Atomic-scale mechanism unlocks thermal-stable high-κ performance in HfO₂ via coherent interfaces

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:Hf_0.6Zr_0.4O₂) 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 E_u 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 bandgap, and excellent compatibility with silicon-based integrated circuit technology^1,2,3,4,5,6. 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 P2₁/c (m) phases^7,8, 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 era^1,11. 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 ceramics^13,14,15,16. 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)^{18,19,20,21,22,23,24,25,26,27,28,29,30}. 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 endurance^17,31,32. 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.

Fig. 1: Schematic diagram of the OFZ growth strategy and associated Raman data for the as-grown Lu:HZO bulk crystals.

a Free energy distributions of t, o-AFE and o-FE phases. ΔE_t/o-AFE and ΔE_t/o-FE denote the energy barriers of the phase transitions from t to o-AFE and o-FE phases, respectively^6,35,63. The cyan and orange vertical arrows represent the polarization directions. b MPB schematic diagram between the t and o-AFE phases⁶³. The yellow region represents the connected interface. c Designed growth strategy for stabilizing t/o-AFE MPBs to room temperature. The as-grown crystal (cyan shaded frame inside the figure) is moved along the growth direction. T denotes temperature, and T_C corresponds to the Curie temperature. The blue curves represent the temperature distribution along the growth direction. The cyan region denotes the t-phase, while the gray spheres correspond to the formed o-AFE phase. d Photograph and room-temperature position-dependent Raman spectra of the as-grown Lu:HZO bulk crystals with different d values corresponding to the d = 0 mm, 5 mm, and d = 10 mm, respectively. (d represents the distance from the uppermost position of the as-grown crystal to the highest heating temperature point (Supplementary Fig. 1)). The theoretical Raman vibrational modes of the t, o-AFE, and o-FE phases are from Ref. ⁴¹.

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) phases^32,35. 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:Hf_0.6Zr_0.4O₂, 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 E_u 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 technologies^36,37.

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 nanoparticles^38,39. 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 temperature^32,35. 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 Hf_0.6Zr_0.4O₂ (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 (T_C) 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 A_1g and B_1g Raman modes around 270 cm^-1, while the o phases manifest strong bond vibrations in the vicinity of 370 cm^–1, including the A_g 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 interface^35,43, 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.

Fig. 2: Phase evolution diagram within the HfO₂-based bulk crystals and the corresponding structural, component, and dielectric properties.

a Phase evolution from the c to t/t + o(MPB) phases within Lu:HZO bulk crystals⁶³. The atom arrangements refer to the standard cards: ICSD No. 173964 (m), ICSD No. 79913 (o-AFE), ref. ³⁵ (o-FE), ICSD No. 173966 (t), 173967 (c). b Enlarged view of room-temperature X-ray powder diffraction (XRPD) data of the top (S_t) and bottom (S_t+o) part of Crystal 2. The blue regions correspond to the diffraction signals at ~53° and 56°. The complete XRPD data are provided in the Supplementary Fig. 5. c Room-temperature position-dependent (distance to the left side of the black dashed box) EPMA data of Crystal 2. d Room-temperature dielectric constant (κ_r) comparison of HfO₂-based bulk crystals with different polymorphs. m-HfO₂ and m-HZO are polycrystalline samples, o-AFE, t + o-AFE, t-HZO, c-HfO₂, and c-ZrO₂ correspond to the Lu:HfO₂ (10 at%), S_t section of Crystal 2, S_t+o section of Crystal 2, Lu:HfO₂ (16 at%), and Y:ZrO₂ (YSZ) bulk crystal samples, respectively. t/o-FE represents the annealed t-phase part of Crystal 2 (composed of t, o-FE, and o-AFE, where the o-FE phase is the predominant o phase). t/o-AFE denotes the phase boundary between the t and t + o-AFE section within Crystal 2. e, f Temperature-dependent κ-values of the t/o-FE and t/o-AFE samples measured at 100 kHz, respectively. The peak at the lower temperature range corresponds to t/o-FE transition temperature, while the peak at the higher temperature range represents the t/o-AFE phase transition. The inset is a partial enlarged detail.

To further analyze the phase difference between the pure t and mixed t + o-AFE regions with as-grown Lu:HZO crystals, we took Crystal 2 as a representative case and collected XRPD data from the t-phase (S_t) and t + o-AFE (S_t+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 S_t 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^o and 56^o are observed in S_t+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 S_t and S_t+o was analyzed by performing Rietveld refinement characterization (Supplementary Figs. 4 and 6). As shown in Supplementary Table 1, the t-phase c/(2^0.5a) of S_t is determined to be 1.010, a value smaller than that of the theoretically standard t-phase (1.028) but larger than that within S_t+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 films^45,46,47. 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 (κ_r) values in contrast to other polymorphs, being in good agreement with the theoretical calculations⁹. The o-AFE sample exhibits an κ_r 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 κ_r 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 T_C (~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 devices^49,50. 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 κ_r = 55.1 after thermal cycling, nearly identical to the pre-test value of 57, and retain κ_r = 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 counterparts^32,35.

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 transition^6,51. 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)).

Fig. 3: Schematic diagrams of t/o-AFE MPB configurations and their associated strain distributions in the t-phase.

a–c Coherent interfaces between the t-phase {001} plane and different o-AFE phase planes (from Type Ⅰ to Type Ⅲ). d–i Coherent interfaces between the t-phase {110} planes and different o-AFE phase planes (from Type Ⅳ to Type Ⅸ). The red and gray arrows denote the tensile and compressive strains, respectively. For instance, Type Ⅰ (<110>_t // c_o-AFE) designates a c_oherent interface under horizontal observation, with the <110> direction of the t-phase parallel to the b-axis of the o-AFE phase. j, Horizontal (S_t-H) and vertical (S_t-v) strain variations of the t-phase across different MPB types. The cyan- and pink-shaded regions represent the strain states of the t-phase {001} and {110} planes, respectively. The red and gray symbols correspond to the tensile and compressive strains, respectively. Case-(1) (<110>_t // b_o-AFE), Case-(2) (c_t // b_o-AFE), Case-(3) (<110>_t // c_o-AFE), Case-(4) (<110>_t // a_o-AFE), Case-(5) (c_t // c_o-AFE), and Case-(6) (c_t // a_o-AFE) describe the different crystallographic correlati_ons of the coheren_t interfaces between the t and o-AFE phases (a–i), and the strain magnitudes quantified in (j). For instance, Case-(1) can be found in Type Ⅰ, Type Ⅲ, Type Ⅵ and Type Ⅶ.

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 layers^33,34. 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.

Fig. 4: Structural schematics and atomic-resolution iDPC-STEM images of the t/t + o-AFE phase boundary within Crystal 2⁶³.

a, b Atomic arrangement along the b- and c-axis directions of the o-AFE phase according to the standard card of ICSD No. 79913. The pink and light blue arrows in (a) represent the polarization direction. c, d Atomic arrangement along the c-axis and <110> directions of the t-phase according to the standard card of ICSD No. 173966. e Observed iDPC-STEM image along the b_o-AFE direction. The pink and light blue arrows represent two reversed c-axis polarization states. f Observed iDPC-STEM image along the c_o-AFE direction. The experimental data in (e, f) coincide with the b-axis and c-axis theoretical structural arrangements of the o-AFE phase shown in (a, b), respectively. g R-value calculation rule of the t-phase (R = (h₁ + h₂)/(v₁ + v₂)). h₁ and h₂ represent the horizontal spacing between adjacent cations, while v₁ and v₂ correspond tothe vertical spacing between adjacent cations. h, R-value distribution corresponding to the observed iDPC-STEM image along the c_t direction (Supplementary Fig. 14a). i R-value distribution corresponding to the observed iDPC-STEM image along the <110>_t direction (Supplementary Fig. 14c). All the scale bars correspond to 1 nm.

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 (t_t), 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 t_t-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 t_t-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 t_t-phase presence. Within the t_t-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, t_t, and o-AFE phases.

Fig. 5: Observed coherent interfaces and strain analysis at the t/t + o-AFE phase boundary of Crystal 2, with the o-AFE observed along the c-axis direction.

a iDPC-STEM image showing the t/t + o-AFE interface with corresponding Hf-Hf distance distribution. b Phase segmentation of the iDPC-STEM image in (a) based on Hf-Hf distance variations. The orange-, cyan-, and purple-shaded regions represent the t, t_t, and o-AFE phases, respectively. c Hf-Hf distance evolution across Rows 4, 21, and 34 during phase transition. The circle and square symbols denote the Hf-Hf distances of odd (d_o) and even (d_e) columns, respectively. d Strain analysis of the t-phase for Rows 2–9, 16–23, and 34–41 during the phase evolution process. Data points represent averaged Hf-Hf distances of eight rows. e Proposed phase evolution pathway from t to o-AFE⁶³, illustrating the coherent interface, as described in Case-(1) (<110>_t // b_o-AFE) in Fig. 3j. d₁ and d₂ denote the horizontal spacing between adjacent cation columns, corresponding to contraction and expansion behaviors, respectively. Scale bars: 1 nm.

Fig. 6: Two types of observed coherent interfaces and strain analysis at the t/t + o-AFE phase boundary of Crystal 2, with the o-AFE observed along the b-axis direction.

a iDPC-STEM image of the t/t + o-AFE interface revealing a distinct Hf-Hf distance distribution, with the t-phase observed along the c-axis direction (Supplementary Fig. 22). b Structural schematic diagram of the strain relationship on the t-phase induced by the o-AFE phase⁶³, as described Case-(3) in Fig. 3j. c iDPC-STEM image of the t/t + o-AFE interface revealing a distinct Hf-Hf distance distribution, with the t-phase observed along the <110> direction (Supplementary Fig. 23). d Structural schematic diagram of the strain relationship on the t-phase induced by the o-AFE phase⁶³, as described Case-(6) in Fig. 3j. Scale bars: 1 nm.

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 t_t-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 t_t-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% (t_t-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) (c_t // b_o-AFE) and Case-(4) (<110>_t // a_o-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. 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 deciphers 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 (κ_s) mainly contains the electronic contribution (κ_∞) and the ion contribution (κ_ion). Although different HfO₂-based polymorphs exhibit a similar κ_∞ value (~5), they show an evident discrepancy in κ_ion originating from distinct infrared-active phonon vibrational modes^54,55. The calculation of κ_s can be expressed as,

$${\kappa }_{s}={\kappa }_{\infty }+{\kappa }_{ion}={\kappa }_{\infty }+\frac{4\pi {e}^{2}}{{M}_{0}V}\frac{{Z}^{\ast 2}}{{\omega }_{{{{\rm{TO}}}}}^{2}}$$

(1)

where e, M₀, and V correspond to the electronic charge, a reference mass, and the lattice volume, respectively. ω_TO represents the vibration frequency of infrared-active transverse optical (TO) phonons, and Z* denotes the relevant mode Born effective charge. Note that the κ_ion contribution is positively proportional to the Z*/ω_TO², implying that the variation of ω_TO 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 materials^56,57, 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 E_u modes (~129 cm⁻¹ and ~460 cm⁻¹) and an A_2u mode (~321 cm⁻¹)⁴¹. Notably, the low-frequency E_u 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 E_u 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 E_u 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 E_u mode softening^58,59. 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 E_u phonon mode will significantly enhance the κ_ion⁴¹. This enhancement originates from the dominant contribution of the low-frequency E_u mode to κ_ion, which is typically two-fold greater than that of the A_2u mode and five-fold larger than the high-frequency E_u mode. 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.

Discussion

The MPB engineering paradigm brings the transformative potential for HfO₂-based dielectric systems, delivering exceptional performance enhancement beyond conventional single-phase configurations^5,26. While current research on HfO₂-based MPB systems predominantly targets t/o-FE coherent interfaces, insufficient study of the microstructural enhancement mechanism obscures fundamental structure-property correlations, leaving the intrinsic origin poorly understood. Furthermore, electric-field cycling or high-temperature operation often induces a phase transition between the t and o-FE phases, destabilizing the optimal phase composition and degrading dielectric properties^17,31. In contrast, the t/o-AFE MPB configuration offers an alternative pathway for optimizing HfO₂-based dielectric performance, owing to its higher energy barrier relative to the t-to-o-FE transition. This enhanced energy barrier promotes long-term functional stability by preserving phase content and phase interface during operation. A major challenge, however, lies in the thermodynamically driven coexistence of o-AFE and o-FE phases in HfO₂-based systems, resulting from their comparable free energies. This coexistence complicates both the establishment and characterization of exclusive t/o-AFE MPBs^33,34. In this study, we address this challenge by employing an integrated composition-growth strategy in Lu:HZO bulk crystals. We achieved controlled fabrication of t/o-AFE MPBs via optimized dopant design and OFZ processing. Crucially, the synergistic application of a large temperature gradient and rapid quenching enables deterministic regulation of t-o phase evolution by kinetically trapping t/o phase interfaces. Comprehensive dielectric characterization confirms that the formed t/o-AFE MPBs in HfO₂-based bulk crystals exhibit a comparable κ-value to reported t/o-FE MPBs, yet remain below the maximum documented value (nearly 70) achieved in optimized thin films (Supplementary Table 2). This limitation is primarily attributed to the synthesis process of t/o-AFE MPBs within Lu:HZO bulk crystals, which necessitates concurrent partial stabilization of the t phase and formation of the o-AFE phase. Moreover, crystallization via melt-solidification traverses complex phase transformations (c → t → o-AFE), imposing challenges for coherent t/o-AFE interface control. Future studies should prioritize the synergistic optimization of dopant composition and growth parameters, guided by proven modulation strategies from HfO₂-based thin films, to systematically enhance dielectric performance.

The subsequent microstructural characterization deciphers that the t-phase near these t/o-AFE interfaces experiences pronounced tensile strain. The strain modifies the infrared-active phonon modes in the t-phase, influenced by the adjacent o-AFE phase, which directly governs the dielectric properties at t/o-AFE MPBs. Given the well-defined interplay relationship ${\kappa }_{ion}\,\propto \,{Z}^{\ast }/{{\omega }_{{{{\rm{TO}}}}}}^{2}$, the tensile-strain-induced softening of the low-frequency E_u phonon mode can drive a more substantial dielectric enhancement than that of A_2u and high-frequency E_u modes^43,47. This study elucidates the fundamental dielectric enhancement mechanisms in t/o-AFE MPBs by establishing how strain states at coherent t/o interfaces directly govern the κ-value. Among the examined configurations, the Case-(1) strain configuration is more suitable for dielectric enhancement in contrast to other coherent interfaces due to its remarkable tensile strain (2.36%). Extensively studied MPB systems in HfO₂-based films predominantly adhere to the field-induced transition model, relying on the reversible phase transition between the t and o-FE phases²¹. In contrast, coherent t/o-AFE interface engineering offers an alternative strategy for enhancing dielectric properties in HfO₂-based MPBs. Crucially, κ_r in t/o-AFE MPBs significantly outperforms single-phase systems, validating their potential for dielectric enhancement. Substituting the o-FE phase with the o-AFE phase dramatically elevates phase-transition energy barriers between t and o phases³⁴. The typical operational electric field in DRAM capacitors (~1 MV/cm) falls significantly below the coercive field of the o-AFE phase (~4 MV/cm) but approaches or exceeds that of the o-FE phase (1–2 MV/cm)^17,26,60. Consequently, DRAM operating fields readily drive the transition between t and o-FE phases, inducing instability, whereas the transition between t and o-AFE phases remains electrically suppressed. As a result, t/o-AFE MPBs enhance the dielectric constant while simultaneously eliminating field-induced instability. Additionally, t/o-AFE MPBs exhibit superior thermal stability compared to t/o-FE counterparts, directly enhancing long-term operational reliability. Subsequent strain analyses elucidate the underlying mechanism at coherent t/o-AFE interfaces, confirming that dielectric optimization can be achieved without the reversible transition between the t and o-FE phases. Precise strain control in the t-phase—mediated by crystallographic correlations and lattice mismatches at coherent t/o-AFE interfaces—enables concurrent enhancement of both dielectric constant and stability in HfO₂-based dielectrics. These results validate the superior feasibility of t/o-AFE MPBs for optimizing HfO₂-based dielectrics and provide a blueprint for enhancing properties through precise control of interfacial strain states.

Building on the insights gained from Lu:HZO bulk crystals, we can extend these principles to HfO₂-based films—a system widely studied for CMOS compatibility. For HfO₂-based thin films, given their typical textured orientation on an atomic scale³⁹, the configuration of t/o-AFE MPBs can be achieved through layered architecture designs, such as nanolaminates and superlattices. Along with optimal coherent t/o-AFE interface design, each t-phase or o-AFE layer can be tailored according to its specific compositional requirements. For the t-phase segment, codoping with Zr⁴⁺ ions represents a promising strategy, which has been widely adopted in most thin-film applications¹⁰. In contrast, optimizing the o-AFE layer remains challenging due to the large formation energy difference between the t and o-AFE phases. Stabilization of the o-AFE phase can be approached through a combination of ion doping and local strain control. RE doping has proven effective in adjusting the o-phase formation within both bulk and thin-film modifications^6,32. In terms of strain engineering, a comprehensive approach considering adjacent layers and intrinsic modulation induced by ions offers a viable pathway for achieving the desired o-phase formation¹⁷. Moreover, precise control of grain growth is also essential, as the size effect represents a critical factor mediating the t-to-o phase transition, which is directly correlated with the tailoring of t/o-AFE MPB configurations⁶. Electrical cycling represents a critical reliability assessment method for HfO₂-based films, complementing established thermal cycling protocols. Following verification of the optimized t/o-AFE MPB configuration in these films, comprehensive electrical cycling tests should be performed to quantify stability metrics. When coupled with thermal cycling data, this dual-methodology enables a unified reliability assessment of the MPB system under device-relevant operating conditions, which is essential for performance optimization in practical applications. Collectively, this work lays the foundation for high-performance, miniaturized HfO₂-based devices essential for next-generation CMOS technologies. Furthermore, it introduces a bulk-crystal design framework for tailoring fluorite-structured materials, enabling the optimization of dielectric, piezoelectric, and ferroelectric functionalities, beyond just HfO₂-based systems, across diverse fields including data storage, energy harvesting, sensors, and photonic chips.

In brief, this study demonstrates a controlled preparation of t/o-AFE MPBs in Lu-doped HZO bulk crystals and elucidates the origin of their dielectric enhancement. The pronounced thermal gradients and rapid quenching rates inherent to the OFZ growth strategy enable precise control of t/o-AFE MPBs. Dielectric characterization reveals that samples rich in t/o-AFE MPBs exhibit superior performance compared to their single-phase or multiphase-mixed counterparts. Atomic-scale structural analysis identifies a predominant tensile strain over compressive strain within the t-phase localized near t/o phase boundaries. This tensile strain reduces the low-frequency infrared E_u vibrational mode frequency, thereby enhancing the dielectric response. Moreover, t/o-AFE MPBs exhibit superior dielectric thermal stability than the extensively studied t/o-FE MPBs. The multimodal characterization approach developed herein elucidates the atomic-scale mechanisms responsible for the significant dielectric enhancement at t/o-AFE MPBs in HfO₂-based systems. These findings establish a foundation for understanding structure-property relationships in fluorite-structured oxides, providing key insights for the rational design of high-κ components in next-generation CMOS-compatible electronics.

Methods

Crystal growth

The polycrystalline Lu:Hf_0.6Zr_0.4O₂ (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 (Hf_0.6Zr_0.4O₂) 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:Hf_0.6Zr_0.4O₂ (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 κ_r 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 550 L 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 Ab initio 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^-7eV, and ionic relaxations proceeded until the residual forces were below 10^-3eV 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.