfO -based thin films, we provide a detailed discussion in the\n2\ncorresponding section:\nFor HfO -based thin films, given their typical textured orientation on an atomic scale\n2\n[Nature 580, 478–482 (2020)], the configuration of t/o-AFE MPBs can be achieved through\nlayered architecture designs, such as nanolaminates and superlattices. Along with optimal\ncoherent t/o-AFE interface design, each t-phase or o-AFE layer can be tailored according to its\nspecific compositional requirements. For the t-phase segment, codoping with Zr4+ ions\nrepresents a promising strategy, which has been widely adopted in most thin-film applications\n[ACS Appl. Mater. Interfaces 16, 60811–60818 (2024)]. In contrast, optimizing the o-AFE\nlayer remains challenging due to the large formation energy difference between the t and o-\nAFE phases. Stabilization of the o-AFE phase can be approached through a combination of ion\ndoping and local strain control. RE doping has proven effective in adjusting the o-phase\nformation within both bulk and thin-film modifications [Nat. Rev. Mater. 7, 653–669 (2022);\nNat. Mater. 20, 826–832 (2021)]. In terms of strain engineering, a comprehensive approach\nconsidering adjacent layers and intrinsic modulation induced by ions offers a viable pathway\nfor achieving the desired o-phase formation [Adv. Mater. Technol. 10, 2401041 (2024)].\nMoreover, precise control of grain growth is also essential, as the size effect represents a critical\nfactor mediating the t-to-o phase transition, which is directly correlated with the tailoring of\nt/o-AFE MPB configurations [Nat. Rev. Mater. 7, 653–669 (2022)].\nTo summarize, this study introduces an MPB design strategy between the t and o-AFE\nphases to address instability issues prevalent in conventional t/o-FE MPBs. Integrating MPB\ninterface design, dielectric verification, and microstructural strain analysis, we conclusively\ndemonstrate that t/o-AFE MPBs enable thermal-stable, high-κ performance in HfO -based\n2\ndielectrics. Although bulk crystals are not directly transferable to film devices, the revealed\nenhancement mechanism—rooted in universal control of coherent t/o interfaces—provides a\nviable pathway for thin-film dielectric fabrication. We believe this strategic framework can\neffectively tailor the dielectric properties of HfO -based materials, accelerating the\n2\ndevelopment of next-generation CMOS-integrated functional devices.\nRevision: Based on the Reviewers’ comments and suggestions, we have modified the\nmanuscript. The detailed revisions are as follows:\nWe have supplemented the discussion regarding the significance of rapid quenching and\nincorporated phonon-related evidence for the t/o-AFE MPBs. (Pages 8 and 9)\nWe have analyzed the variation of the vibrational Raman peak near 270 cm-1 in position-\ndependent Raman spectra collected from Lu:HZO bulk crystals. This analysis demonstrates\nthat the t/t+o-AFE MPBs significantly modify the vibrational response of the adjacent t-phase\nregion (Supplementary Figs. 2 and 3). (Page 8)\nWe have added a discussion of the XRPD data to further clarify phase identification\nbetween the t-phase (S) and t+o-AFE (S ) regions. (Page 11)\nt t+o\nTo further confirm the stabilization of the t/o-AFE MPBs, we have supplemented the\ndielectric measurement data acquired after thermal processing. Additionally, we have\ncharacterized the frequency-dependent dielectric behavior approximately two months after\nthermal cycling. (Page 12)\nTo further verify the universality of the t/o-AFE MPBs within Lu:HZO bulk crystals, we\nhave prepared five additional STEM specimens sampled around the t/(t+o) phase boundary for\niDPC-STEM characterization. These specimens yielded the data presented in Supplementary\nFigs. 16 (Page 14), 18 (Page 16), 19 (Page 17), 24 (Page 21), and 25 (Page 22). The associated\ndiscussion in the main text has been updated accordingly. (Pages 21-23)\nTo elucidate the dielectric enhancement mechanism at the t/o-AFE MPBs, we have\nsupplemented the theoretical discussion concerning strain-mediated variations in the infrared-\nactive low-frequency E mode within the section “Enhancement mechanism of dielectric\nu\nconstant at t/o-AFE MPBs”. (Pages 24-26)\nIn the Discussion section, we have also supplemented the discussion on how these key\nfindings concerning t/o-AFE MPBs provide guidance for the design and fabrication of high-\nperformance HfO -based thin films. (Pages 26-29)\nthese changes and additions. We believe these revisions have thoroughly addressed the\nReviewer’s valid concerns. Our study now more clearly positions the bulk crystal as a\ndiscovery platform, and the t/o-AFE MPB as a novel design strategy to guide the development\nof thermally stable, high-κ HfO -based thin films for future microelectronics.\nour manuscript.\nReviewer #3 (Remarks to the Author):\nThis study utilizes the quenching technique and Lu-doped Hf Zr O (Lu:HZO) composition\n0.6 0.4 2\npreviously reported in prior works to realize a thermally stable HfO -based morphotropic phase\n2\nboundary (t/o-AFE MPB). The paper provides comprehensive analyses on the structural\nevolution, interfacial characteristics, and dielectric performance of this system. However,\nseveral major revisions are required before this study can be considered for publication.\nResponse: Thanks for the positive feedback. We sincerely appreciate the time and effort the\nReviewer devoted to evaluating our manuscript, as well as the recognition of the\ncomprehensive analyses presented. Their insightful questions have provided valuable guidance\nfor further clarifying the scientific logic of our work. In response to the comments, we have\nrevised the manuscript to enhance the overall quality and clarity of presentation. Below, we\nprovide detailed responses to each point raised. We believe the revised manuscript now\naddresses all of the Reviewer’s concerns, and we hope it meets the journal’s high standards for\npublication.\n1. The main problem statement of this study originates from the insufficient thermal stability\nof HfO -based MPB thin films. However, as also mentioned by the authors, the main\n2\napplication fields of MPB thin films are DRAM capacitors and advanced FET devices. In this\ncontext, the thermal stability analysis in the manuscript focuses on rather extreme temperature\nranges (typically from 400 °C up to 600 °C). It remains unclear what type of application\nrequires such high-temperature stability and how this range correlates with realistic device\noperation or processing conditions. The authors should provide a more detailed explanation of\nthe technological relevance of this temperature window and clarify whether the observed\nimprovement in stability is meaningful for semiconductor integration.\nResponse: Thanks for these valuable comments. We sincerely apologize for any\nmisunderstanding regarding the temperature-dependent dielectric spectra. Our thermal stability\nanalysis focused on comparing the t/o-AFE and t/o-FE samples across the temperature range\nof 30–200oC, which aligns with the practical operating conditions of DRAM capacitors and\nadvanced FETs [Nat. Rev. Mater. 9, 790–807 (2024); IET Nanodielectrics, 1, 32-40 (2018)].\nThe t/o-AFE MPBs demonstrate superior thermal stability of dielectric properties compared to\nthe t/o-FE MPBs, as evidenced by a significantly smaller variation in κ (7% for t/o-AFE MPBs\nversus 17% for t/o-FE MPBs), underscoring their advantage for practical high-κ applications.\nThe temperature range of 200–690oC was selected primarily to highlight the differences in\nthe o-to-t phase transition behavior between the two types of MPB samples, helping to explain\nwhy t/o-AFE MPBs exhibit better thermal stability than their t/o-FE counterparts. The Curie\ntemperature (T ) of the t/o-AFE MPBs (~670oC) is markedly higher than that of the t/o-FE\nC\nMPBs (~425oC), consistent with the difference in energy barriers between the t and o phases\nillustrated in Fig. 1a. Thus, the higher energy barrier associated with the t-to-o phase transition\nin t/o-AFE MPBs contributes to their exceptional dielectric stability across the temperature\nrange of 30–200oC, confirming their feasibility for use in real devices. We hope this\nclarification facilitates a clearer understanding of the temperature-dependent dielectric\nbehavior and the enhanced thermal stability offered by t/o-AFE MPBs.\nRevision: We have modified the sentences “This marked increase is attributed to the larger\nenergy barrier for the t-to-o phase transition inherent in the t/o-AFE MPBs32. Consequently,\nwhen heated from room temperature to 200 °C, the t/o-AFE MPBs exhibit minimal variation\nin κ—only 7%, compared to the 17% change observed in t/o-FE MPBs—directly reflecting\ntheir superior dielectric thermal stability.” as “Our thermal stability analysis compared the t/o-\nAFE and t/o-FE samples across the temperature range of 30–200oC, which aligns with the\npractical operating window of modern DRAM and FET devices49,50. The t/o-AFE MPBs\nexhibit superior dielectric thermal stability compared to t/o-FE MPBs, as demonstrated by\nsignificantly reduced dielectric variation (7% for t/o-AFE MPBs versus 17% for t/o-FE MPBs).\nCritically, these structures maintain κ = 55.1 after thermal cycling, nearly identical to the pre-\nr\ntest value of 57, and retain κ = 55.4 even after two months of aging. This exceptional thermal\nr\nand temporal stability originates from the intrinsically larger energy barrier for the t-to-o phase\ntransition in the o-AFE phase32, confirming their viability for practical high-κ device\nimplementation.” (Page 12).\n2. The room-temperature dielectric constant reported in this study is noticeably lower than the\nvalues reported in several previous studies on HfO -based MPB systems (often exceeding 65–\n2\n70). It would strengthen the manuscript if the authors could clarify the origin of this reduction.\nIn particular, the relationship between the reduced dielectric constant and the improved thermal\nstability should be discussed quantitatively. The authors are encouraged to justify why the\nenhancement of thermal stability, rather than dielectric performance, represents the more\ncritical metric for practical device applications.\nResponse: We appreciate these insightful comments. In HfO -based dielectrics for DRAM\n2\napplications, optimizing thermal stability is as critical as enhancing the dielectric constant κ.\nFor instance, the critical retention assessment in DRAM units necessitates evaluating\nperformance variations across processing temperatures by quantifying temperature-driven\nchanges in κ. High dielectric thermal stability implies minimal temperature dependence of κ\nand thereby suppresses the adverse imprint phenomenon, ensuring outstanding operational\nstability of DRAM devices against thermal variations [Nano Converg. 9, 44 (2022); Adv. Funct.\nMater. DOI: 10.1002/adfm.202522802 (2025)]. As the Reviewer noted, we introduced the t/o-\nAFE MPB strategy to address the stability limitations commonly observed in widely studied\nt/o-FE MPBs, thereby optimizing both thermal stability and dielectric constant simultaneously.\nThe detailed rationale is as follows:\nTo address thermal stability, our coherent phase-interface design was guided by energy\nbarrier differences among the t, o-FE, and o-AFE phases. The energy barrier for the t-to-o-AFE\ntransition (~68.8 meV per f.u.) substantially exceeds that for t-to-o-FE transition (~46.0 meV\nper f.u.), indicating superior dielectric stability in t/o-AFE MPBs. Subsequent temperature-\ndependent dielectric measurements confirm significantly enhanced thermal stability, with t/o-\nAFE MPBs exhibiting less than half the κ variation of t/o-FE MPBs across 30–200 °C. Thermal\nstability hinges primarily on the t-to-o phase energy barrier; hence, the higher phase-change\ntemperature in t/o-AFE MPBs delivers superior thermal dielectric stability over 30–200 °C\ncompared to t/o-FE MPBs.\nOptimizing the dielectric constant proves considerably more complex. It depends not\nonly on coherent t/o interface connectivity, MPB density, and t/o phase ratio, but also demands\nprecise composition control and growth optimization [Adv. Mater. Technol. 10, 2401041\n(2024)]. We successfully achieved t/o-AFE MPBs within bulk crystals and verified their\nadvantages over single-phase counterparts through dielectric characterization and\nmicrostructural strain analysis. Theoretical calculations support the revealed strain-mediated\nenhancement mechanism. However, realizing t/o-AFE MPBs requires both partial stabilization\nof t-phase and partial formation of o-AFE phase, which intrinsically limits dielectric property\noptimization. Furthermore, crystallization from melt to bulk crystals traverses complex c→t→\no-AFE phase transformations, making coherent t/o-AFE interface control challenging.\nConsequently, despite systematic interface optimization, the achieved dielectric constant does\nnot reach the maximum values observed in well-fabricated films.\nTo summarize, the enhancement in dielectric thermal stability is primarily ascribed to the\nestablishment of t/o MPBs using the o-AFE phase rather than the o-FE phase. In contrast,\noptimizing the dielectric constant necessitates comprehensive control of multiple material\nparameters [Adv. Mater. Technol. 10, 2401041 (2024)]. Consequently, variations in thermal\nstability lack direct correlation with dielectric constant changes through simple parametric\nrelationships. Regarding the Reviewer’s concerns about the dielectric constant, we believe that\nfuture studies optimizing t/o-AFE MPBs in HfO₂-based bulk crystals—by concurrently\nadjusting dopant composition (e.g., Zr⁴⁺ and rare-earth ions) and growth parameters (e.g.,\ngrowth direction and rate)—will significantly enhance dielectric performance. Furthermore,\nimplementing the t/o-AFE MPB concept in CMOS-compatible HfO -based films represents a\n2\nparticularly promising direction, leveraging more abundant modulation strategies, including\noxygen-source control, dopant engineering, layered configurations, surface-energy modulation,\nand rapid quenching [Nat. Rev. Mater. 7, 653–669 (2022)].\nRevision: To clarify the origin of the relatively poor dielectric performance compared to the\nwell-defined HfO -based MPB systems, we have modified the sentence “Comprehensive\n2\ndielectric characterization confirms that the formed t/o-AFE MPBs within HfO -based bulk\n2\ncrystal exhibit a comparable κ-value to reported t/o-FE MPBs (Supplementary Table 2).” as\n“Comprehensive dielectric characterization confirms that the formed t/o-AFE MPBs in HfO -\n2\nbased bulk crystals exhibit a comparable κ-value to reported t/o-FE MPBs, yet remain below\nthe maximum documented value (nearly 70) achieved in optimized thin films (Supplementary\nTable 2). This limitation is primarily attributed to the synthesis process of t/o-AFE MPBs\nwithin Lu:HZO bulk crystals, which necessitates concurrent partial stabilization of the t phase\nand formation of the o-AFE phase. Moreover, crystallization via melt-solidification traverses\ncomplex phase transformations (c→t→o-AFE), imposing challenges for coherent t/o-AFE\ninterface control. Future studies should prioritize the synergistic optimization of dopant\ncomposition and growth parameters, guided by proven modulation strategies from HfO -based\n2\nthin films, to systematically enhance dielectric performance.” (Page 27)\n3. The manuscript discusses temperature-dependent dielectric constant κ(T) measured during\nheating, but for MPB-based applications in DRAM/FET stacks the more critical question is\nreversibility after process thermal budgets. In other words, do the dielectric/structural\nproperties fully (or acceptably) recover at room temperature after high-T steps typical of BEOL\nintegration? I recommend adding a post-anneal recovery study that mimics realistic process\nconditions and reports pre/post room-temperature metrics.\nFig. R11. (Supplementary Fig. 12). Frequency-dependent dielectric characteristic for the\nt/o-AFE MPBs sample. a. Frequency-dependent dielectric characterization tested immediately\nafter the temperature-dependent dielectric measurement. b. Frequency-dependent dielectric\ncharacterization tested two months after the temperature-dependent dielectric measurement.\nResponse: We appreciate the Reviewer for their valuable comments. The recovery capability\nof high-κ materials following high-temperature processing is indeed crucial for practical\napplications. In our initial temperature-dependent dielectric measurements, we employed t/o-\nAFE MPBs to assess thermal stability in comparison with t/o-FE MPBs. The maximum\nmeasurement temperature reached approximately 690oC, surpassing the typical BEOL\nintegration temperature of around 400oC [Nat. Rev. Mater. 9, 790–807 (2024)].\nThe t/o-AFE MPBs exhibited a room-temperature dielectric constant (κ ) of 57 and\nr\ndemonstrated significantly superior thermal stability relative to t/o-FE MPBs over the\ntemperature range of 30–200 oC. As shown in Fig. R11, after the temperature-dependent tests,\nwe re-evaluated the frequency-dependent dielectric behavior of the t/o-AFE MPBs, obtaining\na κ value of 55.1—closely matching the pre-thermal measurement value of 57. Additionally,\nr\nwe performed further frequency-dependent dielectric characterization on the same sample\napproximately two months after thermal cycling, yielding a κ of 55.4, which aligns well with\nr\nthe value measured immediately post-thermal treatment. These findings robustly confirm the\nexceptional long-term stability of the t/o-AFE MPBs.\nThe outstanding dielectric stability observed in t/o-AFE MPBs can be attributed to the\nhigh energy barrier associated with the t-to-o-AFE transition (~68 meV per f. u.), which is\nsubstantially greater than that of the t-to-o-FE transition (~48.8 meV per f. u.). This remarkable\nstability and reliability highlight the potential of well-engineered t/o-AFE interfaces in the\ndesign of MPB-based dielectrics, positioning them as highly promising candidates for meeting\nthe stringent demands of real-world dielectric applications.\nRevision: To clarify the reversibility of t/o-AFE MPBs after the thermal processing, we\nmodified the sentences in the revised manuscript “This marked increase is attributed to the\nlarger energy barrier for the t-to-o phase transition inherent in the t/o-AFE MPBs32.\nConsequently, when heated from room temperature to 200 °C, the t/o-AFE MPBs exhibit\nminimal variation in κ—only 7%, compared to the 17% change observed in t/o-FE MPBs—\ndirectly reflecting their superior dielectric thermal stability.” as “Our thermal stability analysis\ncompared the t/o-AFE and t/o-FE samples across the temperature range of 30–200oC, which\naligns with the practical operating window of modern DRAM and FET devices49,50. The t/o-\nAFE MPBs exhibit superior dielectric thermal stability compared to t/o-FE MPBs, as\ndemonstrated by significantly reduced dielectric variation (7% for t/o-AFE MPBs versus 17%\nfor t/o-FE MPBs). Critically, these structures maintain κ = 55.1 after thermal cycling, nearly\nr\nidentical to the pre-test value of 57, and retain κ = 55.4 even after two months of aging. This\nr\nexceptional thermal and temporal stability originates from the intrinsically larger energy barrier\nfor the t-to-o phase transition in the o-AFE phase32, confirming their viability for practical high-\nκ device implementation.” (Page 12)\n4. The authors focus on the thermal stability of the t/o-AFE morphotropic phase boundary\n(MPB), but the stability of HfO -based phases is known to be strongly affected not only by\n2\ntemperature but also by electrical cycling. Recent studies on HfO - and HZO-based\n2\nferroelectric thin films have demonstrated that repetitive polarization switching or bias cycling\ncan induce stress comparable to that generated by thermal annealing, significantly altering the\nphase distribution and energy landscape between the t, o-FE, and o-AFE states. If the main\npurpose of this study is to clarify phase stability and the associated energy differences among\nMPB states, it would further strengthen the work to discuss or experimentally address the effect\nof electrical cycling.\nResponse: Thanks for these insightful comments. As the Reviewer pointed out, electrical\ncycling is a vital method for evaluating the stability and reliability of HfO -based films. The\n2\nassociated performance variation is typically accompanied by strain generation resulting from\nthe phase transition between the t and o phases. Precisely for this reason, fabricated films often\nexhibit changing characteristics under repeated electrical cycling. For the extensively studied\nHfO -based ferroelectric thin films, the typical coercive field ranges from 1-2 MV/cm, with a\n2\nmaximum applicable electric field of 3-4 MV/cm [Nature Commun. 13, 645 (2022)]. This\nrange selection primarily considers the optimization of the MPB between the t- and o-FE\nphases, focusing on parameters such as phase composition and MPB characteristics. Given the\nminimal thickness of HfO -based films (typically around 10 nm), applied voltages of only a\n2\nfew volts suffice to conduct relevant electrical cycling.\nIn contrast, this study presents an alternative optimization avenue for enhancing HfO -\n2\nbased dielectric performance by establishing an MPB configuration between the t and o-AFE\nphases. The optimization of t/o-AFE MPBs was directly achieved during the crystal growth of\nLu:HZO bulk crystals via a high-temperature gradient and rapid quenching strategy. Dielectric\nsamples featuring mixed t+o phases are prone to cracking when processed below a certain\nthickness. To maintain consistency across all samples used for dielectric characterization, a\nuniform thickness of ~0.3 mm was employed. The significantly higher energy barrier between\nthe t and o-AFE phases—compared to that between the t and o-FE phases—results in a\nsubstantially larger coercive field for the o-AFE phase. The reported coercive field of the o-\nAFE phase (~4 MV/cm) is substantially greater than that of the o-FE phase (1–2 MV/cm)\n[Small 21, 2408133 (2025)]. This phenomenon necessitates a much higher electric field during\nelectrical cycling. Combined with the substantial sample thickness, the requisite applied\nvoltages could reach several megavolts (~MV). Given the breakdown electric field of Lu:HZO\nbulk crystals (~MV/cm) and the maximum attainable voltage of our dielectric measurement\nsystem (~kV) [Nature Commun. 16, 3745 (2025)], conducting electrical cycling tests on t/o-\nAFE MPBs under current experimental conditions was challenging. Consequently, we\nprimarily verified the stability of t/o-AFE MPBs through thermal cycling dielectric\ncharacterization. This approach parallels the electrical cycling test, as both methodologies\nconcentrate on verifying phase stability at the MPB position.\nThe operational electric field in DRAM capacitors (typically ~1 MV/cm) falls significantly\nbelow the coercive field of the o-AFE phase (~4 MV/cm) but approaches or exceeds that of the\no-FE phase (1–2 MV/cm) [IEEE Electr. Device L. 42, 517-520 (2021); Adv. Mater. Technol.\n10, 2401041 (2024); Small 21, 2408133 (2025)]. Consequently, this field readily drives the\ntransition between t and o-FE phases, inducing instability issues, whereas the transition\nbetween t and o-AFE phases remains electrically suppressed. The strain-engineered dielectric\nenhancement in t/o-AFE MPBs thereby circumvents the inherent instability of t/o-FE systems,\ndirectly improving DRAM stability under operational conditions. The dielectric performance\nat the MPB in HfO -based materials is critically dependent on coherent t/o interfaces. In future\n2\nstudies, further enhancement of t/o-AFE MPB dielectric properties will necessitate optimizing\nthe interface formation between these two phases. Extending this concept to fabricate thin-\nfilm-based dielectrics and evaluating stability through combined thermal and electrical cycling\ncharacterizations would provide a comprehensive assessment of this MPB configuration for\noptimizing HfO -based dielectrics.\nthe discussion section: “Electrical cycling represents a critical reliability assessment method\nfor HfO -based films, complementing established thermal cycling protocols. Following\n2\nverification of the optimized t/o-AFE MPB configuration in these films, comprehensive\nelectrical cycling tests should be performed to quantify stability metrics. When coupled with\nthermal cycling data, this dual-methodology enables a unified reliability assessment of the\nMPB system under device-relevant operating conditions, which is essential for performance\noptimization in practical applications.” (Page 29)\n5. There are several different interpretations regarding the origin of the dielectric constant\nboosting effect observed near the morphotropic phase boundary (MPB). Among these, the most\nwidely accepted mechanism for HfO -based MPB thin films attributes the enhanced dielectric\nx\nresponse to a reversible, field-induced phase transition—in which a portion of the\nantiferroelectric phase is converted into the ferroelectric phase under an applied bias, due to\nthe relatively low energy barrier between these states (see Kai Ni et al., IEDM 2019, DOI:\n10.1109/IEDM19573.2019.8993495).\nFrom this perspective, the proposed t/o-AFE MPB in this work represents an AFE-to-AFE\nboundary, which makes it difficult to rationalize the observed dielectric constant boosting using\nthe conventional field-induced phase transition model. In most previous MPB systems, the\nenhancement arises precisely because of the low energy barrier between the coexisting FE and\nAFE phases that facilitates field-induced switching.\nIn this manuscript, the authors briefly mention a different origin for the dielectric enhancement,\nreferring to strain–phonon coupling at the coherent t/o interface. However, the current explanation and literature discussion appear too brief to fully convince readers of the validity of this alternative mechanism. The manuscript would benefit from a more detailed and quantitative discussion comparing the proposed strain–phonon mechanism with the established field-induced transition model, supported by experimental or theoretical evidence (e.g., phonon mode softening vs polarization switching data).\nResponse: We sincerely appreciate the Reviewer’s insightful comments. Indeed, extensive\nresearch over the past decade has focused on t/o-FE MPBs, driven by in-depth studies of o-FE\nphase stabilization. As noted in MPB-related references (e.g., DOI:\n10.1109/IEDM19573.2019.8993495), reversible t-to-o-FE phase transitions under electrical\ncycling typically enhance dielectric constants. However, this process also induces wake-up and\nfragile effects due to the change of phase composition and coherent interfaces, leading to\ninstability in t/o-FE MPBs. Furthermore, a fundamental understanding of the atomic-scale\nenhancement mechanisms at MPB interfaces remains limited, hindering insight into\nenhancement origins and compromising long-term stability and reliability.\nBuilding on this context, our study established t/o-AFE MPBs through rigorous analysis of\nenergy-level distributions across t, o-FE, and o-AFE phases, combined with metallurgical\nquenching principles. The results confirm that, similar to well-established t/o-FE MPBs, t/o-\nAFE MPBs significantly outperform single-phase systems, validating dielectric enhancement\nvia coherent t/o-AFE interfaces. Importantly, t/o-AFE MPBs exhibit a ~58% reduction in κ-\nvariation over 30–200oC compared to t/o-FE MPBs, demonstrating superior thermal stability.\nCrucially, we systematically uncovered the underlying mechanism from a strain-mediated\nperspective by evaluating the effects of coherent t/o-AFE interfaces on dielectric modulation.\nThe fundamental distinction resides in our selection of o-AFE versus o-FE in the field-\ninduced transition model. Our proposed t/o-AFE MPB strategy demonstrates superior stability\ncompared to t/o-FE MPBs, primarily due to the increased phase-transition difficulty resulting\nfrom the enhanced t-to-o transition energy barriers and larger coercive fields [Nature Commun.\n13, 645 (2022)], thereby stabilizing coherent t/o interfaces. Regarding the dielectric\noptimization at t/o MPB interfaces, strain generation in the t-phase—originating from adjacent\no-phases (o-AFE or o-FE)—stems primarily from crystallographic correlations and lattice\nmismatches at coherent interfaces.\nFig. R9. (Supplementary Fig. 3). Position-dependent shift behavior of the Raman peak of\nt-phase around ~270 cm-1 with different d values. The black dashed line denotes the t/t+o\nphase interface within as-grown bulk crystals, as determined by Raman characterization. a. For\nd = 0 mm, b. For d = 5 mm, c. For d = 10 mm.\nAccording to these suggestions, we compared Raman spectra across Lu:HZO bulk crystals\nwith varying d values (defined in Fig. 1d) to substantiate the phonon-related evidence for the\nimpact of t/o-AFE MPBs on the adjacent t-phase. In t-phase HfO or ZrO , the vibrational\n2 2\nRaman peak near 270 cm-1 arises from Zr/Hf-O stretching modes, serving as a direct indicator\nof local structural variations [J. Am. Ceram. Soc. 80, 1453–1460 (1997)]. As depicted in Fig.\nR9, all three crystals exhibit a comparable trend for the t-phase Raman mode proximal to the\ninterface between t and t+o-AFE phase regions. Traversing the crystal from left to right, this\nmode displays an initial decline followed by an increase, demonstrating that the presence of\nt/o-AFE MPBs significantly alters the vibrational characteristics of the adjacent t-phase [J. Am.\nCeram. Soc. 80, 1453–1460 (1997)]. This spectral variation confirms that the introduction of\nt/o-AFE MPBs modulates the strain state within the neighboring t-phase, which is strongly\ncorrelated with changes in dielectric properties.\nFig. R10. (Supplementary Fig. 27). Strain-induced frequency variation of the infrared-\nactive low-frequency E mode of the t-phase. a, Applied strain along the <110> direction. b,\nu\nApplied strain along the c-axis direction.\nTheoretical calculations were also performed to further clarify how strain mediates the\ndielectric property of the t-phase, elucidating strain-induced variations in the infrared-active\nlow-frequency E mode. These variations correlate with strain distributions along the t-phase\nu\nc-axis and <110> directions (Fig. 3). As shown in Fig. R10, compressive strain along either the\nc-axis or <110> direction increases the vibrational frequency of the low-frequency E mode,\nu\nwhereas tensile strain decreases it. This trend aligns with prior theoretical predictions [Chem.\nMater. 37, 1820–1825 (2025)]. STEM measurements reveal a maximum tensile strain of 2.53%,\napproximately twice the magnitude of the maximum compressive strain (−1.27%).\nFurthermore, averaging strain data from coherent t/o-AFE interfaces (Supplementary Table 3)\nshows the mean tensile strain (1.67%) is roughly triple the magnitude of the mean compressive\nstrain (−0.54%), confirming tensile strain predominance at t/o MPBs within as-grown Lu:HZO\nbulk crystals. This substantial tensile strain induces significant softening of the low-frequency\nE phonon mode, thereby driving the observed dielectric enhancement in Lu:HZO bulk crystals,\nu\n4e2 Z*2\nas described by Equation (1) (      ). This analysis further\ns  ion  M V 2\nsubstantiates the feasibility of dielectric optimization via engineered interfacial connections\nbetween t- and o-AFE phases. This strain-mediated mechanism can be further extended beyond\nbulk-crystal dielectrics to thin-film systems, as both depend on coherent t/o interface formation.\nIn summary, unlike field-induced transition paradigms, this work establishes an alternative\napproach for enhancing HfO -based MPB dielectric properties via coherent t/o-AFE interface\n2\ndesign. The t/o-AFE MPBs exhibit superior interfacial stability relative to t/o-FE systems,\nowing to higher t-to-o phase-transition energy barriers. The typical operational electric field in\nDRAM capacitors ( ~1 MV/cm) falls significantly below the coercive field of the o-AFE phase\n(~4 MV/cm) but approaches or exceeds that of the o-FE phase (1–2 MV/cm) [IEEE Electr.\nDevice L. 42, 517-520 (2021); Adv. Mater. Technol. 10, 2401041 (2024); Small 21, 2408133\n(2025)]. Consequently, DRAM operating conditions readily drive the transition between t and\no-FE phases, inducing instability, whereas the transition between t and o-AFE phases remains\nelectrically suppressed. The strain-engineered dielectric enhancement in t/o-AFE MPBs thus\neliminates this fundamental instability mechanism inherent to t/o-FE systems, directly\nimproving DRAM operational stability. Furthermore, the detailed strain-mediated analysis\nelucidates the mechanism underlying MPB enhancement and reveals its fundamental origin.\nOur findings establish a feasible pathway for simultaneously enhancing both dielectric constant\nand stability in HfO -based dielectrics. For future studies, implementing optimized t/o-AFE\nlong-term operational stability and reliability, accelerating the integration of HfO -based\n2\nmaterials into next-generation CMOS devices.\nRevision: To clarify the phonon-related evidence of the t/o-AFE MPBs on the adjacent t-phase,\nwe have supplemented the main text with the following discussion: “Additionally, to\nsubstantiate the phonon-related evidence of the t/o-AFE MPBs on the adjacent t-phase, we\ncompared the position-dependent Raman spectra collected from Lu:HZO bulk crystals with\nvarying d values. In t-phase HfO or ZrO , the vibrational Raman peak near 270 cm-1 arises\n2 2\nfrom Zr/Hf-O stretching modes, serving as a direct indicator of local structural variations42. As\ndemonstrated in Supplementary Fig. 3, the Raman mode (around 270 cm-1) of all three bulk\ncrystals exhibits a similar trend near the phase interface between the t and t+o-AFE regions.\nFrom left to right within the crystal, this Raman mode shows a declining trend followed by an\nincrease. The inversion point reflects the critical boundary for o-AFE phase formation,\ndemonstrating that t/o-AFE MPBs drastically reconfigure the vibrational behavior of the t-\nphase. Due to the emergence of the o-AFE phase, the leftmost t+o phase region exerts an\ninfluence comparable to that of the rightmost t-phase (Supplementary Fig. 3a,b), even though\nits location before quenching is at a significantly lower temperature. This variation in Raman\nspectra confirms that the introduction of t/o-AFE MPBs can modulate the strain state of the\nadjacent t-phase.” (Page 8)\nIn the section (Enhancement mechanism of dielectric constant at t/o-AFE MPBs) of the\nmain text, we have revised the sentence “Notably, the maximum observed average tensile and\ncompressive strains in the t-phase reach 2.53% and -1.27 %, respectively, demonstrating a\npronounced dominance of tensile strain effects over compressive strain contributions.” as\n“Notably, STEM measurements reveal a maximum tensile strain of 2.53%, approximately\ntwice the magnitude of the maximum compressive strain (−1.27%). Furthermore, averaging\nstrain data from coherent t/o-AFE interfaces (Supplementary Table 3) shows the mean tensile\nstrain (1.67%) is roughly triple the magnitude of the mean compressive strain (−0.54%),\nconfirming tensile strain predominance at t/o MPBs within as-grown Lu:HZO bulk crystals.”\n(Page 24)\nAdditionally, we have also updated the content “This experimental finding aligns with first-\nprinciples predictions……while underscoring the critical need for interface engineering in\ntailoring dielectric responses by selectively modulating specific phonon modes.” as\n“Theoretical analysis of strain-mediated variations in the infrared-active low-frequency E\nu\nmode was performed to elucidate the mechanism by which strain modulates the dielectric\nproperties of the tetragonal phase, with the result shown in Supplementary Fig. 27. These\nfrequency shifts correlate strongly with anisotropic strain distributions along the c-axis and\n110 crystallographic directions of the t-phase (Fig. 3). As shown in Supplementary Fig. 27,\n< >\ncompressive strain along either direction increases the low-frequency E mode frequency,\nu\nwhile tensile strain reduces it—a trend consistent with prior theoretical predictions in HfO -\n2\nbased systems43. Within Lu:HZO bulk crystals, substantial tensile strain at t/o-AFE MPBs\ninduces significant low-frequency E mode softening58,59. This phonon softening directly drives\nu\nthe enhanced dielectric response observed in Lu:HZO systems via the strain-polarization\ncoupling mechanism described by Equation (1). The comparable magnitudes of Z* among the\nthree infrared-active TO vibrational modes suggest that the frequency blueshift of the t-phase\nlow-frequency E phonon mode will significantly enhance the κ 38. This enhancement\nu ion\noriginates from the dominant contribution of the low-frequency E mode to κ , which is\nu ion\ntypically two-fold greater than that of the A mode and five-fold larger than the high-frequency\n2u\nE mode. This strain-mediated mechanism underpins the dielectric enhancement at t/o-MPBs\nu\nand establishes a pathway for property optimization through engineered coherent t/o-AFE\ninterfaces. Our findings demonstrate that interface engineering enables selective tuning of\nmode-specific phonon contributions, providing a universal strain-mediated framework for\ncontrolling dielectric responses.” (Page 25)\nTo clarify the comparison between our strain-mediated model and the field-induced\ntransition model, we have modified the associated content in the discussion part “Moreover,\nthe larger energy barrier for the t-to-o transformation in t/o-AFE MPBs compared to … both κ\nand dielectric thermal stability in HfO₂-based systems.” as “Extensively studied MPB systems\nin HfO -based films predominantly adhere to the field-induced transition model, relying on the\n2\nreversible phase transition between the t and o-FE phases21. In contrast, coherent t/o-AFE\ninterface engineering offers an alternative strategy for enhancing dielectric properties in HfO -\n2\nbased MPBs. Crucially, κ in t/o-AFE MPBs significantly outperforms single-phase systems,\nr\nvalidating their potential for dielectric enhancement. Substituting the o-FE phase with the o-\nAFE phase dramatically elevates phase-transition energy barriers between t and o phases34. The\ntypical operational electric field in DRAM capacitors (~1 MV/cm) falls significantly below the\ncoercive field of the o-AFE phase (~4 MV/cm) but approaches or exceeds that of the o-FE\nphase (1–2 MV/cm)17,26,60. Consequently, DRAM operating fields readily drive the transition\nbetween t and o-FE phases, inducing instability, whereas the transition between t and o-AFE\nphases remains electrically suppressed. As a result, t/o-AFE MPBs enhance the dielectric\nconstant while simultaneously eliminating field-induced instability. Additionally, t/o-AFE\nMPBs exhibit superior thermal stability compared to t/o-FE counterparts, directly enhancing\nlong-term operational reliability. Subsequent strain analyses elucidate the underlying\nmechanism at coherent t/o-AFE interfaces, confirming that dielectric optimization can be\nachieved without the reversible transition between the t and o-FE phases. Precise strain control\nin the t-phase—mediated by crystallographic correlations and lattice mismatches at coherent\nt/o-AFE interfaces—enables concurrent enhancement of both dielectric constant and stability\nin HfO -based dielectrics.” (Page 27)\ncalculation “All first-principles density functional theory (DFT) calculations were performed\nusing Vienna Ab initio Simulation Package (VASP) within the projector–augmented-wave\n(PAW) formalism and the PBEsol generalized-gradient approximation3. A plane-wave cutoff\nenergy of 600 eV was employed. Electronic convergence was set to 10-7 eV, and ionic\nrelaxations proceeded until the residual forces were below 10-3 eV/Å. A 12 × 12 × 8\nMonkhorst–Pack k-point mesh was used for the t phase4. Phonon properties were computed\nusing the finite-displacement method as implemented in the PHONOPY package. A 4 × 4 × 2\nsupercell was used to generate symmetry-inequivalent displacements, and Hellmann–Feynman\nforces from VASP static calculations were used to construct the force-constant matrices.\nPhonon-mode symmetries and irreducible representations were obtained using the PHONOPY\npackage.” in the Experimental section of Supplementary Information. (Page 4)\n6. While the authors cite prior work from their group, lutetium (Lu) still remains a relatively\nunfamiliar dopant in the HfO /HZO community compared with more established options. To\n2\nmake the manuscript more convincing and broadly useful, please clarify the specific role of Lu\nin this study and substantiate its CMOS compatibility and competitiveness relative to\nconventional dopants.\nResponse: Thanks for these valuable comments. For HfO /HZO-based materials, rare-earth\n2\n(RE) doping represents a crucial strategy for stabilizing metastable phases. Regarding bulk\ncrystal growth, the HfO -RE O phase diagram serves as a critical reference standard because\n2 2 3\nthe as-grown crystals must undergo a drastic temperature transition from the melt temperature\nto room temperature. During cooling from the liquid phase, the material crystallizes and\nexperiences multiple phase transitions. However, different RE3+ ions exhibit distinct phase\nmodulation behaviors in RE-doped HfO systems. RE3+ ions with larger ionic radii (e.g., La3+,\n2 2 7 2\nThis yields mixed RE Hf O and m-phase HfO crystals, making the fabrication of the o-phase\n2 2 7 2\nchallenging due to multi-phase interference. In contrast, selecting RE3+ ions with relatively\nsmaller ionic radii (from Gd3+ to Lu3+) provides a viable pathway to address the influence of\nRE Hf O . To prevent m-phase formation, careful consideration of the eutectoid reaction at\n2 2 7\napproximately 1760°C (t → c + m) is essential, as it directly correlates with ion doping\nconcentration. For RE-mediated HfO /HZO systems, achieving o-phases (o-FE and o-AFE)\n2\ntypically requires RE doping concentrations below 10 at.% [Nat. Rev. Mater. 7, 653–669\n(2022)]. Higher doping levels tend to stabilize the t-phase, complicating t/o MPB formation.\nComparing the minimal doping concentrations for avoiding m-phase formation across Gd3+ to\nLu3+ ions, Lu3+ demonstrates a distinct advantage due to its lower required concentration.\nConsequently, we employed Lu doping to investigate t/o-AFE MPBs in this study, and the\nresults confirm the feasibility of this design strategy.\nRegarding RE-doped HfO films, La3+, Gd3+, and Y3+ ions have demonstrated efficacy in\n2\nstabilizing metastable o-phases. Notably, Y3+ achieves exceptional o-FE phase stabilization at\nlow doping concentrations (~5 at.%), whereas achieving the Y3+-stabilized o-FE phase in bulk\ncrystals requires substantially higher doping (12 at.%) due to eutectoid reaction constraints\n[Nat. Mater. 20, 826–832 (2021); Nat. Mater. 21, 903–909 (2022)]. This underscores the\nimportance of selecting RE3+ ions whose ionic characteristics align with the doping window\noptimal for HfO -based films (below 10 at.%), thereby facilitating the design and performance\n2\noptimization of t/o MPBs. Recently, Lu doping has been validated as a stabilizer for modulating\nferroelectricity in thin-film applications, exhibiting CMOS compatibility and tuning effects\ncomparable to widely used RE3+ ions such as La3+, Gd3+, and Y3+. This further underscores the\npromising utility of Lu doping within the HfO /HZO research domain [Mater. Today Nano 25,\n2\n100458 (2024); Nanotechnology 35, 385705 (2024)].\nRevision: To clarify the purpose of selecting Lu3+ ions, we have supplemented the sentences\nin the revised manuscript: “Lu3+ offers a distinct advantage for o-phase stabilization: the doping\nconcentration needed to suppress the detrimental m-phase formation (via the t → c + m\neutectoid reaction) is lower than that required for larger RE3+ ions and falls within the typical\nrange for o-phase stabilization in HfO systems6” (Page 6)\naddressed, I believe this work would be suitable for publication in Nature Communications\nResponse: We really appreciate the Reviewer’s constructive and inspiring comments. We have\ncarefully reviewed the comments and have thoroughly addressed each of their questions in the\nrevised manuscript. We have supplemented experimental details, clarified the core scientific\nlogic, and optimized the presentation of figures and text to improve clarity. We sincerely hope\nthat the revised version has satisfactorily addressed all questions from the Reviewer. Thanks\nagain for the valuable support in promoting the progress of our work."}, {"round": 2, "reviewer_comments": {"reviewer_1": "The authors have adequately responded to my concerns and I recommend publication.", "reviewer_2": "Thank you for your thoughtful response. It clarified some of the unclear points in the first draft. I believe the discovery of a new MPB in a bulk crystal is the highlight of this paper. While this is of great interest to the field of ferroelectrics, my impression is that it doesn't fit well with Nature Communications. Your assertion that the only way to apply it to CMOS and DRAM is to create an array structure of MPBs is correct. Such a breakthrough is eagerly awaited.", "reviewer_3": "In my previous review, I asked the authors to clarify why this work is significant in the broader context of HfO₂-based high-κ dielectrics and device applications, and to sharpen several points that were conceptually interesting but not yet clearly communicated. In the revised manuscript, these issues have been addressed much more explicitly. The authors now articulate more clearly what the central contribution is – namely, the use of a coherent t/o-AFE morphotropic phase boundary as a discovery platform for thermally stable high-κ behavior and a general design strategy for HfO₂-based dielectrics – and how this complements, rather than duplicates, prior t/o-FE MPB thin-film studies.\nThe narrative has also become substantially clearer. Several previously vague or ambiguous passages have been rewritten so that a reader can follow the logical flow from the problem statement, through the choice of a bulk model system, to the key mechanistic findings and their implications for thin-film and device design. The distinction between the practically relevant operating temperature window and the higher-temperature analysis used to understand phase stability is now made explicit, which makes the main message considerably easier to grasp.\nIn addition, the authors have provided a substantial amount of new and more detailed analysis. The extended temperature-dependent dielectric measurements (including post-anneal and long-term room-temperature recovery), the additional STEM statistics on t/o-AFE interfaces, the position-dependent Raman measurements, and the phonon calculations together form a coherent and technically convincing response to the questions raised in the first round. Overall, the authors have responded carefully and comprehensively to the reviewers’ comments, and I do not have remaining major concerns. I am satisfied with the revision and support publication of the manuscript in its present form."}, "author_response": "Responses to Reviewers’ comments\n“Atomic-scale mechanism unlocks thermal-stable high-κ performance in HfO via\n2\ncoherent interfaces” (NCOMMS-25-76784A)\nBy Y. H. Shen, et al.\nWe sincerely appreciate the insightful comments and constructive feedback from all\nreviewers. Your valuable guidance has significantly improved the quality of our\nmanuscript.\nReviewer #1 (Remarks to the Author):\nThe authors have adequately responded to my concerns and I recommend publication.\nResponse: We are deeply appreciative of the reviewer’s supportive feedback and\nfavorable decision. The insightful comments and constructive suggestions offered\nduring the review were immensely valuable and have profoundly strengthened our work.\nReviewer #2 (Remarks to the Author):\nThank you for your thoughtful response. It clarified some of the unclear points in the\nfirst draft. I believe the discovery of a new MPB in a bulk crystal is the highlight of this\npaper. While this is of great interest to the field of ferroelectrics, my impression is that\nit doesn’t fit well with Nature Communications. Your assertion that the only way to\napply it to CMOS and DRAM is to create an array structure of MPBs is correct. Such\na breakthrough is eagerly awaited.\nResponse: We are grateful for the reviewer’s valuable observation. We are in complete\nagreement that the development of MPB array structures is a necessary step toward the\npractical implementation of this discovery in CMOS and DRAM technologies. This\nobservation rightly highlights a pivotal focus for our subsequent research, and we are\ndedicated to pursuing this path to realize the transformative potential that the field\nawaits.\nReviewer #3 (Remarks to the Author):\nIn my previous review, I asked the authors to clarify why this work is significant in the\nbroader context of HfO -based high-κ dielectrics and device applications, and to\n2\nsharpen several points that were conceptually interesting but not yet clearly\ncommunicated. In the revised manuscript, these issues have been addressed much more\nexplicitly. The authors now articulate more clearly what the central contribution is –\nnamely, the use of a coherent t/o-AFE morphotropic phase boundary as a discovery\nplatform for thermally stable high-κ behavior and a general design strategy for HfO -\n2\nbased dielectrics – and how this complements, rather than duplicates, prior t/o-FE MPB\nthin-film studies.\nThe narrative has also become substantially clearer. Several previously vague or\nambiguous passages have been rewritten so that a reader can follow the logical flow\nfrom the problem statement, through the choice of a bulk model system, to the key\nmechanistic findings and their implications for thin-film and device design. The\ndistinction between the practically relevant operating temperature window and the\nhigher-temperature analysis used to understand phase stability is now made explicit,\nwhich makes the main message considerably easier to grasp.\nIn addition, the authors have provided a substantial amount of new and more detailed\nanalysis. The extended temperature-dependent dielectric measurements (including\npost-anneal and long-term room-temperature recovery), the additional STEM statistics\non t/o-AFE interfaces, the position-dependent Raman measurements, and the phonon\ncalculations together form a coherent and technically convincing response to the\nquestions raised in the first round. Overall, the authors have responded carefully and\ncomprehensively to the reviewers’ comments, and I do not have remaining major\nconcerns. I am satisfied with the revision and support publication of the manuscript in\nits present form.\nResponse: We extend our sincere gratitude to the reviewer for their meticulous\nassessment and supportive feedback on our revised manuscript. Their insightful\ncomments proved invaluable to the revision process. We also wish to express our\ngratitude for the reviewer’s insightful comments, positive assessment, and encouraging\nendorsement for publication."}]

Decision letter