Discovery of Nanoscale Electric Field‐Induced Phase Transitions in ZrO2

The emergence of ferroelectric and antiferroelectric properties in the semiconductor industry's most prominent high‐k dielectrics, HfO2 and ZrO2, is leading to technology developments unanticipated a decade ago. Yet the failure to clearly distinguish ferroelectric from antiferroelectric behavior is impeding progress. Band‐excitation piezoresponse force microscopy and molecular dynamics are used to elucidate the nanoscale electric field‐induced phase transitions present in ZrO2‐based antiferroelectrics. Antiferroelectric ZrO2 is clearly distinguished from a closely resembling pinched La‐doped HfO2 ferroelectric. Crystalline grains in the range of 3 – 20 nm are imaged independently undergoing reversible electric field induced phase transitions. The electrically accessible nanoscale phase transitions discovered in this study open up an unprecedented paradigm for the development of new nanoelectronic devices.


Introduction
As the means by which states of matter and energy change forms, phase transitions emerge at the boundaries of human DOI: 10.1002/adfm.2023036363] Hidden within all modern computer chips is a dielectric bearing an enigmatic phase transition that has eluded direct observation, yet could lead to far-reaching transformations in computing, transducing, and energy technologies.[11] However, the operating physics of AFE behavior in these high-k dielectrics is still not well understood, unlike the ferroelectric behavior in HfO 2 and ZrO 2 .Scientists have not been able to provide direct evidence to rule out competing theories of AFE behavior, largely due to the similarities in many experimental features of fluorite-structured FEs and AFEs.This confusion is impeding state-of-the-art advancements in modern digital and emerging computing technologies, such as neuromorphic computing and artificial intelligence. [12,13]erroelectricity in these fluorite-structured dielectrics originates from the polar orthorhombic (o) Pca2 1 phase. [14,15][17] Density functional theory (DFT) calculations and phenomenological Landaubased models have shown that the small energy difference between the ground states of the t-and o-phases in HfO 2 and ZrO 2 can be reversibly changed by electric fields. [15,18]By applying a strong enough electric field, the energy minimum of the o-phase is lowered until it becomes the stable ground state of the material system and a tetragonal to orthorhombic phase transition occurs.Conversely, removing the electric field reconfigures the energy landscape making the nonpolar t-phase the stable ground state, causing a reverse orthorhombic to tetragonal phase transition.
[21][22][23][24][25] The first-order nature of the phase transition is predicted by Landau theory and supported by experimental observations of temperatureinduced phase transitions of the ferroelectric o-phase to the nonpolar t-phase. [18,26,27]The electric field-induced phase transitions generating AFE behavior, however, have remained hidden from view despite theoretical and supporting experimental evidence.][22]28] The ability to probe the piezoelectric behavior of FEs and AFEs at the microscopic scale makes piezoresponse force microscopy (PFM) a suitable technique to investigate the physics of AFE device behavior more clearly.PFM has been previously applied to distinguish the nonlinear piezoelectric response of AFE ZrO 2 with respect to FE La-doped HfO 2 . [22]Although the nonlinear piezoelectric response during PFM hysteresis excitation experimentally indicated the active role of electric field-induced phase transitions, PFM imaging of the AFE capacitor surface conspicuously revealed little detail. [22]y using band excitation piezoresponse force microscopy (BE-PFM), [29] we have discovered direct evidence of an electric fieldinduced phase transition operating at the nanoscale in ZrO 2based antiferroelectrics.The significance of this discovery not only gives us an unprecedented physical view of antiferroelectricity in fluorite-structured materials, but even allows us to unambiguously distinguish AFE from its closely resembling FE counterparts.Microscopic insight is furthermore provided by comparing ZrO 2 and Zr 0.87 Hf 0.13 O 2 , showing that Hf-doping enhances the piezoelectric response and lowers the phase-transition fields due to the material's closer proximity to the tetragonal and orthorhombic morphotropic phase boundary.

Distinguishing AFE ZrO 2 from Pinched FE La-Doped HfO 2
FE doped HfO 2 , such as La-doped HfO 2 , often exhibits an AFElike characteristic marked by a pinched polarization-electric field (P-E) hysteresis loop [30,31] that resembles AFE ZrO 2 , as seen in Figure 1a.La-doped HfO 2 has a notably pinched P-E hysteresis loop and four switching currents as shown in Figure 1b, bearing similar overall features as ZrO 2 during dynamic hysteresis measurements.Despite having a pinched P-E hysteresis loop, Ladoped HfO 2 still exhibits a nonzero remanent polarization, in contrast to ZrO 2 .Moreover, ZrO 2 switching currents are found in all four quadrants, while La-doped HfO 2 has four switching peaks that are only located in two quadrants.The location of the four switching peaks in only two quadrants is frequently associated with internally biased or pinned FE domains, whereas four switching peaks in four quadrants are characteristic of AFE behavior. [32]espite the differences, the similarities between AFE and pinched FE hysteresis loops have led to theories that challenge the authenticity of AFE in fluorites-structured materials.35] The challenge of distinguishing between FE and AFE in fluorite-structured materials, which is critical for advancing technology, stems from not one but several experimental limitations: i) The FE polar orthorhombic (o) Pca2 1 phase is structurally similar to the nonpolar tetragonal (t) P4 2 /nmc phase, obfuscating clear identification of the phases in thin films by grazing incidence x-ray diffraction (GIXRD). [36]ii) AFE behavior is widely attributed to a reversible electric field-induced tetragonal to polar orthorhombic phase transition, but it has been challenging to obtain unambiguous structural identification of the phase transition under applied fields. [36,37]iii) An irreversible electric-field driven tetragonal to orthorhombic phase transition has been observed and may cause "wake-up". [38]iv) FE domains cannot be directly observed from electrical device measurements, but must be inferred from behavioral models at the device terminals. [33,39]o overcome these experimental limitations, BE-PFM can be utilized as a powerful technique to directly image FE domains at the microscopic scale with enhanced sensitivity. [40]Figure 2 presents BE-PFM images of La-doped HfO 2 and ZrO 2 , which clearly shows the presence of FE domains in La-doped HfO 2 .In contrast, no discernible features are observed in ZrO 2 .The lack of FE domains in ZrO 2 provides conclusive evidence that the double hysteresis loop of ZrO 2 does not originate from FE domain pinning, [41] despite sharing qualitatively similar "pinched" hysteresis characteristics with La-doped HfO 2 .This result firmly rules out any involvement of FE domains in the pinched hysteresis loop characteristics originating from AFE in ZrO 2 .

Piezoelectric Response of Electric Field-Induced Phase Transition in ZrO 2
To further investigate AFE films using BE-PFM, we conducted hysteresis spectroscopy measurements on ZrO 2 and Zr 0.87 Hf 0.13 O 2 .Hf-doping pushes ZrO 2 closer to the t-and omorphotropic phase boundary (MPB) which improves the visibility of the tetragonal to polar orthorhombic field-induced phase transition by reducing the phase transition field. [12]The choice of these two ZrO 2 -based compositions is motivated by the goal to approach the MPB without causing electric field-induced irreversible phase transitions ("wake-up").Polarization versus electric field characteristics of ZrO 2 and Zr 0.87 Hf 0.13 O 2 show that both films exhibit double hysteresis loops, as seen in Figure 3a.The magnitude of switching charge is enhanced and the phase transition fields are smaller in Zr 0.87 Hf 0.13 O 2 compared to ZrO 2 , confirming Hf-doping causes the films to be in closer proximity to the t/o-phase MPB.The non-switching regions of the current density versus electric field curve shown in Figure 3b indicate that the relative permittivity is quite similar between the two AFE films.44] Grazing incidence x-ray diffraction (GIXRD) shows that the two ZrO 2 -based films are consistent with the tetragonal phase with the major (011) t diffraction peak showing up at ≈30°, as seen in Figure 3c.Due to the polycrystalline nature and thinness of the 8 nm ZrO 2 -based films, it is very difficult to unambiguously distinguish the tetragonal and orthorhombic phase with certainty. [45]The low-k monoclinic (m) phase is not present in   is expected from the increased magnitude of switched charge and closer proximity to the morphotropic phase boundary with Hfdoping.
The enhanced amplitude of the piezoresponse agrees with the larger switched polarization charge observed in the polarizationelectric field double hysteresis loops.The asymmetry found with electric field polarity manifests again at the microscopic scale in the piezoelectric response, where the larger magnitude of switched charge associated with the positive field-induced phase transition leads to a larger amplitude and piezoresponse as seen in Figure 4a,c, further confirming the piezoelectric dependence on the switched charge.As shown in Figure 4b, the phase is 0°up to applied field strengths of 2 -2.5 MV cm −1 then jumps to 180°i n both films at higher strengths above the phase transition field.The converse phase response is observed with negative applied electric fields.Phase calibration was performed with reference to AlScN and La-doped HfO 2 films, which are shown to have opposite signs of the piezoelectric coefficient, d eff (see Supporting Information). [46]igure 5a shows unipolar BE-PFM hysteresis measurements on the ZrO 2 -based films.A significant peak in piezoresponse is observed that decreases and eventually reverses sign at higher electric fields, which is in agreement with the phase jump observed at high fields during the bipolar BE-PFM hysteresis measurements.Molecular dynamics (MD) simulations were performed to calculate the piezoresponse-electric field characteristics of ZrO 2 caused by the evolution of the electric field induced tetragonal to polar orthorhombic phase transition.Figure 5b shows the MD simulated piezoresponse where distinct behavior in three electric field ranges is observed.At low fields, the simulated piezoresponse originates from electrostriction of the tphase, which is low in magnitude and positive.The magnitude of the piezoresponse increases by a factor of roughly 5 at the tetragonal to polar orthorhombic field-induced phase transition due to the volume expansion of the lattice cell, as depicted in Figure 5c.Simulations show that as the electric field is increased beyond the phase transition, the d 33 originates from the inverse piezoelectric effect of the polar orthorhombic phase, which has roughly the same magnitude as the electrostriction effect of the t-phase but is negative in sign.
From the atomistic modelling perspective, the PFM data offer an unexpected opportunity to validate the quantum mechanical models describing the kinetic barrier for solid-state phase transformations which are related to the electric field needed for the phase transition.It turns out that the used PBEsol density functional, which has been optimized for excellent lattice size, overestimates the kinetic barrier by about a factor of two (as shown in Figure S2, Supporting Information).Despite the overestimation of the kinetic barrier from the adopted density functional, there is excellent agreement between the experimentally observed and simulated piezoresponse as a result of an electric field induced tetragonal to polar orthorhombic phase transition, thus confirming the physical mechanism responsible for AFE behavior in ZrO 2 -based films.

Imaging Electric Field Induced Phase Transitions at the Nanoscale
Antiferroelectrics are generally difficult to experimentally probe because structural relaxations occur once the applied electric field is removed.In Figure 2 and as reported elsewhere, no discernable piezoelectric features are present in a zero-DC field PFM scan of AFE ZrO 2 . [22]To overcome this limitation, BE-PFM imaging was performed with the bottom electrode grounded and with a DC electric field offset through the conducting PFM cantilever tip as it is scanned across the surface of the ZrO 2 -based capacitors.By modifying BE-PFM imaging with a DC field, features of electric field-induced phase transitions that were previously invisible now become apparent, as shown in Figure 6.
In contrast to FEs that exhibit a well-defined piezoresponse from the retained polarization state, AFEs lose their polar state when the electric field is removed.As the DC electric fields are lowered below the phase transition fields, and then are removed completely, BE-PFM imaging shows the amplitude and piezoresponse approach zero due to the loss of the polar state in ZrO 2 , as seen in the 350 nm × 350 nm BE-PFM images in Figure 6.However, when DC fields near the phase transition fields are applied, granular regions on the order of 3-20 nm show significant amplitude, phase, and piezoresponse contrast compared to surrounding regions because of the phase transition to a polar state.The red-blue contrast in the piezoresponse across the film surface shows that the electromechanical response of the film is not uniform and that the phase transitions are highly localized.The nanoscale regions undergoing phase transitions first displace in one direction during the phase transition, then reverse sign as the electric field is increased beyond the phase transition field, which is in excellent agreement with molecular dynamic simulations and PFM hysteresis spectroscopy.
Using the same experimental approach, BE-PFM imaging was again performed but this time on Zr 0.87 Hf 0.13 O 2 with a 100 nm × 100 nm area to obtain higher resolution of the nanoscale electric field-induced phase transitions, as shown in Figure 7.When a −1.88 MV cm −1 DC electric field is applied through the cantilever tip, the negative electric field-induced phase transition becomes pronounced with a 180°phase and contraction of the film surface.This observation is in complete agreement with the series of images of the phase transition on top of the undoped ZrO 2 surface.The positive electric field-induced phase transitions are more clearly visible in the 100 nm × 100 nm images, with the red-colored piezoresponse of single grains undergoing phase transitions gradually weakening and inverting in sign as the DC electric field is increased.
A closer inspection of the 350 nm × 350 nm BE-PFM images of ZrO 2 near the field-induced phase transition at −1.25 MV cm −1 is provided in Figure 8.The nanometer-sized grains undergoing phase transitions show extraordinary amplitude contrast compared to regions that appear electrostrictive, as shown in Figure 8a.A phase transition at −1.25 MV cm −1 DC field induces a 180°phase transition, whereas the phase of the rest of the film is poorly defined and noisy, as shown in Figure 8c.The piezoresponse image shows the film contracting when the AC field through the cantilever acts against the DC field polarity that "freezes" the phase transition in place, in contrast to surrounding regions that appear to show a weak piezoresponse, as seen in Figure 8e.

Results and Discussion
Upon closer inspection of the higher resolution 100 nm × 100 nm BE-PFM images, regions undergoing phase transitions in Hfdoped ZrO 2 exhibit a strong amplitude and a 180°phase  (Figure 8b,d).Regions that show phase transitions exhibit contraction of the film surface (Figure 8f).Small crystallites can impede the ability to induce a phase transition by increasing the phase transition field (Supporting Information).To confirm that the BE-PFM images reflect the true nature of the AFE electromechanical response of ZrO 2 , negative unipolar measurements of the piezoresponse were obtained independently from BE-PFM hysteresis spectroscopy as shown in Figure 8g.The piezoresponse sign and magnitude from hysteresis are in agreement with the sign and magnitudes found in the phase transitions during imaging, providing unequivocal evidence that the BE-PFM images accurately capture the AFE behavior of the capacitor surface.Therefore, these BE-PFM images under varying DC fields provide a clear snapshot of all the features of the phase transition obtained during hysteresis spectroscopy on the capacitor surface.

Conclusion
Nanoscale phase transitions in AFE ZrO 2 have been imaged for the first time by BE-PFM, providing undeniable evidence that reversible electric field-induced phase transitions are responsible for the unique nonlinear dielectric behavior in ZrO 2 -based AFE films.Molecular dynamics simulations demonstrated the characteristic electromechanical response of electric field-induced phase transitions in ZrO 2 that arise from the progressive evolution of i) the electrostrictive effect from the tetragonal phase, ii) the lattice cell volume expansion generated from the tetragonal to orthorhombic phase transition, and then iii) the piezoelectric response of the polar orthorhombic phase as the magnitude of the electric field was increased beyond the transition field.Each characteristic change in piezoresponse found by simulation was in remarkable agreement to the piezoresponse probed experimentally by BE-PFM.
The agreement of two independent measurements in BE-PFM, hysteresis spectroscopy and imaging under DC fields, further confirmed the authentic nature of the reversible field induced phase transitions responsible for AFE behavior in ZrO 2based films.BE-PFM was also used to unambiguously distinguish pinched La-doped HfO 2 from AFE ZrO 2 , clearly illustrating that FE domains are not responsible for the double P-E hysteresis loop.The discovery of independent and reversible phase transitions in nanometer-sized grains under applied electric fields opens up new possibilities for nanoelectronic devices.

Experimental Section
Capacitor Fabrication: Thin film capacitors consisting of a W/TiN/Zr 1-x Hf x O 2 /TiN/Ti/Pt stack were deposited on (100) Si wafers.An ultra-high vacuum Bestec cluster physical vapor deposition tool (PVD) was used to sputter W and TiN.Approximately 30 nm of W was sputter deposited on the Si substrate at room temperature.The W layer serves as a low resistance contact to the bottom electrode.An ≈12 nm TiN layer was sputtered on top of the W layer at room temperature.An Oxford Instruments atomic layer deposition (ALD) tool was used to grow 8 nm thick Zr 1-x Hf x O 2 at 280 °.The precursors used for Zr and Hf were ZyALD (CpZr[N(CH 3 ) 2 ] 3 ) and HyALD (CpHf[N(CH 3 ) 2 ] 3 , respectively.A Zr:Hf cycling ratio of 8:1 was used to grow Zr 0.87 Hf 0.13 O 2 .An ≈12 nm TiN layer was sputtered on top of the Zr 1-x Hf x O 2 films to form the top electrode at room temperature.The blanket ZrO 2 metal-insulator-metal capacitor structure was then annealed at 500 °C for 20 s in N 2 .The ≈13 nm La-doped HfO 2 films were processed with a 10:1 Hf:La ratio with further processing conditions described elsewhere. [30]ithography was performed using a Heidelberg Instruments μPG 101 laser lithography patterning tool.Ti (5 nm) and Pt (10 nm) were deposited using an evaporator from Bestec GmbH.Pt was deposited to act as hard mask during the inductively coupled plasma (ICP) etching process.The top contacts were defined by lift-off in acetone followed by ICP etching to remove the TiN in between the Ti/Pt top contacts.The etching step was performed at room temperature using a Plasmalab System133 from Oxford Instruments with an RF power of 120 W and an ICP power of 1200 W at 10 mTorr.The ICP etch chemistry was a 3:2:1 ratio of SF 6 :O 2 :Ar.A variety of capacitors areas ranging from 10000 -25 μm 2 were available for electrical probing.Band-excitation piezoresponse force microscopy (BE-PFM) was performed on the smallest capacitors.
Physical and Electrical Characterization: A Bruker D8 Discover was used to perform x-ray reflectivity (XRR) and grazing incidence x-ray diffraction (GIXRD) to determine the thickness and crystalline structure of the ZrO 2 -based thin films respectively.Both ZrO 2 -based films were determined to be ≈8 nm thick.Dynamic hysteresis measurements were performed on an Aixacct ferroelectric measurement instrument to acquire polarization versus electric field (P-E) and current density versus electric field (J-E) at a measurement frequency of 1 kHz.All dynamic hysteresis measurements were performed on pristine devices without cycling.
In this study, a commercial Cypher AFM (Asylum Research an Oxford Instruments company, Santa Barbara, CA) was used to conduct PFM measurements with Pt-coated cantilevers (ElectriMulti75-G, Budget Sensors) having a nominal spring constant of ≈3 N m −1 and a resonance frequency of ≈75 kHz.BE-PFM was performed with external data acquisition electronics based on a NI-6115 fast DAQ card controlled by custom-built Labview software.BE-PFM measurements were performed on the top electrode surface of ZrO 2 -based capacitors as shown in Figure S3 (Supporting Information).The BE-PFM experimental data was saved in h5 files and processed using the python pycroscopy package.BE-PFM measurements were performed on pristine capacitors that did not receive any pre-poling.
Molecular Dynamics Description: The molecular dynamics simulations were conducted using the Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS).The utilized interatomic force potential was machine learned using the DeepMD-Kit [47] based on the Perdew-Burke-Ernzerhof revised for solids (PBEsol) potential and is described in detail in. [48]By stacking one monolayer of tetragonal (t) phase with 5 × 5 × 1 12 atomic unit cells surface on top of ferroelectric polar orthorhombic (o) phase with a size of 5 × 5 × N (N = 6-12) 12 atomic unit cells, with the o-phase being polarized in direction of the t-phase, varying surface to volume ratios can be generated.To prevent the decay of the smaller t-phase portion into the "bulk" o-phase, the oxygen atoms were fixed, parallel to the polarization direction of the o-phase, using the fix spring/atom command from LAMMPS.Simulating a 3,5 nm thick layer of ZrO 2 results in a Curie-temperature of below 100 K and AFE behavior at room temperature, at which simulations of the evolution of the phase structure under electric fields were performed, as seen in Figure S7 (Supporting Information).The interfacial t-phase was constrained as a way to force the ground state of the rest of the ZrO 2 crystallite into the t-phase through the depolarization effect at zero field, [49] thus allowing MD to identify if phase transitions would proceed in the presence of an electric field.This method results in stress in the oxygen sublattice leading to a reduction of the Curie-temperature from ≈600-700K, from free energies calculations for "bulk"-phases, to below room temperature for a fixed oxygen sublattice in the monolayer.By assigning Born-charges to the atoms, derived from Berry-phase calculations (Zr = 5.10e, O = −2.55e), a homogeneous external electric field could be applied to the material during the simulations which introduces an error from the charges changing during the transformation on the order of 10%.To improve the model for the description of thermal expansion, [48] a quantum thermal bath model was added.The simulations were carried out using an anisotropic Nose-Hoover style NPT ensemble as implemented in the LAMMPS code.The time-step was chosen to be 1 fs, the thermostat damping parameter 400 fs, the barostat damping parameter to be 10 ps with a drag factor of 2, the transient times were 3 ps for calculations below the phase-transition temperature and 8 ps above the phase-transition temperature to allow the simulation to reach equilibrium after the phasetransition.The final results were obtained after averaging 40 ps.The raw data from the molecular dynamics simulation are time-averaged can be seen in Figure S8 (Supporting Information).

Figure 1 .
Figure 1.a) Polarization versus electric field and b) current density versus electric field dynamic hysteresis measurements of ZrO 2 and La-doped HfO 2 .Both films share similar shaped hysteresis curves with characteristic pinching in polarization near low fields and four switching current peaks.

Figure 2 .
Figure 2. BE-PFM images on top of a La-doped HfO 2 and a ZrO 2 capacitor.a,b) Amplitude, c,d) phase, and e,f) piezoresponse showing ferroelectric domains are present in La-doped HfO 2 , but such features are not resolvable for ZrO 2 .

Figure 3 .
Figure 3. a) Polarization versus electric field, b) current density versus electric field, and c) GIXRD counts versus 2 of ZrO 2 and Zr 0.87 Hf 0.13 O 2 .The double hysteresis loop behavior and diffraction pattern are consistent with a reversible tetragonal to orthorhombic field-induced phase transition.

Figure 4 .
Figure 4. PFM mean a) amplitude-, b) phase-, and c) piezoresponse versus electric field for ZrO 2 and Zr 0.87 Hf 0.13 O 2 .The mean is calculated only from pixels undergoing the phase transitions identified by the quadpeaked amplitude response.The phase transition electric fields are lower while the amplitude and piezoresponse are higher in magnitude in Hfdoped ZrO 2 .

Figure 5 .
Figure 5. Piezoelectric response measured by BE-PFM and calculated by molecular dynamics.a) Experimental unipolar piezoresponse versus electric field measured on ZrO 2 and Zr 0.87 Hf 0.13 O 2 by BE-PFM.b) Simulated piezoresponse and polarization versus electric field produced from molecular dynamic simulations of the electric-field driven tetragonal to polar orthorhombic phase transition.c) Molecular dynamic simulations showing the change in lattice with an electric field-induced phase transition from the nonpolar tetragonal to the polar orthorhombic phase.The inversion of the sign of the piezoresponse is consistent with the sign inversion of the simulated d 33 from the polar orthorhombic phase.The overestimation of the simulated phase transition field is a result of the density functional used.

Figure 6 .
Figure 6.BE-PFM images of 350 nm × 350 nm of ZrO 2 with DC electric field biases to provide a snapshot-by-snapshot evolution of the electric fieldinduced phase transitions.Without a DC electric field, ZrO 2 is not piezoelectric.

Figure 7 .
Figure 7. BE-PFM images of 100 nm × 100 nm of Hf-doped ZrO 2 with DC electric field biases.Phase transitions occur in regions that show a sign change in phase and piezoresponse as the electric field magnitude is increased.

Figure 8 .
Figure 8. BE-PFM images capturing phase transitions in ZrO 2 -based films near the phase transition fields.350 nm × 350 nm BE-PFM a) amplitude, c) phase, and e) piezoresponse images of ZrO 2 under a −1.25 MV cm −1 DC field.100 nm × 100 nm BE-PFM b) amplitude, d) phase, and f) piezoresponse images of Zr 0.87 Hf 0.13 O 2 under a −1.88 MV cm −1 DC field.g) Piezoresponse versus electric field measured locally with BE-PFM hysteresis.The DC fields applied during imaging are near the peak piezoresponse of the phase transition.