Ultrathin ferroic HfO2–ZrO2 superlattice gate stack for advanced transistors

With the scaling of lateral dimensions in advanced transistors, an increased gate capacitance is desirable both to retain the control of the gate electrode over the channel and to reduce the operating voltage1. This led to a fundamental change in the gate stack in 2008, the incorporation of high-dielectric-constant HfO2 (ref. 2), which remains the material of choice to date. Here we report HfO2–ZrO2 superlattice heterostructures as a gate stack, stabilized with mixed ferroelectric–antiferroelectric order, directly integrated onto Si transistors, and scaled down to approximately 20 ångströms, the same gate oxide thickness required for high-performance transistors. The overall equivalent oxide thickness in metal–oxide–semiconductor capacitors is equivalent to an effective SiO2 thickness of approximately 6.5 ångströms. Such a low effective oxide thickness and the resulting large capacitance cannot be achieved in conventional HfO2-based high-dielectric-constant gate stacks without scavenging the interfacial SiO2, which has adverse effects on the electron transport and gate leakage current3. Accordingly, our gate stacks, which do not require such scavenging, provide substantially lower leakage current and no mobility degradation. This work demonstrates that ultrathin ferroic HfO2–ZrO2 multilayers, stabilized with competing ferroelectric–antiferroelectric order in the two-nanometre-thickness regime, provide a path towards advanced gate oxide stacks in electronic devices beyond conventional HfO2-based high-dielectric-constant materials. In the standard Si transistor gate stack, replacing conventional dielectric HfO2 with an ultrathin ferroelectric–antiferroelectric HfO2–ZrO2 heterostructure exhibiting the negative capacitance effect demonstrates ultrahigh capacitance without degradation in leakage and mobility, promising for ferroelectric integration into advanced logic technology.

With the scaling of lateral dimensions in advanced transistors, an increased gate capacitance is desirable both to retain the control of the gate electrode over the channel and to reduce the operating voltage 1 . This led to a fundamental change in the gate stack in 2008, the incorporation of high-dielectric-constant HfO 2 (ref. 2 ), which remains the material of choice to date. Here we report HfO 2 -ZrO 2 superlattice heterostructures as a gate stack, stabilized with mixed ferroelectric-antiferroelectric order, directly integrated onto Si transistors, and scaled down to approximately 20 ångströms, the same gate oxide thickness required for high-performance transistors. The overall equivalent oxide thickness in metal-oxide-semiconductor capacitors is equivalent to an effective SiO 2 thickness of approximately 6.5 ångströms. Such a low effective oxide thickness and the resulting large capacitance cannot be achieved in conventional HfO 2 -based high-dielectric-constant gate stacks without scavenging the interfacial SiO 2 , which has adverse effects on the electron transport and gate leakage current 3 . Accordingly, our gate stacks, which do not require such scavenging, provide substantially lower leakage current and no mobility degradation. This work demonstrates that ultrathin ferroic HfO 2 -ZrO 2 multilayers, stabilized with competing ferroelectric-antiferroelectric order in the two-nanometre-thickness regime, provide a path towards advanced gate oxide stacks in electronic devices beyond conventional HfO 2 -based high-dielectric-constant materials.
With the two-dimensional scaling of silicon field-effect transistors reaching fundamental limits 1 , new functional improvements to transistors 4 , as well as novel computing paradigms and vertical device integration at the architecture level 5 , are currently under intense investigation 1,4,6 . Gate oxides have a critical role in this endeavour as a common performance booster for all transistor devices based on a wide range of materials, including silicon 2 , new high-performance channel materials 7,8 , and even materials suitable for three-dimensional integrated transistors 9,10 . Indeed, the gate oxide transition from SiO 2 to high-κ dielectrics is considered a paradigm shift in computing technology (κ, dielectric constant).
In this context, ferroelectric (FE) oxides offer new functionalities 11 that are considered promising for energy-efficient electronics 4,9 . The advent of atomic layer deposition (ALD)-grown doped-HfO 2 FE films 12 has overcome much of the material compatibility issues that plague traditional perovskite-based FE materials 2 . In addition, ferroic order persists down to a thickness of 1 nm in this system [13][14][15] , fostering integration into the most aggressively scaled devices in which the state-of-the-art high-κ oxide thickness is less than 2 nm.
In an advanced silicon transistor, the gate oxide is a combination of two distinct layers. The first is an interfacial SiO 2 formed with a Article self-limiting process, resulting in approximately 8.0-8.5-Å thickness 16 . The next is the high-κ (HK) dielectric HfO 2 layer that is typically approximately 2 nm in thickness. Higher capacitance of this series combination is desirable to suppress short channel effects. The capacitance is conventionally represented by equivalent oxide thickness, t t ε ε EOT = + /( / ) SiO H K H K SiO 2 2 , where lower EOT represents higher capacitance. Therefore, the EOT minimum value is limited by the interfacial SiO 2 thickness. Typically, with HfO 2 as the high-κ layer, the EOT is approximately 9.5 Å. To go below this value 17,18 , the semiconductor industry has implemented sophisticated scavenging techniques 16,18,19 to reduce the SiO 2 thickness after the full gate stack has been deposited. Although this technique is effective in scaling EOT, the thinner SiO 2 results in undesirable leakage 20 , mobility degradation 2,16 and reliability issues.
In this work, we present an ultrathin HfO 2 -ZrO 2 superlattice gate stack that exploits mixed ferroelectric-antiferroelectric (FE-AFE) order (Fig. 1a, b), stabilized down to 2-nm thickness-the same high-κ oxide thickness used in advanced transistors. When integrated on silicon, the gate stack shows an overall EOT of 6.5 Å, even though both transmission electron microscopy (TEM) and electrical characterization reveal an 8.0-8.5 Å interfacial SiO 2 thickness, as is typically expected from a chemically grown interfacial layer without scavenging. No scavenging of the interfacial SiO 2 results in substantially lower leakage current for the same EOT compared to benchmarks established by major semiconductor industries 3 . In addition, no mobility degradation is observed as EOT is scaled with these HfO 2 -ZrO 2 ferroic gate stacks. Therefore, ultrathin HfO 2 -ZrO 2 gate stacks exploiting ferroic order offer a promising pathway towards advanced energy-efficient transistors.

Ultrathin FE-AFE HfO 2 -ZrO 2 superlattices
Thin films of HfO 2 -ZrO 2 are grown using ALD, in which the nanolaminate periodicity is dictated by the sequence of Hf:Zr (4:12) ALD cycles before the Hf-Zr superstructure is repeated various times (Fig. 1c In-plane grazing-incidence diffraction (a.u.) Composition Electric eld Temperature Con nement (Superlattice) Fig. 1 | Atomic-scale design of negative capacitance in ultrathin HfO 2 -ZrO 2 . a, Energy landscape flattening. An FE double-well energy landscape is flattened by the depolarization field energies originating from electrostatic and elastic inhomogeneities present in the laterally arranged polar-nonpolar (orthorhombic FE-tetragonal AFE) thin-film system. The energy landscape flattening increases the permittivity of the overall system, as susceptibility is proportional to the inverse landscape curvature; such flattening is analogous to negative capacitance stabilization 29,30,49 . The stable energy minimum of the composite free-energy landscape, corresponding to the negative curvature (that is, negative capacitance) regime of the ferroelectric energy landscape, is highlighted in pink. b, Engineering ferroic phase competition in the HfO 2 -ZrO 2 fluorite-structure system. Beyond the conventionally studied tuning parameters-composition, electric field, temperature 32,38 -here we introduce dimensional confinement via superlattice layering to tailor ferroic phase competition at the atomic scale. c, Schematic of the HZH fluorite-structure multilayer on Si; the heterostructures maintain distinct layers (that is, not solid-solution alloys) based on EELS, XRR and depth-resolved XPS (Extended Data Fig. 1). The role of the layering on the underlying ferroic order and capacitance is studied by electrical measurements as a function of HfO 2 -ZrO 2 stacking structure and annealing temperature (Extended Data Figs. 4 and 5, respectively). d, High-resolution TEM images of the atomic-scale HZH trilayer (top) and extracted d-lattice spacings (bottom, determined from the solid white box regions) corresponding to the fluorite-structure AFE tetragonal (P4 2 /nmc, left) and FE orthorhombic (Pca2 1 , right) phases, respectively. The layer delineations are approximate, as the HfO 2 -ZrO 2 and SiO 2 interlayer thicknesses are more rigorously determined by XRR and TEM analysis (Extended Data Figs. 1 and 6, respectively). Note that imaging the crystallinity of the HfO 2 -ZrO 2 layers requires mistilt with respect to the Si lattice (Methods). Scale bars, 5 nm. e, Synchrotron in-plane grazing-incidence diffraction demonstrating the presence of both the AFE T-phase (101) t and FE O-phase (111) o reflections, the d-lattice spacings of which are consistent with those extracted from TEM. Detailed indexing for structural identification is provided by wide-angle synchrotron diffraction (Extended Data Fig. 2a). a.u., arbitrary units.
We note here that the original Kittel view of an 'antipolar' crystal structure 21 does not apply to the nonpolar tetragonal lattice attributed to fluorite-structure antiferroelectricity. Instead, the field-induced tetragonal-to-orthorhombic (nonpolar-to-polar) phase interconversion as the origin of antiferroelectricity has been examined in both ZrO 2 22,23 and HfO 2 22,24 . Therefore, at low electric fields, the mixed FE-AFE behaviour is analogous to an FE-dielectric (polar-nonpolar) heterostructure, which can impart depolarization fields on the FE layer 25 . The laterally intertwined nonpolar-polar phases present in the ultrathin HZH heterostructure are conducive to flattening the FE energy landscape through the aforementioned depolarization fields 26-28 (Fig. 1a). Furthermore, heterogeneous elastic energies in structurally inhomogeneous systems have been shown to destabilize long-range polarization, suppress polarization, and thereby flatten energy landscapes 28 .
Additionally, the polarization in the ultrathin HZH multilayer exhibit an in-plane component. 2D reciprocal space maps indicate a strong out-of-plane (111) texture (Extended Data Fig. 2b), which is consistent with TEM images demonstrating vertically stacked planes of 111-interplanar lattice spacing (Extended Data Fig. 2f). Therefore, considering that the polarization is directed along a principal lattice direction for the Pca2 1 orthorhombic structure, the highly oriented out-of-plane (111) texture indicates an in-plane projected polarization.   Fig. 6), providing evidence of capacitance enhancement via negative capacitance. Furthermore, these 2-nm ferroic gate stacks demonstrate amplified charge from pulsed I-V measurements relative to the SiO 2 interlayer (Extended Data Fig. 7), marking, to our knowledge, the thinnest demonstration of charge and/or capacitance enhancement (Extended Data Fig. 7).

Article
The in-plane polarization introduces additional depolarization field, owing to the electrostatic coupling with the nonpolar AFE phases in the lateral direction. Notably, exploiting inhomogeneity to induce depolarization fields and enhance susceptibility has been demonstrated for perovskites exhibiting heterogeneous polar-nonpolar regions 28 . Following the same underlying mechanisms, our work demonstrates that it is possible to stabilize a mixed nonpolar-polar phase competition in 2-nm-thick binary oxide films and enhance its permittivity. We also note that flattening of the energy landscape via depolarization fields is the same underlying principle of the negative capacitance effect 11,29 , in which depolarization fields stabilize the FE locally at a higher energy state compared to the ground state of an isolated, homogeneous FE, leading to negative-curvature energy landscapes 30,31 .
To confirm the higher susceptibility in the mixed AFE-FE system directly, we have performed capacitance-voltage (C-V) hysteresis loops in metal-insulator-metal capacitor structures on thicker films with the same superlattice periodicity (Fig. 2a). Besides features indicative of mixed FE-AFE order, the total capacitance for the superlattice is larger than both conventional AFE ZrO 2 and FE Zr:HfO 2 of the same thickness (Fig. 2a), demonstrating enhanced susceptibility. To quantify the permittivity, capacitance measurements were performed across the superlattice thickness series. These measurements yield an extracted    to extract the radio-frequency g m (Extended Data Fig. 9).
permittivity of approximately 52 (Fig. 2b, Methods), which is larger than both the FE orthorhombic Zr:HfO 2 and AFE tetragonal ZrO 2 values 32 . To further understand the ferroic evolution in these HZH superlattices, we performed low-temperature measurements where enhanced FE phase stabilization is expected. Indeed, temperature-dependent C-V loops for thicker HZH demonstrate an evolution from mixed-ferroic to FE-like hysteresis upon cooling slightly below room temperature (approximately 240 K, Fig. 2c), consistent with temperature-dependent X-ray spectroscopy indicating transition from mixed tetragonalorthorhombic phase to predominately orthorhombic structure at similar temperatures (Extended Data Fig. 3c). That the capacitance decreases upon cooling as the system moves away from the highly susceptible mixed ferroic phase is consistent with previous work on negative capacitance in FE-dielectric systems 29 , which establishes the energy landscape link between enhanced capacitance and susceptibility near phase transitions. Notably, the intertwined FE-AFE phases within the superlattice and the resulting enhancement in susceptibility from the competition of FE and AFE phases are analogous to negative stiffness composites of ferroelastics within a metal matrix 33,34 , that is, the mechanical analogue to negative capacitance.
Notably, the composition in our films is close to where several previous reports have postulated a possible morphotropic phase boundary (MPB) in thicker HfO 2 -ZrO 2 solid-solution films 35 . We note that MPB systems follow strict symmetry requirements 36 , which have not been established for the HfO 2 -ZrO 2 system. In our ultrathin HZH multilayers, the negative free-energy curvature of the polar FE O phase compensates the positive curvature of the nonpolar AFE T phase (Fig. 1a), leading to a flattened energy landscape. Similarly, energy landscape flattening is postulated as the thermodynamic origin of enhanced piezoelectric response in canonical perovskite ferroelectrics 36 , in which multiple crystal symmetries are nearly degenerate across a composition phase boundary (MPB). However, a critical distinction is that here the overall energy landscape flattening, and corresponding increase in capacitance, is determined by the stacking of the atomic-scale HfO 2 -ZrO 2 layers, and not the volume fraction of the constituent elements 37 : solid solution of the same Hf:Zr composition does not provide the same high capacitance (Fig. 2e). Furthermore, compared to HfO 2 -ZrO 2 solid solutions across a range of typically reported Zr-rich 'MPB-like' compositions 35 , the HZH multilayer demonstrates larger capacitance (Extended Data Fig. 4). This indicates that the enhanced capacitance in HZH films is not simply driven by doping 32,38 , but can instead be tuned by the configuration of the multilayer structure (Extended Data Figs. 4,5). In the ultrathin regime, surface energies become a more dominant consideration for determining polymorphic phase stability 22 ; accordingly, the importance of stacking is amplified.
To quantify the observed capacitance, we have performed EOT simulations of MOS capacitors using the industry-standard Synopsys simulation platform (Methods). The Hf:Zr:Hf 4:12:4 trilayer stacks vary between 6.5-7.0-Å EOT (Fig. 2f), consistent over many measured capacitors. Notably, this EOT is smaller than the expected thickness of the interfacial SiO 2 layer (8.0-8.5 Å), as mentioned. To investigate further, high-resolution TEM of the gate stacks (Extended Data Fig. 6) illustrates that the SiO 2 thickness is indeed approximately 8.5 Å. To supplement this physical characterization, we next implemented electrical characterization of the interfacial layer via inverse capacitance versus thickness analysis of conventional dielectric HfO 2 and Al 2 O 3 thickness series grown on the same SiO 2 (Methods, Extended Data Fig. 6). All thermal processing is kept the same as the HfO 2 -ZrO 2 superlattice gate stack. The extracted HfO 2 and Al 2 O 3 permittivities-19 and 9, respectively-are consistent with the typical dielectric phases of these two materials. Therefore, one can reliably extract the SiO 2 layer thickness, yielding 8 Å (Extended Data Fig. 6), consistent with the high-resolution TEM results and values established by the semiconductor industry 3 .
Moreover, the consistent interlayer thickness extracted from both material systems indicates that neither Hf nor Al encroaches into the interfacial SiO 2 , which would reduce its thickness and/or increase its permittivity. This is expected considering that the gate oxides are processed at much lower temperature than that needed for silicate formation 39 and works reporting an increased SiO 2 interlayer permittivity 40 . Furthermore, XRR, EELS and XPS data indicate that for both the undoped control HfO 2 gate stack and the superlattice gate stack, the HfO 2 layer sits right on top of SiO 2 , leading to the same interface in both cases (Extended Data Fig. 1). Therefore, considering the interfacial layer thickness as 8 Å, the HZH multilayer gate stack demonstrates an overall EOT approximately 1.5 Å lower than the constituent SiO 2 thickness. We note that, for simplicity, we have used an EOT to quantify the capacitance of the superlattice stack; however, for a rigorous description, one should solve for the non-linearities that are expected to emerge from the ferroic nature of the gate oxide 41 .
To supplement the C-V evidence of capacitance enhancement, pulsed current-voltage (I-V) measurements of MOS capacitors integrating the approximately 2-nm HZH gate stack-which can quantify the amount of charge as a function of voltage 26 (Methods, Extended Data Fig. 7)-demonstrate larger stored charge than if just interfacial SiO 2 was sitting on top of Si. This provides further electrical evidence of charge enhancement in the ultrathin mixed-ferroic gate stack (Extended Data Fig. 7e). Furthermore, from these measurements, the extracted polarization-electric field relationship for just the HZH multilayer (Extended Data Fig. 7f) exhibits a regime of negative slope, which mathematically corresponds to negative capacitance stabilization 26 .

Ultrathin FE-AFE HfO 2 -ZrO 2 device results
The practical implication of this capacitance enhancement can be clearly seen in Fig. 3b, which shows leakage current versus EOT behaviour. The leakage current is measured at V g − V fb = −1 V, where V fb is the flatband voltage of the semiconductor and V g is the gate voltage. All other data points on this plot are taken from reported industrial gate stacks 3 . The leakage current for the Hf:Zr:Hf 4:12:4 stack is substantially lower at the same EOT. Note that below 9 Å, the other gate stacks need sophisticated scavenging techniques to reduce the thickness of the interfacial SiO 2 (ref. 3 ). On the other hand, the ferroic gate stack can achieve approximately 6.5 Å without any scavenging, resulting in the lower leakage current (Fig. 3b).
Furthermore, the scavenging of the interfacial SiO 2 leads to a loss of mobility of approximately 20 cm 2 V −1 s −1 per every Å of scavenged SiO 2 , owing to an increase in remote phonon scattering 3,16 . To examine how the mobility evolves with EOT, we compared transistors implementing the lower-EOT HZH gate stack compared to higher-EOT conventional HfO 2 gate stack, both of the same physical thickness (Methods). Notably, the mobility remains essentially the same for both stacks, demonstrating that there is no fundamental change in electron transport as a result of the mixed-ferroic multilayer gate stack compared to the standard high-κ dielectric gate stack (Extended Data Fig. 8d). Furthermore, this work demonstrates no penalty in mobility below 9 Å EOT, the point where Article conventional high-κ gate stacks display the mobility degradation due to scavenging that is necessary for lowering EOT (Fig. 3c, Extended Data Fig. 8d). Indeed, raw mobility extracted from long-channel transistors integrating the 2-nm HZH mixed-ferroic heterostructure gate stack exceed that of industry-reported long-channel transistors integrating standard 2-nm HfO 2 high-κ dielectric gate stacks 42 at the same EOT (Fig. 3c).
To examine how the capacitance enhancement in the 2-nm HZH gate stack behaves at high frequency, radio-frequency measurements were performed on the same long-channel (gate length L G = 1 μm) devices (Methods, Extended Data Fig. 9) to extract device parameters up to approximately 800 MHz for our devices (close to the cut-off frequency). Of particular interest is the transconductance( g m ), which is proportional to the product of capacitance and electron velocity (mobility). From Y-parameter measurements one can find alternating current (a.c.) transconductance as Re(Y 21 ) = g m + af 2 , where f is the frequency (Methods). This yields an a.c. transconductance as a function of applied gate voltage (V g ). Plotting this dependence, together with direct current (d.c.) transconductance (∂I d /∂V g from d.c. I d -V g ; Fig. 3h), illustrates that the d.c. and a.c. transconductance are similar, with a.c. transconductance roughly 15% larger at the peak value. This slightly larger a.c. transconductance may result from the fact that certain interface traps, which affect the d.c. behaviour, cannot respond at frequencies larger than 100 MHz, leading to better gate control. More importantly, these radio-frequency results show that the observed capacitance enhancement is not limited to the low-frequency regime 43,44 .
Next, shorter-channel (L G = 90 nm) devices, fabricated on a silicon-on-insulator (SOI) transistor with 18-nm SOI thickness, were examined. The transfer and output characteristic of a typical transistor are shown in Fig. 3e, f. Note that the threshold voltage of this device is 0.55 V, which is consistent with the work function of W used as the gate metal. Because of this, the transistors have been driven up to 1.6-V gate voltage so that an overdrive voltage (V ov = V g − V T ) of approximately 1 V can be applied (V T , threshold voltage). It is found that at a drain voltage (V d ) and V ov of 1 V, the drain current exceeds 1 mA μm −1 . Additionally, the measured extrinsic transconductance of approximately 1.1 mS μm −1 (Fig. 3g) corresponds to an intrinsic transconductance of approximately 1.75 mS μm −1 (Methods, Extended Data Fig. 10). The transconductance is substantially larger than conventional 90-nm transistors. In addition, it is larger than control devices with a HfO 2 gate stack of the same physical thickness, demonstrating the dual benefits of the HZH mixed-ferroic gate stack: low EOT without adversely affecting the electron transport.
Finally, to probe the interface quality, especially trap-induced effects 45 relevant for MOS field-effect transistor (MOSFET) reliability-a very crucial aspect for commercial application-we performed positive-bias temperature instability measurements on nFET transistors (Extended Data Fig. 8e-h). The results demonstrate very similar behaviour for both the HZH and control HfO 2 stacks of the same physical thickness, and similar to those reported in literature for high-κ HfO 2 stacks 46 . This is not unexpected; reliability characteristics are predominantly determined by the interfacial oxide and its high-κ interface 46 ; here both stacks have the same un-scavenged SiO 2 interlayer (Extended Data Fig. 1). Furthermore, stress measurements on capacitors demonstrate negligible V fb shift and non-existent capacitance degradation with increased stress time (Extended Data Fig. 8i, j).

Discussion
Capacitance enhancement via negative capacitance has been demonstrated for FE-dielectric superlattices in many single-crystalline perovskite-structure systems 30,31,47,48 . This work demonstrates that the same enhancement is possible in HfO 2 -ZrO 2 fluorite-structure superlattices on Si, which exhibit mixed FE-AFE (polar-nonpolar) order in films as thin as just approximately 2 nm. The ability to go down to such thickness and still stabilize competing ferroic order, conducive for negative-capacitance-mediated capacitance enhancement, is very important for advanced electronic devices, because dimensional scaling requires ultrathin gate stacks. Furthermore, this work establishes the critical role of atomic-layer stacking-as opposed to conventional doping techniques 32,38 -in controlling the ferroic phase space and permittivity of fluorite-structure oxides down to ultrathin limits, leveraging its unique size effects [13][14][15] and rich AFE-FE polymorphs 22,23 . When this mixed phase HfO 2 -ZrO 2 multilayer is integrated on Si, the gate stack exhibits a capacitance enhancement, lowering the EOT below a threshold that traditionally required careful scavenging of interfacial SiO 2 , which would otherwise degrade mobility 3 . Additionally, the low EOT is achieved at over an order of magnitude lower leakage current. Therefore, harnessing atomic-scale layering in ultrathin HfO 2 -ZrO 2 ferroic gate oxides presents a promising materials design platform for future Si transistors beyond the conventional high-κ dielectrics that have spurred semiconductor industry scaling over the past two decades.

Online content
Any methods, additional references, Nature Research reporting summaries, source data, extended data, supplementary information, acknowledgements, peer review information; details of author contributions and competing interests; and statements of data and code availability are available at https://doi.org/10.1038/s41586-022-04425-6.  Fig. 1), and maintains the mixed-ferroic behaviour, as high-temperature annealing would induce purely FE behaviour (Extended Data Fig. 5). X-ray diffraction and TEM confirm the presence of crystalline ultrathin films despite the low deposition temperature, afforded by the low crystallization temperature of ZrO 2 50 . In fact, non-post-annealed ALD-grown ZrO 2 has previously demonstrated crystallization into the FE orthorhombic phase on Si 51 . Bulk transistors. The n-type bulk transistors were fabricated by a non-self-aligned gate-last process on bulk silicon wafers (10 17 cm −3 ) with local oxidation of silicon (LOCOS) as device isolation technique. First, 10 nm of SiO 2 thermal oxide and 30 nm of low-pressure chemical vapour deposition (LPCVD) Si 3 N 4 were grown on the Si substrates. After the active region was defined by photolithography and Si 3 N 4 /SiO 2 etching, dry oxidation was performed to form the LOCOS isolation. Next, the source/drain regions were defined by photolithography and ion implantation with an ion dose of 3 × 10 15 ions per cm 2 . The dopants were then activated by a rapid thermal anneal (RTA) at 900 °C for 7 min in N 2 ambient. The gate stacks with the sub-nm chemically grown SiO 2 , 2-nm HZH heterostructure, and 100 nm of sputtered W gate was then deposited. After the gate fingers (from 500 nm to 50 μm) were patterned by photolithography and etched by inductively coupled plasma (ICP) metal etching, the 400-nm-thick interlayer dielectric (ILD) SiO 2 was deposited using plasma-enhanced CVD (PECVD). Last, after the contact hole opening, the Ti/TiN contact metal was deposited by sputtering, defined by photolithography, and then etched by ICP metal etching.

Short-channel SOI transistors.
The n-type short-channel transistors were fabricated by a non-self-aligned gate-last process on SOI substrates with a gate length (L G ) down to 90 nm. First, the device layer was thinned down to 20 nm and the active regions were defined by photolithography with expose regions etched slightly into the buried oxide. The hydrogen silsequioxane (HSQ) negative resist were written by e-beam lithography as a hard mask for the ion implantation with a dose of 5 × 10 15 ions per cm 2 . The dopant activation was conducted in an RTA at 900 °C for 15 s in N 2 ambient. The gate stacks with the sub-nm chemically grown SiO 2 , 2-nm HZH heterostructure, 1.5 nm of PEALD TiN, and 100 nm of sputtered W were sequentially deposited. The gate region (250 nm) was then patterned by photolithography. Similar to the back-end process for the bulk transistors, 400 nm of ILD and sputtered Ti/TiN contact metal were deposited and defined by photolithography and ICP etching.

Microscopy
Transmission electron microscopy. Electron microscopy was performed at the National Center for Electron Microscopy (NCEM) facility of the Molecular Foundry at Lawrence Berkeley National Laboratory (LBNL). The high-resolution bright field TEM images of HZH thin films were performed by FEI ThemIS 60-300 microscope with image aberration corrector operated at 300 kV (Fig. 1d, Extended Data Fig. 2e, f). To prepare cross-sectional TEM samples of HZH thin films, mechanical polishing was employed by using an Allied High Tech Multiprep at a 0.5° wedge to thin down the total thickness of samples down to 10 μm. Later, Ar ion milling of the Gatan Precision Ion Milling System was used to make an electron-transparent sample, starting from 4 keV down to 200 eV as final cleaning energy. For high-resolution imaging, in order to capture the crystallinity of the HZH layers, the zone axis alignment required varying degrees of mistilt with respect to the Si lattice, explaining the slightly obscured Si atomic columns (Fig. 1d, Extended Data Fig. 2e, f).
The local interplanar d-spacing in the ultrathin HZH films (Extended Data Fig. 2e, f) was measured by DigitalMicrograph software using its line profile plus integration width analysis. For the 2-nm HZH multilayer film, the extracted interplanar lattice spacings were averaged over multiple lattice periodicities and confirmed across various local regions of the film (Extended Data Fig. 2e, f). The SiO 2 interlayer thickness from low-magnification wide field-of-view (FOV) imaging was determined by the same method (Extended Data Fig. 6a). In particular, the intensity line scan from the wide FOV image (Extended Data Fig. 6a) is obtained from averaging across the entire FOV specified by the teal-coloured box (~150 nm). Next, the inflection points of the intensity peak were used as the criteria to set the boundaries of the SiO 2 interlayer (Extended Data Fig. 6a). This methodology was also utilized to determine the boundaries of the HZH layers from the EELS spectrum (Extended Data Fig. 1c). Regarding the wide FOV cross-sectional TEM (Extended Data Fig. 6a), both the low atomic weight and lack of crystallinity of the SiO 2 layer contribute to its weak scattering (bright colour), which aids in the visual delineation of the layer boundaries and the thickness extraction from the corresponding averaged intensity line scan. Fig. 2d) were performed with a Ti:sapphire femtosecond laser (Tsunami, Spectra Physics, λ ≈ 800 nm, frequency ≈ 80 MHz). The linearly polarized femtosecond laser beam was focused through 50× objective lens (numerical aperture (NA) ≈ 0.42) which results in a focal spot size of 2 μm. The generated SHG signal was collected through the same objective lens and separated from the fundamental beam by the harmonic separator. After passing through the optical bandpass filter, the SHG signals were registered to the photon multiplier tube (PMT) without a polarizer. The fundamental beam was mechanically chopped, and the signal collected by the PMT was filtered by a lock-in amplifier to reduce the background noise. For SHG spatial mapping, a two-axis piezo stage was used and the coordinate was synchronized with the PMT signal. The SHG intensity was obtained by averaging the mapping signals across a 100 μm × 100 μm sample area.

Optical microscopy. Second harmonic generation (SHG) measurements (Extended Data
X-ray characterization X-ray reflectivity. Synchrotron X-ray reflectivity (XRR)-performed at Sector 33-BM-C beamline of the Advanced Photon Source, Argonne National Laboratory and at Beamline 2-1 of the Stanford Synchrotron Radiation Lightsource, SLAC National Accelerator Laboratory-confirmed the thickness of HZH heterostructures (Extended Data Fig. 1b). The overall thickness of the HZH heterostructures is consistent with the growth rate (~1 Å per cycle) of ALD-grown Zr:HfO 2 as demonstrated in our previous work 13 . Furthermore, the presence of irregularly spaced fringes in the thicker HZH heterostructures suggests the presence of well separated HZH layers, that is, not a solid solution. This is confirmed by XRR fitting (Extended Data Fig. 1b) performed with the python package GenX 52 which considers factors such as density, roughness, and thickness.
In-plane grazing-incidence diffraction. Synchrotron in-plane grazing-incidence diffraction (GID) (Fig. 1e and Extended Data Fig. 2a) was performed at Sector 33-ID-D beamline of the Advanced Photon Source, Argonne National Laboratory. A Pilatus-II 100K area detector mounted on the del-arm was used to collect diffraction signal with a grazing-incidence geometry. The region of interest on the detector was set such that the ring-like signal was fully integrated. In-plane GID was collected by sweeping the in-plane angle ν (8-50°) with a fixed out-of-plane grazing angle δ (δ = 0.9°); the corrected Bragg angle (2θ) over which the data are plotted and indexed is determined from the relationship cos(2θ) = cos(ν)cos(δ) set by the geometry of the diffractometer. The X-ray source was fixed at 16 keV (λ = 0.775 Å). In-plane diffraction yields more diffraction peaks with better defined width, probably owing to the preferred orientation and disc-shape domains in the film. Therefore, in-plane GID enables clear indexing to the FE orthorhombic (Pca2 1 ) and AFE tetragonal (P4 2 /nmc) fluorite structure in the ultrathin HZH films, as the presence of many reflections from the in-plane GID spectra (Fig. 1e, Extended Data Fig. 2a) enables clear distinction from other nonpolar fluorite-structure polymorphs. Such diffraction spectra would be otherwise prohibited in typical out-of-plane geometry owing to the lack of vertical diffraction planes and the large linewidth inherent to ultrathin films. Two-dimensional diffraction. Two-dimensional reciprocal space maps (Extended Data Fig. 2b) were measured at Beamline 11-3 of the Stanford Synchrotron Radiation Lightsource, SLAC National Accelerator Laboratory. Rayonix MX225 CCD area detector collected diffraction flux in grazing-incidence (<0.20°) geometry; the X-ray source (50 μm vertical × 150 μm horizontal beam size) was fixed at 12.7 keV. The sample-detector work distance was set to 80 mm to enable detection of a wide region of reciprocal space (Q range 0.2 to 5 Å −1 ) at the expense of reciprocal space resolution, set by the pixel size. The two-dimensional diffraction scans-in which a wide portion of the entire reciprocal space was collected simultaneously, rather than at discrete regions in Q x -Q y space-were averaged over data collection time and for repeated scans. These measurement features, in tandem with the high X-ray flux afforded by the synchrotron source, enabled sufficient diffraction signal detection and contrast in films just 2 nm in thickness. Data analysis was performed Nika, an Igor Pro package for correction, calibration and reduction of two-dimensional areal maps into one-dimensional data 53 . Two-dimensional reciprocal space maps on bare HZH heterostructures confirm the presence of crystalline ultrathin films despite the low deposition temperature, afforded by the low crystallization temperature of ZrO 2 on Si 50 . Ferroic phase identification from diffraction. For fluorite-structure thin films, the main phases to consider are the dielectric monoclinic (P2 1 /c), AFE tetragonal (P4 2 /nmc), and FE orthorhombic (Pca2 1 ) phases. Various diffraction reflections from the wide-angle in-plane GID spectra enable indexing to the orthorhombic Pca2 1 phase. Lattice parameters (a, b, c)-determined via Bragg's law from the d 200 family of reflections-are self-consistently checked against the (111) lattice spacing ( = + + ) as well as other higher-order reflections present in the in-plane diffraction spectra (Extended Data Fig. 2a). For example, the lattice parameters extracted from the {200} reflections were a = 5.36 Å, b = 5.23 Å, c = 5.47 Å. This corresponds to a d 211 lattice spacing of 2.209 Å, which agrees well with the lattice spacing (2.205 Å) obtained from Bragg's law based on the reflection position.
The monoclinic phase was ruled out owing to a lack of two {111} peaks in the diffraction spectra and the (111) o and (101) t reflections being substantially offset from its expected peak position in the monoclinic phase. With regards to the indexing of tetragonal (101) t peak (Extended Data Fig. 2a), it is always reported that the tetragonal (101) t reflection has a smaller d spacing 54 in thicker HfO 2 -based films 55 , and is therefore expected to be present at a higher angle compared to the orthorhombic (111) o reflection, which is the case in the indexed diffraction spectra (Extended Data Fig. 2a), based on the result that the self-consistent indexing methodology outlined above provides.
In terms of extracting the phase fraction of the tetragonal and orthorhombic phases, although Rietveld refinement has been applied to grazing-incidence X-ray diffraction of thick (10 nm) Zr:HfO 2 56 to determine the orthorhombic phase fraction, that methodology cannot be applied in the ultrathin regime, as the films are highly oriented, as opposed to fully polycrystalline (Extended Data Fig. 2b), which is a requirement to apply Rietveld refinement.
Regarding strain effects: strain-induced ferroelectricity in antiferroelectrics is a key consideration; strain-induced ferroelectricity has been predicted in ZrO 2 23 , which is indeed what we observe in certain lateral regions of our film. From the cross-sectional TEM (Fig. 1d, Extended Data Fig. 2e, f), the presence of both the FE orthorhombic Pca2 1 phase grains and AFE P4 2 /nmc tetragonal phase grains can be locally identified to persist throughout the entire HZH thickness. Considering that the 2-nm HZH heterostructure has distinct layers (evidenced by XRR, EELS and XPS characterization in Extended Data Fig. 1), that means the middle ZrO 2 layer has local regions where it is stabilized in the FE orthorhombic phase, and other local regions where it is stabilized in the AFE tetragonal phase.
Regarding structural indicators of such strain effects, again we look to the measured d 111 (O phase) and d 101 (T phase) lattice spacings for the ~2-nm HZH film-structural markers for distortion and strain in this fluorite-structure system 13 . Note that truly stress-free values cannot be obtained because bulk ferroelectricity is not stabilized in this material system, so we compare against DFT values 22 for HfO 2 , ZrO 2 and Zr:HfO 2 (HZO) 22 , which closely match experimental values for thicker HfO 2 -ZrO 2 ferroic films 57 .
In particular, the FE O-phase d 111 -spacing for HZH (3.09 Å) is larger than typical values for thick FE HZO films (2.95 Å) 22 , demonstrating that the individual HfO 2 and ZrO 2 layers in the HZH multilayer are in fact strained, that is, have increased rhombic distortion. This is consistent with the ultrathin enhanced lattice distortions trend observed in previous ALD-grown highly oriented orthorhombic FE HZO films 13 , as well as epitaxial orthorhombic FE HZO films 58 . On the other hand, we observe that the d spacing for the tetragonal (101) reflection (2.95 Å) is nearly the same as is expected for prototypical AFE T-phase ZrO 2 (2.94 Å) 22 . This is expected: when the tetragonal phase is strained, it transitions to the lower-symmetry orthorhombic phase as opposed to remaining in the tetragonal phase, as it does not have the same tolerance of the FE O phase to maintain its symmetry when strained. Consequently, the larger d spacing is always attributed to the FE O phase 57 , as confirmed by self-consistent indexing to higher-order reflections (Extended Data Fig. 2a). These diffraction-based d spacings are confirmed by cross-sectional TEM (Extended Data Fig. 2e, f). Furthermore, the presence of the ZrO 2 layer developing ferroelectricity is supported by the presence of orbital polarization at the Zr L edge from synchrotron X-ray linear dichroism (Extended Data Fig. 2c).

X-ray absorption spectroscopy.
Hard and soft synchrotron X-ray spectroscopy (Extended Data Fig. 2c) was measured at beamline 4-ID-D of the Advanced Photon Source, Argonne National Laboratory and Beamline 4.0.2. of the Advanced Light Source, Lawrence Berkeley National Laboratory, respectively. Spectroscopy measurements were taken at the oxygen K edge (520-550 eV), zirconium M 3,2 edge (325-355 eV), hafnium M 3 edge (2,090-2,150 eV), and zirconium L 3,2 edge (2,200-2,350 eV). X-rays were incident at 20° off grazing. XAS (XLD) was obtained from the average (difference) of horizontal and vertical linearly polarized X-rays. To eliminate systematic artefacts in the signal that drift with time, spectra measured at ALS were captured with the order of polarization rotation reversed (that is, horizontal, vertical, vertical and horizontal) in successive scans, in which an elliptically polarizing undulator tuned the polarization and photon energy of the synchrotron X-ray source 59 . Spectra measured at ALS were recorded under total electron yield (TEY) mode 59 from room temperature down to 100 K. Spectra measured at APS were recorded under various modes: total electron yield (TEY), fluorescence yield (FY) and reflectivity (REF).
Ferroic phase identification from spectroscopy. X-ray spectroscopy provides various signatures to distinguish the competing FE orthorhombic (Pca2 1 ) and AFE tetragonal (P4 2 /nmc) phase. Simulated XAS spectra at the oxygen K edge (Extended Data Fig. 3d) for ZrO 2 in the various fluorite-structure polymorphs (orthorhombic Pca2 1 and tetragonal P4 2 /nmc) were computed through the Materials Project 60 open-source database for XAS spectra 61 . The T-phase (P4 2 /nmc) nonpolar distortion (D 4h , 4-fold prismatic symmetry) from regular tetrahedral (T d , full tetrahedral symmetry) fluorite-structure symmetry does not split the degenerate e-bands d d ( , ) x y z r − 3 − 2 2 2 2 , as confirmed by experiment 62 and the aforementioned XAS simulations 13 . Meanwhile, the O-phase (Pca2 1 ) polar rhombic pyramidal distortion (C 2v , 2-fold pyramidal symmetry) does split the e-manifold based on crystal field symmetry, providing a spectroscopic means to distinguish the T and O phases. The additional spectroscopic feature present between the main e and t 2 absorption features due to orthorhombic symmetrylowering distortion is illustrated by its crystal field diagram (Extended Data Fig. 3b). This provides a spectroscopic fingerprint for phase identification beyond diffraction which can often be ambiguous owing to the nearly identical T-phase and O-phase lattice parameters. For the 2-nm HZH trilayer, the experimental O K edge XAS spectra demonstrates tetrahedral and rhombic splitting features closely matching the polar O phase (Pca2 1 ) emerge slightly below room temperature, indicative of the mixed tetragonal-orthorhombic to orthorhombic phase transition upon cooling. This temperature-dependent tetragonal-orthorhombic structural evolution is expected for fluorite-structure thin films 63 and is consistent with temperature-dependent capacitance measurements (Extended Data Fig. 3f). Further XAS phase identification details are provided in previous work on ultrathin Zr:HfO 2 films 13 .
X-ray photoelectron spectroscopy. Angle-resolved photoelectron spectroscopy (ARPES) was performed using a Phi Versaprobe III at the Stanford Nano Shared Facilities (Extended Data Fig. 1d). A monochromatic aluminium source was used to give a photon energy of 1,486.6 eV. Data were fitted and analysed using CasaXPS. Angle-dependent XPS at various incident grazing angles enabled depth-resolved composition analysis to help confirm the HZH multilayer structure.
Dielectric measurements MOS capacitance. Capacitance-voltage (C-V) measurements were performed using a commercial Semiconductor Device Analyzer (Agilent B1500) with a multi-frequency capacitance measuring unit (MF-CMU). 19-μm W tips (DCP-HTR 154-001, FormFactor) made electrical contact within a commercial probe station (Cascade Microtech); voltage was applied to the W top electrode and the lightly doped Si bottom electrode was grounded. To eliminate contributions from series and parasitic resistances, frequency-dependent C-V measurements were performed. In particular, C-V data were analysed at two frequencies (100-500 kHz regime) to allow for the extraction of accurate frequency-independent C-V via a three-element circuit model consisting of the capacitor and the parasitic series and parallel resistors 64 . The frequency-independent capacitance is given by where C i and D i refer to the measured capacitance in parallel mode (C p -R p ) and dissipation values at frequencies f i . The dissipation factor is given by D = −cotθ, where θ is the phase. To maximize the accuracy of this method, it is important the dissipation factors are small (≪1) at the frequencies chosen; therefore, high frequencies were selected.
Permittivity extraction. The permittivity of Al 2 O 3 and HfO 2 dielectric layers was extracted from thickness-dependent MOS C-V measurements on lightly doped p-substrates (Extended Data Fig. 6). In the accumulation region of the MOS C-V measurements, the MOS capacitor can be modelled as three capacitors (Al 2 O 3 or HfO 2 dielectric layer, SiO 2 interlayer, and Si space charge layer) in series using the following equation where t HK is the thickness of the high-κ (Al 2 O 3 or HfO 2 ) layer, t SiO phys 2 is the physical SiO 2 thickness, and t CL is the charge-layer thickness in silicon. The physical SiO 2 thickness is constant across all the thickness series (Al 2 O 3 and HfO 2 single layers). Additionally, the capacitance values were extracted at various values of fixed charge (Q = 0 to −3 μC cm −2 ) which ensures that the charge-layer thickness is constant across all thicknesses and in the accumulation region. Therefore, the inverse capacitance at a fixed charge as a function of film thickness should result in a line and the permittivity can be extracted from the slope. This yielded extracted permittivities of 9 and 19 for the Al 2 O 3 and HfO 2 thickness series, respectively, as expected for these systems. Note that for the HfO 2 thickness series, thicknesses of 6 nm and higher were used to ensure HfO 2 stabilizes in the dielectric monoclinic phase (κ ≈ 18) 22 . Similarly, the permittivity of the HZH heterostructures was extracted from thickness-dependent MIM C-V measurements (Fig. 2b). The inverse capacitance is a linear function of the film thickness, and the permittivity can be extracted from the slope.
Electrical interlayer thickness extraction. The thickness of the SiO 2 interlayer was determined not only by TEM (Extended Data Fig. 6a), but also electrically via C-V measurements of both dielectric HfO 2 and Al 2 O 3 thickness series on SiO 2 -buffered Si (Extended Data Fig. 6f). The inverse capacitance at a fixed charge as a function of dielectric thickness should result in a line and the capacitance-equivalent thickness (CET) of the SiO 2 interlayer and Si charge layer can be extracted from the y intercept. By extracting the CET at different charge values, the Q-V relation of the SiO 2 interlayer and Si charge layer can be calculated through the following equation where V fb is the flatband voltage (Extended Data Fig. 6b, d). To confirm this methodology, another method for determining the Q-V relation of the SiO 2 interlayer and Si charge layer was extracted from the Q-V relations of both the dielectric HfO 2 and Al 2 O 3 thickness series. At a fixed charge, the corresponding voltage values of each thickness were fitted to a line and the y intercept corresponds to the voltage value for the SiO 2 interlayer and Si charge layer Q-V relation (Extended Data Fig. 6c, e). As expected, both methods lead to the same extracted Q-V relation (Extended Data Fig. 6c, e), corresponding to 8 Å EOT (Extended Data Fig. 6f)-close to the SiO 2 physical thickness of 8.5 Å obtained via TEM (Extended Data Fig. 6a)-based on technology computer-aided design simulation (TCAD) Q-V relations of different SiO 2 thicknesses on lightly doped Si.
Hysteretic C-V measurements. Capacitance-voltage (C-V) measurements on MIM capacitors were performed using a commercial semiconductor device analyser (Agilent B1500) with a multi-frequency capacitance measuring unit. 19-μm W tips (DCP-HTR 154-001, FormFactor) made electrical contact within a commercial probe station (Cascade Microtech); voltage was applied to the W top electrode, and the W bottom electrode was grounded.
Transistor transfer and output characteristics. Transistor I d -V g and I d -V d characterization of short-channel and long-channel transistors were performed using a commercial semiconductor device analyser (Agilent B1500). 19-μm W tips (DCP-HTR 154-001, FormFactor) made electrical contact within a commercial probe station (Cascade Microtech); voltage was applied to the gate and drain contacts, whereas the source and Si substrate were grounded.
Mobility extraction. The low-field transistor mobility for SOI transistors integrating ~2-nm HZH ferroic multilayers and standard high-κ HfO 2 gate stacks of the same physical thickness (Fig. 3c, Extended  Data Fig. 8c) is calculated on the basis of the channel resistance (R ch ) and inversion sheet charge density (Q inv ), which are extracted respectively from transfer characteristics (I d -V gs , Extended Data Fig. 8b; V gs , gate-to-source voltage) and from the intrinsic gate capacitance-voltage (C gg versus V gs − V fb , Extended Data Fig. 8a) measurements. Given the device aspect ratio of channel length (L) and channel width (W), we have ch gs eff gs inv gs First, the channel resistance is extracted at 50-mV drain-to-source bias (V ds ) by subtracting the parasitic resistance (R p ) from the measured drain-to-source resistance (R ds ). where R p is ascribed to the resistance of the source and the drain contacts and the n+ extension regions that are extrinsic to the channel region. When the overdrive voltage (V ov = V gs − V T , where V T is the threshold voltage) is sufficiently large, R ch is known to be inversely proportional to V ov . Therefore, R p can be extracted using a linear extrapolation of the R ds − 1/V ov relationship, which is derived from the I d -V gs (Extended Data Fig. 8b) from which V T can be characterized with the max-g m method. Second, the C gg versus V gs − V fb (Extended Data Fig. 8a) is integrated and normalized to the channel area to estimate the inversion charge.
inv gs −∞ gg gs gs gs Finally, we combine the above characterizations to obtain the effective mobility ( Fig. 3c and Extended Data Fig. 8c).
Transconductance extraction from d.c. measurements. The measured transconductance (g m = ∂I d /∂V gs ) and the output conductance (g ds = ∂I d /∂V ds ) are affected by the series resistance on the source (R s ) and the drain sides (R d ), as they reduce the voltage drops on the channel region, where V gs,i and V ds,i are the gate-to-source and the drain-to-source voltages intrinsic to the channel, respectively. R s ≈ R d ≈ R p /2 because the transistor is symmetric. R p can be extracted from the R ds − 1/V ov relationships as discussed in Methods section 'Mobility extraction'. Besides, devices with different gate length (L G ) series are fabricated on silicon-on-insulator (SOI) wafers, which enables another extraction method with R sd -L G relations. At low V d and a given V ov , Q inv and μ eff are unchanged across different L G if short-channel effects are not considerable, making R ch proportional to the channel length. Such condition is confirmed by the consistency of V T across measured L G (Extended Data Fig. 10a). Therefore, the L G offset as well as the R p can be found at the intersection of the linear relations of R sd -L G with different V ov (Extended Data Fig. 10c). The two R p extraction methods yield consistent results.
The following equation is solved to extract the intrinsic g m,i = ∂I d /∂V gs,i and g ds,i = ∂I d /∂V ds,i without the degradation due to R s and R d . where g m and g ds are measured, and R s ≈ R d ≈ R p /2 from the above-discussed characterizations. Using this methodology, the intrinsic g m,i and intrinsic g ds,i are extracted ( Fig. 3g and Extended Data Fig. 10d, e).
Transconductance extraction from radio-frequency measurements.
Next, to decouple the effect of series pad resistance and inductance of DUT, Z 2 is subtracted from Z 1 and the resulting difference is converted back to admittance parameters, Y corr : Y corr represents the de-embedded admittance parameters of the DUT. This de-embedding procedure is schematically represented in Extended Data Fig. 9a.
To extract the transconductance (g m ) from the de-embedded admittance parameters, a small-signal model of the transistor was assumed (Extended Data Fig. 9b). Under this small-signal model, the Y parameters can be written in terms of model parameters and frequency (assuming R s = R d = 0, C gg = C gs + C gd , and The transconductance (g m ) can therefore be extracted at a fixed d.c. bias via the following relation (Fig. 3h, Extended Data Fig. 9c).
Reliability. Positive-bias temperature instability (PBTI) measurements were performed on bulk nMOSFET devices integrating the ~2-nm mixed-ferroic HZH and conventional high-κ dielectric HfO 2 gate stacks at 85 °C at electric fields up to 9 MV cm −1 (Extended Data Fig. 8f, g). A measure-stress-measure (MSM) voltage scheme (Extended Data Fig. 8e) was used to apply the PBTI bias, where the drain current was measured with a minimized delay time (600 μs) at V ds = 50 mV to minimize the recovery effect 67 . The measured drain current was then converted to a ΔV T shift by comparing it to the drain current measured on the virgin device. Additionally, the time exponent, n, was extracted by noting that 67 ΔV T = At n . The extracted time exponent, n, was found to similar to those reported in literature for high-κ HfO 2 stacks 67 , which is expected considering the reliability characteristics are predominantly determined by the interfacial oxide and interfacial-high-κ interface 46 ; both stacks with different EOT have HfO 2 sitting on the same SiO 2 interfacial (Extended Data Fig. 1). Furthermore, the d.c. lifetime 67 -the stress time needed to induce a 50-mV ΔV T shift-was extracted as a function of electric field from the PBTI measurements for the HZH and HfO 2 gate stacks. Both HZH and HfO 2 show comparable rates of degradation as a function of field (Extended Data Fig. 8h), which is expected for the aforementioned reasons related to the consistent SiO 2 interfacial. Additionally, the extracted time exponent for HZH (n = 0.14, Extended Data Fig. 8f) is closer to the ideal value 67 of n = 0.16 compared to HfO 2 (n = 0.10, Extended Data Fig. 8g), indicating that there are initially a smaller number of interface traps for HZH. When field stress is applied, trap generation accelerates until the number of traps reaches a certain threshold beyond which it eventually saturates. As a result, the relative degradation is larger for HZH at smaller fields, although the absolute degradation is always slightly smaller than HfO 2 . This can also be seen directly from the extracted d.c. lifetimes (Extended Data Fig. 8h) as the d.c. lifetime is slightly better for HZH at intermediate field stresses before it becomes similar to HfO 2 at high field stresses. We again note that extracted n values are similar to what has been reported in literature for HfO 2 -based high-κ metal gate stacks 67 .
Stress measurements were also performed on lightly doped p-type MOS capacitors with the ~2-nm mixed-ferroic HZH and conventional high-κ dielectric HfO 2 gate stacks at room temperature (Extended Data Fig. 8i, j) at V g − V fb = −1 V. The stresses were applied again with a MSM voltage scheme, where the accumulation C-V was measured in between bias application at 500 kHz. The stress-induced effect was found to be minimal (Extended Data Fig. 8i, j) and no EOT degradation was observed after 10 3 s of stress at V g − V fb = −1 V (Extended Data Fig. 8i, j).

Charge boost measurements.
Pulsed charge-voltage measurements (Extended Data Fig. 7) were conducted on p-Si/SiO 2 /HZH (2 nm)/TiN/W capacitor structures to extract the energy landscape of the ferroic HZH heterostructure, following the measurement scheme detailed in previous works 26, [68][69][70] . The capacitor structures were connected to an Agilent 81150A pulse function arbitrary noise generator and the current and voltage was measured through an InfiniiVision DSOX3024A oscilloscope with 50-Ω and 1-MΩ input impedances, respectively. Short voltage pulses (500 ns) with increasing amplitudes were applied to the capacitor (Extended Dat a Fig. 7c). From the integration of the measured disch arging current, a charge versus voltage relationship was extracted (Extended Data Fig. 7d). The voltage was calculated by max(V − IR), where V is the applied voltage pulse, I is the measured current, and R is a combination of the oscilloscope resistance (50 Ω) and parasitic resistances associated with the set-up and lightly doped substrate (220 Ω). Fast voltage pulses were applied in order to minimize charge injection into the FE-dielectric interface, which could mask the observation of the negative capacitance regime 26,69 . Additionally, short voltage pulses help prevent electrical breakdown of the SiO 2 layer. The Q-V relation of the series capacitance of the SiO 2 interlayer and Si charge layer was determined via thickness-dependent C-V measurements of Al 2 O 3 and HfO 2 (Extended Data Fig. 6, Methods section 'Electrical interlayer thickness extraction'), which corresponded to 8-Å SiO 2 on lightly doped Si. The charge boost was calculated by integrating the difference between the Q-V relations of the 2-nm HZH heterostructure and the series combination of the SiO 2 interlayer and the Si charge layer (Extended Data Fig. 7e).
To determine the polarization-electric field (P-E F ) relation of just the 2-nm HZH heterostructure (Extended Data Fig. 7f), the electric field across the ferroic HZH heterostructure was calculated by subtracting the voltage across the series capacitance of the SiO 2 interlayer and Si charge layer (V d ) at a fixed charge value, where t is the thickness of the HZH heterostructure.

Modelling
Energy landscape considerations. One can write the total free energy (F) of the system as: where V is the volume, f bulk is the bulk free energy (Landau), f elas is the elastic energy density, f elec is the electrostatic energy density, and f grad is the gradient energy density. For the laterally arranged mixed FE-AFE phase present in our material, all of the above terms are important, especially the gradient terms, which are by default present owing to the mixed polar-nonpolar (FE-AFE) phase distribution. Additionally, heterogeneous elastic energies in structurally inhomogeneous systems-such as our mixed orthorhombic-tetragonal (FE-AFE) system-have been shown to destabilize long-range polarization, leading to suppressed polarization and a flattened energy landscape 28, 71 . Furthermore, considering that the polarization in our films has an in-plane component (as described in the text), this leads to an additional depolarization field on the FE grains, similar to an FE-dielectric heterostructure (albeit in the in-plane direction). At low electric fields, the mixed FE-AFE behaviour is analogous to an FE-dielectric (polar-nonpolar) heterostructure-owing to the nonpolar parent structure of fluorite-structure antiferroelectricity-which has been shown to impart depolarization fields on the FE layer 25,72 . The laterally intertwined nonpolar-polar phases present in the ultrathin HZH heterostructure are conducive to flattening the FE energy landscape through the aforementioned depolarization fields 26-28 (Fig. 1a).
Overall, the above contributions all lead to a suppression of the bulk polarization via depolarization fields. As it has been shown 26-28 , the depolarization field essentially flattens the bulk energy landscape for the FE (E d ∝ −P, hence ⋅ >0 E P ) and leads to a permittivity enhancement (ε ∝ (∂ 2 F/∂D 2 ) −1 ). Depolarization field-induced flattening of the energy landscape is also the underlying physics of the negative capacitance effect 26,27,29,30,49 .
Technology computer-aided design simulations. The measured C-V curves are calibrated to Sentuarus technology computer-aided design simulations (TCAD) device simulator which solves the electrostatics, electron and hole transport, and the quantum confinement effect self-consistently 73 . MOS capacitors with 10 15 cm −3 p-type substrate doping and planar SOI MOSFETs are simulated with finite-element methods. The EOT and the metal work function (φ m ) are the only two parameters that are fit to the MOS capacitor measurement results, yet the slope of the accumulation capacitance can be successfully captured by the model (Fig. 2f, Extended Data Fig. 6). Similarly, the intrinsic C gg versus V gs − V fb extracted from SOI transistors can be successfully model by the TCAD model with appropriate EOT and φ m (Extended Data Fig. 8a).

Atomic-scale HZH mixed-ferroic heterostructure
Thickness limits and atomic-scale heterostructures. Recent perspectives on HfO 2 -based ferroelectricity for device applications 9,74-77 posed the technological challenges stemming from thickness limit concerns of HfO 2 -based ferroelectricity, and thereby, negative capacitance. The use of short-period superlattices, that is, nanolaminates, is common in the high-κ field to enhance permittivity [78][79][80][81][82] ; in particular, rutile-structure TiO 2 is often paired with fluorite-structure HfO 2 and/ or ZrO 2 in dynamic random-access memory (DRAM) capacitors 83 . Recently, fluorite-structure nanolaminates were used to tune the FE behaviour of HZH films [84][85][86] . However, all of these works have studied nanolaminates with thick periodicity, going as thin as 10 ALD cycles (~1.1 nm) per superlattice sublayer 84 . In this work, we scale down to a much thinner thickness limit while still maintaining physical separation of the individual layers (Extended Data Fig. 1). The reasoning behind using a short-period superlattice structure to scale down the ferroic behaviour of HZH rather than simply thinning down a solid solution stems from the notorious thickness-dependent FE behaviour in Zr:HfO 2 at fixed composition 38,57,63 . Here, the use of nanolaminated structures can help provide thickness-independent scaling of ferroic order, as has been previously demonstrated to overcome the upper thickness limit of HfO 2 -based ferroelectricity 86 . The persistence of high capacitance for these 2-nm films is notable considering that other high-κ dielectric systems suffer from considerable permittivity degradation in the thin film (sub-10 nm) regime, particularly TiO 2 -and SrTiO 3 -based oxides 83,87 . Sustaining the mixed ferroic order underlying negative capacitance to the 2-nm regime is extremely relevant for advanced technology nodes 88 which budget only ~2 nm for the oxide layer.
Iso-structural polycrystalline multilayer. Previous attempts to heterostructure FE Zr:HfO 2 with dielectric Al 2 O 3 26,69,70 failed to demonstrate capacitance enhancement, which was attributed to the fixed charges at the FE-dielectric interface. These charges can screen the FE polarization, pushing the stable point of the energy well to one the minimum points, and thereby preventing stabilization of negative capacitance regime via depolarization fields from the dielectric. Here, the use of iso-structural HZH to serve as both the nonpolar (AFE) and polar (FE) layers and leveraging the high (low) onset crystallization temperature of HfO 2 (ZrO 2 ) on Si 50 , enables interfaces with diminished defects, allowing for the polar layer to experience the depolarization fields and stabilize in the 'forbidden' negative capacitance regime. Regarding the polycrystalline nature of the ultrathin multilayers, it has been experimentally 48 and theoretically 89 established that negative capacitance can be stabilized in the presence of FE domains, as recently reviewed 76 .

Data availability
The experimental data contained in the manuscript are available for download at https://doi.org/10.5281/zenodo.5797030. Fig. 2 | Ferroic phase insights from structural characterization. a, Left, in-plane synchrotron grazing-incidence diffraction (IP-GiD) of a bare 2-nm HZH trilayer indexed to the tetragonal P4 2 /nmc and orthorhombic Pca2 1 phases. Right, magnification of the spectrum about the orthorhombic (111) o and tetragonal (101) t reflections, confirming the co-existing structural polymorphs in the 2-nm film. These two peaks were differentiated via self-consistent indexing of the entire spectrum, in which interplanar lattice spacings-determined from the {200} o family of reflections-closely match the d spacings for all other reflections-(111) o , (120) o , (211) o , (202) o -determined by Bragg's law (Methods). b, Two-dimensional reciprocal space map of the bare 2-nm HZH trilayer, indexed by integrating the diffraction spectrum. The lack of fully polycrystalline rings illustrates that the 2-nm HZH trilayer is highly oriented, consistent with TEM imaging. c, Synchrotron spectroscopy (XAS) of the bare 2-nm HZH trilayer at the Hf M 3 edge (left) and Zr L 3,2 edge (centre); right, the presence of linear dichroism (orbital polarization) provides further evidence of symmetry-breaking in these oriented thin films. d, Second harmonic generation (SHG) mapped across the bare 2-nm HZH trilayer; the presence of SHG intensity confirms broken inversion symmetry in these ultrathin ferroic films. e, f, Additional cross-sectional TEM providing complementary evidence of the tetragonal P4 2 /nmc (e) and orthorhombic Pca2 1 (f) phases, in which the extracted (101) t lattice spacing (~2.95 Å) and (111) o lattice spacing (~3.08 Å) extracted from IP-GiD are consistent with the average lattice spacings extracted from the periodicity of the TEM-imaged planes. The white scale bars in all the TEM images represent 1 nm. Fig. 3 | Ferroic phase insights: proximity to temperaturedependent phase transition. a, Schematic of temperature-dependent AFE-FE phase evolution in fluorite-structure oxides. At lower temperatures, the higher symmetry tetragonal phase is expected to transition to the lower symmetry orthorhombic phase. b, Schematic crystal field splitting diagram for fluoritestructure polymorphs; the symmetry-induced e-splitting (rhombic distortion, ∆ R ), besides the typical t 2 -e splitting (tetrahedral distortion, ∆ T ) present in all fluorite-structure phases, provides a spectroscopic signature for the polar O phase (Methods). c, Temperature-dependent XAS at the oxygen K edge for a 2-nm HZH bare film demonstrating clearer spectroscopic signatures of the FE O phase emerge slightly below room temperature.d, Simulated oxygen K-edge XAS spectra (Materials Project) for the respective O and T phases. XAS provides spectroscopic signatures to distinguish between the O and T phases (difficult to resolve from GI-XRD). e, Prototypical C-V behaviour for mixed AFE-FE (shoulder-like features in addition to the characteristic butterfly-like shape) and FE films (just butterfly-like) in MIM capacitor structures. f, Temperaturedependent C-V for thicker HZH multilayers of the same periodicity (in MIM capacitor structure) demonstrating an evolution from mixed-ferroic to FE-like hysteresis upon cooling slightly below room temperature. Thinner HZH multilayers films suffer from leakage limitations, preventing such hysteretic C-V measurements. The thicker HZH multilayers of the same periodicityannealed at the same low-temperature condition to maintain the multilayer structure-demonstrate a similar mixed ferroic to FE phase transition slightly below room temperature as the thinner 2-nm multilayer (c).

Extended Data
HZH superlattice (60% Zr) compared to solid-solution films of the same thickness (6 nm) and composition (60% Zr), as well as solid-solution films of the same thickness and higher Zr composition (67%-100% Zr). Hf:ZrO 2 solid-solution films with higher Zr content (60%-75%) are around the range attributed to the 'MPB' in thicker Hf:ZrO 2 alloys 35,55,90-93 . These results indicate that the capacitance enhancement in multilayer films is not simply driven by Zr content 32,38,57,63 , but instead the atomic-scale stacking, as the solid-solution films with subatomic superlattice period do not demonstrate the same mixed-ferroic behaviour and enhanced capacitance as the superlattices. Fig. 5 | Solid solutions versus superlattice structure: role of annealing temperature. a, Schematic of HfO 2 -ZrO 2 multilayer and Hf:ZrO 2 solid-solution films. Under a high-temperature anneal, the multilayer structure transitions towards a Hf:ZrO 2 solid-solution-like structure demonstrating more FE-like behaviour. The solid-solution state yields diminished capacitance owing to the lack of both the higher-permittivity AFE phase and the mixed-ferroic-induced capacitance enhancement (Fig. 1a). b, Comparison of MOS capacitor accumulation C-V characteristics in HZH multilayers, where the superstructure was repeated (left) one, (centre) two, or (right) three times, under both low-and high-temperature anneals. c, Comparison of mixed-ferroic behaviour in low-temperature treated MIM HZH multilayers versus FE behaviour in the same multilayers annealed at high temperatures, where the superstructure was repeated (left) three, (centre) four, or (right) five times. In all instances, the high-temperature anneal (>500 °C) results in diminished accumulation capacitance compared to the low-temperature anneals, as the multilayered mixed-ferroic films presumably transition to more FE-like solid-solution alloys.