Superflexible and Stretchable Ferroelectric Memory on a Biocompatible Platform

Next‐generation flexible electronics for healthcare applications require biocompatible flexible non‐volatile memory for data storage. Ultra‐thin ferroelectric hafnium oxide films offer great potential for flexible memories due to their potential flexibility and perfect compatibility with modern technologies. This study presents ultra‐flexible and stretchable memory devices based on 10‐nm‐thick Hf0.5Zr0.5O2 film fabricated by an innovative technology involving encapsulation of the devices in a biocompatible organic package. They exhibit high memory functionality (remanent polarization of 27 µC cm−2) and withstand extreme mechanical conditions, including folding in half, multiple bending up to 150 000 bending cycles as well as tension with loads up to 1.5 kg. Further, flexible devices are employed as a platform to elucidate the fundamental role of mechanical stress in ferroelectricity of hafnia both experimentally and theoretically. Direct in situ experiment demonstrates that in‐plane tension causes changes in spontaneous polarization, coercive voltage, permittivity, and conductivity. First‐principle calculations explain the role of mechanical stress in ferroelectric and dielectric properties of hafnia. In applications, this work establishes a foundation for the implementation of biocompatible, high‐performance flexible ferroelectric memory, and in the field of ferroelectric materials fundamentals, it provides insight into the critical role of the residual mechanical stress that is inevitably present in thin films.


Introduction
Flexible electronics have suggested tremendous potential to shape human lives for more convenience and health.Strenuous efforts have been devoted to developing technologies and devices for flexible gadgets, electronic textiles, wearable devices and a number of healthcare applications, including medical skin sensors and medical implantable devices. [1]The next generation of healthcare and wearable electronic devices directly contacting DOI: 10.1002/aelm.202300449 the human body requires the development of flexible active elements on a biocompatible platform, potentially microcontrollers, including non-volatile memory for data storage. [2,3]Currently, several concepts of flexible non-volatile memory are under consideration.Some of the most attractive concepts are ferroelectric memories due to their high speed, low power consumption, and high endurance.
Thin polycrystalline HfO 2 ferroelectric films have great potential for the development of flexible ferroelectric memory devices since they exhibit ferroelectric properties being very thin (4-30 nm), [4] and therefore, when bent, the internal mechanical stresses can be small.Several flexible ferroelectric memory devices based on Hf 0.5 Zr 0.5 O 2 (HZO) have been demonstrated, including ferroelectric capacitors, [5,6] transistors [5][6][7] and a memristor. [8]It is remarkable that most of the devices have been constructed on mica -an inorganic solid substrate, [6][7][8] though for healthcare applications organic substrates are needed, because of their good biocompatibility.The choice of non-biocompatible mica as a substrate was determined by the specific properties of HZO films.Indeed, in the as-deposited state, the HZO film is amorphous, and a subsequent annealing process is required to crystallize it into ferroelectric structural phase. [9]Meanwhile, organic substrates degrade upon rapid thermal annealing at high temperatures (400 °C and more), and, as will be discussed below, a special temperature profile during annealing is necessary.Thus, the development of flexible ferroelectric memory devices with high performance on a biocompatible platform remains a significant challenge.
Another important challenge that has not been addressed yet is the effect of mechanical stress acting during the practical use of flexible ferroelectric devices on their characteristics.Flexible electronics used in healthcare requires high bending and tensile strength.To date, the critical radius of bending is not found, the effect of tensile stress is unknown, and thus the real application conditions have not been realized.Therefore, the real potential of HfO 2 -based memory for flexible electronics is still unclear.
From a fundamental point of view, it is important to note that the creation of stretchable ferroelectric devices would open a direct path to establish the contribution of mechanical stresses to ferroelectricity in hafnium oxide, a fundamental question that still remains unanswered.12] In this work, we elucidate the power of ultra-thin ferroelectric HZO films to create biocompatible ultra-flexible non-volatile memory and reveal the crucial role of mechanical stress in properties of this material.We develop an innovative semiconductorcompatible technology and fabricate superflexible ferroelectric memory devices based on a 10 nm thick HZO film.The devices are completely encapsulated in a stretchable organic polyimide package with good biocompatibility and routed to terminals for connection via a connector to measuring equipment, which allows to make automated in situ measurements of functional properties under various mechanical strains.The devices demonstrate excellent memory and mechanical performance.They operate steadily for 150 000 cycles of bending and when folded in half maintain a large remanent polarization (27 μC cm −2 ).Under tensile stress applied to the stretchable sample, fully reversible changes in the ferroelectric and dielectric properties are revealed.In addition to its applied significance, the effect discovered directly reveals that the mechanical stress, always present in rigid functional hafnia structures, causes decrease or increase in the spontaneous polarization.Theoretical calculations of spontaneous polarization, dielectric permittivity and bandgap energy explain the mechanical performance of flexible ferroelectric memory based on Hf 0.5 Zr 0.5 O 2 and open the way for intelligent engineering of mechanical stresses in ferroelectric memory devices.

Fabrication of Flexible Ferroelectric Memory Devices
Figure 1 presents the development of the devices.In situ measurements under mechanical strain require routing of the electrodes to the contact pads, which, in turn, require using an isolating layer.For this purpose, we use a polyimide layer.The polyimide also serves as a biocompatible flexible substrate and encapsulation layer required for packaging of the devices.Polyimide films are fabricated from the liquid precursor by its centrifuging on a rigid silicon carrier substrate and further drying.
First, the tungsten film is deposited on a silicon carrier substrate.It is used as a sacrificial layer, which is etched off at the very end of the technological route in order to peel off the final sample encapsulated in the polyimide package.Second, a ≈15 μm thick polyimide substrate layer is fabricated.Then the functional W, HZO and TiN layers are grown (Figure 1a), and crystallization of the initially amorphous HZO is conducted by means of thermal annealing at 390 °C for 3 h with gradual increase and decrease in temperature (inset in Figure 1a).Al square pads 25, 50, 100 μm in size and 150 nm in thickness are formed by means of electron-beam sputtering and optical lithography (Figure 1b).They are used as a hard mask for further patterning of the top TiN electrode (Figure 1c) and also serve as a low-resistive electric contact to the devices.Then the bottom W electrode and HZO film are patterned (Figure 1d) and the sample is coated by a second polyimide layer.This layer serves to electrically insulate the bottom and top electrodes wiring (Figure 1e).By means of another tungsten hard mask, the insulating polyimide layer is removed over the top electrodes (Figure 1f).Then it is thinned to a thickness of 2-3 μm (Figure 1g), and Al routes to the top electrodes are fabricated (Figure 1h).Then third, encapsulating layer is fabricated, covering the sample from above (Figure 1i).The encapsulating layer is removed above the contact pads (terminals) that end the wiring paths from the structures (Section S1, Supporting Information).Using the next tungsten hard mask, perforation holes over the sample are made by etching all three polyimide layers (Figure 1j).At the end of etching, the bottom layer is also partially etched, after which the sacrificial tungsten layer is completely etched away (Figure 1k) and the sample is torn off from the silicon carrier substrate.The original sample is ≈30 μm thick and is therefore very flexible (Figure 1l).In its as-prepared form, the sample is employed to determine the ultimate bend radius and to study the ferroelectric properties under the tensile stress.Since the sample is too thin to bend to controllable radii, for the bending test it is glued onto a 200 μm thick polyethylene carrier substrate.
For in situ measurements of the device characteristics under mechanical stress, an automatized setup are constructed (Section S2, Supporting Information).It allows measurements of polarization, leakage currents, and capacitance during voltage sweep and with controlled static bending (with specified radii) and tension (with specified load or deformation).The method of measuring the radius of bending is described in the Section S2 (Supporting Information).The same characteristics can be measured during multiple bending and tension cycles performed automatically.To connect wired structures to the measuring equipment, the geometry of the structure's terminals was designed to match the pin geometry of commercially available connectors.Thus, the sample is simply inserted into the connector so that the terminals would connect to the pins.
Therefore, ferroelectric memory devices compatible with complementary metal-oxide-semiconductor structure (CMOS) technology are encapsulated in an organic polyimide package, which exhibits several excellent characteristics, including good biocompatibility, high mechanical strength and flexibility, and excellent electrical insulation properties.In addition, the polyimide has good temperature stability, i.e., it withstands the annealing required for the crystallization of HZO into the ferroelectric phase.
The memory performance of flexible ferroelectric capacitors (wake-up, endurance, switching time, retention time) is presented in the Section S3 (Supporting Information).Now let us focus on the influence of mechanical strains and stresses on the functionality of flexible ferroelectric memory.

Effect of the Bending Stress
The remanent polarization of the flexible ferroelectric HZO capacitor measured after the wake-up procedure is ≈27 μC cm −2 (Figure 2a).This value is ≈20 times higher than the remanent  polarization previously achieved for a 10 nm thick HZO film on flexible organic substrate. [5]The large polarization is a rather unexpected result for a device on a flexible inorganic substrate.In the case of a rigid substrate with a smaller coefficient of thermal expansion, the HZO film experiences a compressive stress during annealing.[12] In particular, the compressive stress reduces the temperature of the phase transition from the parent nonpolar phase to the metastable polar orthorhombic phase and, thus, promotes ferroelectricity.However, in a case when an organic polyimide substrate is used, a soft and ductile thick polyimide layer separates the capacitor layers from the Si carrier substrate during annealing.Therefore, it can be concluded that the substrate and its thermal expansion do not play a dominant role in inducing ferroelectricity in hafnia, at least when long thermal annealing is employed.The study of the structural properties of a similar sample by X-ray diffraction (XRD) shows that the fraction of nonpolar monoclinic phase in the film is negligibly small, and the polar orthorhombic Pca2 1 phase dominates (Section S4, Supporting Information).This is in agreement with the measured large remanent polarization.
Static bending with any controllable radius does not result in any changes in the remanent polarization and coercive voltages (Figure 2a), which indicates that the mechanical bending stresses in our device structures are minor.This is caused by the small elastic modulus of polyimide and polyethylene substrates.However, previously, no change in switchable polarization was also observed for HZO capacitors constructed on a flexible mica substrate. [7]o examine the strength to multiple bending, we measure the polarization dynamics in situ during 150 000 bending cycles using an automatized measuring setup (Figure 2b).During the first 50 000 cycles the bending radius is 2 cm, during the second 50 000 cycles it is reduced to 1 cm, and then, consequently, to 0.5 cm.The switchable polarization is measured after certain numbers of cycles when the sample is flat.It remains constant throughout entire bending cycling, although careful inspection of Figure 2b reveals a slight increase in the value of the switchable polarization.We attribute this behavior to a wake-up effect that continues after 10 4 bipolar wake-up pulses.
Since no impact of bending on the functional properties is detected, we try to find a critical bending radius.To ensure an extremely small radius (to allow bending to an extremely small radius), the original thin (≈30 μm in thickness) sample is placed into the automatized measuring setup and is folded in half so that all memory structures are located at the fold line.In Figure 2c, the orange arrows indicate the fold line where the structures under test are located.As it is measured more precisely, the bending radius of a tightly folded sample is 0.5 mm (for details, see Section S2, Supporting Information).Although from the point of view of flexible electronics applications, the sample can be considered as folded in half, in fact the bending radius is finite, albeit extremely small.
The P-V and switching I-V curves are measured before, after and during folding.As can be seen in Figure 2d, bending with an extremely small radius does not lead to any change in functional properties.Therefore, in the most direct and obvious way we prove that the internal mechanical stress in ultrathin HfO 2 films under bending and even folding is negligible, so this material has great potential for implementation in flexible non-volatile memory.

Effect of the Tensile Stress
In many applications of flexible devices, they are subjected to tensile mechanical stress, and therefore it is necessary to investigate the stability of the functional properties of HZO-based memory cells under tension.For this experiment, the edges of the original thin sample are locked in the fixed and movable parts of an automatized measuring setup (Figure 3a) and the functional properties are characterized under different tensile loads and, consequently, during different tensile deformations.As the load increases, polarization current peaks gradually decrease in magnitude, which means a decrease in the switchable polarization (Figure 3b,c).At a load of ≈1 500 g, the switchable polarization drops by ≈10 %.The positions of both peaks gradually shift towards higher voltages, i.e., mean coercive voltages increase.The positive mean coercive voltage increases from 1.5 to 1.7 V, whereas the negative -from −1.3 to −1.4 V.After the load is removed, the reverse process takes place, i.e., the switchable polarization increases and coercive voltages decreases.Therefore, the deformation of the functional layer under the tensile load up to 1 500 g is elastic, and the changes in the ferroelectric properties are reversible and recover after load removal.
It can be noted that at the end of this experiment the switchable polarization slightly increases compared to the beginning.This is due to the wake-up effect, which continues during the measurement of functional characteristics.Indeed, it is known that the growth of switchable polarization during bipolar cycling accelerates significantly with an increase in pulse duration. [13]Meanwhile, at each tensile load, we measure several characteristics, and some of them (C-V and quasistatic I-V curves) by means of a slow sweeping of bias voltage, i.e., at large voltage duration.Thus, despite the wake-up procedure is performed before the measurements, the growth of the switchable polarization take place during further measurements.
To examine the strength to multiple tensions, we in situ measure the polarization dynamics over 900 tension cycles using our automatized measuring setup.The tensile load is increased from 320 g to 600 g as shown in Figure 3g.The switchable polarization is measured after certain numbers of cycles when the sample is at the non-strained state.It remains constant throughout the entire experiment on tension cycling.
Therefore, the ferroelectric properties retain under tensile stress.Changes in the switchable polarization and switching voltages are evident; however, they are quite small and only marginally affect the memory window.This indicates the feasibility and promise of developing flexible HZO-based memory operating under pulling loads, e.g., for wearable electronics and biomedical skin sensors.
To get further insight into the physical properties of ferroelectric HZO capacitors under tensile stress and deformation, we measure the evolution of the C-V and quasistatic I-V curves under increasing and decreasing load (since the curves evolved reversibly, only the curves for increasing load are shown in Figure 3d,e).In the monodomain state of HZO film, the dielectric permittivity increases with increasing load (Figure 3d,f), while in the polydomain state, its behavior is more complicated.
The evolution of current polarization peaks on the quasistatic I-V curves (Figure 3e) is similar to the evolution of peaks on the switching AC I-V curves (Figure 3b).From both measurements, one could conclude that coercive voltages rise with increasing tensile load.As for the leakage current, it slightly decreases with tension (Figure 3e,f).Overall, as well as changes in ferroelectric properties under load, changes in dielectric permittivity and leakages are small and reversible, and it does not spoil the functionality of flexible devices.
In addition to practical significance for applications in flexible electronics, the described results are of fundamental interest.Indeed, information on the effect of mechanical stress on the ferroelectric properties of the film is usually obtained from indirect data.For example, residual mechanical stresses are calculated from lattice constants measured by X-ray diffraction, [10][11][12] or tensile stresses are induced by bending films grown on flexible solid inorganic substrates and then evaluated from finite element analysis. [6,7]In the present work, the experimental information is obtained in the most direct way.It is noteworthy that in our experiment, the sample is subjected to the uniaxial in-plane stress (Figure 3a), whereas the strained films grown on rigid substrates and then studied via XRD analysis are under biaxial in-plane stress.
While information about the effect of loading is more important for applications, information about the effect of mechanical deformations is more important for fundamentals of ferroelectricity.Therefore, we measure the uniaxial tensile deformation induced by tensile load.In order to measure the movements of the shifting part of the setup in real time, the setup is equipped with a high precision optical microscope (Section S1, Supporting Information).It is confirmed that the deformation linearly depends on the load (i.e., it is elastic), and therefore the uniaxial relative deformation can be calculated for any load (on the top horizontal axes in Figure 3c,f).For example, 1 500 g causes a deformation of ≈3 %.It should be noted that the limiting load for our samples is ≈2 000 g, and the polyimide ruptures at a higher load.Due to the Hook's law, a load of 2 000 g corresponds to a relative deformation of ≈4 %, which is very close to the elastic limit deformations of solid polycrystalline films. [14,15]Therefore, our results cover almost the maximum possible range of HZO deformation.

Theoretical Investigation
To get a deeper insight into effect of mechanical stress on the ferroelectric and dielectric properties of ferroelectric HfO 2 , we perform a series of first-principles calculations.Based on simulations, we present a confirmation of the experimental results.
We started with structural relaxation for the polar Pca2 1 orthorhombic phase of HfO 2 (o-HfO 2 ) to obtain an equilibrium configuration for both cell parameters and atomic positions.Our calculated lattice constants for the a, b and c crystal axes are 5.20, 4.99, and 5.01 Å, respectively; the atomic coordinates are given in Table S1 (Supporting Information) (Section S5, Supporting Information).The polar axis here is c-axis.The obtained solution is in good agreement with previous experimental [16] and theoretical [17] results.
In order to more naturally imitate the experimental setup (axial tension of the HZO thin film perpendicular to the vertical direction), we apply an uniaxial strain to the unit cell along the longest a-axis, while along the other two spatial directions the cell remains relaxed (Figure 4a).To do this, we run structural optimizations in which the lattice constant a value is fixed to a = a 0 (1 +  ax ), and the other two lattice constants as well as atomic positions are allowed to vary; here a 0 is the previously calculated equilibrium cell parameter and  ax is the axial physical strain.In our calculations,  ax varies in a small range from -1.5% to 1.5%, in which the physical properties of HfO 2 would change linearly, without reaching the yield strength, much less transformation of the ferroelectric phase into other structures and reaching the ultimate tensile strength.Figure 4b shows that the energy minimum corresponds to no stretch, so the equilibrium geometry is obtained correctly.

Spontaneous Polarization
In the relaxed state, the computed spontaneous polarization P sp of the o-HfO 2 phase is P sp = 54.6 μC cm −2 , which matches the previously published results. [17,18]However, this theoretical result does not take into account polycrystallinity of film.Misorientation of grains leads to the smaller average polarization.Figure 4c shows the dependence of the spontaneous polarization on the axial strain  ax .Theoretical calculations demonstrate that a change in the tensile strain of the order of 1% leads to a decrease in polarization by 2-3%, and given linear dependence, polarization decreases down to ≈6-9% at tensile strain of 3 %, which is similar to the experimental results (Figure 3c).
Let us note that our experimental switchable polarization of HZO (54-55 μC cm −2 ) is very large compared to the polarization in the bulk of works dealing with films on rigid substrates.During annealing, due to difference in coefficients of thermal expansion ordinary substrates and underlayers (Si, SiO 2 , mica, W, TiN, etc.) induce a large compressive stress in HZO, which promotes formation of ferroelectric Pca2 1 phase.It is reasonable that HZO crystallizes under compressive strain in such way that its polycrystalline structure compensates the stress and, after cooling, it turns out under tensile stress.Therefore, the large switchable polarization of our flexible ultra-thin samples may be due to less tensile strain in the HZO.

Leakage Current and Bandgap
In any of the possible mechanisms of current transport in thin hafnium oxide films, whether it is thermionic emission, Poole-Frenkel mechanism or trap-assisted tunneling, the leakage current exponentially depends on the barrier height, which, in turn, determined by the bandgap. [19]Specifically, the leakage current grows with a decline in the bandgap.Therefore, by analyzing how various factors affect the bandgap width, one could predict changes in the leakage current.The bandgap obtained for the o-HfO 2 equilibrium cell is equal to 4.7 eV.Standard Density Functional Theory (DFT) calculation gives lowered correlation of the d-and f-bands in transition metal oxides, resulting in an underestimation of the bandgap value compared to the experimental ones.This can be resolved by running DFT+U calculation, which treats the strongly correlated electronic states (d orbitals) with an additional Hubbard U parameter while describing the rest of the electrons with the classic DFT approach. [20]ith Hubbard U set to 6 eV, the achieved bandgap value is 5.6 eV, which agrees with previous experimental data of 5.3-5.7 eV. [21,22]s shown in Figure 4d, we find that the bandgap grows with increasing strain, which explains the decrease in modulus of leakage current upon tension of the HZO film (Figures 3e,f).

Dielectric Permittivity
Based on first-principles calculations via finite-fields approach, [23,24] one could compute static dielectric permittivity ɛ stat of the insulator, which is experimentally obtained through the capacitance measurement of the insulator-based capacitor.In the finite-fields method, the wave functions and, as a consequence, the electronic structure of the system in the presence of a finite homogeneous electric field  is derived by minimizing the energy functional where E 0 [{ i }] is the usual energy functional in the absence of an external electric field, P ion and P el [{ i }] are the ionic and electronic polarizations along the direction of , respectively.P macr = P ion + P el is the macroscopic polarization.The electronic component is determined through the Berry phase theory of polarization, [25] and the ionic component is given as , where R i is the position coordinate in the direction of the applied field and Z i is the charge of the ionic core.The described finite-fields approach allows us to calculate the electronic structure in the presence of a finite electric field for a system obeying periodic boundary conditions.Moreover, this approach is applicable whether the internal displacements are either clamped or unclamped.If the ions are kept fixed, one could obtain the electronic high-frequency contribution ɛ ∞ to the dielectric permittivity; if both electrons and ions are allowed to relax in response to the field, the static (also called total) dielectric constant ɛ stat is obtained: where variation of the polarization Δ P  = P  − P 0 corresponds to the vanishing field (both permittivity ɛ and polarization P are along the direction of ).In turn, the lattice-mediated part ɛ ion is defined as the difference ɛ stat − ɛ ∞ .
In the undeformed state of o-HfO 2 , the calculated electronic and static dielectric constants along the polar direction are equal to ɛ ∞ = 4.86 and ɛ stat = 21.72,respectively, which satisfies the previous experimental [21,22] and theoretical [26] data.The static dielectric permittivity increases slightly under the tensile strain (Figure 4d).This is both qualitatively and quantitatively in line with experimental results (Figure 3d,f).It is noteworthy that the increase in static permittivity, measured experimentally, is associated only with a change in the lattice-mediated contribution, while the electronic contribution remains constant.Thus, the change in the dielectric properties of HZO with tension is due precisely to the lattice response.
Therefore, the first-principles calculations elucidated the role of mechanical stress in the ferroelectric and dielectric properties of hafnium oxide films.On the one hand, they explained the experimentally revealed behavior of flexible ferroelectric memory devices under mechanical stress.On the other hand, theoretical calculations have quantitatively demonstrated that the difference in the ferroelectric properties of rigid hafnia-based capacitors, even nominally the same, can be due to different residual mechanical stresses.

Conclusion
In summary, we elucidate the potential of ferroelectric HZO ultra-thin films to create a superflexible non-volatile memory.We report inorganic, CMOS-compatible, highly flexible and resistant to tensile load ferroelectric HZO-based memory devices fabricated on a biocompatible polyimide platform.The devices are fully encapsulated in a biocompatible polyimide package that also serves for protection and electrical insulation.Ferroelectric performances do not change during static bending with an extremely small radius (down to 0.5 mm), and are retained during 150 000 bending cycles with the radius down to 0.5 cm.Under static tensile deformation, the ferroelectricity retains, but the switchable polarization decreases by up to ≈10%.Changes in ferroelectric properties are sufficiently small and reversible, so that only marginally affect the memory window, which paves the way for the application of our technology in next-generation flexible electronics.
For fundamentals of ferroelectric materials, the straightforward experimental information on ferroelectric and dielectric parameters during tensile load and strain is very prominent, because it clarifies the role of the mechanical stress and deformation in ferroelectric and dielectric properties of hafnia, includ-ing hafnia-based structures on rigid substrates.The theoretical analysis explains the experimental results and elucidates the role of mechanical stress from first principles calculations.Our research marks a milestone in the development of flexible ferroelectric memory with excellent functional properties and outstanding flexibility, and has great potential to trigger a new version in healthcare electronics.

Experimental Section
The HZO film 10 nm in thickness was grown via thermal atomic layer deposition at a 230 °C substrate temperature using Hf[N(CH 3 )(C 2 H 5 )] 4 and H 2 O as precursors and N 2 as a carrier and a purging gas.Both bottom 20 nm thick W and top 20 nm thick TiN layers were deposited via reactive magnetron sputtering.
Crystallization of the HZO film was induced by post-metallization thermal annealing for 3 h in argon atmosphere at 390 °C with gradual increase and decrease in temperature.At higher temperatures (400 °C or more), the polyimide underlayer degrades, whereas at lower temperatures (380 °C or less) HZO film was non-ferroelectric.Long-term annealing was chosen because rapid (20-30 s) thermal annealing usually used for inducing ferroelectricity in hafnium oxide leads to deformation of the polyimide layers even at temperatures of 380 °C.It was assumed that the polyimide experiences thermal shock during rapid annealing as opposed to long-term annealing.Previously, Yu et al. came to a similar conclusion. [5]he remanent polarization of the flexible ferroelectric HZO capacitor measured after the wake-up procedure was ≈27 μC cm −2 (Figure 2a).It should be note that in previous work on HZO on polyimide substrate, [5] the remanent polarization of 10 nm thick HZO film was ≈1 μC cm −2 , and it reached ≈13 μC cm −2 for 35 nm thick HZO film.Yu et al. also reported the degradation of polyimide substrate under rapid thermal annealing, [5] and therefore they performed annealing for 2 min at 380 °C on a hot plate.Thus, this work indicates that increasing the annealing time had a promoting effect on the ferroelectric properties of HZO films grown on polymer substrates.Unlike silicon substrates, polymer substrates did not induce mechanical stress in the HZO film during annealing; meanwhile, the stress reduces the temperature of phase transition from the parent nonpolar phase to the metastable polar phase, i.e., it promotes ferroelectricity.Additional studies of this issue are desirable.
For electrophysical characterization, the semiconductor parameter analyzer Agilent B1500A (for the tension test and test on folding in half) or Keithley Source Meter 2450 (for the bending test) connected to the sample via home-made setup were used.P-V curves were measured through the dynamic positive-up negative-down (PUND) technique. [27]To wake up the fresh HZO film, the ferroelectric capacitors were cycled 10 4 times by applying bipolar voltage double triangular pulses with an amplitude of ±3 V and a duration of 10 μs.Dielectric permittivity was acquired for cycled structures through C-V curves measured at an excitation voltage of 10 kHz, 50 mV and series capacitor-series resistor (Cs-Rs) equivalent scheme.The leakage current was obtained using quasistatic I-V curves measured by the stepwise sweeping of the bias voltage.
For mechanical characterization, an automatized setup for electrophysical measurements under mechanical stress was developed and fabricated, as described in the Section S2 (Supporting Information).
Structural characterization was performed by X-ray diffraction (XRD) study using a Rigaku SmartLab diffractometer.Incident angle was 0.6°to maximize signal-to-noise ratio.For XRD study, a large area sample was fabricated using a simplified technique, by only steps a-b of Figure 1.The P-V curves and XRD pattern are presented in the Section S4 (Supporting Information).
Density Functional Theory (DFT) calculations were carried out via Quantum ESPRESSO 7.1 package. [28]In this calculations, the Perdew-Burke-Ernzerhof formulation was considered for solids (PBEsol) [29] of the generalized gradient approximation to describe the exchange-correlation functional.The projector-augmented wave pseudopotentials was used. [30]The electronic wave functions were expanded in a plane-wave basis with a kinetic energy cutoff of 610 eV.For structural optimization of HfO 2 , the Brillouin zone was sampled with a 6 × 6 × 6 k-point grid (corresponding to a 12-atom periodic unit cell).Spontaneous polarization was calculated using the modern theory of polarization (Berry phase approach). [25,31,32]This approach requires a higher-density k-mesh in the polar direction: 6 × 6 × 8 grid.To obtain the dielectric permittivity, the finite-fields approach was employed, [23,24] in which a regular mesh of 3 × 3 × 7 k-points was used, and an electric field of 0.036 V Å −1 was applied along the polar Cartesian axis.The structure was fully relaxed until all ionic forces and cell stresses drop below 0.003 eV Å −1 and 0.05 GPa, respectively.

Figure 1 .
Figure 1.Preparation of ultra-flexible ferroelectric structures.Letters indicate the technological steps described in the text.

Figure 2 .
Figure 2. Results of the bending test.a) P-V curve for non-bent and bent sample (bending radii are notated).b) Evolution of switchable polarization during multiple bending with different radii.c) Sample folded in half so that the structures are located on the fold line.Note that the folding line marked with arrows is perpendicular to the bending axis in the sketch of the sample in Figure 1l.d) P-V and switching I-V curves measured before folding and in folded state.

Figure 3 .
Figure 3. Results of the tensile test.a) Sample mounted to the setup.b) Switching I-V curves measured during the increase and decrease in tensile load.c) Dependences of switchable polarization and absolute coercive voltages on tensile load.d) C-V curves and e) quasistatic I-V curves measured with different tensile load.f) Dependences of dielectric permittivity and leakage current on tensile load and tensile deformation.The values are measured at the definite voltages marked in (d) and (e); g) Evolution of the switchable polarization during multiple tensions with different load.

Figure 4 .
Figure 4. Theoretical investigation of the effect of axial strain on the properties of the ferroelectric Pca2 1 structure of HfO 2 .a) Illustration of applying axial strain  ax perpendicular to the polar direction.Lattice constant a is fixed to a = a 0 (1 +  ax ), while the other two lattice constants as well as atomic positions are allowed to vary b) Dependency of energy from strain.Minimum corresponds to the relaxed structure.c) Computed spontaneous polarization P sp as a function of axial strain.Modification of the d) bandgap and e) dielectric permittivity.The total static permittivity ɛ stat is the sum of the high-frequency electronic (frozen-ion) part ɛ ∞ and the lattice-mediated part ɛ ion .