Epitaxial Ferroelectric HfO2 Films: Growth, Properties, and Devices

About ten years after ferroelectricity was first reported in doped HfO2 polycrystalline films, there is tremendous interest in this material and ferroelectric oxides are once again in the spotlight of the memories industry. Great efforts are being made to understand and control ferroelectric properties. Epitaxial films, which have fewer defects and a more controlled microstructure than polycrystalline films, can be very useful for this purpose. Epitaxial films of ferroelectric HfO2 have been much less investigated, but after the first report in 2015 significant progress has been achieved. This review summarizes and discusses the main advances on epitaxial HfO2, considering growth, study of structural and ferroelectric properties, identification of the ferroelectric phase, and fabrication of devices. We hope this review will help researchers investigating epitaxial HfO2. It can also help extend the interest of the ferroelectric HfO2 community, now basically focused on polycrystalline samples, to epitaxial films.


Introduction
Ferroelectric perovskites are widely used in the electronics industry, in particular BaTiO3 is used in multilayer ceramic capacitors and lead zirconate titanate (PZT) in piezoelectric devices. 1 Additionally, ferroelectric random access memories (Fe-RAM), which currently use PZT, are on the market for about 30 years. These memories offer very high speed, low power consumption, and high retention and endurance. However, the difficulties in scaling the size below the 130 nm node make them not cost competitive and its use is restricted to niche applications. Various perovskite oxides are also used in emerging memories such as ferroelectric field effect transistors (Fe-FETs) and ferroelectric tunnel junctions (Fe-TJs), 2 but after several decades of research, they are far from being used in commercial devices. Therefore, ferroelectric perovskites do not have a big impact on the memory device market. Limited success stems from the complexity of these oxides. Ferroelectric perovskite films must be no less than tens of nanometer thick to exhibit good properties, and deposition techniques as atomic layer deposition (ALD) allowing conformal growth are not easily implemented. The compatibility with CMOS processes is restricted by the thermal budget required for its crystalline growth and by its sensibility to hydrogen.
The recent discovery of ferroelectricity in simple oxides based on HfO2 has renewed the interest in ferroelectric memories. [2][3][4][5][6][7] HfO2 is already used in CMOS lines and the deposition techniques and conditions to form the ferroelectric phase can be compatible with CMOS technology. Very shortly after the first publication in 2011 reporting on ferroelectricity in HfO2, 8 prototypes of Fe-RAMs and Fe-FETs 9 were produced. This was followed by the fabrication of 3D Fe-RAMs 10 and Fe-FETs with 22 nm node. 11 Doped-HfO2 is also promising for the development of Fe-TJs. 12 Research on HfO2 has basically been done with polycrystalline films, mostly made by ALD at room temperature followed of rapid thermal annealing using TiN/doped-HfO2/TiN capacitor heterostructures.
The experimental demonstration of ferroelectricity in HfO2 was unexpected since its monoclinic phase (space group P21/c) is nonpolar. Other crystalline phases that form at high temperature, the tetragonal (P42/nmc) and cubic (Fm3m) polymorphs, are also nonpolar. It was observed that the presence of a capping layer before HfO2 annealing was essential to stabilize the ferroelectric phase. It was proposed that the film crystallized in tetragonal phase, transforming into an orthorhombic polar phase during cooling. In absence of the capping layer, it transformed into the monoclinic phase. 8,13 The films with capping layer and annealed were not pure orthorhombic and the monoclinic phase was also present. The relative amount of the monoclinic phase increases with thickness in films thicker than around 10 nm. [14][15][16] The experimental results suggested that surface and strain energy were important factors in the stabilization of the metastable ferroelectric phase. Experimental structural characterization indicated that the Pca21 phase was the origin of the ferroelectricity in HfO2, 17 and density functional theory (DFT) calculations support this. [18][19][20][21][22] However, the formation of the ferroelectric phase does not depend only on thermodynamics, and the kinetics in the preparation process seems to be determinant. 23 Progress in the preparation, understanding of structural and ferroelectric properties of HfO2, and fabrication of devices has been enormous (see, for instance, reviews in refs. [3][4][5][6][7][24][25][26][27][28][29][30][31]. This progress has been achieved mainly with polycrystalline films. Epitaxial films have been much less investigated. The polycrystalline ferroelectric films are formed by annealing of amorphous or quasi-amorphous doped HfO2 in heterostructures such as TiN/doped-HfO2/TiN. Instead, epitaxial films generally nucleate on the surface of single crystals or bottom epitaxial layers. The relative contribution of the interface energy during nucleation is greater than in the case of crystallization in bulk by annealing. This has allowed the epitaxial stabilization of metastable phases of other materials that rarely form in polycrystalline films. 32 Epitaxial films can also undergo phase transformations when cooled, but the contribution of the (semi)coherent interfaces can be much relevant than in polycrystalline films. Therefore, the stabilization mechanisms of the ferroelectric phase of HfO2 in epitaxial films may differ significantly from those widely investigated for polycrystalline films, offering the opportunity to stabilize films of enhanced quality and concomitantly better functional properties. Epitaxial films, with better control of microstructure, can also be of great interest to better understand the ferroelectric properties of HfO2, as well as for prototyping devices. Despite this interest, it was not until 2015 when researchers at Tokyo Institute of Technology and Tohoku University reported by the first time on epitaxial growth of ferroelectric films of doped HfO2. 33 Afterwards the research on epitaxial ferroelectric HfO2 films increased exponentially. Table I summarizes the ferroelectric properties reported for epitaxial films of doped HfO2. Excellent properties have been achieved, and differences between polycrystalline and epitaxial films have been observed (Table II). Here, we review on the main results obtained in epitaxial ferroelectric HfO2 films. We will first revise results on the epitaxial films grown on yttria-stabilized zirconia, epitaxial films obtained by the crystallization of amorphous films, epitaxial films grown on perovskite substrates and, finally, epitaxial films grown on Si. We will discuss on the different polymorphs that have been proposed as ferroelectric phase in epitaxial films. We will analyze in detail the functional properties reported for epitaxial films, i.e. the Pr and Ec obtained values and the endurance and retention. Finally, we will focus on the results obtained in the characterization of devices made of epitaxial doped HfO2 films.

Epitaxial ferroelectric doped HfO2 films on yttria-stabilized zirconia
Shimizu et al. 33 prepared Y-doped (0, 7, and 15 %) HfO2 (YHO) films, 20 nm thick, on (001)oriented yttria-stabilized zirconia (YSZ) by pulsed laser deposition (PLD) at 700 C and 0.01 Torr of O2. Symmetric X-ray diffraction (XRD) measurements signaled that the films presented (001) orientation, as the substrate. The close position of the XRD symmetric reflections made phase identification difficult. The authors used a two-dimensional (2D) detector to measure asymmetric reflections. There are additional weak diffraction spots as lower the crystal symmetry is, and the absence of some reflections permits excluding first the monoclinic phase and second the orthorhombic phase. They concluded that the crystal phases in the films were monoclinic for the pure HfO2 film, tetragonal or cubic for the Y(15%):HfO2 film, and orthorhombic for the Y(7%):HfO2 film. Therefore, the metastable orthorhombic phase was only stabilized in the epitaxial Hf0.93Y0.07O2 film. Shimizu et al. performed also XRD measurements of this sample at high temperature ( Figure 1a). 33 The weak asymmetric orthorhombic (o) o-YHO(110) reflection was measured from room temperature to 600 C (Figure 1b). The peak vanished at around 450 C, signaling a transition to paraelectric tetragonal or cubic phase, and thus indicating that the Curie temperature of the film was around 450 C.
Orthorhombic films on cubic substrates are expected to present crystal variants. This was experimentally observed by XRD in YHO films on YSZ(001). 34 Local analysis by transmission electron microscopy (TEM) revealed a lateral size of the crystallites of around 10 nm, and that grain boundaries were along {100} or {110} planes. 35 Shimizu et al. 36 observed that films on indium-tin oxide (ITO) buffered YSZ(001), presenting only b-and c-oriented domains (c-axis was considered the polar axis), had large polarization of around 30 µC/cm 2 . This suggested that ferroelectric switching should imply ferroelastic domain switching, which was later confirmed experimentally by micro-diffraction, focusing a synchrotron radiation beam on poled and pristine capacitors ( Figure 2) where vanishing of (0l0) reflections was observed after junction cycling indicating a polarization rotation from in-plane to out of plane.

Control of film orientation on yttria-stabilized zirconia
Funakubo and collaborators prepared also epitaxial Hf0.93Y0.07O2 films, around 15 nm thick, on ITO buffered YSZ (110) 37 and YSZ (111) 38 substrates. YHO films and ITO electrodes were epitaxial and presented cube-on-cube like epitaxial relationship with the substrate. Ferroelectric polarization loops were measured, being the remanent polarization around 10 and 16 µC/cm 2 for (111) and (110) oriented films, respectively. The coercive field Ec of both films was similar, around 2 MV/cm. XRD measurements at high temperature of a YHO(110) film 37 signaled Tc around 450 C, similar to YHO(001) films. 33 Recently, the same research group has extended this analysis to (111)-oriented epitaxial films and polycrystalline films, also characterizing films with different thickness. 39 Although the investigated thickness ranges and growth conditions were not coincident, the results suggest small orientation and thickness dependence on Tc in films thicker than around 10 nm, with Tc around 500 C, and reduction of Tc in thinner films, t  5 nm, up to 350 C (Figure 1c).
Shiraishi et al. prepared epitaxial Fe-doped HfO2 41 and Ce-doped HfO2 42 films. Films were grown on ITO/YSZ(001) by ion-beam sputtering at room temperature followed by rapid thermal annealing. Fe-doped films presented the greatest amount of orthorhombic phase for a Fe content of around 6%. The polarization loops, not saturated, showed Pr of around 8.8 µC/cm 2 . The Curie temperature, estimated from XRD measurements at high-temperature, was around 500 C. In the case of Ce-doped films, XRD and TEM characterization suggested that films doped with 3 to 10% Ce are orthorhombic. The polarization loops showed low remanent polarization, being the estimated value around 5 µC/cm 2 .

Solid phase epitaxy
Kiguchi et al. 43 reported epitaxy of HZO by crystallization of amorphous films. A HZO film, deposited by ion-beam sputtering at room temperature, was crystalized by rapid thermal annealing (RTA) at 800 C for 10 min under oxygen flow. The film was 30 nm thick. The authors concluded, from high-angle annular dark-field imaging (HAADF) scanning transmission electron microscopy (STEM) images compared with simulations, that the crystallized epitaxial film included both monoclinic and orthorhombic phases. However, the measured XRD scan showed a very broad peak that did not allow to confirm the stabilization of the orthorhombic phase. A similar growth process was done by Mimura et al., 39 using PLD to grow non-ferroelectric Y-doped HfO2 films at room temperature on YSZ (111) (Figure 3a) and subsequent RTA at around 1000 C under N2 atmosphere (Figure 3b). The ferroelectric properties were similar to those of films grown by PLD at 700 C. 34,37 Films around 15 nm present orthorhombic phase, while there is coexistence of orthorhombic and monoclinic phases in films around 30 nm thick. In-situ XRD 5 during annealing of 15 nm thick Hf0.93Y0.07O2 films on ITO/YSZ(111) allowed identifying the evolution of crystal phases during heating to 1000 C and cooling to room temperature. 44 The film deposited at room temperature was monoclinic, and phase transformation was not detected up to 600 C. Above this temperature monoclinic and tetragonal phases coexisted, being the film purely tetragonal above around 950 C. Cooling the film, it remained tetragonal up to around 400 C, when both tetragonal and orthorhombic coexisted. Finally, only the orthorhombic phase is detected below 200 C (Figure 3c,d,e).
Suzuki et al. 45 investigated the influence of the atmosphere in sputtering at room temperature and rapid thermal annealing for crystallization. They deposited Hf0.93Y0.07O2 films, around 24 nm thick, by RF magnetron sputtering under 200 mTorr of pure Ar or Ar/O2 = 100. Crystallization was done at 1000 C for 10 s under N2 or O2 flow. The orthorhombic phase was present in all samples, but the ferroelectric properties were very different. The film deposited in pure Ar and crystallized under N2 flow showed well saturated polarization loops, while loops could not be measured in the films grown in Ar gas with around 1% O2 due to leakage. The film deposited under pure Ar and annealed under O2 showed ferroelectric loops, but with significant imprint and low breakdown field. Current leakage curves of films deposited with partial pressure of O2 or crystallized under O2 flow were asymmetrical and showed large leakage. Similar influence of oxygen is observed in polycrystalline films prepared by sputtering. [46][47] Recently, Mimura et al. 48 reported the unexpected epitaxial growth of orthorhombic Hf0.93Y0.07O2 films at room temperature without annealing. The films were deposited by sputtering in pure Ar atmosphere. The absence of O2 in the sputtering gas was found to be critical in the formation of orthorhombic phase, and films deposited under Ar/O2 = 100 were monoclinic. This result, which suggests that oxygen vacancies are convenient to stabilize the metastable orthorhombic phase, are in agreement with observations done with polycrystalline films [46][47] and epitaxial films obtained by RTA of amorphous films. 45 Mimura et al. 48 confirmed ferroelectricity by polarization loops, with high Pr of 14.5 µC/cm 2 in films on ITO/YSZ (111), and much lower polarization in films on ITO/YSZ(001). Although it is known that some fluorite oxides as CeO2 can grow epitaxially at room temperature, 49 the result reported by Mimura et al. 48 was surprising and further studies are required to understand the mechanism that allow epitaxial growth of the metastable phase at room temperature.

Epitaxial ferroelectric HfO2 films on perovskite single crystals
Si has been widely used as a dopant to stabilize the ferroelectric phase in polycrystalline films. This is achieved for a narrow range of Si content of around 4 %, while for slightly higher content the tetragonal phase stabilizes and the films are antiferroelectric. 8,24 The epitaxial growth of Sidoped HfO2 was reported by Li et al. 50 They deposited Si(4.4%):HfO2 films (Si:HO), with thickness in the 1.5-15 nm range, on (001), (110) and (111) (Figure 4). The coercive fields were huge around 5 MV/cm and with little dependence on thickness and sizeable leakage contribution probably related to the use of Nb:STO as an electrode. Ferroelectric loops for 3 nm thick films were also reported without clear evidence of ferroelectric polarization.
An alternative to semiconducting Nb:STO perovskite substrates is the use of conducting epitaxial perovskite electrodes. Various groups have reported on epitaxial ferroelectric HZO films on La0.67Sr0.33MnO3 (LSMO) electrodes grown epitaxially on STO(001) and other single crystalline perovskite substrates. Wei et al. 51 and Lyu et al. 52 reported ferroelectric HZO films on LSMO/STO(001) in 2018. The films were grown by PLD at 800 C and 0.1 mbar of oxygen. The epitaxial films were (111) oriented, being the (111) diffraction peak in the -2 scans located at around 30 (Cu K radiation), while the peak is usually at around 30.5 in polycrystalline films. The films present four in-plane crystal variants (Figure 5a), as expected considering the 3-fold symmetry of HZO (111) and the 4-fold symmetry of LSMO(001). Wei et al. 51 deposited films, having thickness in the 4 -27 nm range, and showed polarization loops for t = 9 nm and t = 5 nm films, with remanent polarization of 18 µC/cm 2 in the t = 9 nm and huge 34 µC/cm 2 in the t = 5 nm. There was not wake-up effect, although the films presented very strong fatigue and polarization was very low after 10 3 cycles. The coercive fields were great, above 3 and 5 MV/cm in the t = 9 and 5 nm, respectively. On the other hand, Ec was higher in the thinner film, as usually observed in ferroelectric perovskite oxides. Lyu et al. 52 compared two films, t = 9 and 18 nm thick, (111) oriented and with four in-plane crystal variants too. The presence of monoclinic phase coexisting with the polar orthorhombic phase was evident in XRD measurements of the thicker film using a 2D detector (Figure 5b). It was observed that the monoclinic phase has much higher mosaicity than the o-phase. Thus, the relative amount of monoclinic phase in HZO films on LSMO/STO(001) can be underestimated by XRD -2 scans using a point detector. The increase of monoclinic phase with thickness in epitaxial films is commonly observed too in polycrystalline HZO films. 14-16 Lyu et al. 52 reported ferroelectric loops, without wake-up effect ( Figure 6a). The t = 9 nm film exhibited huge coercive field above 3 MV/cm and imprint field of 0.5 MV/cm directed towards the LSMO bottom electrode. The remanent polarization was around 20 µC/cm 2 in this film, and less than 7 µC/cm 2 in the t = 18 nm film. These polarization values, and those reported by Wei et al. 51 for t = 5 and 9 nm films, pointed to a decrease of polarization increasing HZO thickness, which could be connected with the larger amount of nonpolar monoclinic phase.
Lyu et al. 52 demonstrated that epitaxial HfO2 can present high endurance and retention. The t = 9 nm film was cycled for more than 10 8 cycles without breakdown, although exhibited fatigue, i.e. polarization decreased from 2Pr = 25 to 9 µC/cm 2 after 10 8 cycles of amplitude 4.5 V (Figure 6b,c). The dielectric permittivity showed too monotonic reduction with the number of cycles (Figure 6c, inset). Leakage current was constant during the first 10 4 cycles, but it increased monotonously with additional cycles. 52 The retention was measured at room temperature after poling the film at 5.5 V up to 10 4 s. Extrapolation of the experimental data pointed to retention well beyond 10 years.

Growth window for epitaxial stabilization
The growth window (substrate temperature and oxygen pressure) for epitaxial stabilization by PLD was reported by Lyu et al. 53 They grew t = 9 nm HZO films on LSMO/STO(001) varying substrate temperature in the Ts = 650 -825 C range (at fixed PO2 = 0.1 mbar) and varying oxygen pressure in the PO2 = 0.01 -0.2 mbar range (at fixed Ts = 800 C). The orthorhombic phase was formed in all the Ts range, increasing the intensity of the o-HZO(111) peak with Ts, signaling increased amount of polar phase and/or reduced mosaicity. The out-of-plane lattice parameter, do-HZO(111), decreased from around 2.98 Å to around 2.96 Å. All films were very flat, with root mean square roughness (rms) roughness less than 4 Å. The oxygen pressure has a great effect in the crystallinity of the films. Films deposited at 0.05 mbar or higher PO2 exhibited an intense o-HZO(111) diffraction peak, while there were no diffraction peaks in the PO2 = 0.01 mbar film. In the case of the PO2 = 0.02 film there was a low intensity o-HZO(111) peak, and XRD measurements using a 2D detector revealed a coexisting high-mosaicity monoclinic phase. The amount of the monoclinic phase was lower in films deposited at higher PO2. do-HZO(111) decreased with PO2, from close to 2.99 Å in the 0.02 mbar film to around 2.95 Å in the 0.2 mbar film. The rms roughness was less than 4 Å in films deposited at PO2 up to 0.1 mbar, increasing in the 0.2 mbar film up to around 7 Å.
Substrate temperature and oxygen pressure have a notorious influence on the ferroelectric properties. Lyu et al. 53 reported that remanent polarization Pr and coercive electric field Ec of HZO films (t  9 nm) increased with Ts, from 14 µC/cm 2 and 1.9 MV/cm to 21 µC/cm 2 and 2.9 MV/cm. Pr increased also with PO2, from negligible value in the 0.01 mbar film to around 20 µC/cm 2 in the 0.1 mbar film, being around 18 µC/cm 2 in films grown under higher PO2. The dependence of Vc on PO2 was similar, with values in the 0.8 -2.8 MV/cm range. Considering both Ts and PO2 series, there was clear correlation of polarization with amount of orthorhombic phase, while there was not an evident dependence with do-HZO (111). Similar correlation between polarization and orthorhombic phase amount had been reported for polycrystalline doped HfO2 films. 54 On the other hand, leakage current decreased more than one order of magnitude with Ts (from  10 -5 A/cm 2 (Ts = 650C) to less than 10 -6 A/cm 2 (Ts = 825C) at E = 1 MV/cm), while it increased more than three orders of magnitude with PO2 (from  10 -7 A/cm 2 (PO2 = 0.02 mbar) to more than 10 -4 A/cm 2 (PO2 = 0.2 mbar) at E = 1 MV/cm). The dependence on PO2 suggests that leakage in these epitaxial films arises from other factors in addition to oxygen vacancies The leakage of HZO films exhibiting high polarization is around 10 -6 A/cm 2 at E = 1 MV/cm, similar to other polycrystalline HZO films of equivalent thickness, although an extremely low leakage current of less than 10 -8 A/cm 2 at E = 1 MV/cm has also been reported for t = 10 nm polycrystalline HZO films. 55

Interfacial layer and epitaxy mechanisms
Wei et al. 51 characterized by cross-sectional STEM a HZO/LSMO/STO(001) sample and observed an interfacial HZO layer around 2-3 monolayers thick at the interface with LSMO. The layer, coherently strained, was identified as tetragonal phase. Later, Nukala et al. 56 determined by electron energy loss spectroscopy that the interfacial layer was oxygen deficient. They proposed that this oxygen deficient layer could be conducting, and that it could yield an additional screening mechanism for the stabilization of the polar phase. There was no interfacial layer in films on LSMO/LaAlO3(001). Since it is known that the formation of oxygen vacancies is favored under tensile stress, the authors suggested that tensely strained LSMO was responsible for the formation of the tetragonal interfacial layer. Estandía et al. 57 also observed by STEM an interfacial layer in HZO/LSMO/STO(001). It was a pseudomorphic HZO layer, one monolayer thick, separated from the rest of the HZO film by a semicoherent interface. Similar interfacial layers were previously reported in interfaces between other highly mismatched oxides. 58 Epitaxy generally happens by matching of atomic columns at the interface between two materials. Cube-on-cube epitaxy, or other simple epitaxial relationships as 45 in-plane rotation of the crystal lattices, are common. These conventional epitaxy habits are not viable in case of symmetry dissimilarity and high lattice mismatch, as it is the case of orthorhombic HZO(111) on (001) surfaces of LSMO or other perovskites of similar lattice parameter. However, unconventional mechanisms, as tilted epitaxy 59 or domain matching epitaxy (DME), 60-61 can permit epitaxy in some of these cases. Tilted epitaxy of HZO(111) occurs on Nb:STO(001), with a misorientation of about 15 with respect to the surface normal. 56 In the case of orthorhombic HZO(111) on LSMO(001), Estandía et al. 57

Polar phase stabilized on LSMO
Wei et al. 51 observed that the out-of-plane d(111) lattice parameter was larger in the thinner films. They performed -scans and -2 scans around asymmetric {111} reflections, using synchrotron radiation and measured d(11-1) = d(1-11) = d(-111) = 2.94 Å, smaller than the d(111) = 2.98 Å. The values were consistent with a rhombohedral unit cell, and the authors considered it a R3m rhombohedral metastable polymorph stabilized by the epitaxy. This was based on DFT calculations that simulated a R3m structure that was strongly polar (P  15 µC/cm 2 ) under high epitaxial compressive stress causing an out-of-plane d(111) lattice parameter of 3.25 Å ( Figure  8). Another polar rhombohedral phase, R3, was simulated for pure HfO2, but it was less stable for HZO. Thus, it was concluded that ferroelectricity in epitaxial films on LSMO(001) was due to the polar R3m rhombohedral phase. More recent DFT calculations by Zhang et al. 62 confirmed high polarization in the R3m phase under huge compressive strain of around 5%, although the rhombohedral phase was only more stable than the orthorhombic Pca21 for extremely small thickness less than 5 five Hf-O2 monolayers.
The DFT calculations 51 determined that the R3m phase should be under huge out-ofplane strain, d(111) > 3.25 Å, to present the high polarization observed experimentally. Huge out-of-plane strain was experimental reported by Wei et al. 51 , but only for an ultra-thin film of 1.5 nm. The polarization of that film was not reported, likely because the extremely low thickness did not allow the measurement. Experimental data of polarization of epitaxial HZO(111) on LSMO/STO(001) are reported for films of thicknesses ranging around 4.5 -40 nm. [51][52][53]63 The experimental d(111) out-of-plane lattice parameters of these films, 2.96 -3.05 Å, are much smaller than the very high values (d(111) > 3.25 Å) that the DFT calculations found necessary for high polarization 51 . Besides, polarization shows moderate dependence on strain (and decreasing with d111 instead of increasing) in films deposited on substrates with varying lattice parameter 64 or prepared varying growth condition ( Figure 8). 53 Moreover, the d(111) extracted parameter is below 2.99 Å for any sample and thus far from the calculated necessary distortion to achieve large remanent polarization. Moreover, as shown below in Section 5, epitaxial HZO films on buffered Si(001), under great in-plane tensile stress when are cooled after growth due to the mismatch in thermal expansion coefficients between HZO and Si, present outof-plane d(111) 2.94 -2.96 Å, 63, 65-66 significantly smaller than equivalent films on STO(001), 53,63 but contrary to DFT predictions for R3m phase, 51 the polarization is larger. The experimental reports on evaluation of remanent polarization and d(111) out-of-plane lattice parameters similar to that found necessary for high polarization by DFT calculations 51 are non-existent. Wei et al., 51 noted the possibility that some effects (crystallite size; surfaces and interfaces; local deviations from the average composition) could help to stabilize particular phases. Therefore, further studies are needed to conclude that the rhombohedral unit is a genuine phase, which could present ferroelectric properties different to those of the Pca21 orthorhombic phase, and not a simple structural distortion caused by epitaxial stress as commonly occur in other heteroepitaxial systems.
Materlik et al. 20 performed DFT calculations to compare the total energy of different polymorphs, including strain with an estimation of the surface energy. They concluded that strain was not the major cause of stabilization of the ferroelectric Pca21 phase, and that the stability of this phase in epitaxial HZO films was limited to size below 5 nm. Later, Liu et al. 67 considered epitaxial films of different orientation and strain and evaluated by DFT calculations the energy of two orthorhombic phases (the polar Pca21 and the non-polar Pbca) in comparison with the energy of the monoclinic P21/c. They concluded that the orthorhombic phases were more stable than the monoclinic phase in (111) films in a wide range of strain. The stable phase at high temperature would be tetragonal, and although the non-polar orthorhombic phase presented slightly lower energy than the polar phase, its transformation from the tetragonal phase was assumed to be slow and thus its formation could be suppressed by kinetics. Other recent DFT calculations evaluated epitaxial (111)-oriented films on STO(001) substrates and predicted that the phase responsible of the ferroelectricity was the polar orthorhombic phase Pnm21. 68 The authors proposed that the distinct Pnm21 phase would be the reason of the absence of wake-up effect in these epitaxial films. However, it has to be noted that wake-up effect is not a property genuine of a phase, [69][70][71] and different mechanisms can produce it. 3,[72][73][74][75] Assumptions of Qi et al., 68 which can be extended to the other authors reporting DFT calculations of ferroelectric HfO2 and other polymorphs, are based on strain states that differ to the experimental data revealed by XRD and STEM. 53, 57, 64

Epitaxial stress engineering
Estandía et al. 64 deposited LSMO electrodes and t = 9.5 nm HZO films on a set of ten (001)oriented cubic or pseudo-cubic single crystalline oxide substrates (YAlO3, LaAlO3, NdGaO3, LSAT, SrTiO3 DyScO3, TbScO3, GdScO3, DyScO3, NdScO3 and MgO), with lattice parameter ranging from 3.71 Å (YAlO3) to 4.21 Å (MgO). The t = 25 nm LSMO electrodes grew coherently for lattice mismatch from around -2% (LSMO on LaAlO3) to +2% (LSMO on TbScO3), and were partially or fully relaxed on more mismatched substrates. XRD measurements using a 2D detector demonstrated that the in-plane parameter of LSMO determines the relative amount of orthorhombic and monoclinic phases in the HZO film. When LSMO (aLSMO = 3.874 Å in bulk) is compressively strained (aLSMO smaller than around 3.86 Å), HZO crystallizes in monoclinic phase. When LSMO is relaxed or under tensile strain, the metastable orthorhombic phase is stabilized, increasing the o/m ratio with aLSMO. LSMO electrodes on scandate substrates were highly tensely strained (aLSMO 3.95 Å), and the HZO films were almost purely orthorhombic. STEM characterization allowed to confirm the increased amount of orthorhombic phase for increasing substrate lattice parameter (Figure 9a,b,c). The films on LSMO/LSAT, LSMO/STO and LSMO/GdScO3 showed single monoclinic phase, coexisting monoclinic and orthorhombic phases, and single orthorhombic phase, respectively. It is noted that grains are observed even in single phase films, due to the crystal variants existing in both monoclinic and orthorhombic phases. The grain boundaries between crystal variants are coherent, while those between monoclinic and orthorhombic phases are incoherent. 76 Estandía et al. 64 reported polarization loops of the films deposited on the ten oxide substrates. The ferroelectric polarization was very low in the film on substrates (YAlO3, LaAlO3 and NdGaO3) causing compressive strain to LSMO, and it was low (Pr  5 µC/cm 2 ) in the film on LSAT, on which LSMO is practically unstrained. Polarization increases in films on substrates with larger lattice parameter, being Pr  24 µC/cm 2 on TbScO3. LSMO relaxes plastically on substrates with lattice parameter greater than TbScO3, and the polarization of the HZO film on these substrates is lower. In the case of ferroelectric perovskites, polarization usually depends on the lattice strain of the ferroelectric film. It allows the control of the ferroelectric polarization by selection of a substrate that causes a certain elastic strain. This is usually called strain engineering. 77 However, in the case of epitaxial HZO films, the great influence of the substrate on the ferroelectric polarization is not mainly due to HZO strain (i.e., strain engineering). Figure  9d shows that do-HZO(111) does not vary significantly in the HZO films and this small variation does not produce a significant Pr variation. In fact, the small decrease of Pr with do-HZO(111) appreciated in Figure 9d is against the increase of polarization with do-HZO(111) theoretically predicted and discussed in the previous section. Thus, other contributions play a more important role. In this series of HZO films on ten substrates, Estandía et al. 64 observed that films on scandate substrate had the greater amount of orthorhombic and the larger ferroelectric polarization (Figure 9e). Therefore, in epitaxial growth of HZO/LSMO on oxide substrates, the selection of scandate substrates causing tensile strain is critical to have the highest ferroelectric polarization. The different substrates cause different strain in LSMO, which determines the relative amount of monoclinic and orthorhombic phases. Therefore, the impact on the properties of HZO is due to epitaxial stress engineering, but not to epitaxial HZO strain engineering.
Nukala et al. 56 deposited t = 6 nm HZO films on a set of six different oxide substrates (YAlO3, LaAlO3, NdGaO3, LSAT, SrTiO3 and DyScO3) buffered with a t = 40 nm LSMO electrode. The HZO films on the two substrates with larger lattice parameter, STO and DSO, presented single polar rhombohedral phase, (111)-oriented. This phase was present too in films on LSAT and LaAlO3, substrates with intermediate lattice parameters, but it was accompanied of (001)oriented crystallites, attributed to mixture of monoclinic and tetragonal phases. These results confirmed that epitaxial stress engineering, 64 allows controlling the stabilization of the ferroelectric phase in HZO films enough thin: tensely strained LSMO electrodes favors it, while compressively strained LSMO suppresses it.
Epitaxial stress engineering is thus limited to substrates having moderately high lattice mismatch with LSMO, to allow its coherent growth. In addition to lattice mismatch, LSMO coherence or relaxation can depend on LSMO deposition parameters and thickness. Nukala et al. 56 grew HZO films on LaAlO3(001) substrates buffered with t = 10 and 40 nm LSMO electrodes. HZO on the fully strained t = 10 nm electrodes, it presented only non-polar phases, while there was mixture of non-polar and polar phases in the HZO film on the partially relaxed t = 40 nm LSMO. However, Yoong et al. 78 reported divergent results for a t = 10 nm HZO film on fully strained 10 nm LSMO on LaAlO3(001). From XRD measurements around asymmetrical reflections and STEM characterizations, the authors confirmed epitaxy in spite of the low growth temperature of 550 C, and concluded that the film presented single polar orthorhombic phase, being (00l) oriented. The low deposition temperature could maybe favor the stabilization of the orthorhombic phase and its (001)-orientation under compressive stress, although other studies have shown that crystallization of films on STO(001) is inhibited decreasing substrate temperature below to around 650 C. 53 Polarization loops confirmed that the (001)-oriented phase was polar, measuring remanent polarization around 20 µC/cm 2 , with coercive fields of -2 and + 2.8 MV/cm.

Impact of bottom electrode
Epitaxy of ferroelectric HfO2 has been reported using only a few bottom electrodes. ITO is the bottom electrode that is commonly used to grow epitaxial Y-doped HfO2, 26, 36-38, 44-45, 48, 79-80 Cedoped HfO2, 42 and Fe-doped HfO2 41 films. Semiconducting Nb:STO substrates were used to deposit epitaxial Si-doped HfO2 films. 50 In the case of HZO, the epitaxial stabilization of the ferroelectric phase is achieved using a LSMO bottom electrode. 51-53, 56-57, 63-66, 76, 78, 81-89 Very recently, Estandía et al. 89 investigated the influence of the bottom electrode on the stabilized phases and the ferroelectric polarization of HZO films. They compared films on LSMO/STO(001) with others on conducting LaNiO3 (LNO), SrRuO3 (SRO), LSMO, and Ba0.95La0.05SnO3 (BLSO) electrodes grown on STO(001), and also with a HZO film on a doped Nb:STO(001) semiconducting substrate. The orthorhombic phase does not form on LNO and SRO, but on Nb:STO and BLSO, showing an unusual tilted epitaxy. There was not ferroelectric polarization in the films on LNO and SRO, while in the films on Nb:STO and BLSO it was much smaller than that of films on LSMO. It was ruled out that the impact of the electrode was due to the epitaxial stress effects described in previous section. To get insight on the cause of the impact, LSMO electrodes covered with 3 unit cells (u.c.) of LNO or SRO were used. The formation of the orthorhombic phase was suppressed. In contrast, when LNO or SRO electrodes were covered with 3 u.c. of LSMO, the orthorhombic phase was epitaxially stabilized and the films showed high polarization. The results pointed that the different chemical composition and atomic structure of the surface of the electrodes was a relevant factor. Finally, Estandía et al. 89 compared four La1-xAxMnO3 (A= Sr, Ca; x= 0.33, 0.5) electrodes, and it was found that the amount of the orthorhombic phase did not depend on the divalent atom (Sr or Ca), but it was greater for La0.67A0.33MnO3 than for La0.5A0.5MnO3. Taken together, the results pointed to a complex interface, critically influencing the epitaxial stabilization. Detailed studies of the atomic structure are necessary to determine the causes.

Epitaxial integration on Si
Lee et al. 90 deposited Y-doped HfO2 films (thickness and Y content were not indicated) on YSZ/Si(001) by PLD. Symmetric -2 XRD scans (Cu K radiation) showed a peak at around 35, indexed as (001)/(010) reflections of the orthorhombic phase. This diffraction peak can also be ascribed to the YSZ(002) peak, as well as {200} peaks of the monoclinic phase. The authors also measured -scans and reciprocal space maps around asymmetrical reflections, but overlapping with other reflections is also expected. Films were characterized electrically and, although the absence of bottom electrode, their ferroelectric nature was evidenced in spite of important leakage current contributions. Hf0.93Y0.07O2 films, as thick as 900 nm, were also integrated epitaxially on ITO/YSZ/Si(001) by deposition at room temperature and RTA. 91 The films presented properties similar to the films of similar thickness on YSZ(001) with Pr around 4 µC/cm 2 and coercive electric field of 1 MV/cm. Other authors deposited HZO films on bare YSZ(001) single crystals and reported the formation of monoclinic phase, without presence of orthorhombic phase. 92 L. Bégon-Lours et al. 93 deposited epitaxial HZO films on GaN/Si (111) and reported structural characterization. The films were (111) oriented and from measurements of d{111} lattice distances, the unit cell was found to be rhombohedral. The films were characterized by STEM, and the authors suggested that the R3 rhombohedral phase matched better than R3m.
Nukala et al. 82 deposited HZO (x = 0.5, 0.7 and 0.85) directly on Si (111), and a x = 0.7 film was also grown on Si(001). Zr atoms likely reduced the native amorphous SiOx, allowing epitaxy as occurs in epitaxial growth of yttria-stabilized zirconia. 94 They deposited epitaxial films by PLD, at Ts = 800 C under 0.005 mbar of Ar. From XRD and STEM characterization, the authors concluded that the phase of the film on Si(001) was orthorhombic, while the films on Si (111) presented mixture of monoclinic and rhombohedral phases, the latter more abundant in the HZO films with higher Zr content. I-V loops measured at 5 K evidenced ferroelectric character of films on Si (111) although the presence of large leakage currents.
SrTiO3 is a natural option as buffer layer for epitaxial integration of ferroelectric HfO2 on Si(001). On one hand, STO(001) substrates have been used extensively to grow ferroelectric HZO film. On the other hand, STO can be grown epitaxially on Si(001) by molecular beam epitaxy (MBE) 95 and other techniques as PLD 96 or atomic layer deposition. 97 Si(001) coated with a MBE grown STO layer was used to deposit by PLD a LSMO electrode and a t = 7.7 nm HZO film, 65 using same deposition parameters that in equivalent films on STO(001). 52 XRD confirmed epitaxial stabilization of the orthorhombic phase, with diffraction spots of the monoclinic phase barely observable. The out-of-plane interplanar spacing, do-HZO(111) = 2.940 Å, smaller than that of the equivalent HZO films on LSMO/STO(001), was probably a consequence of the thermal expansion mismatch between the oxide layers and the Si(001) substrate. Topographic AFM images showed a flat surface with rms roughness of 3.5 Å. Polarization loops confirmed very large remanent polarization of 34 µC/cm 2 , significantly larger than the 24 µC/cm 2 of films t  9 nm thick on STO(001) perovskite substrates. 53 The dielectric constant showed an hysteretic loop, with the butterfly shape characteristic of a ferroelectric, and permittivity at saturation of 31-32. The film presented excellent endurance behavior up to 10 9 cycles of 4.0 V amplitude, although with fatigue that reduced 2Pr from 30 µC/cm 2 in the pristine state to 4.5 µC/cm 2 after the 10 9 cycles.
Remarkably, capacitors poled with the same voltage of 4.0 V retain ferroelectric polarization for more than 10 years.
YSZ, contrary to STO, can be (relatively) easily grown epitaxially on Si(001) by PLD. 94 For this reason, YSZ is probably the most popular buffer layer for epitaxial growth of functional oxides on Si(001). However, HZO/LSMO bilayers cannot be directly grown on YSZ/Si(001) due to the large lattice mismatch between LSMO and YSZ. This is solved by inserting oxide films to accommodate progressively the mismatch, and HZO/LSMO bilayers were grown epitaxially on LaNiO3/CeO2/YSZ/Si(001). 65 It is noted that the top buffer layer, LaNiO3, is a conducting oxide with lattice parameter (3.84 Å) close to that of LSMO (3.875 Å). However, HZO films directly grown on LaNiO3 were not orthorhombic . 65 This points to the critical role of the LSMO(001) surface on stabilization of the orthorhombic phase. Lyu et al. 85 reported the dependence on thickness in the t = 4.6 -18.6 nm range. XRD measurements confirmed the epitaxial stabilization of the orthorhombic phase, and symmetric -2 scans showed the o-HZO(111) reflection in all the samples. XRD 2- frames were measured to detect the monoclinic phase. The spots corresponding to this phase increased strongly in intensity with thickness. All HZO films showed ferroelectric polarization hysteresis loops, with remanent polarization decreasing with thickness. The dielectric constant also showed hysteresis. The hysteresis decreases with thickness, and the permittivity at saturation reduces from 33.5 to 28. The observed increase of paraelectric monoclinic phase in thicker films is probably the cause of loss of polarization and decrease in dielectric constant. Figure 10a shows that remanent polarization decreases monotonically with thickness from 33 µC/cm 2 (t = 4.6 nm) to 10 µC/cm 2 (t = 18.6 nm). The monotonic dependence contrast with the usual peaky dependence reported for polycrystalline HZO films (empty symbols in Figure 10a). The increase in polarization with decreasing thickness of the epitaxial HZO films on Si(001) suggests that ferroelectricity could be maintained in extremely thin films. This is in agreement with theoretical calculations. 98 This was recently confirmed by Cheema et al., 99 measuring ultrathin (t = 1 nm) Hf0.8Zr0.2O2 polycrystalline films grown directly on Si(001) by piezoresponse force microscopy and demonstrating switchable polarization.
Remarkably, epitaxial HZO films on Si(001) show a higher remanent polarization than equivalent films on STO(001) substrates. It has been shown in Section 4.4, for HZO/LSMO grown on different oxide substrates, that the selection of GdScO3 or TbScO3 as substrate is critical to obtain the highest ferroelectric polarization. This was correlated with the tensile epitaxial stress that the scandate substrates cause on HZO/LSMO. In the case of the films on Si(001) substrates, the stress was not due to mismatch between lattice parameters, but to the lower thermal expansion coefficient of Si(001) that caused the compression of the out-of-plane parameter of orthorhombic HZO when the film was cooled after deposition.

Dependence of Pr and Ec on thickness
In polycrystalline doped-HfO2 films, the relative amount of paraelectric monoclinic phase respect the ferroelectric orthorhombic phase is found to increase with film thickness. [14][15][16] This dependence, which can influence critically the ferroelectric properties, has been observed too in epitaxial YHO 80 and HZO films 53, 85 films.
Mimura et al. 80 prepared epitaxial YHO films of thickness in the 10-115 nm range on ITO/YSZ (111). The coercive field, similarly as it occurs in polycrystalline films of doped HfO2, 100 did not change significantly with thickness. The polarization of the films showed small dependence on thickness. More recently, Shimura et al. 91 prepared Hf0.93Y0.07O2 films as thick as 340 and 1080 nm. The films were deposited at room temperature by RF magnetron sputtering on ITO/YSZ(001) and ITO/YSZ(111), followed by RTA (800 C, 10 s, N2). Epitaxy was confirmed by XRD (2- frames recorded with a 2D detector and pole figures). Films on YSZ(001) were epitaxial and single (001) oriented, although the {100} diffraction spots in the t = 1.08 µm were highly elongated along , signaling high mosaicity. Films on YSZ(111) presented coexistence of (111) and (001) orientations, and the diffraction spots corresponding to both orientations were very elongated for both thicknesses. Polarization loops confirmed ferroelectricity in all samples, with constant remanent polarization (5 µC/cm 2 ) and coercive electric field (1 MV/cm) irrespective of film thickness and orientation (Figure 10b-c). The same group reported also high ferroelectric polarization (15 µC/cm 2 ) in polycrystalline Hf0.93Y0.07O2 films of around 1 µm in thickness prepared on Si(001) by PLD at room temperature and subsequent RTA. 44 These results contrast with the common observation of degradation of ferroelectricity increasing thickness of doped HfO2 films. Usually, either polycrystalline 16 or epitaxial 53, 63, 85 doped-HfO2 films show low or negligible polarization for thickness above a few tens of nanometers. On the other hand, the Ect dependence of the YHO epitaxial films (Figure 10c), and polycrystalline films of doped HfO2 films, 48,100 differ to the behavior of conventional ferroelectric perovskites. In high quality ferroelectric perovskite films, Ec decreases with thickness, very usually following the Ec  t -2/3 scaling law. [101][102][103] Thus, the preservation of ferroelectricity in polycrystalline 44 and epitaxial 91 Hf0.93Y0.07O2 films could be likely consequence of the particular microstructure of films deposited at room temperature and crystallized by RTA. However, ferroelectricity in bulk crystals of Ydoped HfO2 has been reported very recently, 104 demonstrating that this property is not restricted to nanometric sizes. The orthorhombic phase was kinetically stabilized in crystals that were quenched very rapidly. The ferroelectric polycrystalline 44 and epitaxial 91 1 µm thick Hf0.93Y0.07O2 films were crystallized by a RTA process. However, polycrystalline HfO2 films, doped with Y or other dopants, prepared by similar RTA processes show usually severe degradation of polarization when they are thicker than a few nanometers. Moreover, similar degradation is observed in films grown epitaxially in-situ and cooled much slowly. It remains to be determined the microstructural characteristics (oxygen vacancies and other defects, residual stress, etc.) that allow preservation of ferroelectricity in thick films.
In the case of epitaxial HZO films, Lyu et al. 53 reported critical impact of the thickness on the ferroelectric properties. A series of HZO films, with thickness in the 2.3 -37 nm range, on LSMO/STO(001) was characterized. Increasing thickness, the amount of non-polar monoclinic phase increases. Films thinner than around 14 nm were very flat, with rms roughness less than 4 Å. In thicker films rms increased up to around 8 Å in the t = 37 nm film. Polarization loops were measured for films thicker than 4.6 nm (leakage of thinner films impeded ferroelectric measurements). The remanent polarization showed a peaky dependence on thickness, with the largest polarization of 24 µC/cm 2 for films around 7 nm thick (Figure 10a). Similar dependence is reported for polycrystalline films (Figure 10a 15,100,[105][106][107]. The coercive field of the loops varies with thickness. The log-log plot of Ec against thickness (Figure 10d) shows linear dependence with slope -0.61, in agreement with the Ec  t -2/3 scaling law. The same dependence of coercive field on thickness was observed for epitaxial HZO films on Si(001) 85 and La-doped HZO films on STO(001) and Si(001). 63 It signals that crystal grain size along the out-of-plane direction is not smaller than the film thickness. In contrast, Ec does not change significantly with thickness in epitaxial YHO films obtained by annealing of amorphous layers, 80,91 or usually in polycrystalline HfO2 films, 100 but yes (showing Ec  t -2/3 ) for polycrystalline films thinner than around 30 nm and grains spanning across the entire thickness. 108

Endurance and retention
A ferroelectric used in a memory has to show, in addition of high polarization, high retention and endurance. Endurance is perhaps the main limitation of ferroelectric hafnia for its future use in commercial devices. Endurance can be limited by hard breakdown (device failure) or by fatigue (polarization decrease upon cycling up to an undetectable value). Significant progress achieved in the last few years has permitted achieving endurance up to 10 11 cycles, 85, 109 which is promising but still far of the 10 15 cycles achieved with perovskites. 2 Further improving of endurance is also challenged due to the polarization -endurance dilemma: when a capacitor is optimized to enhance its endurance, this is accompanied of a reduction of the remanent polarization. 3 Moreover, it is convenient for memory reliability that polarization remains as constant as possible during its operational use. However, both wake-up effect and fatigue cause that polarization varies with number of cycles.
The first measurements of endurance in epitaxial HZO films revealed that fatigue was important. 52 Fatigue and retention can depend on thin film deposition parameters, and thus these properties have to be considered to determine the growth window of the thin films. 84 Fatigue and retention were measured in the series of films on LSMO/STO(001) deposited at varied Ts and PO2, and which polarization, coercive field and current leakage were previously reported. 53 To quantify fatigue, films were cycled 10 7 times. Tiny wake-up effect was only observed in the films deposited at 700 C or lower temperature, and there was absence of wakeup in the other films. This confirmed that epitaxial films are more robust against wake-up than polycrystalline films. In contrast, all the epitaxial films suffered fatigue (Table II). The relative polarization decrease upon cycling with respect the initial Pr value increases with either Ts or PO2. In the case of the Ts series, the remanent polarization of the 650 C (825 C) sample was 47% (27%) after 10 7 cycles. In the case of the PO2 series, the remanent polarization of the 0.02 mbar (0.15 mbar) sample was 42% (25%) after 10 7 cycles. The 0.2 mbar sample was more fatigued before hard breakdown after only 10 3 cycles. On the other hand, retention measurements showed asymmetry, being more stable the capacitor poled applying positive voltage to the top Pt electrode. The asymmetry was very high in the films deposited at low Ts, while asymmetry was moderately low at high Ts independently of PO2. Retention was short, for negative poling, in the films with combined high asymmetry and low coercive field. Excluding these films, polarization was very stable, with more than 40% of the initial value retained after 10 years at room temperature. Retention and fatigue made the growth window of the epitaxial films narrower than considering only polarization, but optimal Ts and PO2 ranges are still sufficiently wide. Figure 11 summarizes the effects of Ts and PO2 on polarization, retention and fatigue obtaining the best performance for Ts around 750 o C and PO2 = 0.10-0.15 mbar.
Lyu et al. 85 reported endurance and retention properties in epitaxial HZO films of thickness in the t = 4.6 -18.4 nm range, deposited on LSMO/LaNiO3/CeO2/YSZ buffered Si(001). The retention (Figure 12a) after 10 years was extrapolated by fitting the remanent polarization measured at room temperature as a function of delay time td to the Pr = Po td -k dependence. All films presented net ferroelectric polarization after ten years, being retention longer in the thinnest films. It was argued 85 that the smaller fraction of monoclinic phase in these films could reduce the depolarizing field. Endurance measurements showed only tiny wake-up effect in the thinnest film. However, all samples presented fatigue. The loss of normalized polarization of the epitaxial HZO films on Si(001) with number of cycles did not depend on the electric field. 65 The thinner films presented significantly higher endurance than the thicker ones 85 and the sub-5 nm film showed excellent endurance (2Pr was 6 µC/cm 2 after 10 11 cycles of 2.5 V amplitude). Applying higher poling voltage, the initial polarization was higher, but hard breakdown occurred after a number of cycles (smaller as higher the voltage was). The authors measured permittivity hysteresis loops and current leakage during the endurance tests. The permittivity reduced gradually, similarly as observed in polycrystalline capacitors. 73,110 Current leakage did not vary significantly initially, but it increased suddenly after high number cycles. The threshold occurred earlier as higher was the electric field, and it was not observed for low enough electric field. A gradual reduction of the imprint field was also observed during the endurance measurements. Evolution in the charge defects, mainly oxygen vacancies, were proposed to cause the observed variation in polarization, imprint and leakage, as suggested for polycrystalline hafnia films. 73 Figure 12b compares the polarization and endurance of the epitaxial sub-5 nm HZO film on Si(001) with data reported for polycrystalline films. The combination of high endurance and polarization in the epitaxial films equals the best results reported for polycrystalline films, which was achieved doping HZO with La. 109 A dilemma between endurance and retention 111-113 could constitute a bottleneck for further reliability improvement. Retention and endurance are generally evaluated considering different samples or different poling fields, while both properties should be optimal under same operation conditions. The epitaxial films reported by Lyu et al. 85 presented endurance of at least 10 11 cycles and retention longer than 10 years using same poling field. The thickness of the films, less than 5 nm, can allow its use in tunneling devices.
Adkins et al. 114 measured endurance of an epitaxial HZO film, t = 5.6 nm, on LSMO/LaNiO3/CeO2/YSZ/Si(001) at cryogenic temperatures. The fatigue present at room temperature diminished reducing temperature, and there was not loss of polarization at 33 K in the explored range of 10 7 cycles, even for huge applied field of around 10 MV/cm. The authors estimated an activation energy of around 23.4 meV associated with fatigue. The value appeared to be too low for oxygen vacancies diffusion, and diffusion of trapped injected charges was proposed as main cause of fatigue.
In polycrystalline HZO films, La doping causes reduction of the coercive field and leakage, allowing endurance enhancement. 109,115 Epitaxial 1% mol La doped HZO films, with thickness in the 4.5 -13 nm range, were grown by PLD on LSMO/STO(001) and LSMO/STO/Si(001). 63 The coercive field was not reduced respect to equivalent epitaxial undoped HZO films, although leakage diminished by around one order of magnitude (leakage of t = 8.3 nm films was 10 -7 A/cm 2 at 1 MV/cm). The remanent polarization was higher than in equivalent undoped epitaxial HZO films, particularly in films thicker than around 10 nm, probably due to lower amount of monoclinic phase. The epitaxial La-doped films thinner than around 8 nm exhibited wake-up effect, although only for around 100 cycles, while in polycrystalline La-doped films it can occur up to 10 7 cycles. 111 Endurance in the epitaxial films was limited by fatigue or hard breakdown, the latter occurring earlier as higher the cycling field is. A 4.6 nm thick La-doped HZO film on LSMO/STO(001) showed the highest endurance, without breakdown after 5x10 10 cycles of 5.4 MV/cm, but with 2Pr reduced to around 3 µC/cm 2 due to fatigue. Films thicker than 5 nm presented long retention, with high remanent polarization extrapolated after 10 years at room temperature. This was measured after poling at different voltages, including the low voltages that allowed high endurance. Also, retention longer than 10 years was measured at 85 C of t = 8.3 nm films on LSMO/STO(001) and LSMO/STO/Si(001). The results demonstrated that wakeup effect and endurance-retention dilemma are not intrinsic in La-doped HZO. Very recently, it has been reported on the epitaxial stabilization of the orthorhombic phase in La-doped HfO2 films. 88 Films t = 12 nm thick on STO and DyScO3 substrates showed remanent polarization of around 16 µC/cm 2 , while t = 8 nm films were very leaky and t = 16 nm films showed smaller polarization. The retention was more than 10 years and the endurance about 10 7 cycles. The authors investigated in detail the influence of pulse voltage amplitude and width, and interval between pulses, on the endurance, observing a big impact on wake-up and fatigue. Contrary to the observations that fatigue does not depend on pulse amplitude in epitaxial HZO 65,85 and Ladoped HZO films, 63 fatigue in La:HfO2 depended strongly on the applied electric field, being more severe for the applied voltage and pulse width smaller. Li et al. 88 considered domain wall pinning as the main mechanism of fatigue, and that high amount of domain walls in case of partial switching accelerated fatigue.
Measurements of the endurance of epitaxial doped HfO2 films confirm a different behavior from that of polycrystalline films. Polycrystalline films exhibit a recurrent wake-up effect, even up to around 10 7 cycles, but can be fatigue-free. 109 The wake-up effect in epitaxial films on LSMO electrodes is negligible, or limited to a few cycles in ultra-thin films. 63, 116 LSMO is not expected to induce formation of oxygen vacancies in the doped HfO2 film, unlike the TiN electrodes that are commonly used in polycrystalline capacitors. This can be a major factor in the near absence of a wake-up effect in epitaxial films. In contrast, fatigue is a serious problem and epitaxial films without fatigue have not yet been reported. Wake-up and fatigue have been extensively investigated in polycrystalline films, and different mechanisms have been reported for both phenomena, including domain depinning/pinning at oxygen vacancies or other charged defects and paraelectric -ferroelectric phase changes. 73,[117][118] The multiple mechanisms observed experimentally suggest that the microstructure of the film may be critical. Paraelectric monoclinic and ferroelectric orthorhombic phases usually coexist in epitaxial films. The dependence of the fatigue of HZO films on LSMO/STO(001) with the deposition conditions (Ts and PO2), shown in Figure 11, reveals less fatigue in films grown at low Ts or low PO2, despite the fact that these films presented the highest amount of monoclinic phase, i.e less initial remanent polarization . It should be noted that the parasitic phase can promote fatigue through domain pinning, but could also suppress the propagation of pinned domains. Measurement of the endurance of epitaxial films on LSMO buffered scandate substrates, almost free of paraelectric phase, 64 would give insight on this. Table I summarizes the ferroelectric properties of epitaxial films of doped HfO2. Among the chemical compositions investigated, the highest remanent polarization of around 30-34 µC/cm 2 is reported for Hf0.5Zr0.5O2, 51,66,116 La-doped Hf0.5Zr0.5O2 63 and Si-doped HfO2 films. 50 High endurance of up to 10 11 and 5x10 10 cycles has been measured for Hf0.5Zr0.5O2 116 and La-doped Hf0.5Zr0.5O2 63 films, respectively. Retention of more than 10 years was shown using writing voltage pulses of the same amplitude to those used to measure the endurance. Therefore, epitaxial doped HfO2 films simultaneously allow high polarization, endurance and retention.

Devices
Ferroelectric HfO2 is very interesting for memory devices and it has already used to fabricate 3D Fe-RAMs 10 and Fe-FETs with 22 nm node. 11 However, the development of Fe-TJs has been less successful, and very low endurance was reported. 119 Epitaxial films, with lower surface roughness and defects than polycrystalline films, single orientation and possibility of control of parasitic polymorphs, may offer opportunities to develop these challenging devices.
Electroresistance (ER) loops were soon measured in epitaxial HZO films a few nanometers thick. 76,81,83,87 Sulzbach et al. 87 reported electroresistance loops with the same coercive voltage (Figure 13a) than the corresponding polarization loops (Figure 13b), indicating the close relation between ferroelectric switching and electroresistance. The Brinkman model was used to fit I-V characteristics pointing to tunneling current as predominant conduction mechanism. However, it was found that whereas short writing times or few cycling voltages result in below 1 order of magnitude electroresistance, the use of longer writing pulses or further sample cycling results in irreversible electroresistance. Thus, genuine tunneling ER resulting from ferroelectric switching can be accompanied by ER resulting from other transport mechanisms. They are associated to ions motion, and cause huge ER values up to 10 5 % 87 or even 10 6 %. 83 Noheda and coworkers 83,86 proposed that the huge ER is connected to oxygen vacancy migration between bottom LSMO electrode and HZO film. However, other mechanisms can be considered too, as the widely studied filamentary resistive RAM devices based in Hf and Zr oxides suggest. 2,120 It is understood that in these devices different resistance states are stabilized, because the formation of conducting channels, which are confined at the grain boundaries. [121][122][123] Therefore, filamentary ionic conduction can also play an important role in the found irreversible large electroresistance. Sulzbach et al. 76,87 have followed two strategies to overcome this effect. The first is based in the control of the amount of orthorhombic phase by epitaxial stress. 64 It was observed that ionic conduction mechanism is less active (higher voltage is necessary to activate it) in HZO films grown on scandate substrates where predominant orthorhombic phase is found. 76 This points to the fact that monoclinic-monoclinic and orthorhombic-monoclinic, but not orthorhombic-orthorhombic, grain boundaries can favor ionic motion. 76 Second, conduction at the grain boundaries was also claimed to be reduced by covering the HZO layer with an insulating paraelectric layer. 87 The insulting layer blocks the ionic conduction channels resulting in tunneling electroresistance driven by ferroelectric polarization almost completely avoiding ionic conduction. Thus, as in polycrystalline films, important coexistence between ionic and ferroelectric contributions to electroresistance exists; however, epitaxial films have been proved to be unique to disentangle the FE and non-FE contributions to tunnel electroresistance. 76,87 The effect of the ionic exchange between the electrodes and the HZO has been used to manipulate not only the tunneling current, but also the tunneling magnetoresistance in FM/HZO/FM tunnel junctions, where FM layers act as electrodes. 81,83 In Figure 13c, 83 it can be observed that the TMR inverts its sign for cycled samples, where ionic contributions are relevant. More relevant from applications point of view is that TMR is also modulated for samples where less ionic contribution is expected, thus indicating an intrinsic, but low, magnetoelectric coupling between the HZO and FM electrodes Figure 13d. 81 Electroresistance is not only present in tunnel junction of ferroelectric materials. Thicker films can show conductivity due to thermionic injection at the interface which can be modulated by ferroelectric polarization. 124 Yoong et al.,78 demonstrated this effect in 10 nm epitaxial HZO films. As expected in thick films, the electroresistance is much larger than in tunnel juntions. Interestingly, brain-like memristive activity was demonstrate with a throughout characterization. In Figure 13e,f it is shown the asymmetric Hebbian and paired-pulse facilitation results.
Stable negative capacitance effect has recently emerged as a phenomenon that can enable sub 60mV/dec gain in FeFET. Most of the literature reporting on genuine negative capacitance effects make use of epitaxial perovskite films. 125 This finds its origin on the strong dependence of stable negative capacitance, and the nucleation and propagation of ferroelectric domains, which is intrinsically linked to the film quality. However, epitaxial HfO2 films have not been explored on this regard so far. Up to now, it has been shown that strain imposed by the top electrode in a polycrystalline doped hafnium oxide film can have a relevant role on the fine tuning of negative capacitance effects 126 being possible to achieve sub-60mV/dec gain with extremely small hysteresis. Being epitaxial strain highly controllable by the use of f.i. piezoelectric substrate, it is of the highest interest the study of negative capacitance effects in epitaxial films. On the other hand, spatial homogeneity is required, as recently emphasized by Hoffmann et al. 127 Epitaxial HZO films grown on selected substrates (GdScO3 or TbScO3), present pure orthorhombic phase. 64 The recent demonstration of ferroelectricity in ultrathin ferroelectric (epitaxial HZO) / paraelectric (STO or AlOx) on GdScO3 substrates 128 suggests that HfO2 epitaxial ferroelectric films may be excellent candidates for prototyping and exploring negative capacitance devices.

Conclusions and outlook
Epitaxial films have been much less investigated than polycrystalline films, but they have already demonstrate that can allow excellent ferroelectric properties, and can help to better understand the properties of ferroelectric HfO2 and, in some cases, they can be a guide to improve properties of polycrystalline films. However, the research on epitaxial films is still incipient and many important questions are still open.
The kinetics effects are critical in the crystallization of the metastable orthorhombic phase in polycrystalline films. The balance between thermodynamics and kinetics in the epitaxial growth of ferroelectric HfO2 films could influence the relative amount of phases or the grain size of the epitaxial orthorhombic phase. Epitaxial films are grown primarily by PLD. This technique allows the thermodynamics / kinetics balance to be controlled by adjusting the growth temperature, growth rate (instantaneous or average), and plasma energy (by laser fluence, target substrate distance or gas processing pressure). These studies have yet to be addressed. In this regard, it is also important obtaining epitaxial films by other deposition techniques, including MBE and ALD. Relevant results achieved with epitaxial films include the growth of Ydoped HfO2 with controlled out-of-plane orientation and the estimation of their polarization and Curie temperature. It has been also reported that epitaxial Y-doped HfO2 films as thick as around 1 µm can be ferroelectric, without the degradation of polarization usual in films thicker than a few tens of nanometers. Epitaxial Hf0.5Zr0.5O2 films have evidenced a very weak wake-up effect, contrary to polycrystalline that generally exhibit pronounced wake-up. Epitaxial Hf0.5Zr0.5O2 films have also allowed achievement of simultaneous high polarization, retention, and endurance up to 10 11 cycles, demonstrating that there is not intrinsic dilemmas between P and endurance and between endurance and retention. In contrast, epitaxial Hf0.5Zr0.5O2 appears to suffer more pronounced fatigue. It could be favored because the coercive field of epitaxial films is higher than in polycrystalline films. Understanding the cause of the higher coercive field, and identifying the mechanisms of fatigue in epitaxial films, requires more research. The control of coercive field could allow improvement of endurance.
Most of the research on epitaxial hafnia has been focused on two specific chemical compositions, Y0.07Hf0.93O2 and Hf0.5Zr0.5O2, using mostly ITO and LSMO bottom electrodes, respectively, and usually top Pt electrodes. The properties of other compositions (dopant atom and content), and the effect of other top electrodes, has to be investigated.
Detailed studies of endurance and retention have been reported for Hf0.5Zr0.5O2 films, but scarcely for other compositions. The influence of the relative amount of the parasitic paraelectric phase on the endurance and retention of epitaxial doped HfO2 films is also unknown.
The ferroelectric phase in polycrystalline films is considered to be orthorhombic Pca21. In the case of epitaxial films there is not consensus and, while some authors consider that the ferroelectric phase is the orthorhombic Pca21 too, others have proposed rhombohedral phases (R3m and R3) or the orthorhombic Pnm21. However, there is an important mismatch between DFT calculations and films properties (required strain for the measured polarization), and there is not evidence of differences in specific intrinsic ferroelectric properties in the epitaxial films respect to polycrystalline (Pca21) films. Deeper characterization of the epitaxial films would be relevant. For example, imaging of dipoles by scanning transmission electron microscopy. Also, there are not reports on ferroelectric switching dynamics in epitaxial films.
Epitaxial Hf0.5Zr0.5O2 have allowed detangling and controlling electronic and ionic contributions to electroresistance in FeTJs or resistive RAMs. However, epitaxial growth impact on other devices has not been investigated in detail. Regarding, FeTJ or ReRAM although complementary ferroelectric and electroresistance characterization signals their connection, resistance switching at faster time scales and their retention and endurance characterization are needed to set potential applications of these type of devices. Fabrication of Fe-FETs based in epitaxial HfO2, and the evaluation of negative capacitance effects in these devices, has not done yet. Near-pure orthorhombic epitaxial HZO films deposited on LSMO/GdScO3 or LSMO/TbScO3 may be useful for prototyping Fe-FETs and exploring negative capacitance effects.
The progress achieved in few years on epitaxial HfO2 films has been outstanding. It is however in a nascent state and probably epitaxial films will be very important in the development of the scientifically exciting and technologically highly relevant ferroelectric HfO2. Figure 1. (a)