Intrinsic ferroelectricity in Y-doped HfO2 thin films

Ferroelectric HfO2-based materials hold great potential for widespread integration of ferroelectricity into modern electronics due to their robust ferroelectric properties at the nanoscale and compatibility with the existing Si technology. Earlier work indicated that the nanometer crystal grain size was crucial for stabilization of the ferroelectric phase of hafnia. This constraint caused high density of unavoidable structural defects of the HfO2-based ferroelectrics, obscuring the intrinsic ferroelectricity inherited from the crystal space group of bulk HfO2. Here, we demonstrate the intrinsic ferroelectricity in Y-doped HfO2 films of high crystallinity. Contrary to the common expectation, we show that in the 5% Y-doped HfO2 epitaxial thin films, high crystallinity enhances the spontaneous polarization up to a record-high 50 {\mu}C/cm2 value at room temperature. The high spontaneous polarization persists at reduced temperature, with polarization values consistent with our theoretical predictions, indicating the dominant contribution from the intrinsic ferroelectricity. The crystal structure of these films reveals the Pca21 orthorhombic phase with a small rhombohedral distortion, underlining the role of the anisotropic stress and strain. These results open a pathway to controlling the intrinsic ferroelectricity in the HfO2-based materials and optimizing their performance in applications.


Introduction
Ferroelectric materials exhibit switchable spontaneous electric polarization, which makes them promising for application in modern electronics, especially for information storage and processing 1 . Conventional ABO3 perovskite ferroelectrics suffer from poor scalability due to the increasing depolarization field at reduced thicknesses and incompatibility with the current Sitechnology 2-5 . The recent discovery of robust ferroelectricity at the nanoscale in hafnium oxide (HfO2) based materials, which have long been used as high-k dielectrics, makes the widespread integration of ferroelectricity into nanoscale electronics feasible. 6,7 Earlier reports suggested that to establish ferroelectricity, it is crucial for the HfO2-based materials to consist of nanometer-sized crystal grains, because the ferroelectric orthorhombic structural phase (Pca21, o-phase, Fig. 1a) is unstable in ambient conditions. All the stable structural phases of HfO2, i.e., the monoclinic phase (P21/c, m-phase) at room temperature, the tetragonal phase (P42/mnc, t-phase) above 2100 K, and the cubic phase (Fm-3m, c-phase) above 2800 K 8 are not ferroelectric. The small crystal grain sizes lead to proliferation of structural defects (low crystallinity) in the form of grain boundaries, which are expected to undermine and obscure ferroelectric properties. 9 Indeed, it has been challenging to elucidate the crystal structure of the ferroelectric o-phase; to date, most of the experimentally observed spontaneous polarization values are significantly lower than the theoretically predicted ones (40-60 μC/cm 2 ) 10-14 .
Being able to fabricate HfO2-based ferroelectrics with the minimally possible defect density, or high crystallinity, will not only allow elucidation of intrinsic ferroelectric properties, but also enable better performance in device applications. The key is to enhance the stability of the ferroelectric o-phase, which is typically achieved by constraining the grain size making use of the two main mechanisms. (1) The small grains size enhances the stability of the o-phase because the surface energy of the o-phase is larger than that of the m-phase. 10,[15][16][17][18][19] (2) HfO2-based ferroelectrics are typically obtained by fast cooling from the high-temperature t-phase taking advantage of the smaller energy of the o/t interface compared with that of the m/t interface, even though the bulk m-phase is more stable; the size of the crystal grains is then limited by the rapid cooling process. 17,19-30 On the other hand, when the stability of the o-phase is enhanced by additional mechanisms, such as doping and epitaxial growth, the ferroelectricity may reconcile with high crystallinity in HfO2-based materials. Among various dopants of HfO2 6,15,29,31-34 , yttrium stands out for stabilizing the o-phase HfO2 in thick films 35,36 and even in bulk 20 . In addition, in ultra-thin epitaxial films, the large surface area and the anisotropic stress and strain have been suggested to enhance the stability of the o-phase 10,15-19 .
In this work, we challenge the common belief that the smaller grain size is required to stabilize the ferroelectric o-phase in HfO2-based thin films. We investigate molar 5% YO1.5 doped HfO2 (YHO) films, focusing on high-temperature epitaxial growth on LSMO (001) / STO (001) and LSMO (110) /STO (110) substrates, where LSMO and STO stand for La0.7Sr0.3MnO3 and SrTiO3, respectively. We demonstrate that higher crystallinity of the films actually enhances spontaneous polarization up to a record-high value of 50 μC/cm 2 at room temperature. We show that the high polarization only moderately decreases at low temperature suggesting the dominant contribution from the intrinsic ferroelectricity.

Results and Discussion Positive correlation between Pr and crystallinity
A typical θ-2θ x-ray diffraction (XRD) scan for YHO (111) /LSMO (001) thin films grown at substrate temperature Ts = 890 °C in O2 pressure of 70 mTorr (optimal condition for spontaneous polarization, same below) is shown in Fig. 1b. The clear Laue oscillations around the YHO peak indicate smooth surface and interfaces. The thickness of the LSMO and YHO layers are ≈ 25 nm and ≈ 10 nm, respectively, according to x-ray reflection (XRR) (Supplementary Fig. S1). The peak at 2θ ≈ 30° can be assigned to the diffraction of the pseudo cubic (111)pc plane [24][25][26][27][28]37 . Fig. 1c shows the remanent Polarization-Voltage (P-V) loop measured using the positive up and negative down (PUND) method at room temperature for the YHO films grown at optimal condition. The spontaneous or remanent polarization (Pr) value is approximately 36 μC/cm 2 , which is larger than all polarization values reported for Y-doped HfO2 films. [20][21][22]35,36,38 The coercive voltage (Ec) is much larger than Ec of the polycrystalline films 6,15,16,20,35 and slightly larger than Ec of the 5-nm-thick HZO (111) /LSMO (001) films. 24 The in-plane size of the crystal grains was estimated using x-ray diffraction rocking curves, which measures the size of reciprocal lattice point along the in-plane direction and in turn the inplane size of the crystallites for epitaxial films. As shown Fig. 1b inset for the films grown at optimized condition (see also Fig. S2), the rocking curves clearly consist of a narrow peak sitting on a broad peak, corresponding to small (≈ 10 nm) and large (≈ 100 nm) crystal grains respectively, according to the Scherrer formula 39 . The large grain is an order of magnitude larger than the typical grain size (< 10 nm) found in polycrystalline films 16,17 and previously reported epitaxial films. 24,28 To elucidate whether the high crystallinity contributes to the large polarization, we studied YHO films with different growth temperature Ts, which is expected to be critical for the microstructure of the HfO2-based films with multiple competing phases. 27 The O2 pressure is fixed at 70 mTorr, similar to the optimal oxygen pressure (0.1 mbar) in the growth of HZO on LSMO (001) 24,27 . At lower temperature (≤ 800°C), the films contain traces of m-phase as indicated by the (-111)m peak at 2θ ≈ 28.5° ( Supplementary Fig. S3), which disappears at higher temperature (≥ 850°C).
As temperature changes, the rocking curves ( Fig. S2) remain comprised of the narrow peak and the broad peak while their relative weight changes dramatically, corresponding to a large change of the volume fraction of the small and large grains. Since more large grains means less grain boundary defects, here we define the large/small grain ratio (area ratio of the narrow and broad peaks) as a quantitative measure of the crystallinity.
The Ts dependence of the crystallinity (large/small grain ratio) shows a non-monotonic trend, with a peak at Ts = 890°C, as shown in Fig. 1d. Below 890°C, the crystallinity increases with temperature, most probably due to the reduction of the m-phase. Above 890°C, the crystallinity decreases with temperature, likely due to the decay of the LSMO layer ( Supplementary Fig. S4). The Pr as a function of Ts is also plotted in Fig. 1d, which shows a nonmonotonic trend in perfect match with the Ts-dependence of crystallinity (large/small grain ratio).
In contrast, the YHO (111) peak shifts monotonically to higher 2θ at higher temperature, indicating reduced d(111), which is consistent with previous studies in HZO epitaxial films 27 .
To confirm the positive correlation between crystallinity and Pr, we studied YHO films grown on LSMO(110) / STO(110), which has not been reported in the literature. It turns out, the YHO epitaxial films also grow along the (111) direction, as shown in Fig. 1e. At the optimal growth condition, the YHO(111) / LSMO(110) films also show clear Laue oscillations indicating the sharp surface and interfaces; the spontaneous polarization reaches ≈ 50 μC/cm 2 , as displayed in Fig. 1c. The rocking curve of the films displayed in the inset of Fig. 1e is dominated by the sharp peak that represents the large crystal grains, indicating high crystallinity. Combining the data of YHO(111) films grown on LSMO(001) and those on LSMO(110), a clear positive correlation can be observed in Fig. 1f between the crystallinity (large/small grain ratio) and the spontaneous polarization. Overall, the spontaneous polarization increases with the crystallinity and appears to saturate at a value close to 50 μC/cm 2 .

Local switching and temperature dependence of polarization
To cross-check ferroelectricity in the YHO films, samples were measured using piezoresponse force microscopy (PFM) as well as temperature-dependent measurements of the polarization hysteresis loops.  Figure 3a shows the remanent P-V loops for the YHO(111) /LSMO(001) sample grown at the optimal condition, which shows a weak temperature dependence between 20 and 300 K. For the YHO(111) /LSMO(110) sample grown at the optimal condition, the Pr increased from 37 μC/cm 2 at 20 K to about 50 μC/cm 2 at 300 K as shown in Fig. 3b. Comparison of the Pr as a function of temperature for the two different films is shown in Fig. 3c. The increase of Pr with temperature is opposite to that of the conventional ferroelectric materials since the ferroelectric order is expected to be higher at low temperature. One possibility is the extrinsic contributions to the polarization switching process such as oxygen migration 41,42 . Recently, in-situ STEM was employed to study the ferroelectric switching process in the HZO(111) / LSMO(001) thin film structures, where HZO stands for Hf0.5Zr0.5O2. It was reported that most of the polarization in the HZO(111) / LSMO(001) structures could be attributed to oxygen vacancy migration, 41 with the intrinsic ferroelectric polarization estimated to be less than 9 μC/cm 2 . In addition, it was reported that Pr in the 5.6-nm-thick HZO films grown on LSMO/LaNiO3/CeO2/YSZ/Si(100) decreases by a factor of 3 from 300 K to 20 K. 43 On the other hand, for the YHO(111) films studied in this work, Pr exhibits a large value at low temperature and stays nearly constant below 100 K. This suggests that the extrinsic contributions are minimal to the measured Pr at low temperature. The moderate overall change of Pr with temperature also indicates that the contribution from the intrinsic ferroelectricity dominates even at room temperature.
Further evidence for the minimal effect of the oxygen vacancies migration was obtained by comparing the imprint behavior at 300 K (Fig. S6a) and at 20 K (Fig. S6b,c). Recently, it was reported that the imprint in HfO2-based films is strongly dependent on their poling history, i.e., positive (negative) imprint would develop if the last switching pulse would set the capacitor to the upward (downward) polarization state 44 . This so-called fluid imprint could also be observed in our samples at room temperature (Fig. S6a). However, upon cooling to 20 K, the imprint remained 'frozen-in', which can be attributed to the minimal movement of internal charges (such as oxygen vacancies) at low temperatures.
Finally, remanent P-V loops were measured at 20 K for the YHO(111) /LSMO(001) samples with different crystallinity, to verify if the trend of increasing Pr with crystallinity was intrinsic in origin. As shown in Fig. 3d, strong correlation between the high Pr and high crystallinity observed at room temperature could be reproduced at 20 K (see also Fig. 1d), suggesting the intrinsic nature of the observed features.

o-phase with a rhombohedral distortion and the t→o structural transition
The high crystallinity of the YHO films allows for determination of the crystal structure, which is critical for understanding the ferroelectricity. Previously, the ferroelectric HZO(111) / LSMO(001) films have been found to be the o-phase [25][26][27]  The lattice constants of the YHO were probed by measuring the spacing of the {200} pc planes. For the YHO(111) / LSMO(001) films, due to the 4-fold rotational symmetry of LSMO (001), the (111) oriented YHO films contain four structural domains rotated by 90° relative to each other along the film normal 37,45 , which multiplies the three tilted {200} pc planes (tilt angle χ≈55°) to twelve (see Supplementary Fig. S13a). For the YHO(111) / LSMO(001) films, as shown in Fig.  4a, after averaging the twelve directions, the {200} pc diffraction profiles show two distinct peaks, corresponding to lattice constants of 5.20 ± 0.01 and 5.07 ± 0.01 Å, respectively. Overall, the peak at smaller 2θ has about ½ of the area of the other peak, indicating that one lattice constant (assigned as a) is 5.20 Å, while the other two lattice constants (assigned as b and c) are 5.07 Å (see Table 1), because the structural factors of the three {200} pc planes are similar due to the nearly cubic structure. The substantial difference between a and { , } but very close value between b and c is consistent with the orthorhombic Pca21 ferroelectric phases 10,11,46 .
For the YHO(111) / LSMO(110) films, the 2-fold rotational symmetry of LSMO (110) surface generates two structural domains rotated by 180° relative to each other along the film normal ( Supplementary Fig. S13b). Since the structural domain boundaries are like "built-in" defects of the films which reduces the crystallinity, the less structural domains in the YHO(111) / LSMO(110) films may explain their higher crystallinity compared with that in the YHO(111) / LSMO(001) films. The double-peaks feature has also been observed for the {200} pc planes (Fig.  4a), corresponding to lattice constants a = 5.21 ± 0.01 Å and b ≈ c = 5.08 ± 0.01 Å.
Besides the lattice constants, what distinguishes the o-phase from the t-phase and the mphase is the space group symmetry including a two-fold screw axis along the polar (c) axis and two glide planes perpendicular to the other two axes (a and b). As a result, the o-phase has two important distortions (Fig. 4b, c)  Previously, the appearance of the {110} pc x-ray diffraction peak was employed to measure the 47,48 t→o phase transition in YHO films. Here we measured the temperature dependence of the (1-10)pc diffraction peak using RHEED. As shown in Fig. 4f, both the (1-10)pc and the (11-2)pc diffraction intensities appear as weak streaks in the RHEED images at room temperature. As shown in Fig. 4g, at high temperature, the (1-10)pc diffraction is absent while the (11-2)pc diffraction peak is present, indicating the t phase. When the film was cooled, the (1-10)pc peak appears at about 450 °C, while the intensity of the (11-2)pc diffraction peak also increases, indicating a transition to the o phase, which is consistent with the range of transition temperature 350 to 550 °C found in previous studies on YHO 23,[47][48][49] .

Theoretical modeling
To explore the effects of the rhombohedral distortion on the structural stability and ferroelectric polarization of the YHO, we performed density-functional theory (DFT) calculations 50 . We started from the orthorhombic Pca21 unit cell of undoped HfO2 where the interaxial angles were α = β = γ = 90°. A small rhombohedral distortion was then introduced by reducing the angles while keeping them equal, i.e., α = β = γ < 90°. Throughout the calculations, the experimental values of the lattice parameters were assumed and fixed to be a = c = 5.07 Å and b = 5.20 Å, and only inner atomic positions were relaxed. Similar calculations were also performed for the 5% Ydoped HfO2, where effects of doping were modelled by the Virtual Crystal Approximation 51 (see Methods for details).
The calculated ferroelectric polarization of the orthorhombic Pca21 phase of HfO2 is about 50.2 μC/cm 2 , which is consistent with the previous theoretical studies. [10][11][12][13][14] The polarization is directed along the c-axis, as enforced by the symmetry of the crystal, so that the a-and bcomponents of polarization are zero. The 5% Y doping slightly reduces the polarization down to about 49.9 μC/cm 2 , which indicates that Y does not play a decisive intrinsic role in high polarization values observed in our experiments, but rather helps to stabilize the orthorhombic Pca21 phase of hafnia. Figure 5a shows the calculated c-component of the ferroelectric polarization Pc as a function of angle α. With a larger rhombohedral distortion (smaller α), the Pc remains large, but slightly reduces. This reduction is just ~ 0.1 μC/cm 2 for the degree of distortion relevant to our experiment. At the same time the broken Pca21 symmetry allows the appearance of non-vanishing a-and b-components of polarization, Pa and Pb. Figure 5b demonstrates that the absolute values of both Pa and Pb increase with decreasing α, but the magnitudes are much smaller than Pc. Ydoped HfO2 exhibits the same tendency as the pristine HfO2 (compare the red and blue lines in Fig.  5a and b), implying an idle role of the doping in the polarization enhancement.
Overall, our DFT calculations reveal that the rhombohedral distortion observed in our experiments is not intrinsic to the bulk HfO2 and most likely results from the strain imposed by the substrate. In addition, the rhombohedral distortion of the degree observed in our experiments does not much affect the large ferroelectric polarization value of the orthorhombic Pca21 phase of the pristine and YHO.
Importantly, comparing the results of our DFT calculations and experimental data indicates that we observe the intrinsic ferroelectricity of Y-doped HfO2 at low temperature. Experimentally, the remanent polarization saturates with increasing crystallinity at low temperature values ranging from 32 μC/cm 2 to 37 μC/cm 2 , corresponding to the of YHO(111) grown on LSMO(001) and LSMO(110), respectively (Fig. 1f). These values represent the projection of polarization of YHO pointing along the c axis to the out-of-plane (111)pc direction. This implies that the total spontaneous polarization along the c axis is in the range from 55 μC/cm 2 to 64 μC/cm 2 , which is in good agreement with the results of our DFT calculations.

Discussion
Stabilization of the o-phase has been a core issue for the ferroelectricity in the HfO2-based materials. Thermodynamic stabilization requires that the o-phase has lower energy than all the other phases, especially the m-phase. However, the theoretically predicted critical size is smaller than was observed experimentally 17 . Therefore, kinetic stabilization is necessary. During cooling from the high-temperature t-phase, formation of the o-phase is favored since its interfacial energy with the t-phase is smaller compared with that of the m-phase 19,20 . This process is more effective if the initial t-phase has high crystallinity because the structural defects lead to ill-defined o/t and m/t interfaces. Since the high growth temperature of epitaxial thin films enhances the crystallinity of the t-phase, it is expected to promote the stabilization of the o-phase and allows formation of the o-phase with high crystallinity during cooling, which explains the results of this work.
Two factors are critical for enhancing the stability of the o-phase YHO studied in this work. The first factor is the large surface area and anisotropic strain of the ultra-thin epitaxial films, as suggested previously by theory 12,15 . Experimentally, no rapid annealing is necessary for growing ferroelectric HfO2-based epitaxial films, indicating more effective kinetic stabilization 19, [21][22][23][24][25][26][27][28]47,52 . In this work, a small rhombohedral distortion in YHO suggests a presence of anisotropic strain, which could enhance the stability of the o-phase by increasing the energy of the m-phase. The second factor is Y doping, which has been shown to reduce the energy of the high-temperature symmetric phase. 48,53,54 More importantly, Y doping appears to have a superior effect on enhancing the o-phase stability, which has been highlighted recently by the demonstration of ferroelectricity in YHO of 1-μm-thick films 35,36 and even in bulk 20 .

Summary and Outlook
We have demonstrated that the spontaneous polarization of the YHO(111) films grown on both LSMO(001) and LSMO(110) increases with improving crystallinity, which is opposite to the common expectation that the stabilization of the ferroelectric Pca21 structure requires formation of nanograins. The measured spontaneous polarization was found to be higher and having a much weaker temperature dependence than that reported in the previous studies, indicating the dominant contribution from the intrinsic ferroelectricity. The highly crystalline YHO(111) films contained the orthorhombic ferroelectric Pca21 structure with a small rhombohedral distortion. Overall, our results demonstrate that Y doping and the anisotropic strain in epitaxial films grown at high temperature strongly enhance the stability of the orthorhombic ferroelectric phase and thus offer a viable approach to HfO2-based ferroelectrics with high crystallinity. This marks a milestone in understanding and tuning the intrinsic properties as well as expanding the application potential of the HfO2-based ferroelectric materials.

Methods
Sample preparation. The YHO thin films on La2/3Sr1/3MnO3 (LSMO) bottom electrodes were grown by pulse laser deposition (PLD) with a wavelength of 248 nm on SrTiO3 (STO) substrates. The base pressure of PLD chamber is around 3×10 -7 mTorr. Before depositions, the STO substrates were pre-annealed at 650°C for 1 hour in PLD chamber. LSMO layer with thickness of ~25 nm was deposited at 600°C under a 60 mTorr oxygen atmosphere. The ceramic 5% Y-doped HfO2 target was synthesized at 1400°C by solid-state reaction using HfO2 (99.99% purity) and Y2O3 (99.9% purity) powders. The growth temperature from 750°C to 970°C, a repetition rate of 2 Hz and an oxygen pressure of 70 mTorr were employed to grow the YHO films. The typical thickness of YHO films is about 9-11 nm. At the end of deposition, the temperature of the films decreases to room temperature with a cooling rate of 10°C/min under an oxygen pressure of 70 mTorr. The platinum top electrodes with thickness of ~15 nm were deposited ex-situ by PLD using shadow mask in vacuum at room temperature. The diameter of top electrodes is from 75 μm to 400 μm. Electrical measurements. For the measurements of the ferroelectric properties at room temperature, a solid Pt tip (RMN-25PT400B, RockyMountain Nanotechnology) in contact with the platinum top electrode was used to apply the voltage pulses using a Keysight 33621A arbitrary waveform generator while the transient switching currents through the bottom electrode were recorded by a Tektronix TDS 3014B oscilloscope. In all measurements, the bias was applied to the top electrode (diameter from 75 μm to 400 μm) while the LSMO bottom electrode was grounded. The low-temperature measurements with temperature range from 20 K to 300 K are implemented using Cryostat, Sumitomo Cryogenics, and the top electrodes are connected using silver paint and silver wires.
Scanning probe microscopy. PFM measurements were carried out using a commercial AFM system (MFP-3D, Asylum Research) using Pt-coated tips (PPP-EFM, Nanosensor) in the resonance tracking mode by applying an ac modulation signal of 0.8 V amplitude and a frequency of ~ 350 kHz. The bias was applied through the conductive tip and the bottom electrode was grounded.
Electron microscopy. For the images with the view along YHO [11 ̅ 0] (same as LSMO [001]): The TEM foil was prepared by conventional cutting, grinding and polishing followed by a precision ion polishing (Gatan PIPS695 tool). (S)TEM images with EDS mappings were obtained by a high-resolution transmission electron microscope (HRTEM) FEI TALOS-F200X equipped with high-angle annular dark-field (HAADF) detectors and energy dispersive X-ray spectrometer (EDX). For the images with the view along YHO [112 ̅ ] (same as LSMO [11 ̅ 0]): An electron transparent cross section of sample of HfO2/LSMO thin film on STO substrate was prepared using Helios NanoLab Dual Beam 660 SEM. The cross-section sample was mounted on a copper FIB lift-out grid. The thinning of the cross-section sample was started from the bottom of the sample to avoid damaging the top part of the sample where the thin films were deposited. Thus, sample was tilted 52±7°, 52±5°, 52±3°, 52±1.5° and was thinned from 2 μm to less than 100 nm by ion beam with 15 kV and 0.42 nA, 8 kV and 0.23 nA, 5 kV 80 pA, and 3 kV and 20 pA, respectively. The final polishing was done at 2 kV and 20 pA. The sample was characterized using a FEI Tecnai Osiris S/TEM. Density-functional theory (DFT) calculations. First-principles DFT calculations were performed using the plane-wave pseudopotential method implemented in the Quantum-ESPRESSO package 50 . Generalized gradient approximation (GGA) for the exchange and correlation functional and an energy cutoff of 544 eV were used in the calculations. The atomic relaxations were performed with an 8×8×8 k-point mesh until the Hellmann-Feynman forces on each atom became less than 1.3 meV/Å. A 10×10×10 k-point mesh was used for the subsequent self-consistent calculations. The Berry phase method was applied to calculate the ferroelectric polarization. The effects of Y doping was modelled by Virtual Crystal Approximation (VCA) 51 , by simulating each Hf-site with a pseudopotential of fractional valence. To neutralize the charge in the structures, O-sites are also treated by VCA.

Data availability
The data that support the findings of this study are included in the main text and Supplementary Information.