Distinguishing the Rhombohedral Phase from Orthorhombic Phases in Epitaxial Doped HfO2 Ferroelectric Films

Epitaxial strain plays an important role in the stabilization of ferroelectricity in doped hafnia thin films, which are emerging candidates for Si-compatible nanoscale devices. Here, we report on epitaxial ferroelectric thin films of doped HfO2 deposited on La0.7Sr0.3MnO3-buffered SrTiO3 substrates, La0.7Sr0.3MnO3 SrTiO3-buffered Si (100) wafers, and trigonal Al2O3 substrates. The investigated films appear to consist of four domains in a rhombohedral phase for films deposited on La0.7Sr0.3MnO3-buffered SrTiO3 substrates and two domains for those deposited on sapphire. These findings are supported by extensive transmission electron microscopy characterization of the investigated films. The doped hafnia films show ferroelectric behavior with a remanent polarization up to 25 μC/cm2 and they do not require wake-up cycling to reach the polarization, unlike the reported polycrystalline orthorhombic ferroelectric hafnia films.


INTRODUCTION
−9 Recently discovered ferroelectricity in doped hafnia ultrathin films opens new perspectives for the realization of special devices like ferroelectric field-effect transistors and ferroelectric tunnel junctions 10,11 due to their compatibility with the Si technology.
Single-crystal Y-doped HfO 2 ferroelectric films deposited on yttrium-stabilized zirconia have already been reported, exhibiting the orthorhombic polar phase with the space group Pca2 1 (o-phase) and a polarization of 16 μC/cm 2 , generally considered responsible for ferroelectricity in thin doped hafnia films. 12On the other hand, epitaxial Hf 0.5 Zr 0.5 O 2 films deposited on La 0.7 Sr 0.3 MnO 3 /SrTiO 3 (substrate) by pulsed laser deposition (PLD) have recently been reported. 13,14These films do not crystallize in the commonly reported o-phase, but in a polar rhombohedral phase (r-phase), stabilized via epitaxial strain, and was identified with a large P r of 34 μC/cm 2 .Moreover, these rhombohedral films do not require "wake-up" cycling for establishing ferroelectric switching unlike most of the reported polycrystalline films with an orthorhombic polar phase.Recently, polycrystalline Hf-(Zr) 1+x O 2 crystallizing in a rhombohedral ferroelectric phase with a low coercive field have been reported. 15Meanwhile, epitaxial doped hafnia films were reported by some authors, being deposited on several single crystal substrates like yttriastabilized zirconia (111)YSZ, (100)YSZ, 16 LSMO-buffered LaAlO 3 , 14,17,18 SrTiO 3 , 13,14,18,19 NdScO 3 , NdGaO 3 , MgO, 18 YAlO 3 , (LaAlO 3 ) 0.3 −(Sr 2 AlTaO 6 ) 0.7 (LSAT), DyScO 3 , 14,18 SrTiO 3 -buffered Si, 20 and GaN-buffered Si. 21An interesting study on epitaxial doped hafnia films deposited on various La 0.7 Sr 0.3 MnO 3 (LSMO)-buffered substrates reveals that TbScO 3 and GdScO 3 are very good candidates for epitaxial stress stabilization of the ferroelectric phase. 18In most of these studies, the stress-stabilized metastable polar orthorhombic phase (Pca2 1 ) was reported to be responsible for the ferroelectricity in doped hafnia films, 12,17,19,20,22−26 whereas the rhombohedral (space groups R3m or R3) phases are less reported.The reason might be the fact that the orthorhombic phase is hard to distinguish from the rhombohedral phase.In this article, we focus on the challenge of distinguishing between these phases.
Apart from the epitaxial hafnia films deposited on sapphire, ITO-buffered YSZ, and GaN, only epitaxial films deposited on LSMO-buffered substrates have been reported to be ferroelectric.
A study on other buffer layers like LaNiO 3 , La 0.5 Ca 0.5 MnO 3 , SrRuO 3 , and Ba 0.95 La 0.05 SnO 3 showed a low or no stabilized ferroelectric phase, except for those with manganite electrodes. 27n addition to the epitaxial strain imposed by the substrate, factors such as deposition temperature, partial gas pressure, and film composition also play an important role in determining the formation of crystal phases.For example, Kaiser et al. reported that either a monoclinic or a rhombohedral phase is stable in HfO 2 thin films grown by molecular beam epitaxy on c-cut sapphire depending on the oxygen partial pressure.DFT simulations have shown that the rhombohedral phase is stabilized by oxygen vacancies, not due to the epitaxial strain. 28Furthermore, it was discussed that a zirconium substitution may have the same effect.
Superlattice and layer structures provide a further improvement of the ferroelectric performance of hafnia-based films.Thus, "wake-up" free ferroelectric capacitors based on HfO 2 / ZrO 2 superlattices 29 or capacitors with improved ferroelectric and dielectric performances have been reported. 30,31n this work, the focus will be on ferroelectric epitaxial doped hafnia films deposited on three different substrates to compare their structural properties and to determine their crystal structure.Thus, Zr/Y:HfO 2 /La 0.7 Sr 0.3 MnO 3 /SrTiO 3 (100), Zr/Y:HfO 2 /La 0.7 Sr 0.3 MnO 3 /SrTiO 3 /Si (100), and Zr/ Y:HfO 2 /Al 2 O 3 (0001) systems are investigated here.The structural characterization of each of these three systems (comprising XRD and TEM results) is presented in a separate subsection, and the electrical characterization is shown in the last section of the results.

EXPERIMENTAL METHODS
2.1.Materials.Hf 0.5 Zr 0.5 O 2 and Hf 0.93 Y 0.07 O 2 thin films of thicknesses varying from 2.5 to 12 nm were deposited by pulsed laser deposition (PLD) on La 0.7 Sr 0.3 MnO 3 -buffered SrTiO 3 (001) (STO) substrates, La 0.7 Sr 0.3 MnO 3 -buffered Nb (0.5%)-doped SrTiO 3 (001), SrTiO 3 -buffered Si substrates, and sapphire (0001) substrates.The doped HfO 2 and the LSMO films were deposited in a single process without breaking the vacuum.The Hf 0.5 Zr 0.5 O 2 -and Hf 0.93 Y 0.07 O 2 -sintered ceramic targets were purchased from EVO-CHEM whereas the LSMO target was purchased from PraxAir.A KrF excimer laser of 248 nm in wavelength was used for ablation in a commercial PLD system from Surface GmbH.The La 0.7 Sr 0.3 MnO 3 films were deposited at a substrate temperature of 780 °C, under 0.15 mbar O 2 , and at a laser fluence and frequency of 1.4 J/cm 2 , and 2 Hz, respectively.The doped HfO 2 films were deposited at a substrate temperature of 800 °C, under 1.5 × 10 −2 mbar O 2 , and at a laser fluence of 1.4 J/cm 2 and a frequency of 5 Hz.After deposition, the films were cooled at 5 C/min to room temperature under 3 mbar of oxygen pressure.Epitaxial 20 nm SrTiO 3 buffer layers were deposited on Si(100) substrates by molecular beam epitaxy (MBE) at Texas State University.The epitaxial oxide growth on silicon was achieved using a codeposition process in which both the alkaline earth metal and the Ti shutters were opened in a controlled oxygen environment.Since, under these growth conditions, the sticking coefficient of the individual elements is unity, careful calibration of the fluxes was performed for stoichiometric oxide films.The growth rate used was approximately 2A/min and was calibrated using RHEED intensity oscillations.

XRD Characterization.
The XRD measurements including wide-range reciprocal space maps (RSMs) and pole figures were acquired with a SmartLab diffractometer (Rigaku) equipped with a 9 kW Cu anode X-ray tube and a 2D HyPix-3000 X-ray detector.A twobounce monochromator was used for high-resolution XRD scans.

TEM Sample Preparation and Analysis.
Cross-sectional TEM samples were prepared from the SrTiO 3 and Al 2 O 3 substrates using focused ion beam (FIB) milling in an FEI Helios Nanolab system.Before Ga-ion etching, a protective Pt coating was deposited with a gas injection source inside the FIB system.A plan-view sample on a Si substrate with epitaxial SrTiO 3 and LSMO layers was prepared with a Precision Ion Polishing System (PIPS, Model 691 from Gatan Inc.).
The FIB samples were analyzed using a JEOL JEM-2100 with electrons accelerated to 200 kV extracted from a LaB6 cathode, while the PIPS sample was analyzed with an FEI Tecnai F30 G 2 at 300 kV and a field emission gun.
2.4.Device Fabrication.Ferroelectric capacitors were fabricated by depositing Cu top electrodes by thermal evaporation through a stencil mask.The device size varies from 25 to 225 μm 2 .Other ferroelectric capacitors on Si substrates were patterned by using UV optical lithography and Ar + ion beam etching.
2.5.Electrical Characterization.The ferroelectric hysteresis loops (P−V loops) of the ferroelectric capacitors were measured by using a Radiant Technologies Premier II ferroelectric tester.The test signal used here consists of a linear ramp waveform with a period in the range of 0.1 to 150 ms.Additional ferroelectric hysteresis loops were measured with an aixACCT TF Analyzer 3000.Nb:STO Substrates.3.1.1.1.X-ray Diffraction Analysis.An Xray diffraction (XRD) scan of a Hf 0.5 Zr 0.5 O 2 (HZO) film on LSMO-buffered (001)-oriented Nb:STO substrates is depicted in Figure 1a.The specular reflections 001, 002, and 003 of the Nb:STO substrate are the most intense ones, followed by the specular reflections of the epitaxial LSMO film.The 003 and 006 reflections of the HZO film are also present.Figure 1b shows the magnified 003 HZO region, where the thickness oscillations are clearly visible, demonstrating good crystalline   parallel to the sample surface), θ is its corresponding diffraction angle, λ is the X-ray wavelength, and n is the film thickness in the number of interplanar spacing.The theoretical diffractogram is plotted with a red line as shown in Figure 1b.A similar analysis for the LSMO film revealed an LSMO film thickness of 27.4 nm, as illustrated in Figure 1c.The rocking curve of the Hf 0.5 Zr 0.5 O 2 003 reflection illustrated in Figure 1d shows a FWHM of 0.032°, indicating a good crystalline quality for these films.

RESULTS AND DISCUSSION
Next, wide-range reciprocal space maps (RSMs) and pole figures were measured for the same stack to determine the crystallographic phase and the orientation of the HZO films.Thus, in the reciprocal space map of the Hf 0.5 Zr 0.5 O 2 / La 0.7 Sr 0.3 MnO 3 /SrTiO 3 (substrate) heterostructures shown in Figure 2a, the substrate reflections 001, 002, and 003 are identified and labeled in dark blue color on the RSM.The reciprocal space spots corresponding to the epitaxial LSMO layer could not be distinguished from those of the STO substrate, due to lack of resolution in the wide range RSM measurements.Here, we like to specify that the sample was on purpose in-plane rotated by an angle φ = 15°(with respect to the in-plane a-direction of the STO substrate) to avoid the contribution of nonspecular spots of the STO/LSMO).For more clarity, a wide-range RSM of the same sample measured at φ = 45°is shown in Figure S1, where the 111, 112, 113, and 221 spots of the STO/LSMO are also present.The HZO films grow epitaxially out-of-plane on the LSMO/STO template, and the films appear to consist of four kinds of domains, belonging to the same crystallographic R3m phase, first reported by Wei et al., 13 having four kinds of in-plane orientations, rotated by 90°with respect to one another.A similar domain structure was reported by Nukala et al. for such heterostructure. 14The reason for this domain configuration could be explained by the 4-fold symmetry imposed by the substrate, as also described by Estandi ́a et al. 18 and observed in heteroepitaxy of oxides 33 or semiconductors. 34The results are illustrated in Figure 2a.The angles marked next to the HZO spots in the wide-range RSM represent the in-plane rotation of the corresponding HZO domains.From the 022 HZO spot, we extracted the lattice parameter values of a = 7.17 and c =  8.82 Å.More precise values will be extracted from the highresolution in-plane and out-of-plane scans.
A pole figure of the HZO/LSMO/STO (substrate) heterostructure is shown in Figure 2b.The radial direction represents χ, which ranges between 51°and 85°, while the azimuthal direction represents φ, which ranges between 0°and 360°.Please note that the pole figure presented here is not measured for a single reflection but for a two-theta range between 23°and 37°.Thus, the HZO {201} and HZO {022} families of reflections are seen here.The 12 poles of the HZO {201}, measured at a 2θ angle of 30.5°and the 12 poles of the HZO {022} measured at a 2θ angle of 35.6°are clearly visible in the pole figure.From the crystal symmetry of the R3m phase, one expects three poles for each, spaced by 120°, but the presence of four kinds of crystallographic domains rotated 90°with respect to one another would give us the observed 12 poles.To reproduce the measured data, we considered four domains of the R3m phase having the (001) orientation and an in-plane rotation of 90°with respect to one another and simulated the pole figure using the MTEX 35 simulation tool.The simulated pole figure is presented in Figure 2c.As can be seen, both {201} (at chi = 71.15°)and {022} (at chi = 55.7°) spot families could be reproduced in the simulation of the R3m phase.If one considers the orthorhombic Pca2 1 phase with a single (111)-oriented domain, three poles rotated by 120°are expected for the HZO{1 11}, from the crystal symmetry, as simulated with MTEX and also experimentally reported, 18 and one pole for each of the {020}, {200}, and {002} reflections.The HZO{1 11} of the Pca2 1 phase would be the corresponding HZO{201} spots of the R3m phase, and the HZO{020} of the Pca2 1 phase would be the corresponding HZO{022} spots of the R3m phase.Furthermore, if one considers (111) grown films consisting of four domains having four in-plane orientations rotated 90°with respect to one another and simulates the pole figure, one can reproduce the 12 spots corresponding to HZO {1 11}, as shown in the simulated pole figure from Figure 2d.To enhance clarity, the poles from each domain in the simulation from Figures 2c,d are indicated with an arrow of a specific color.Thus, we have black, red, blue, and green arrows to indicate the four domains.Additionally, 12 poles are expected at a two-theta angle of about 35.6°, each of the {020}, {200}, and {002} reflections contributing with four spots in the simulation, separated by a 90°angle in phi.The corresponding two-theta angles of the nonsymmetry equivalent 020, 002, and 200 reflections of the Pca2 1 phase are close to each other.Thus, it is difficult to distinguish between the R3m and Pca2 1 phases based on the (low resolution) wide-range RSM and pole figures.One way to distinguish the R3m phase from the Pca2 1 phase is to compare the interplanar spacing of the 12 spots measured at a chi angle of 71.15°with the interplanar distance of the specular 111 spot of the Pca2 1 phase.In the case of the Pca2 1 phase, all spots should have the same d-spacing (due to the symmetry), whereas for the R3m phase, the specular spot (the 003 reflection) should have a larger d-spacing value. 13,14Symmetric two-theta scans of the 12 poles measured at chi = 71.15°areplotted together with the out-of-plane reflection (chi = 0°) as shown in Figure 3a.The 12 spots share nearly the same 2θ values, whereas the out-of-plane reflection has a smaller 2θ (larger d-spacing), which is an indication for the R3m phase.
Another possibility to distinguish between the two polymorphs is to measure symmetric 2θ scans at around 35°f or the 12 spots at a chi angle of 55.7°.In the case of the R3m phase, the {022} spots should have the same 2θ values, whereas for the Pca2 1 phase, the {020}, {200}, and {002}, each contributing with four spots (from the four domains) separated by 90°in φ with respect to one another (see Figure 2d), should have slightly different 2θ values.Similarly, one can analyze the 12 spots measured at chi = 35°at a 2θ of about 50°.Thus, for the R3m phase, the {204} spots should show the same 2θ values whereas for the Pca2 1 phase, the {022}, {202}, and {220} each contributing with four spots separated by 90°i n φ with respect to one another should have slightly different 2θ values.The symmetric two-theta scans of the 12 poles measured at chi = 55.7°and a 2θ value around 35°are presented in Figure 3b, and the 12 poles measured at chi = 35°a nd a 2θ value of around 50°are shown in Figure 3c.To improve the ease of understanding for the reader, the 2θ scans of each {020}, {200}, and {002} as in Figure 3b and {022}, {202}, and {220} reflections as in Figure 3c corresponding to the Pca2 1 phase are depicted using distinct colors: red, green, and blue.Thus, in the case of the Pca2 1 phase, the reflections of the same color (separated in phi by 90°) should share the same 2-theta value and should be slightly different for each color.When these 2θ values are all equal, assuming the ferroelectric Pca2 1 phase, would imply a = b = c, which contradicts the reported metrics of this crystallographic phase, making it unlikely that the investigated films are in the Pca2 1 phase.These results are instead in good agreement with the metrics of the R3m phase.However, the existence of a separate ferroelectric rhombohedral phase which is not just a structural distortion caused by epitaxial stress distortion of the Pca2 1 orthorhombic phase is still under debate, as suggested by Fina and Sańchez. 36o gain a clearer understanding of how the scans from Figure 3c relate to particular reflections and domains, simulated pole figures for both R3m and Pca2 1 phases of the 12 spots at chi = 35°and a 2θ of about 50°are shown in Figure S5.

Transmission Electron Microscopy Characterization.
The same HZO film on the LSMO-buffered (001)oriented Nb:STO substrate analyzed by XRD was used for TEM characterization.The HRTEM micrograph in Figure 4a shows the LSMO back electrode growing along (012) planes while the HZO thin film grows mainly in the [003] direction of the R3m phase.However, a minority growing direction along [ 222] was also observed (marked with an orange ellipse in the FFT in Figure 4b, as also reported by Wei et al). 13This minority growth direction is not observed in XRD measurements.Different domains of the HZO were present with (022) planes oriented to the right or the left, these planes are indicated by a black and a red arrow, respectively.Frequently both orientations superimpose, as can be seen in the FFT in Figure 4c.This pattern can be explained by a 2-fold twin rotation around the [003] growing direction.Accordingly, we can see here at least two of the four domains observed in XRD.The missing two domains cannot be distinguished in this orientation because they have the same diffraction pattern.For instance, the [110] zone axis (ZA) is equivalent to the [100] ZA in a rhombohedral symmetry.A clear view of the boundary of the domains, however, was not found in many micrographs examined.
The selected area electron diffraction (SAED) pattern in Figure 4d was aligned parallel to the [100] ZA of the STO.In this orientation, the LSMO is in the [221] ZA and the epitaxial growth of all films is clearly visible.The diffraction patterns of STO and LSMO are indicated by black horizontal lines.For HZO, the (003) reflections in the growing direction are most prominent, while in-plane no reflections can be evidenced, and also the diagonal planes are very faint (marked with orange circles).
Furthermore, from this SAED pattern, a difference in the dvalues of (006) and (042) can be observed, as illustrated by the dashed ring around the (006) reflections.These reflections would correspond to the {222} planes of the ferroelectric orthorhombic phase, which cannot have a d-value difference (in a relaxed structure) due to the orthorhombic symmetry.An effect of an elliptical distortion of the diffraction pattern by unprecise adjustments of the projector lens system can be     37,38 The Hf 0.93 Y 0.07 O 2 /La 0.7 Sr 0.3 MnO 3 epitaxial stack was deposited by PLD, using the same deposition parameters as those deposited on Nb:SrTiO 3 substrates.The wide-range RSM of the doped hafnia films deposited on La 0.7 Sr 0.3 MnO 3 /SrTiO 3 / Si (substrate) shows features similar to those deposited on La 0.7 Sr 0.3 MnO 3 /SrTiO 3 (substrate), an out-of-plane orientation, and the presence of four kinds of domains with different in-plane orientations, as described before.The wide-range RSM was acquired at φ = 0°, and besides the specular Si(004), the Si(022) spot was visible in this diffraction geometry.The nonspecular STO/LSMO diffraction spots 111, 112, and 221 are also present.The results are shown in Figure 5a.A pole figure of HYO{022}, HYO{201}, STO/LSMO{011}, and Si{111} measured for a 2θ ranging from 34.8°to 47.8°is shown in Figure 5b.The 12 spots of the HYO{022} and HYO{201} arising from the four domains are present on the pole figure, similar to the results from doped hafnia films deposited on LSMO-buffered STO substrates.

Transmission Electron Microscopy Characterization.
The TEM preparation of plan-view samples grown on the STO substrates was not successful because in 3 trials the samples broke apart during mechanical polishing before finishing the preparation.As a result, a Zr/Y:HfO 2 sample on SrTiO 3 -buffered Si was prepared.This sample should be  representative, as indicated by the XRD analysis.A SAED pattern of the plan-view sample with Si oriented in the [100] ZA is shown in Figure 6a.Here, the HYO forms a similar diffraction pattern as reported by Wei et al. 13 with 12 {120} reflections which can be explained by HYO having at least two domains rotated in plane by 90°.The green and red circles in Figure 6a indicate two domains.The domains marked with green circles are oriented with the STO (110) planes while the domains marked with red circles are oriented with the STO (101) planes.Adding the 2-fold twin rotation observed in the cross-sectional TEM analysis results in the four domains observed in XRD pole figures.These four types of domains may form during the crystal nucleation during PLD, where each nucleus can be oriented with STO (110), (−110), (1− 10), or (−1−10).The same color code is used in the FFT shown in Figure 6c of the HRTEM micrograph in shown Figure 6b.These colored circles were used for the filtered inverse FFT in Figure 6d which illustrates the granular microstructure of the HYO thin film.However, all individual grains are epitaxial.
A TEM image in a different orientation, tilted away from the [100] zone axis of Si, is shown in Figure S4.Here, strong Moiréfringes appear which were again used for a filtered inverse FFT.From these false color images, the average width of 20 domains can be roughly estimated to be 10 nm ±3 nm.The high crystallinity of the HZO, as indicated by the rocking curve, argues for coherent interfaces between these 10 nmsized domains as would be the case for twins.
In addition to the observed majority reflections in the SAED pattern shown in Figure 6a from HYO with the [003] out-ofplane orientation, a minority is observed in the FFTs (see yellow circles in Figure 6c and blue circles in Figure S4b) that is oriented with the STO (200) planes.7a allowed for the precise measurement of the c lattice parameter, listed in Table 1, and determination of the film thickness based on the thicknessoscillation period, which in this case was 4.7 nm.A wide-range RSM shown in Figure 7b was measured at an in-plane rotation angle of φ = 30°.Thus, in addition to the specular 006 spot, the 113, 116, and 119 spots of the Al 2 O 3 substrate are observed at this in-plane phi angle.The HZO film appears to consist of two kinds of domains, belonging to the same r-phase R3m no.160, rotated in-plane by 180°with respect to one another and by 30°with respect to the Al 2 O 3 crystallographic cell.The corresponding angles of these two domains, which were obtained from the simulation of the RSM are denoted next to indexed HZO spots in the figure.The pole figure of the same sample is presented in Figure 7c.The HZO {201}, HZO {022}, sapphire {102} and sapphire {104} spots from the lattice planes symmetrically equivalent are marked on the pole figure.The 2θ ranges from 25°to 37.8°.
The sapphire {102} and {104} spots reflect the trigonal symmetry of the phase, resulting in three spots on the pole figure for each family.The HZO {201} and HZO {022} spots should also show three spots each, according to the crystallographic symmetry of the R3m phase, but six spots are observed experimentally.This can be explained by the presence of two kinds of domains, belonging to the same trigonal phase R3m, rotated in-plane by 180°with respect to one another, as deduced for the wide-range RSM simulation discussed above.This domain configuration has been reported in prior studies on HZO films deposited on GaN and sapphire, 14 also being imposed by the symmetry of the substrate.To verify that, a pole figure of the HZO films was simulated using MTEX, according to the proposed assumption, and the results are shown in Figure 8a.The simulation corresponds to the findings obtained from the experiments.
The simulation for the Pca2 1 phase of a (111) oriented monodomain film gives three poles from the {111}, and one poles from each {020}, {002} and {200} reflection families.If one considers two (111) domains rotated in-plane by 180°w ith respect to one another, the simulations reproduce the observed six {111} poles, as well as the six poles of the {020}, {002}, and {200} ones, as shown in Figure 8b.Also, in this case, it is difficult to distinguish between the R3m and Pca2 1 crystallographic phases from the pole figure XRD measurements.
Considering the relatively uniform intensity distribution of the reflections corresponding to a specific family of spots, one can state that the volume fraction of the two types of HZO domains appears to be equally distributed.
The measured wide-range RSM of the HZO deposited on sapphire could also be assigned to a ferroelectric orthorhombic phase like, for example, the one reported by Xu et al. 39 With this assumption, the films are epitaxial and have an (111) outof-plane orientation.Such an example is illustrated in Figure S2, where the observed spots in the RSM from the HfO 2 films deposited on sapphire are assigned to the above-mentioned crystallographic phases.
To precisely determine the in-plane lattice parameters of the deposited films, we performed in-plane X-ray diffraction measurements.Thus, in the case of doped hafnia films deposited on sapphire, the HYO (220) and Al 2 O 3 (300) reflections were observed, as can be seen in Figure 9a.This means that the (220) crystallographic planes of the epitaxially doped hafnia films are parallel with the (300) planes of the underlying sapphire substrates and perpendicular to the HYO (003) planes which are parallel with the sample surface.The epitaxial relationship in this case considering the R3m crystallographic phase is [220] HZO(001) //[300] Al 2 O 3 (001).If one would consider the ferroelectric orthorhombic phase Pca2 1 instead of the trigonal phase (R3m), the (111) crystallographic plane is parallel with the sample surface, whereas the (202) plane forms an angle of 89.84°with the (111) plane, very close to 90°.For this reason, based on the inplane XRD measurements, one cannot distinguish between the ferroelectric orthorhombic phase and the rhombohedral one.
From these high-resolution in-plane scans, one can precisely determine the in-plane lattice parameter of the rhombohedral HYO films deposited on sapphire, which is 7.207 Å. Next, the 2-ThetaChi/Phi axis was fixed at the HYO(220) peak position, and a phi-scan was performed, with a complete 360°phi-axis scan range.The 3-fold in-plane symmetry expected for the rhombohedral films combined with the presence of the two 180°in-plane rotated domains is consistent with the observed six reflections spaced by 60°from this scan and with the results from the pole figures of the HZO films deposited on sapphire, discussed above.The in-plane phi scan shown in Figure 9b is equivalent to an in-plane rocking curve, and the width of the reflections gives us a measure of the in-plane mosaicity.In the case of 6.2 nm HYO films deposited on sapphire, the FWHM of the in-plane rocking curve is 4.1°.
A table with the precisely measured lattice parameters of the epitaxially doped hafnia films, extracted from high-resolution specular and in-plane scans, for films deposited on different heterostructures/substrates with different film thicknesses is shown below.The R3m crystallographic phase including the structure parameters is taken from Wei et al. 13 3.1.3.2.Transmission Electron Microscopy Characterization.The TEM analysis of HZO on sapphire is shown in Figure 10.HZO on sapphire is divided into two domains, both growing in the [003] direction (considering the R3m phase) with a 2-fold twin rotation as shown in the HRTEM micrograph and the corresponding FFTs in Figure 10b,c.On sapphire, however, no additional growing direction was observed.In comparison to HZO on an STO substrate, the out-of-plane (003) reflections in the SAED pattern have a weak intensity, while for the in-plane (030) reflection, a higher intensity is observed.For both substrates, the intensities of the diffraction pattern is comparable.This may suggest a stronger in-plane epitaxial relation of (120) of Al 2 O 3 and (030) or (300) of HZO in comparison to those deposited on STO substrates.
3.2.Electrical Characterization.Ferroelectric dynamic polarization hysteresis loops of the HZO films deposited on STO (substrate)/LSMO and Si (substrate)/STO/LSMO were measured to test the ferroelectric behavior of the doped hafnia films.The capacitor devices have a Cu top electrode, and the device area is 225 μm 2 for the films deposited on STO substrates and 50 μm 2 for those deposited on the Si substrate.No correction or leakage current compensation was used for the dynamic polarization hysteresis loop measurements.The results are listed in Figure 11.All of the measured samples show ferroelectricity, with a remanent polarization ranging from 14 to 26 μC/cm 2 .These polarization values are comparable with those reported in the literature for epitaxial doped HfO 2 films. 13,18he "wake-up" effect in these ferroelectric capacitors was investigated by acquiring the first 9 consecutive P−V cycles on a pristine capacitor, as presented in Figure 11d.The samples show ferroelectricity from the first P−V cycle, and after the third cycle, there is no significant change in the shape of the P−V ferroelectric loops.

CONCLUSIONS
In conclusion, ultrathin epitaxial ferroelectric Y-and Zr-doped HfO 2 films are successfully deposited on three different systems: La 0.7 Sr 0.3 MnO 3 -buffered SrTiO 3 substrates, La 0.7 Sr 0.3 MnO 3 SrTiO 3 -buffered Si (100) wafers, and trigonal Al 2 O 3 substrates.To distinguish between the commonly reported orthorhombic phase and other possible ferroelectric polymorphs like the rhombohedral R3m phase employing XRD methods, combining θ-2θ symmetric scans, in-plane scans, wide-range reciprocal space maps, and pole figure measurements turned out to be a difficult task due to the structural similarities of the polymorphs.However, extensive XRD characterization indicates that the majority of the investigated films consist of the trigonal phase (R3m, no.160) with c-axis orientation.The films deposited on La 0.7 Sr 0.3 MnO 3 -buffered SrTiO 3 substrates and La 0.7 Sr 0.3 MnO 3 SrTiO 3 -buffered Si (100) wafers consist of four kinds of domains, rotated inplane with 90°with respect to one another, whereas the films deposited on sapphire consist of two kinds of domains, rotated in-plane with 180°with respect to one another, the domains having an equal volume-fraction.TEM analysis supports these conclusions.However, for the doped HfO 2 films deposited on La 0.7 Sr 0.3 MnO 3 -buffered SrTiO 3 substrates, a minority growing direction ([222]) could be detected by TEM, whereas only the majority [003] growing direction was observed for those deposited on sapphire.By the analysis of HRTEM micrographs of a plan-view of doped hafnia films deposited on STObuffered Si, a domain size of about 10 nm could be estimated.The ferroelectric characterization of capacitors based on Y-or Zr-doped HfO 2 films deposited on La 0.7 Sr 0.3 MnO 3 -buffered SrTiO 3 substrates and SrTiO 3 -buffered Si substrates show a remanent polarization ranging from 15 μC/cm 2 to 26 μC/cm 2 with no "wake-up" effects.
A wide-range RSM of the HZO/LSMO/STO heterostructure at a φ angle of 45°; wide-range RSM assigned to the R3m and Pca2 1 phases; the explanation for the shifts in the φ angle observed in the measured wide range pole figures; HRTEM micrograph of the HYO/ LSMO/STO/Si thin film stack; simulated pole figures for the R3m and Pca2 1 phases at a 2-theta of about 50°, and a chi angle of 35°(PDF)

Figure 1 .
Figure 1.(a) The XRD pattern of the Hf 0.5 Zr 0.5 O 2 /La 0.7 Sr 0.3 MnO 3 / SrTiO 3 (substrate) heterostructure; (b) the detailed Hf 0.5 Zr 0.5 O 2 003 region with thickness oscillations; the blue line represents the experimental data, and the red line is the simulation of the diffractogram showing a film thickness of 8 nm.(c) Simulation of the La 0.7 Sr 0.3 MnO 3 001 region (red line), the film thickness is found to be about 71 unit cells, i.e., 27 nm.(d) Rocking curve of the Hf 0.5 Zr 0.5 O 2 003 reflection; FWHM = 0.032°.

Figure 2 .
Figure 2. (a) Wide range RSM of the HZO/LSMO/STO (substrate) heterostructure.The spots belonging to LSMO/STO are denoted in dark blue, whereas the spots from the HZO film are denoted in red.The angles marked next to the HZO spots represent the in-plane rotation of the corresponding HZO domains; the hkl Miller indices are assigned here to the R3m phase.(b) Pole figure of the HZO {201} and HZO {022} spots; the black, red, blue, and green arrows indicate the four domains with the families of spots associated with them.Pole figure simulation of the HZO films: (c) phase R3m, considering (001) out-of-plane orientation and presence of four domains, with an in-plane rotation of 90°with respect to one another; (d) phase Pca2 1 considering (111) out-of-plane orientation and presence of four domains, with an in-plane rotation of 90°with respect to one another, and the presence of {200}, {020}, and {002} spots.

Figure 4 .
Figure 4. (a) HRTEM micrograph showing an LSMO back electrode in ZA [542] growing along (012) planes.An FFT analysis shown below in (b) and (c) was performed on the two HZO regions marked with circles.The left grain is in [100] ZA, and the right FFT shows a superposition of a [100] and a [100] ZA which could be explained by a twin with a 2-fold rotation at the [003] direction.These domains are indicated by yellow and red rectangles.The orange ellipse in the left FFT in (b) marks the additional [222] minority growing directions to the main [003] growing direction.The SAED pattern in (d) is similar to that of FFT in (c).

Figure 5 .
Figure 5. (a) Wide-range RSM of a 5.6 nm thick HYO film deposited on La 0.7 Sr 0.3 MnO 3 /SrTiO 3 /Si (substrate); here, the observed spots from the HYO film are assigned to (001)-oriented films of the ferroelectric R3m phase, consisting of four types of domains with 0°, 90°, 180°, and 270°inplane orientation.The measurement was acquired at φ = 0°.(b) Pole figure of the HYO {022}, HYO {201}, STO/LSMO {011}, and Si {111} reflections; the yellow, red, white, and green arrows indicate the four domains with the families of spots associated with them.The measured 2θ range is 24.9−37.4°.The radial direction represents the χ axis ranging from 0°to 90°, whereas the azimuthal direction represents the φ axis with a range from 0°to 360°.

Figure 6 .
Figure 6.(a) Plan-view SAED pattern of Si/STO/LSMO/HYO.The substrate Si is oriented in the [100] zone axis as well as the STO which is rotated by 45°with respect to Si. HYO shows mainly two types of reflections.The red circles depict the HYO [001] zone axis with {220} reflections aligned with the STO (101) planes (red arrow) while the reflections marked by the green circles are aligned with the STO (110) planes (green arrow).(b) shows a high-resolution TEM micrograph in the same viewing direction which is confirmed by the FFT in (c) showing the same diffraction pattern as in a).In (c), the green, red, and yellow circles were used for filtering the FFT and building a colored inverse FFT shown in (d).The majority of the domains have an [003] out-of-plane orientation with {220} reflections marked by red and green circles.The minority (yellow) is oriented with STO (200).

Figure 7 .
Figure 7. (a) High-resolution 2θ/ω scan of a 4.7 nm thick HZO film deposited on sapphire.(b) Wide range RSM of the same film on sapphire.The spots belonging to sapphire are denoted in black, whereas the spots from the HZO film are denoted in red.The angles denoted next to the HZO spots represent the in-plane rotation of the corresponding HZO domains assigned to the R3m phase.The sapphire substrate was rotated by phi = 30°during the RSM measurement.(c) Pole figure of the HZO {201}, HZO {022}, sapphire {102} and sapphire {104} spots.The radial direction represents the χ axis ranging from 0°to 90°, whereas the azimuthal direction represents the φ axis with a range from 0°to 360°.

Figure 8 .
Figure 8. Pole figure simulation of the HZO films using MTEX.(a) Phase R3m, considering (001) out-of-plane orientation and presence of two domains (indicated by the red and the blue arrows), with an in-plane angular rotation of 180°with respect to one another.(b) Phase Pca2 1 considering (111) out-of-plane orientation, and the presence of two domains, with an in-plane angular rotation of 180°with respect to one another.

Figure 9 .
Figure 9. In-plane XRD of the HYO(6.2nm)/Al 2 O 3 : (a) in-plane scan showing the HYO(220) and Al 2 O 3 (300) reflections; the lattice parameters and the FWHM are given in the inset.(b) In-plane phiscan of the HYO(220) region showing a 6-fold in-plane symmetry; the FWHM is 4.1°.

Figure 10 .
Figure 10.(a) HRTEM micrograph of Al 2 O 3 in [210] ZA and HZO in [100] ZA.Two different domains were found via FFT analysis in (b) and (c); again, the [100] ZA is mirrored at the (003) plane.The SAED pattern in (d) shows both domains, and the Al 2 O 3 [210] ZA is indicated by vertical black lines.In this system, the (003) reflections are rather weak compared to the STO/LSMO system, and the (060) reflection is visible in-plane.In FFTs even the (030) planes.The diffraction rings originate from the Pt coating which was used to protect during FIB preparation.

Table 1 .
a and c Lattice Parameters of the Strained Doped HfO 2 Films Deposited on Different systems in this Work Were Extracted from High-Resolution 2θ/ω Scans and In-Plane Scans a a The crystallographic structure is the one reported by Wei et al. in ref 13 adapted to the lattice parameters measured in this work.