Antiferroelectric negative capacitance from a structural phase transition in zirconia

Crystalline materials with broken inversion symmetry can exhibit a spontaneous electric polarization, which originates from a microscopic electric dipole moment. Long-range polar or anti-polar order of such permanent dipoles gives rise to ferroelectricity or antiferroelectricity, respectively. However, the recently discovered antiferroelectrics of fluorite structure (HfO2 and ZrO2) are different: A non-polar phase transforms into a polar phase by spontaneous inversion symmetry breaking upon the application of an electric field. Here, we show that this structural transition in antiferroelectric ZrO2 gives rise to a negative capacitance, which is promising for overcoming the fundamental limits of energy efficiency in electronics. Our findings provide insight into the thermodynamically forbidden region of the antiferroelectric transition in ZrO2 and extend the concept of negative capacitance beyond ferroelectricity. This shows that negative capacitance is a more general phenomenon than previously thought and can be expected in a much broader range of materials exhibiting structural phase transitions.

A ntiferroelectric materials are promising for diverse applications ranging from energy harvesting 1 and solid state cooling devices 2 over electromechanical transducers 3 to energy storage supercapacitors 4,5 . First predicted in 1951 6 , antiferroelectricity was subsequently discovered in the archetypal perovskite oxide, lead zirconate (PbZrO 3 ) 7,8 . Ever since, the range of materials has been expanded to two-dimensional hybrid perovskites 9 , interfacially engineered heterostructures and superlattices 10 , fluorite structure binary oxides 11,12 , and more have been predicted by first principles calculations 13,14 . However, compared to their ferroelectric counterparts, antiferroelectrics have remained less explored and understood so far, despite their intriguing properties and rich phase transition phenomena [14][15][16] . Therefore, antiferroelectric materials hold a large untapped potential for the discovery of emergent phases for example in antiferroelectric oxide heterostructures, which have been investigated in this work.
Antiferroelectricity is characterized by a distinctive, double hysteresis loop in the macroscopic electric polarization P vs. electric field E a characteristics as shown in Fig. 1a based on a Kittel-model (see Supplementary Methods) 6 . From a thermodynamic perspective, such a macroscopic response can be described by a free energy (G)-polarization landscape as shown in Fig. 1b for E a = 0, where the only stable state is the macroscopically non-polar ground state (A) at P = 0. However, when an electric field E a = E 1 is applied, see Fig. 1c, an energy barrier emerges between the non-polar state M and the polar state N. This forbidden region of negative free energy curvature (d 2 G/ dP 2 < 0) between points B and C is thermodynamically unstable 6,15 . Note that the relative energies of the non-polar and polar states in Fig. 1c, d are dependent upon the antiferroelectric material and also the magnitude of the electric field, i.e. the polar phase will become lower in energy than the non-polar phase for even higher applied fields. According to theory, the non-linear permittivity and thus capacitance of a material is proportional to (d 2 G/dP 2 ) −1 , which means that at the antiferroelectric transition the capacitance of the material would become negative if stabilized in a larger system 17,18 . Note that we always mean "negative differential capacitance" when we write "negative capacitance" in this context. Due to the inversion symmetry of the non-polar ground state, the same transition occurs when an opposite electric field E a = −E 1 is applied, see Fig. 1d. Therefore, two separate and symmetric regions of negative capacitance can be predicted at the antiferroelectric non-polar to polar phase transition as shown by the dotted lines in Fig. 1a where dP/dE a < 0.
Similar 'S'-shaped P-E curves have been derived from the Landau-Ginzburg-Devonshire theory of ferroelectric phase transitions many decades ago but were previously understood to be inaccessible to experiments due to their unstable nature 19 . Only recently, it was suggested that one could access these forbidden thermodynamic regions in ferroelectric/dielectric heterostructures using pulsed electrical measurements 20,21 . In such a structure, the positive capacitance of the dielectric layer can stabilize the region of negative capacitance and prevent the screening of bound polarization charge by free electrons in the metal electrodes. Here, we apply a similar approach to first probe the inaccessible region of a non-polar to polar structural phase transition in an antiferroelectric oxide. While experimental insights into such thermodynamic instabilities are of fundamental interest to materials science, they are also useful for prospective applications since the resulting negative capacitance can be used to amplify voltage signals in electronic devices and circuits 18,22 .
Historically, antiferroelectricity has been related to the antipolar alignment of microscopic electric dipoles in the unit cell 6 . For example, in the ground state of antiferroelectric PbZrO 3 , two adjacent columns of Pb ions point in the same direction, while the forbidden forbidden unstable (C < 0) a b c d Fig. 1 Origin of antiferroelectric negative capacitance. a The polarization P-electric field E a characteristics of an antiferroelectric material. The segment BAB' corresponds to the non-polar, antiferroelectric ground state, and segments CD and C'D' correspond to the polar phase. Segments BC and B'C' represent the unstable negative capacitance (C < 0) regions. At Ea = E 1 , the antiferroelectric has two stable states: M and N. b-d The antiferroelectric free energy landscape at E a = 0 (b), E 1 (c) and −E 1 (d). d 2 G/dP 2 < 0 in the P-range corresponding to BC and B'C 'forbidden' regions.
next two columns have antiparallel alignment 7 . The application of a sufficiently large electric field then leads to a spontaneous alignment of the anti-parallel dipoles resulting in a transition to a polar ferroelectric state 23 . In a similar way, first principles calculations of ferroelectric/paraelectric heterostructures have predicted antiferroelectric-like negative capacitance regions due to the transition between a striped domain pattern and a ferroelectric monodomain state 24 . In contrast, the newly discovered HfO 2 and ZrO 2 based antiferroelectrics of fluorite structure transcend the classical definition of antiferroelectricity 11,12 , since their ground state does not exhibit anti-polar order but is microscopically non-polar 25 . Therefore, the original Kittel-model in Fig. 1a might not give a precise microscopic picture of antiferroelectricity in fluorite structure oxides and thus cannot explain the results quantitatively. However, the qualitative prediction of a negative capacitance from the non-polar to polar phase transition still applies. Note that this is fundamentally different from previous investigations in ferroelectrics, where no phase transition or change of symmetry occurs in the forbidden region of the energy landscape 21 .
Here, we investigate this unique type of non-polar to polar antiferroelectric transition in ZrO 2 as a model system, which is of significant technological importance due to its compatibility with semiconductor manufacturing and thickness scalability to the nanometer regime 12 . Additionally, no doping of ZrO 2 is needed to induce antiferroelectricity in contrast to HfO 2 based thin films 11,26 . At room temperature, the stable bulk phase of ZrO 2 is the non-polar monoclinic P2 1 /c phase, which can be suppressed in thin films of around 10 nm thickness and below, which favor the non-polar tetragonal P4 2 /nmc phase 12 . The current understanding of the origin of antiferroelectricity in ZrO 2 is that the non-polar tetragonal P4 2 /nmc phase undergoes a first-order structural phase transition into the polar orthorhombic Pca2 1 phase by application of an electric field of around 2-3 MV cm −1 25,26 . The polar orthorhombic Pca2 1 phase has been shown to be responsible for the ferroelectric behavior observed in HfO 2 based thin films 27 . While obtaining definitive experimental proof of such a fieldinduced first-order phase transition has proved difficult so far 28 , this mechanism is consistent with first principles calculations 25,29 as well as composition-and temperature-dependent experimental results 26 . While the microscopic switching pathway between the P4 2 /nmc and Pca2 1 phases is still unclear, it has been suggested to include an intermediate phase of orthorhombic Pmn2 1 symmetry for Hf 0.5 Zr 0.5 O 2 30 .

Results and discussion
Characterization of antiferroelectricity in ZrO 2 . For basic antiferroelectric characterization, TiN/ZrO 2 /TiN capacitors were fabricated as described in methods. Grazing incidence X-ray diffraction (GIXRD) measurement results presented in Supplementary Fig. 1 confirm that the crystalline ZrO 2 layer is in the non-polar tetragonal P4 2 /nmc phase in the as fabricated capacitors. Figure 2a and Supplementary Fig. 2a show the antiferroelectric double hysteresis loops in the polarization-electric field characteristics for a 10 nm and 5 nm ZrO 2 layer, respectively, measured using a ferroelectric tester. Since the structural data suggests that our ZrO 2 films are fully tetragonal without applied voltage, the measured double hysteresis loops can only be explained by a field-induced structural transformation into a polar ferroelectric phase. While we cannot directly determine the symmetry of this polar phase at high electric field, there is substantial evidence in literature which suggests that it is of orthorhombic Pca2 1 symmetry 26 . For example, a temperaturedependent phase transition from the non-polar P4 2 /nmc phase to the polar Pca2 1 phase in similar ZrO 2 thin films has been experimentally observed with in situ high-temperature X-ray diffraction 31 . Furthermore, ZrO 2 can be stabilized in the Pca2 1 phase even at room temperature under certain processing conditions 32 . Lastly, the field-induced transition from the P4 2 / nmc phase to the Pca2 1 phase has been directly observed in Hf 0.5 Zr 0.5 O 2 thin films 33 . From these experimental data and previous first principles calculations 25,29 , it seems reasonable to conclude that the polar phase observed at high electric field in Fig. 2a is of Pca2 1 symmetry. Furthermore, using high-resolution transmission electron microscopy (HRTEM) with in situ voltage biasing, it was directly shown that antiferroelectric ZrO 2 always returns to its initial non-polar P4 2 /nmc structure after the applied voltage is removed 28 . Since the ZrO 2 film investigated in ref. 28 was fabricated in the exact same way as the ones shown here, it is reasonable to assume that they also return to the initial non-polar P4 2 /nmc phase after each field-induced phase transition.
Antiferroelectric/dielectric heterostructures. However, as expected for a single layer antiferroelectric capacitor in Fig. 2a, the 'forbidden' regions (see Fig. 1) of the structural transition to the polar phase cannot be observed electrically due to their unstable nature. To access these unstable regions, a positive series capacitance can be used in the form of a dielectric layer in contact with the antiferroelectric 18,20,21 . The dielectric layer has two important functions: It prevents the injection of compensating charge which could screen the bound polarization P and it creates a depolarization field in the antiferroelectric which is antiparallel to P, such that E a can decrease while P is increasing. When the antiferroelectric enters the unstable region in such a heterostructure, the resulting negative capacitance would then increase the total capacitance of the dielectric/antiferroelectric stack beyond than that of the dielectric layer alone. Such a capacitance enhancement would thus be a clear signature of the structural transition itself. To test this prediction, we fabricated heterostructure capacitors consisting of the same ZrO 2 layer and a stack of Al 2 O 3 /HfO 2 dielectrics with TiN used as top and bottom electrodes using atomic layer deposition as described in methods. The intermediate Al 2 O 3 layer was introduced to prevent the crystallization of the top HfO 2 layer due to templating effects from the underlying crystallized ZrO 2 . Scanning transmission electron microscopy (STEM) analysis of a representative TiN/ ZrO 2 /Al 2 O 3 /HfO 2 /TiN heterostructure in Fig. 2b confirms that the ZrO 2 layer was stabilized in its non-polar tetragonal phase while the HfO 2 layer remained amorphous. The combined results of our GIXRD measurements together with STEM and nanobeam electron diffraction data (see Supplementary Fig. 3) present strong evidence for a fully non-polar tetragonal ground state of the ZrO 2 layer. As mentioned before, previous in situ HRTEM experiments showed that these ZrO 2 layers always return to their initial non-polar ground state after the applied voltage is removed 28 .
Pulsed electrical characterization. To probe the capacitance of the heterostructure under high applied fields, we adopt a pulsed capacitance measurement technique 20,34 . We apply microsecond voltage pulses and the charge supplied by the voltage source is directly measured by integrating the measured current. Details are described in methods. Note that standard small-signal capacitance-voltage measurements are too slow at the high applied voltages needed, leading to significant charge injection or dielectric breakdown. In contrast, pulsed capacitance measurements can mitigate this, if the pulse duration is shorter (∼1 μs in our experiments) than the time scale for charge injection, breakdown and related mechanisms 20 . Figure 3a shows the experimental setup in which voltage pulses V in (t) (t ≡ time) of T = 1.1 μs duration, different amplitudes V a were applied to the capacitors in series to an external resistor R. Waveforms of V in , measured current I, and integrated charge (=∫Idt) for different amplitudes V a for a HfO 2 (8 nm)/Al 2 O 3 (∼1 nm)/ZrO 2 (10 nm) capacitor are shown in Fig. 3b. For a given V a , Q max is the total charge supplied by the voltage source (i.e., , and accounts for charge injection and leakage. The difference between Q max and Q res is defined as ΔQ, which is the actual amount of charge that is reversibly delivered to and discharged from the capacitor and determines the differential capacitance of the heterostructure as C DE-AFE = ΔQ/ ΔV a . Figure 3c plots Q max , Q res and ΔQ (calculated from Fig. 3b: panel 3) as functions of V a . We note in Fig. 3c for positive V a that Q res is zero, and ΔQ = Q max as expected in the absence of charge injection and leakage for a purely capacitive load. The slope of the ΔQ − V a curve for V a ≥ 10 V (YZ segment) is larger than the capacitance of the constituent dielectric stack C DE which is shown as a slope in Fig. 3c and was measured on a separate HfO 2 (8 nm)/ Al 2 O 3 (∼1 nm) capacitor fabricated under the same processing conditions (see Supplementary Fig. 4). For large negative values of V a , Q res has a non-zero value; however, accounting for the corresponding charge injection and leakage, a similar capacitance enhancement is observed for V a < −9.2 V (Y'Z' segment).
From the inversion symmetry of the measured ΔQ−V a curves in Fig. 3c despite the asymmetric Q res -V a behavior one can conclude that the capacitive behavior is unaffected by leakage currents or charge injection. Furthermore, a symmetric ΔQ-V a curve is expected only for an ideal antiferroelectric/dielectric stack with negligible trapped charges at the interface between both layers. This contrasts with recent reports of similar ferroelectric/dielectric capacitors, where large negative trapped charge densities (comparable to the spontaneous polarization) were found at the interface 20,21 . This indicates that the initial ferroelectric polarization during fabrication in such stacks causes the trapping of charges at the interface, which is not the case for the antiferroelectric heterostructure due to the non-polar antiferroelectric ground state. Therefore, having a nonpolar ground state seems beneficial for avoiding trapped interface charges, which can be detrimental when building negative capacitance devices.
Extracting negative capacitance and energy landscape. For a given V a , the electric field in the antiferroelectric layer E a can be calculated as E a = (V a − V DE )/t AFE , where t AFE is the ZrO 2 thickness and V DE = ΔQ(V a )/C DE (see Methods for details). The corresponding P − E a curve (P = ΔQ/A with A being the area of the capacitor) of the ZrO 2 layer in Fig. 3d shows two separate regions of negative slope (i.e. negative capacitance) which correspond to the capacitance enhancement regions in the ΔQ − V a curve in Fig. 3c. For comparison, the P-E a characteristics of an equivalent, single-layer ZrO 2 capacitor measured using a ferroelectric tester is also plotted in Fig. 3d. The locations of the negative capacitance regions in Fig. 3d coincide with the two hysteresis regions of the polarization-electric field characteristics of the stand-alone ZrO 2 layer, in agreement with the theoretical prediction (Fig. 1a). However, the second positive capacitance branch expected at higher fields is often not observed in experiments, since hard dielectric breakdown of the dielectric layers occurs at these high electric fields. Nevertheless, we were able to observe the second positive capacitance branch in some samples that showed a slightly higher than average breakdown field strength as can be seen in the Supplementary Fig. 9. Furthermore, in Supplementary Fig. 12 we incrementally changed the voltage pulse amplitude from 0 V → 11 V → −11 V → 0 V to investigate the reversibility of the P-E a curve. An asymmetric hysteresis emerges which seems to correlate with the observation of significant Q res for negative voltages in Fig. 3c. This suggests that the hysteresis is not related to the non-polar to polar phase transition itself, but that it is caused by leakage and subsequent charge trapping of a fraction of Q res at the antiferroelectric/dielectric interface, which leads to a shift of the apparent P-E a curve. For positive voltages, where Q res is low, negative capacitance is observed in both forward and backwards sweep directions in Supplementary Fig. 12.
By integrating the P-E a curve, one obtains the antiferroelectric energy landscape (G(P) = ∫E a dP) which is shown in Fig. 3e, where the normally forbidden regions (G′′ < 0) of thermodynamic instability at the non-polar to polar structural phase transition can be accessed in the antiferroelectric/dielectric heterostructure. It is interesting to note here, that previous first principles calculations for the antiferroelectric transition in ZrO 2 found that G" is always positive along the direct switching pathway between the P4 2 /nmc and Pca2 1 phase, corresponding to a cusp in the energy landscape 25 . This is in contrast to our experimental findings, where negative G" regions are clearly observed (see Fig. 3e). However, recent first principles calculations have shown that there could be other switching pathways between the P4 2 / nmc and Pca2 1 phase, which can avoid the cusp in the energy landscape by traversing through an intermediate orthorhombic Pmn2 1 phase 30 . Therefore, our findings provide the first indirect experimental evidence that such an alternative switching pathway might exist in antiferroelectric ZrO 2 . Effect of dielectric layer thickness. Next, we changed the HfO 2 thickness to 5 nm, 6 nm and 10 nm while keeping Al 2 O 3 and ZrO 2 layer thicknesses constant (∼1 nm and 10 nm, respectively). For all different HfO 2 thicknesses, the extracted P − E a characteristics of the ZrO 2 layer have the same quantitative shape as shown in Supplementary Fig. 5-7. We further observed in Fig. 4a that the capacitance enhancement (r = C DE-AFE /C DE > 1) in these samples obeys the ideal capacitance matching equation r= |C AFE | /( | C AFE | − C DE ) with a best fit antiferroelectric negative capacitance C AFE°= −4.75 μF cm −2 , extracted at the polarization value of P = 16 µC cm −2 for all samples. Figure 4b shows the inverse total capacitance (C DE-AFE ) at P = 16 µC cm −2 as a function of the inverse dielectric capacitance (C DE ) with and excellent linear fit (R 2 = 0.9986). Two important conclusions can be drawn from Fig. 4. First, the negative intercept for 1/C DE = 0 and the consistent capacitance enhancement shows that the ZrO 2 capacitance must indeed be negative for all samples. Second, the ZrO 2 and Al 2 O 3 /HfO 2 layers do act as expected for two capacitors in series, i.e., the antiferroelectric negative capacitance is independent of the thickness of the HfO 2 layer. Previous results for multi-domain ferroelectric/dielectric superlattices showed a similar behavior 35 . However, theory suggests that multi-domain ferroelectric negative capacitance can strongly depend on the domain configuration and lateral domain wall motion in the ferroelectric and thus changes, e.g. with the ferroelectric film thickness [36][37][38][39] . On the other hand, the constant C AFE < 0 of our antiferroelectric ZrO 2 films with both HfO 2 and ZrO 2 thickness (see also Supplementary Fig. 8) indicates that it is an intrinsic property of the non-polar to polar structural transition. This suggests that antiferroelectricity in ZrO 2 is indeed caused by a local field-induced inversion symmetry breaking of the unit cell. Our findings do not support the recently proposed Negative capacitance transistor simulations. Finally, we simulated an antiferroelectric negative capacitance field-effect transistor (NCFET) based on our experimental results to investigate what performance improvements might be expected compared to current device technologies. The details can be found in the Supplementary Methods. We find that the antiferroelectric NCFET outperforms the reference device in terms of speed while at the same time consuming 41% less power at almost half the power supply voltage (see Supplementary Fig. 13 and Supplementary Table 1). These results support previous suggestions that antiferroelectrics are indeed promising for ultra-low power electronic devices 42 . Especially since ZrO 2 is already used as the capacitor dielectric in current dynamic random access memory technologies, which has been demonstrated to also be antiferroelectric 43 .
In summary, we have explored the forbidden thermodynamic region of the non-polar to polar antiferroelectric transition in ZrO 2 using pulsed electrical measurements. In contrast to previous reports in multi-domain ferroelectrics, we report a different type of antiferroelectric negative capacitance which seems to be an intrinsic property of the structural instability at the boundary between P4 2 /nmc and Pca2 1 phases in fluorite-type oxides. This is of great interest for applications in energy-efficient electronics since mixtures of these phases have been reported in the widely used HfO 2 and ZrO 2 based ultrathin films, which are present in most semiconductor products today. The observation of negative capacitance in ZrO 2 indicates that the switching pathway between the P4 2 /nmc and Pca2 1 might include an intermediate saddle phase of different symmetry. Furthermore, our findings suggest that the phenomenon of negative capacitance is not limited to polar ferroelectric order but can be expected at any transition with a polarization instability. This includes phase transitions between non-polar and polar phases as shown here, but which should also include transitions between different polar phases or even between different non-polar phases 44 . This opens up opportunities for characterizing structural phase transitions and for building negative capacitance devices from a much broader range of possible materials.

Methods
Sample fabrication. The atomic layer deposition (ALD) of ZrO 2 and bottom TiN layers were conducted in a 300 mm Tokyo Electron thin film formation tool. The ZrO 2 and TiN films were deposited by ALD at 350°C and~430°C respectively by previously described processes 45 . The as-grown ZrO 2 layer was amorphous. With regards to the thickness of ZrO 2 in the ZrO 2 /TiN heterostructure of these samples, there were two differently processed stacks: ZrO 2 /TiN with 10 nm ZrO 2 and 5 nm ZrO 2 , respectively. A post-ZrO 2 deposition annealing was performed on both stacks at 450°C for 30 s in nitrogen atmosphere to stabilize the ZrO 2 layer in the antiferroelectric tetragonal phase. The ZrO 2 /TiN heterostructure was cleaned in standard clean-2 (SC-2) solution. Afterwards, HfO 2 (6, 8, 10 nm)/Al 2 O 3 (~1 nm) heterostructure was deposited on the ZrO 2 /TiN heterostructure in a Cambridge NanoTech Fiji G2 Plasma Enhanced ALD (PEALD) system at Georgia Tech. Subsequently, a top TiN layer was deposited without breaking the vacuum in the same ALD reactor. The deposition was carried out at 250°C using tetrakis (dimethylamido) hafnium, tetrakis (dimethylamido) aluminum and tetrakis (dimethylamido) titanium precursors for HfO 2 , Al 2 O 3 and TiN, respectively. For oxides, water was used as the oxygen source and for TiN, nitrogen (plasma) was used as the nitride source. After the ALD of TiN/HfO 2 /Al 2 O 3 /ZrO 2 /TiN and TiN/ HfO 2 /ZrO 2 /TiN heterostructures, Al (~100 nm) was evaporated and patterned into rectangular electrodes using standard microfabrication techniques. Top TiN layer was wet etched afterwards in H 2 O 2 :H 2 O solution at 50°C using the patterned Al layer as a hard mask.
Electrical characterization. Electrical measurements were conducted on a Cascade Microtech Summit 1200 K Semi-automated Probe Station. Polarization versus electric field curves were measured using an aixACCT TF-3000 ferroelectric parameter analyzer at 1 kHz with dynamic leakage current compensation (DLCC) turned off. The capacitance versus electric field curves were measured by a Keysight E4990A impedance analyzer with a small-signal amplitude of 25 mV and a frequency of 100 kHz. The pulsed measurements on dielectric/antiferroelectric heterostructure capacitors were conducted using a Keysight 81150 A Pulse Function Arbitrary Noise Generator and a Keysight DSOS104A Oscilloscope. The series resistor had a resistance of R = 5.6 kΩ.
Structural characterization. X-ray diffraction (XRD) measurements were performed using SmartLab diffractometer (Rigaku) equipped with 9 kW cooper rotating anode X-ray source (wavelength CuKα = 0.15418 nm). A standard coplanar diffraction geometry with constant angle of incidence (grazing incidence X-ray diffraction: GIXRD) was used for the studies. To perform the GIXRD measurements the diffractometer was equipped with a parabolic multilayered X-ray mirror and a set of axial divergence eliminating soller slits with divergence of 5°in incident and diffracted beam, and parallel plate collimator with acceptance of 0.5°i n diffracted beam. Diffracted intensity was acquired with hybrid-pixel single photon counting 2D detector HyPix 3000. The incidence angle of the X-rays, with respect to the sample surface, was set up slightly above the critical angle of investigated material, ω = 0.6°. Measured diffraction data were fitted using whole powder pattern procedure -Rietveld method. A computer program MStruct was used for the fitting. The investigated samples contain tetragonal ZrO 2 phase (space group P4 2 /nmc, #137). Some minor fractions of other ZrO 2 phases might be present, but in fractions below the detection limit of GIXRD. Scanning transmission electron microscopy (STEM) imaging was performed using a Hitachi aberration corrected STEM HD2700 operating at 200 kV at Georgia Tech. The convergent angle is 35 mrad, and the inner angle of the annular dark field (ADF) detector is 50 mrad. Nano beam electron diffraction (NBED) was performed using a FEI transmission electron microscope (TEM) Technai F30 working at 300 kV. The determination of the phase of ZrO 2 was accomplished by analyzing the NBED patterns.
Extraction of P-E a characteristics from pulsed measurements. Voltage pulses V in of duration T = 1.1 µs with different amplitudes were applied, and the voltage across the dielectric/antiferroelectric capacitor, V DE-AFE and V in were measured using an oscilloscope. The input pulse amplitude V in was changed in 200 mV steps to span the full P-E a curves. At a given applied voltage amplitude V a , voltages across the dielectric layers and the antiferroelectric layer was calculated as V DE = ΔQ/C DE and V AFE = V a -V DE , respectively. For each of the dielectric/antiferroelectric samples, an equivalent dielectric only stack with the same thicknesses of HfO 2 and Al 2 O 3 (~1 nm) layers was deposited under the same process conditions to measure C DE independently (measurements shown in Supplementary  Fig. 4). Figure 3d as well as Supplementary Fig. 5, 6c, 7c and Fig. 8a show the polarization P = ΔQ/A as a function of the extracted electric field in the antiferroelectric E a = V AFE /t a where A and t a are the capacitor area and the ZrO 2 thickness. The details of the calculations are provided below.
The voltage V in applied to the system can be written as with where V DE-AFE , V DE , and V AFE are the voltages across the entire dielectric/ antiferroelectric heterostructure, dielectric combo, and antiferroelectric layer, respectively. The current I(t) flowing through the resistor R in series with the dielectric/antiferroelectric heterostructure is calculated from measured V in (t) and V DE-AFE (t) waveforms. The amount of charge Q on the heterostructure capacitor is calculated by where C para is the parasitic capacitance that appears in parallel to the dielectric/ antiferroelectric capacitor, which was experimentally determined as~20 pF. Three important charges are extracted for each value of V a : the maximum stored charge on the capacitor, Q max = Q(t=T), the residual charge on the capacitor after the applied voltage is zero again, Q res = Q(t=5 µs»T), and the charge that is reversibly stored and released from the capacitor, ΔQ = Q max − Q res . The electric field E a in the antiferroelectric layer can be calculated by where ΔQ is the amount of charges reversed and C DE is the capacitance of the dielectric layer. The relative permittivity ε r of the dielectric layers was extracted from capacitance versus voltage measurements on samples fabricated without the antiferroelectric layer (see Supplementary Fig. 4). The polarization of the antiferroelectric layer was calculated as where A is the area of the dielectric/antiferroelectric capacitor. Using Eqs. (4) and (5), the antiferroelectric P versus E a curve can be calculated. The experimental free energy density G can be obtained from Reporting summary. Further information on research design is available in the Nature Research Reporting Summary linked to this article.
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