Microstructural evolution and ferroelectricity in HfO₂ films

Polymorphs of bulk HfO₂

Bulk HfO₂ crystals present different polymorphs depending on the temperature and pressure. The left branch of Figure 1 lists the stable crystal structures reported in bulk HfO₂ in the sequence based on symmetry reduction from the highest-symmetry cubic phase (C-phase, space group Fm$$\bar 3$$m) that exists above 2773 K^[38]. During the cooling process, the C-phase transforms to a tetragonal phase (T-phase, space group P4₂/nmc) at 2773 K by symmetry reduction and then to a monoclinic phase (M-phase, space group P2₁/c) at 1973 K^[90]. The M-phase is the most stable phase at room temperature and atmospheric pressure. At high pressure, bulk HfO₂ has two orthorhombic polymorphs, denoted as orthoI (space group Pcba) and orthoII (space group Pmna)^[91]. OrthoI is transformed from the T-phase by symmetry reduction under pressures between 4 and 14.5 GPa. OrthoI changes to orthoII with a pressure above 14.5 GPa and the transition pressure is almost independent of temperature^[92]. All of these polymorphs have a center of symmetry, which is marked by the green point in each structure in the left branch of Figure 1. The centrosymmetric feature of these structures cannot induce ferroelectricity.

Figure 1. Symmetry-reduction flowchart of low energy phases of HfO₂, starting from the C-phase. The left branch shows stable non-polar phases and the right branch presents polar phases obtained from first-principles calculations. Dark yellow and red spheres represent hafnium and oxygen atoms, respectively, while green spheres indicate the center of symmetry of the centrosymmetric phases^[38].

Identification of FE HfO₂ phases

Although the stable bulk HfO₂ phases are centrosymmetric, HfO₂ films with a nanoscale thickness, as well as properly doped HfO₂ bulk crystals, can show another landscape. Compared with undoped bulk HfO₂ crystals, atomic layer deposition (ALD) processed undoped HfO₂ films with a thickness of 6 nm have robust ferroelectricity due to the formation of the FE O-phase under a nanoscale grain size effect^[93]. These FE properties can be further enhanced by lowering the oxidant dose^[94] and modulating the water pulse time^[95] during the ALD process. In addition, ferroelectricity can also be stabilized in bulk HfO₂ single crystals after 12% yttrium doping and a fast quenching process^[34]. However, the most common and robust ferroelectricity is observed in nano HfO₂ films doped with various elements.

The first report confirming robust ferroelectricity in HfO₂-based materials was for Si-doped HfO₂ (Si:HfO₂) films with a thickness of 10 nm, in which the formation of a non-centrosymmetric O-phase (space group Pbc2₁) analogous to Mg:ZrO₂ was also observed by grazing incidence X-ray diffraction measurements^[16]. To identify the accurate atomic occupation of this FE structure in HfO₂, density functional theory (DFT) calculations were firstly used to predict polar O-phases. First-principles calculations suggested that the two most viable FE phases are Pca2₁ and Pmn2₁ and that these two non-centrosymmetric equilibrium phases have similar free energies^[38]. As shown in the right branch of Figure 1, the non-centrosymmetric structures with space groups of Pca2₁ and Pmn2₁can be obtained by distorting the P4₂/nmc structure along the [110] and [100] directions, respectively. The lattice parameters of these phases are summarized in Table 1^{[29,32,38,53,74,96-98]}. The polarization of the Pca2₁ and Pmn2₁ phases can be 180° switched with small energy barriers, serving as two topologically equivalent variants with opposite polarization referred to as the “up” and “down” states. The energy barrier between the “up” and “down” states of the Pca2₁ and Pmn2₁ phases at 0 Pa were estimated to be 40 and 8 meV/atom, respectively.

Sang et al.^[32] confirmed the Pca2₁ phase in Gd-doped HfO₂ (Gd:HfO₂) FE thin films by combining scanning transmission electron microscopy (STEM) and position averaged convergent beam electron diffraction (PACBED)^[32,63]. The crystal structures of the centrosymmetric M-phase (P2₁/c) and O-phases (Pbcm and Pbca), non-centrosymmetric O-phases (Pca2₁ and Pmn2₁) and their corresponding atomic projections along the four major zone axes are presented in Figure 2A. The Pca2₁, Pbcm and Pbca phases have the same projected columns of Hf atoms but different projected columns of O atoms along the four main zone axes. Figure 2B shows STEM-high angle annular dark-field (STEM-HAADF) images of FE HfO₂ films along the four main zone axes, which are consistent with the projections of the Hf columns in the Pca2₁, Pbcm and Pbca phases. Because O atoms are much lighter than Hf atoms, it is only possible to image Hf atoms under STEM-HAADF imaging mode, resulting in difficulties in distinguishing these phases. PACBED was then applied to find the difference between the Pca2₁, Pbca and Pbcm phases by the projected symmetry information. Thus, the presence of the Pca2₁ phase in Gd:HfO₂ thin films is indirectly confirmed, which shows a non-centrosymmetry feature and is responsible for ferroelectricity in HfO₂ films^[37,38].

Figure 2. (A) HfO₂ crystal structures for M-phase (P2₁/c), two non-centrosymmetric O-phases (Pmn2₁ and Pca2₁) and two centrosymmetric O-phases (Pbcm and Pbca) and their atom projections along four major zone axes. (B) STEM-HAADF images of Gd:HfO₂ films acquired along four major zone axes, which are the same for the Pca2₁, Pbca and Pbcm phases. Scale bar is 0.5 nm^[32]. STEM-HAADF: Scanning transmission electron microscopy-high angle annular dark-field.

Recently, Luo et al.^[99] provided evidence to distinguish these O-phases in Hf_0.5Zr_0.5O₂ (HZO) thin films by directly mapping oxygen atoms using atomic-scale STEM-HAADF and STEM annular bright-field (STEM-ABF) techniques. Figure 3A-C show the sublattice of the Hf/Zr and O atoms projections along the [010] axis of HZO phases with different space groups. The O atom projections in the blank rectangle are different between the Pca2₁, Pbca and Pbcm phases. Figure 3D and E present atomic-resolution STEM-HADDF and STEM-ABF images of FE HZO films, respectively, in which the Hf/Zr and O atomic columns along the [010] axis match very well with the simulated results of the Pca2₁ phase.

Figure 3. Projections of crystal structures of HfO₂ with three O-phases along the [010] axis. The arrangements of O atoms in the black rectangles are different among (A) Pbcm, (B) Pbca and (C) Pca2₁. (D) STEM-HAADF image of HZO phase projected along [010] zone axis. Scale bar of 1 nm. (E) STEM-ABF image of (D) with the inset being a simulated ABF image. Scale bar is 1 nm^[99]. STEM-HAADF: Scanning transmission electron microscopy-high angle annular dark-field; HZO: Hf_0.5Zr_0.5O₂; ABF: annular bright-field.

With the exception of the Pca2₁structure, a rhombohedral phase (R-phase) with the R3m space group is also non-centrosymmetric. The R3m structure is obtained in epitaxial (111)HZO/(001) La_0.7Sr_0.3MnO₃ (LSMO)/SrTiO₃ (STO) substrates, as shown in Figure 4A and B. Devices based on this phase exhibit a large remanent polarization (P_r) of 34 μC·cm^-2 and are free of a wake-up process. The R3m phase is only observed in epitaxial thin films, while the commonly reported Pca2₁phase can be found in both polycrystalline and epitaxial films. According to DFT calculations, the Pca2₁ phase has lower free energy than the R3m phase and is thus more stable and common in FE HfO₂ films. However, epitaxial strain and size effects favor the R3m phase^[29].

Figure 4. Polar R-phase (R3m) viewed from (A) the [001] axis and (B) the [100] axis of bulk HfO₂ obtained by first-principles calculations. Hf and O atoms are represented by green and blue spheres, respectively^[29].

Film deposition methods

The ALD method, which has been intensively studied for the semiconductor industry, has been widely used for the preparation of FE HfO₂ films^[16]. The precursors are commercially available materials for Hf, Si and Zr, e.g., tetrakis(ethylmethylamino)hafnium and HfCl₄, tetrakis(dimethylamino)silane and SiCl₄, and tetrakis(ethylmethylamino)zirconium. Ozone and water are used as oxygen sources while argon is used as a purge and carrier gas^[19,20,52]. The initial HfO₂ films deposited on TiN or TaN bottom electrodes are amorphous. A subsequent rapid thermal annealing for crystallization is applied after capping a top electrode layer to introduce ferroelectricity. A P_r of up to 35 μC·cm^-2 and a coercive field (E_c) of up to 3.5 MV·cm^-1 were experimentally achieved in ALD-based HfO₂ films with various dopants, including Si, Zr, Y, La, Gd, Sr, Sc and N^{[23,53,75,100]}. In addition, these ALD-based HfO₂ films present a significant reduction of P_r with increasing film thickness and almost lose their ferroelectricity when the film thickness is over 20 nm^[101]. There are some concerns regarding the practical application of the ALD method. First is the chemical reactions between a metal precursor, an oxygen source, a substrate or a previously deposited film, which makes it difficult to control the film processing parameters and leads to a narrow processing window^[102]. In addition, sophisticated and high-cost facilities and the low deposition rate of ALD makes it less viable for practical manufacturing^[21]. In order to solve these problems, other deposition methods, including physical vapor deposition (PVD), chemical solution deposition (CSD) and PLD have been explored^[21,43]. A comparison of these methods is shown in Table 2^[63,103-106].

For PVD methods, the sputtering, sputter power, atmosphere and deposition temperature can be precisely controlled to adjust HfO₂ films with multiple phases with different phase fractions and the corresponding macroscopic FE performance. This not only benefits the exploration of the structure-property relationship of FE HfO₂ films, but is also attractive for revealing how the growth parameters control the phases in obtained HfO₂ films, especially the FE Pca2₁phase^[107]. Mittmann et al.^[108] prepared undoped HfO₂ films using the sputtering method, in which the film thickness, annealing temperature and oxygen content were controllable. After annealing with temperatures higher than 600 °C, the films with thicknesses of 8-30 nm show a stable remanent polarization (P_r). For films with a thickness in the range of 8-20 nm, their P_r values increase with annealing temperature up to 1000 °C. For thicker films, 800 °C is the optimal anneal temperature. In addition, the concentration of oxygen (oxygen deficiency) within the HfO₂ films is responsible for the stabilization of the O-phase by adjusting the nucleation of the nanocrystallite phase in the as-deposited films. The sputtering method is also promising for depositing HfO₂ films at room temperature, because it can significantly change the kinetic energy of the sputtered films to control the phase types at room temperature without subsequent high-temperature processing^[109]. The reduction of deposition temperature is always desirable for decreasing production costs and matching substrates that cannot sustain high temperatures, such as organic flexible substrates^[110].

The CSD method is an inexpensive and flexible deposition technique with good adjustability of concentration and stoichiometry. Therefore, it is widely used for the deposition of FE and piezoelectric ceramic thin films^[111,112]. Using the CSD method, Starschich et al.^[43] successfully prepared Y:HfO₂ films with a thickness of ~70 nm, which still possess P_rover 13 μC·cm^-2. The PLD method has been widely used to prepare highly oriented HfO₂ films. Recently, 930-nm-thick 7%-Y:HfO₂ films were deposited on (111)Pt/TiO_x/SiO₂/(001)Si substrates using this method. Interestingly, the resulting FE structures and properties were insensitive to the film thickness, which also makes HfO₂ films attractive for structural characterization and piezoelectric applications^[29,35,63].

Phase stability

The ferroelectricity in doped HfO₂ films is attributed to the stabilization of the metastable non-centrosymmetric Pca2₁phase^[32,38,99]. The FE phase Pca2₁ can be stabilized by various growth parameters during the film fabrication process with the above mentioned methods, i.e., ALD, PVD, CSD and PLD. The common growth parameters that can be controlled are doping (bulk free energy)^{[45,75,113,114]}, film thickness (grain size effect)^[57,78,93] and capping layer (thermal strain)^[16,115-117]. We will discuss how the polar Pca2₁phase is stabilized by these growth parameters. In addition, the ferroelectricity in HfO₂ films has a strong electric field^[118-121] and temperature dependence^[18,122,123], which has a strong correlation with the phase transformation under external stimuli^[25,122]. While previous reviews^[51,82] focused mainly on the FE properties, we will summarize the microstructure-property relations.

Effects of dopants (bulk free energy)

The ferroelectricity in HfO₂ films can be adjusted by dopant species. Various cations, including Si^[16], Zr^[74], Al^[20], Y^[19] and La^[100,124], and an anion, N^[114], have been incorporated into HfO₂ films. All these dopants can induce ferroelectricity but have different doping sensitivity depending on the dopant size. For films with smaller sized dopants, such as Si and Al, macroscopic paraelectric (PE)-FE-antiferroelectric (AFE) transitions occur with increasing dopant concentration^[16,18,20]. HfO₂ films doped with Si were firstly reported to induce ferroelectricity and exhibited significant potential for industrial applications due to Si already being a standard element with mature technical parameters and contamination control methods^[16]. In HfO₂ films, P_r increases with a Si concentration of 2.6 to 3.1 mol.%. The AFE property gradually appears when the Si concentration is over 4.3 mol.%^[16]. Similar results were observed in Al-doped HfO₂ films. A robust FE behavior is achieved at an Al content of 4.8 mol.% and obvious AFE behavior occurs at an 8.5 mol.% Al content^[20]. Zr is another promising dopant to maintain the FE properties in a wide Zr-content range because the Zr can substitute Hf in the whole composition range^[125]. Figure 5A shows a polarization-electric field (P-E) hysteresis loop for the HZO films. The FE behavior in the HZO system is stabilized when the Zr concentration is 30-50 mol.%^[62,74]. Figure 5B demonstrates how the ZrO₂ content affects the P_r, dielectric constant (ε_r) and M-phase fraction in HfO₂-ZrO₂ solid solutions. The highest P_r is achieved at a 50 mol.% ZrO₂ concentration, while the fraction of the M-phase (P2₁/c) decreases to 0% at this point. This result indicates that the centrosymmetric M-phase is suppressed with increasing doping concentration. The reduced M-phase promises the possibility of forming the non-centrosymmetric phase Pca2₁.

Figure 5. (A) P-E hysteresis at 1 kHz of 9-nm-thick HZO-based metal-insulator-metal capacitors. (B) Evolution of P_r, ε_r and M-phase fraction in the HfO₂-ZrO₂ solid solution with increasing ZrO₂ content (mol.%)^[74]. (C) Contour plot of P_r as a function of dopant radius and concentration^[45]. HZO: Hf_0.5Zr_0.5O₂; P_r: remanent polarization.

The doping sensitivity of various dopants is shown in Figure 5C^[45]. Unlike small-sized dopants, large-sized dopants (e.g., Y, Gd and La) exhibit different PE-FE-PE transitions with increasing concentrations^{[19,21,124,126]}. Müller et al.^[19] prepared HfO₂ films with Y concentrations varying from 2.3 to 12.3 mol.%. The highest P_r of 24 μC·cm^-2 was achieved at a Y concentration of 5.2 mol.%. Unlike the AFE behavior in Si- or Al-doped HfO₂ films, the HfO₂ films with PMA (anneal for crystallization after top electrode deposition) and PDA (anneal for crystallization after top electrode deposition) change to paraelectric again when the concentration of Y increases to 12.3 mol.%, as shown in Figure 6.

Figure 6. P-V hysteresis loops of 10 nm HfO₂ films doped with Y from 2.3 to 12.3 mol.% treated with PMA and PDA processes^[19].

To systematically investigate the dopant effects on phase types and ferroelectricity in HfO₂ films, experiments and theoretical calculations were carried out with different dopant species (ionic size and valence) and concentrations. Schroeder et al.^[45] compared the ferroelectricity of HfO₂ films with various dopants of radii from 54 pm (Si) to 132 pm (Sr). AFE behavior (when T-phase occurs) occurred in HfO₂ films with small-sized dopants, such as Si and Al, and this was attributed to the specific phase transformation path related to small dopants. For small dopants, like Si and Al, M-O-T-C phases transformations occur with increasing doping concentration^[45]. On the contrary, M-O-C phase transformation takes place in HfO₂ films with large dopants, such as Y, Gd, La and Sr, not favoring the formation of the T-phase that leads to AFE-like behavior. The T-phase contains four relatively short and four relatively long Hf-O bonds, which is more favorable with Si or Al doping because the short Si-O or Al-O bonds could form after Si or Al doping, while long X-O bonds are formed by large dopants in the T-phase^[127,128].

Later, more atoms (Al, Ga, Co, Ni, Mg, In, La, Y, Nd, Sm, Er, Sr and Ba) with different ionic radii (from 54 to 135 pm), valences and concentrations were incorporated in CSD-based HfO₂ films^[75]. The P_rin HfO₂ films with large dopants (from La to Sm, P_r≈ 14 μC·cm^-2) is almost four times higher than that of small dopants (from Al to In, P_r ≈ 3.5 μC·cm^-2). This is due to the promotion of the C-phase to O-phase transformation by the large dopants, with the assistance of oxygen vacancy movement under an applied electric field^[75]. Similar results were also obtained in sputtered HfO₂ films doped with Sc, Y, Nb, Al, Si, Ge and Zr^[114]. Figures 7A and B show the switchable polarization (P_SW) and the phase fractions of the O-, T- and C-phases as a function of doping species and concentration. Although these dopants show different doping sensitivities, the switchable polarization peaks remain at ~22 μC·cm^-2. Meanwhile, the corresponding fractions of the O-, T- and C-phases increase to ~100% at high doping levels, indicating a phase transformation from the M-phase to the O-, T- and C-phases. Figures 7C and D show the relationships of P_SW-fraction and 2θ-fraction of the M-phase, respectively. These results present a possible universal route for the formation of the FE HfO₂ phase with increasing dopant concentration: the low symmetric M-phase tends to transform to the higher symmetric T-/C-phases at higher doping concentrations, with O-phase being the intermediate one between them^[114].

Figure 7. (A) Switchable polarization P_SW of HfO₂ films as a function of doping concentration for different dopants: Sc, Y, Si, Ge, Zr and N. (B) O-, T- and C-phase fraction of HfO₂ films as a function of doping concentrations for various dopants. (C) P_SW as a function of the M-phase fraction for HfO₂ films with various dopants. (D) O-, T- and C-phase (111) peak positions as a function of the fraction of the M-phase for various dopants. The red and green arrows represent theoretical values for FE O-phase and non-FE T-phase, respectively^[114]. P_SW: switchable polarization; FE: ferroelectric.

In order to further understand the dopant effect on the stabilization of the Pca2₁ phase, first-principles calculations were carried out with 40 dopants by Batra et al.^[113]. The results indicated a significant decrease in bulk free energy after doping with Ca, Sr, Ba, La, Y and Gd, although the Pca2₁phase could not be solely stabilized by any dopant. In addition, the Pca2₁ phase is more favored by dopants with large radii and low electronegativity due to the specific bonds between the dopant cation and the second nearest oxygen neighbor. Compared with divalent dopants, such as Ba and Sr, trivalent dopants, including La, Gd and Y, are considered to stabilize the polar Pca2₁phase at a lower lattice strain condition. These conclusions are consistent with the experimental results discussed above, illustrating that some dopants from rare earth metals (La, Gd and Y) to alkaline earth metals (Sr) show significant potential in enhancing the ferroelectricity in HfO₂ films.

The understanding of the phase transformation with dopant concentration is interesting for both the fundamental understanding of HfO₂ films and their applications. It is helpful to understand the origin of ferroelectricity in HfO₂ films. In addition, the FE properties in HfO₂ FEs can be manipulated by different dopants to optimize the device performance. For example, Park et al.^[31] reported that the energy storage density was the highest in the Hf_1-xZr_xO₂ system with x = 0.7. Doping is the most flexible method to tailor HfO₂ FE thin films with the desired properties.

Effects of film thickness (surface energy)

According to the bulk free energy theory, the M-phase is more energetically favored compared to the FE Pca2₁phase that can be obtained in films with thicknesses of < 40 nm^[16,19,52]. Park et al.^[76] investigated the FE properties and the fraction of FE O-phase in Hf_0.5Zr_0.5O₂ films with thicknesses from 10 to 25 nm. A consistent reduction of the P_r and O-phase fraction was found with increasing film thickness. Similar results were reported in undoped HfO₂ films with thicknesses from 4 to 20 nm^[93] [Figure 8A]. A reduction of P_rand permittivity in the HfO₂ films was observed when the film thickness increased from 6 to 20 nm. Grains in HfO₂ films with thicknesses from 6 to 20 nm were characterized by TEM, as shown in Figure 8B. The individual grain grew across from bottom to top electrodes, in which the horizontal and vertical dimensions were of the same order of magnitude of film thickness. According to this result, a relation of grain size vs. film thickness was proposed, where the individual grain size in the HfO₂ film depends on its vertical dimension, or in other words, the film thickness. Thus, a larger film thickness results in an enlarged grain size. As indicated by ab initio results, the FE O-phase with the Pca2₁ structure has a lower surface energy than the M-phase^[57]. In the nanoscale HfO₂ films, the existence of a large quantity of nanocrystal grains leads to a high surface-to-volume ratio. Therefore, the surface energy dominates the total Helmholtz free energy, leading to stabilization of the metastable Pca2₁phase that unfavored solely by the bulk free energy. In this case, the surface energy loses its dominant contribution to the total energy in thicker films and the obtained phase is mainly favored by the bulk free energy, resulting in stabilization of the M-phase.

Figure 8. (A) Evolution of polarization-electric field and permittivity-electric field hysteresis with increasing thickness of undoped HfO₂ thin films. (B) TEM micrograph of typical grains in 6 and 20 nm-thick HfO₂ films^[93]. TEM: Transmission electron microscopy.

Benefitting from their unusual size effect, HfO₂ films can maintain spontaneous and switchable polarization, even for thicknesses down to 1 nm^[129], unlike the scaling issues in perovskite FEs. This size effect in HfO₂ FE films not only shifts the search for the fundamental limits from traditional perovskite FEs to next-generation fluorite structured oxides, but is also helpful for developing polarization-driven memories and ultrathin FE-based transistors.

In addition, contradictory reports are available in the literature on the effect of film thickness on E_c, even in epitaxial HfO₂ films. Lyu et al.^[130] reported that E_c decreases remarkably with film thickness in epitaxial HZO films, and the slope of the linear fit to log(E_c) vs. thickness is -0.61, which is consistent with the scaling value of -2/3 that is common in high quality perovskite FEs. A similar thickness-dependent E_cwas observed for epitaxial HZO films on Si(001)^[69] and La-doped HZO films on STO(001) and Si(001)^[131]. In contrast, the E_c was reported to remain almost constant with increasing film thickness in epitaxial Y-doped HfO₂ films^[132]. The microstructural origin for the different thickness-E_c relation is rarely reported. It was believed that microstructures would significantly affect the thickness and E_c relationship, which requires more work to reveal the role of microstructure.

Effects of capping electrodes and annealing (strain and quenching)

As-deposited HfO₂ films from ALD normally consist of an amorphous structure. Crystallization by annealing should be carried out. In the annealing process, a capping layer is a significant promotion to induce ferroelectricity due to the strain effect (the strain is introduced by the different thermal expansion coefficients between the capping layer and the HfO₂ film). Böscke et al.^[16] reported that ferroelectricity only occurs in 10-nm-thick Si:HfO₂ after annealing with a TiN top electrode capping. A more systematic investigation of Al:HfO₂ films was conducted by Mueller et al.^[20] on the FE properties in PMA samples with a TiN top capping layer [Pt/TiN(top)/Al:HfO₂/TiN(bottom)/Si], and PDA samples without a TiN top capping layer. As shown in Figure 9, the PMA and PDA samples show similar PE-FE-AFE transitions with increasing doping concentration, but the P_rof the PMA samples is always higher than that of the PDA samples.

Figure 9. Polarization hysteresis for (A) PMA and (B) PDA samples^[20].

Bottom electrodes also play a significant role in the ferroelectricity of HfO₂ films, which can control the resulting grain orientations and produce in-plane lattice strain. Park et al.^[115] clarified that grains in HZO/TiN (polycrystalline films/electrode) possess random orientations, while HfO₂ films on (111)-oriented Pt bottom electrodes are (111)-textured. A high in-plane tensile strain larger than 1.5% is found in both types of films. For tetragonal grains with proper orientation [(110)-oriented], the transformation to the Pca2₁ phase is possible because the a axis of the O-phase (a_O) could be obtained by elongating the c axis of the T-phase (c_T) under the in-plane tensile strain. However, for (111)-textured films on (111)-oriented Pt bottom electrodes, the transformation from the T-phase to the O-phase requires a larger strain for the c_T to a_O transformation, which is not favored by similar in-plane tensile strain. Shiraishi et al.^[117] investigated the role of in-plane strain on the ferroelectricity of HZO films. Pt bottom electrodes with the (111)-orientation were coated on SiO₂, Si and CaF₂ substrates with thermal expansion coefficients of 0.47 × 10^-6, 4.49 × 10^-6 and 22 × 10^-6/°C, respectively, leading to different strain conditions for HfO₂ film deposition [Figure 10A]. As a result, HZO films on SiO₂ substrates have a smaller in-plane tensile strain than that on Si substrates, while HfO₂ films on CaF₂ substrates have in-plane compressive strain, as shown in Figure 10B. Correspondingly, HZO films on SiO₂ have the highest remanent polarization, followed by those on Si substrates and on CaF₂ substrates, which is consistent with the reduction of the in-plane tensile strain, as shown in Figure 10B. The fraction of the O- and T-phases is also estimated, which increases with in-plane tensile strain.

Figure 10. (A) P-E hysteresis of HZO thin films deposited on SiO₂, Si and CaF₂ substrates. (B) Relationship between remanent polarization and deviation of the lattice spacing^[117]. HZO: Hf_0.5Zr_0.5O₂.

Furthermore, other metal electrodes, such as W, Ru and Ir, have also been used for HfO₂ FE fabrication to improve the endurance of the device or device integration ability^[133-138]. Some field-induced behaviors, such as the wake-up effect and fatigue, are also related to the electrode properties^[25,33].

Temperature

Temperature-dependent ferroelectricity is an interesting topic in FE HfO₂ films. The FE-AFE transition with a temperature increase from 0 to 180 °C was first reported in 3.8 mol.% Si-doped HfO₂ films by Böscke et al.^[18]. A lower transition temperature occurs at higher Si concentrations. Similar temperature-induced FE phase transformations were also reported in HZO solid systems and Al-doped HfO₂ films^[20,74]. This phenomenon is very useful for energy-related applications in nanoscale devices, such as electrocaloric cooling devices^{[31,51,139,140]}. Hoffmann et al.^[23] reported that giant pyroelectric coefficients up to 1300 μC/(m² K) were achieved due to the temperature-induced structural transition. The ultra-high pyroelectric coefficient comes not only from usual pyroelectric behavior but also from a phase transformation associated with a large change of polarization with temperature. Encouraged by the significant potential of energy storage and transfer applications, further fundamental knowledge behind this temperature-induced FE property evolution was explored, especially with its structural mechanism. Park et al.^[122] investigated remanent polarization-microstructure relation from 80 to 400 K. Figure 11A gives an intensity contour map of grazing incidence X-ray diffraction (GIXRD) patterns of Si-doped HfO₂ films from 110 to 410 K. With decreasing temperature, the normalized intensities of the O-phase (110)_o and (120)_o diffraction peaks increase from almost 0 to 0.25 and 1, respectively. This provides direct evidence of the T- to O-phase transformation [Figure 11B-G] and as the origin of the changes of the P-E curves [Figure 11H-M].

Figure 11. (A) An intensity contour map of GIXRD patterns of Si-doped HfO₂ films from 110 to 410 K. GIXRD patterns of Si-doped HfO₂ films measured at (B) 410, (C) 350, (D) 275, (E) 200, (F) 125 and (G) 110 K. P-E curves of Si-doped HfO₂ films measured at (H) 400, (I) 350, (J) 275, (K) 200, (L) 125 and (M) 80 K^[122]. GIXRD: Grazing incidence X-ray diffraction

Electric field

Although HfO₂ FEs show significant potential for resolving critical difficulties that deter the commercialization of FE memories, they also suffer from remarkable instability issues induced by electric fields, namely, wake-up and fatigue^{[25,33,118,141]}. A significant enhancement in ferroelectricity by electric field loading was first reported in Gd-doped HfO₂ films by Mueller et al.^[126]. Later, Zhou et al.^[118] provided detailed experimental results in polarization change and identified it as the wake-up behavior in Si-doped HfO₂ films. At the wake-up stage, P_r increases with electric cyclings and the two previously existing asymmetric coercive voltages tend to be symmetric. After the wake-up stage, the P_rof HfO₂ films show a degradation when the electric cycling continuously increases, leading to device failure (fatigue). Non-volatile FE memory devices are subjected to frequent read-out and write-in operation require robust stability. The electric field induced switching behaviors and phase transformation have side effects on device stability, thus their behaviors and the mechanism behind them should be understood for further device optimization.

The wake-up behavior is attributed to a transition of built-in bias. Pešić et al.^[25] investigated some electrical parameters, including polarization, built-in bias and leakage current, which induce wake-up and fatigue, and concluded some trends during cyclic loadings. In the initial wake-up stage, the polarization increases while the built-in bias diminishes with a constant leakage current [Figure 12]. The constant leakage current indicates that no new defects form at this stage. Therefore, a possible origin for built-in bias is the evolution of the local defect (e.g., oxygen vacancies) distribution and/or phase transformation within a device. These oxygen vacancies are expected to occur at the interface between the TiN electrode and HfO₂ films in the pristine HfO₂ films, which induce the asymmetric distribution of the internal field that results in two peaks in the switching current curve [Figure 12B]. During the electric cycling process, these charged oxygen vacancies can move into the internal film under the electric field. The redistribution of oxygen vacancies improves the asymmetric internal field, which makes the two peaks (pristine state) in the switching current merge into one (wake-up state).

Figure 12. (A) P_r of Sr:HfO₂ FE capacitors as a function of electric cyclings. (B) Current-voltage curves for the pristine, wake-up and fatigue stages. (C) Leakage current-electric field curves measured after different cycling numbers^[25]. P_r: Remanent polarization; FE: ferroelectric.

In addition, a phase transformation is expected with increasing cyclic loadings. The bulk region undergoes an M-phase to O-phase transformation, while the interfacial region undergoes a T-phase to O-phase transformation, as confirmed by TEM characterization^[25]. The field-induced phase changes at the wake-up stage were also observed by TEM in 10-nm-thick Si- and Gd-doped HfO₂ films^[33,119,142]. The O-, C- and T-phase to M-phase ratio is 0.2 for pristine films and increases to 1 after 1000 cycles, representing a phase transformation from the M-phase to the O-, C- and T-phases upon the electric cycle loadings, as shown in Figure 13A^[33]. Similar phase transformations during the wake-up process were also observed by X-ray diffraction. Fields et al.^[121] observed a decrease in the full width at half-maximum of the T- and O-phase superimposed peak, from 0.425 before the wake-up process to 0.406 after wake-up, which indicated the phase change from the T-phase to the O-phase during the wake-up process. A similar result was also reported in undoped and Y-doped HfO₂ films by Nittayakasetwat and Kita^[143].

Figure 13. (A) STEM-HAADF images of HfO₂ films at pristine, wake-up and fatigue stages, showing phase transformation and corresponding phase fractions at different stages^[33]. (B) Proposed physical mechanism behind the field-induced FE behavior by coupling with phase transformation, defect generation and diffusion, and charge injection^[25]. STEM-HAADF: Scanning transmission electron microscopy-high angle annular dark-field; FE: ferroelectric.

It is noteworthy that the redistribution of oxygen vacancies and the phase transformation during the wake-up process should not be considered separately. Previous experimental investigations indicate that the formation of the stable M-phase could be suppressed by an oxygen deficient atmosphere^[62,102], while computational simulations suggest that the O-phase has a lower free energy with increasing oxygen vacancies^[53]. Mittmann et al.^[55] claimed that oxygen vacancies may act as nucleation sites for the polar phase, which promise a large number of nuclei that leads to a small average grain size during the crystallization process and therefore stabilizes the O-phase. During the wake-up process, oxygen vacancies can diffuse into the film interior easily at such a high electric field (in the order of MV cm^-1), which may result in the phase transformation to the O-phase.

After the wake-up process, if the FE HfO₂-based devices are applied with continuous electric cyclic loadings, these devices will reach the fatigue stage. At present, the reported field cycling endurance for devices based on polycrystalline La-doped HfO₂ films^[48] is no more than 10¹¹. This value is much smaller than that of their perovskite counterparts (10¹⁵ for the MSP430 FR573x microcontroller, Texas Instruments^[84]), making it a critical problem for HfO₂-based devices. During the fatigue process, the leakage current increases, along with the reduction of polarization, which is attributed to the formation of new defects, e.g., Hf and O vacancies and their accumulation near grain boundaries. Pešić et al.^[25] investigated the fatigue stage using dielectric-based simulation software and a commercial TCAD Sentaurus device simulator tool. The complete device stack is defined as TiN (top)/TiO_xN_y/TM-HfO_x/FE-HfO₂/TM-HfO_x/TiO_x/TiN (bottom), where TM-HfO_x is the interfacial region consisting of a nonswitchable transitional material. In the fatigue stage, oxygen vacancies are generated at the electrode near the TiO_x interface. The non-switchable regions, TM-HfO_x, reduce the switching electric field for the FE layer and thus the number of switchable domains and polarization decrease.

Park et al.^[84] discussed the limited endurance of FE HfO₂ films and the possible affected factors on this phenomenon. They reported that both grain size and doping concentration influence the endurance property. In the case of polycrystalline FE HfO₂ films, the FE O-phase is stabilized by the nanoscaled grain sizes in HfO₂ films that result in significant grain boundaries for the accumulation of oxygen vacancies. Therefore, HfO₂ films with larger grain sizes are expected to possess higher endurance, while the M-phase fraction also increases, resulting in a reduction in remanent polarization. In addition, the largest 2P_r of 40 μC·cm^-2 is observed when the Zr doping concentration reaches 50%, while the worst endurance of ~10⁷ is also recorded in this doping concentration^[84]. They also noticed a “P_r-endurance dilemma”, a high P_r value usually leads to poor endurance in HfO₂ films. This dilemma is consistent with the above mentioned grain size and doping concentration effects. It can be further explained from the structural aspect if we focus on the oxygen vacancies and grain boundaries that induce the breakdown. In polycrystalline HfO₂ films, the P_r value is almost determined by the FE O-phase fraction. As we mentioned before, the free energy of the O-phase is lowered by increasing oxygen vacancies^[53]. Therefore, if the HfO₂ film has a higher fraction of the O-phase (almost equivalent to higher P_r), it may contain a larger concentration of oxygen vacancies, resulting in devices breakdown under repeated electric cycles. In addition, the O-phase has lower interfacial energy than the M-phase, thus a higher surface-to-volume ratio favors the stabilization of the O-phase. A high surface-to-volume ratio can be achieved by decreasing grain size, which leads to a large P_r but more grain boundaries for the accumulation of oxygen vacancies. Therefore, high endurance and P_r are rarely obtained simultaneously in polycrystalline films.

Retention is another significant parameter for FE devices. FE HfO₂ films can achieve retention times of up to a decade, which is higher than the retention time in perovskite FE materials, e.g., PZT [Pb(Zr,Ti)O₃]^[69,144]. The high retention in HfO₂ films is related to the reduced depolarization field/coercive field and trapping effects. Gong and Ma^[144], Ma et al.^[145] suggested that if the depolarization field is comparable to or smaller than E_c, the polarization decay for retention is low. In HfO₂ FEs, the large E_cof ~1-2 MV cm^-1 results in minimal polarization loss. In addition, the electron injection is induced by the remanent polarization during the device working, which is followed by electron trapping and then diminished polarization in the FE layer. In HfO₂ FE films, the internal defects concentrations, e.g., grain boundaries, domain walls and point defects, are key to the polarization loss. Compared with perovskite FEs that have large thicknesses of ~100 nm, HfO₂ films with thicknesses of ~10-40 nm possess robust ferroelectricity, in which the trap concentration is reduced by the thin film deposition.

As discussed above, the limited endurance and the long retention in HfO₂ films are related to the very large E_cof ~1-2 MV cm^-1, which is much higher than that of conventional perovskite FEs (~0.05 MV cm^-1)^[81]. Such a large E_cbrings both advantages and disadvantages to HfO₂-based FE films. For example, HfO₂ FE devices require a high driving voltage (≥ 3.0 V for 10-nm-thick films) to reach the saturated remnant polarization (2P_r) value due to the large E_c, and thus, degrades the device reliability during the endurance test. However, it improves the scalability of HfO₂ film-based FeFET devices. The memory window (MW) of a FeFET is estimated as MW = 2E_c× t, where E_c is the coercive field and t is the thickness of the FE layer. From this aspect, the higher E_c is helpful to reduce the device dimensions. In addition, higher E_c can improve the retention of the FeFET of HfO₂ films. This makes the E_c value attractive at a certain level.

This electric field-induced FE behavior is normally related to the phase transformation. However, the mechanism behind it is unclear. Pešić et al.^[25] revealed that the existing defects, e.g., oxygen vacancies, can redistribute under the electric field, resulting in a phase transformation, as shown in Figure 13B. However, it is difficult to observe the direct evidence of defect redistribution under the electric field due to the present limitations of film quality and experimental techniques. Recently, FE domain switching behavior was observed due to the epitaxial rhombohedral (R-phase) HfO₂ films with high single crystalline quality. Nukala et al.^[146] showed the drift of oxygen vacancies across the HZO films between two LSMO electrodes by in-situ TEM with the integrated differential phase contrast (iDPC) mode. The oxygen vacancies move to the bottom electrode from the HZO films when the positive bias increases from 0 to 2 V. At a bias of 4 V, a phase transformation from the R-phase to M- and O-phases occurs [Figure 14]. It is noteworthy that the oxygen-reactive top LSMO electrode is the main source and sink of oxygen. This observation clarifies the microstructural origin of phase transformation from the R-phase to the O- and M-phases. However, this phase transformation path is not the most common one between the M- and O-phases. Therefore, further investigations should be carried out for FE HfO₂ films with the O-phase with the Pca2₁ space group.

Figure 14. Oxygenation and deoxygenation of HZO and associated phase transformations. (A) STEM-iDPC images under increasing positive bias showing R-phase evolution of an HZO grain. (B) Out-of-plane displacement of V_O with external bias in the marked supercell (red box) with respect to the positions in (A). Negative values indicate displacement toward bottom electrode. V_O shows both in-plane and out-of-plane (toward bottom electrode) components (inset). (C) A new grain nucleates in the same region at +4 V, giving rise to a polycrystalline nature (FFT in inset). (D) Another region in HZO film back at 0 V showing the O- and M-phases. Note the change of orientation from [111] to [100]. (E) STEM-iDPC image of domains (mutually rotated by 180° about [111]) in R-phase, which is retained when poled at -3 V (imaged at 0 V). Scale bars: 1 nm in (A, C, E), 2 nm in (D). Interfaces between HZO and top and bottom LSMO are marked in orange^[30]. HZO: Hf_0.5Zr_0.5O₂; STEM-iDPC: scanning transmission electron microscopy-integrated differential phase contrast; LSMO: La_0.7Sr_0.3MnO₃.

FE phase stabilization in epitaxial HfO₂ films

Epitaxial HfO₂ films present single-crystalline structures with certain crystallographic orientations, benefiting both promoting FE properties and easing the investigation of fundamental issues due to their simple phase composition. Since the phase types and FE properties of epitaxial films are dominated by substrate types, here, epitaxial HfO₂ films are reviewed according to substrate types. In addition, dopant concentration^[63,147-152], film thickness^{[35,47,66,69,130,132,153-159]} and process parameters, such as oxygen concentration^{[106,109,130,160]} and annealing temperature^[130,161], also have effects on FE phases in epitaxial HfO₂ films. However, their effects are similar to those in polycrystalline films in terms of the microstructural mechanism, thus these parts are not discussed in this section.

Orthorhombic Y-doped HfO₂ films on YSZ substrates

For epitaxial films, the initial film structure and final phase stability are determined by interfacial energy between substrates and HfO₂ films. Normally, the interfacial energy of a coherent or a semi-coherent interface is relatively small, while the incoherent interface has much higher energy. Therefore, the FE O- and R-phases could also be stabilized with proper epitaxial relations.

YO_1.5-doped HfO₂ films were first epitaxially grown on (100) YSZ substrates using the PLD method by the group of Funakubo^[63]. With increasing dopant concentration, the structure of the epitaxial HfO₂ films changes from the non-FE M-phase to the FE O-phase, and finally to a high symmetric T-phase without ferroelectricity. Furthermore, the orientation of epitaxial orthorhombic YO_1.5-HfO₂ films could be adjusted by selecting appropriate substrates. In this case, the deposition temperature (700 °C) is higher than the Curie temperature (450 °C), resulting in the formation of a T-phase at this temperature^[63]. During the cooling stage, high-temperature T-phase transforms to the O-phase. Since the c-axis (c_T) is longer than the a-axis (a_T) in the T-phase, while the O-phase has a longer a-axis (a_O) and relatively shorter b-axis (b_O) and c-axis (c_O), it is likely that a_O is transformed from c_Twhile b_Oand c_O are transformed from a_T, as shown in Figure 15A. Therefore, the orientation of the O-phase is determined by the orientation of the initial T-phase.

Figure 15. (A) Possible phase transformation paths from the T-phase to the O-phase. (B) Crystal parameter matching between HfO₂ films and electrodes/substrates^[162].

In Figure 15B, (001)-oriented (a_T= 0.5115 nm) HfO₂ films with the T-phase can be deposited on a (001)ITO (a_ITO= 0.5135 nm)//(001)YSZ substrate with a lattice mismatch of -0.39% and then transforms to the (100)-oriented O-phase. In addition, the (100)/(010)-oriented tetragonal HfO₂ (sqrt [(a_T² + c_T²)/2] = 0.5185 nm) films can be deposited on (001) YSZ (a_YSZ= 0.5184 nm) by diagonal matching with lattice mismatch of 0.02% and then transforms to the (010)/(001) O-phase^[162]. The thickness-dependent structure and FE performance of (111)-oriented epitaxial 0.07YO_1.5-HfO₂ (YHO7) films were investigated by Mimura et al.^[132]. The dominant phase in obtained for 10-115-nm-thick Y-doped HfO₂ films is the O-phase (Pca2₁), while a small fraction of the M-phase is found in films with a thickness over 68 nm. The average lateral grain sizes are similar regardless of film thickness, e.g., which are 114.5 and 117.7 nm in 10- and 110 nm-thick YHO7 films, respectively, and lead to the significantly small FE domains even in thick YHO7 films. Thus, ferroelectricity could be maintained in these Y-doped HfO₂ films with thickness of up to 115 nm and the thickness dependence of P_r and E_c is relatively small.

Orthorhombic HZO films on LSMO bottom electrode

LSMO has also been used as a bottom electrode and buffer layer for the epitaxial growth of HZO thin films because of the lattice matching and the consideration of interfacial chemistry^[67]. LSMO layers were deposited on various oxide substrates with cubic or pseudocubic structures with lattice parameters in the range of 0.371 to 0.421 nm, resulting in different lattice mismatches for epitaxial (111)-oriented HZO films [d₍₁₁₁₎ = 0.298 nm > d_{(11-1)/(1-11)/(-111)} = 0.294 nm] with different FE properties. The fraction of O-phase increases at larger substrate lattice parameters, indicating that this phase is more favored with tensile LSMO electrodes. A domain-matching mechanism is responsible for high-quality epitaxial HfO₂ films in this (111)HZO//(001)LSMO system, although a structural dissimilarity and large lattice mismatch exist in this (111)HZO//(001)LSMO system, which is revealed by a STEM investigation, as shown in Figure 16^[68]. Estandía et al.^[80] also systematically investigated the effects of bottom electrodes in stabilizing the O-phase. They proposed that surface chemical composition and atomic structure, instead of epitaxial stress, are the dominant causes of the ferroelectricity in HZO films. The interfacial chemistry, especially an LSMO layer with a proper La content, has a significant impact on the stabilization of the polar phase in epitaxial HZO films. Compared with polycrystalline HfO₂ films, epitaxial HfO₂ films need to be further explored to understand the epitaxial mechanisms, which is critical for improving film quality.

Figure 16. (A) Schematic top view of an HZO crystal on a LSMO(001) surface. (B) Cross-sectional STEM-HAADF image of HZO/LSMO heterostructure showing HZO crystal variants of the [$$\bar 2$$11] and [0$$\bar 1$$1] types. Reconstructed image from reflections in Fourier space corresponding to ($$\bar 1$$11) HZO and (110) LSMO planes. (inset) Fast Fourier transformation of both HZO and LSMO. Planes in the HZO layer are shown in yellow, while planes in the LSMO are given in white^[68]. HZO: Hf_0.5Zr_0.5O₂; LSMO: La_0.7Sr_0.3MnO₃; STEM-HAADF: scanning transmission electron microscopy-high angle annular dark-field.

Rhombohedral HZO films on LSMO bottom electrodes

A new epitaxial rhombohedral (R3m) HZO thin film grown on a (001) La_0.7Sr_0.3MnO₃/SrTiO₃ (LSMO/STO) substrate was recently reported by Wei et al.^[29]. Figure 17A presents a plan-view selected-area electron diffraction (SAED) pattern of a 9-nm-thick HZO film, showing 220 superposition spots from at least two domains (as shown in Figure 17C), with yellow and blue circles. The cross-sectional STEM-HAADF image of a 9-nm-thick HZO film in Figure 17B displays the coexistence of majority and minority HZO domains with [111]_HZO and [001]_HZO out-of-plane, respectively. In addition, from the fast Fourier transformation in Figure 17B, the estimated d_111-HZO is around 2.953.01 Å. An interfacial HZO phase with a thickness of 2-3 monolayers is also found between the LSMO and HZO film, which is a (~8%) in-plane tensile strained T-phase (a = 3.60 Å in the unstrained T-phase and here, strained to the STO substrate, a = 3.91 Å), as shown in Figure 17D. A much lower out-of-plane parameter of c/2 = 2.31-2.44 Å is induced by the strained T-phase, leading to the generation of the R-phase under compressive strain (d_111-r-HZO = 2.95-3.01 Å and d_001-t-HZO = 2.31-2.44 Å). The obtained HZO film with the R-phase has a large FE polarization of up to 34 μC·cm^-2 and no requirement for a wake-up stage.

Figure 17. (A) Plan-view SAED pattern and (B) representative cross-sectional STEM-HAADF image of a 4-nm-thick film. (C) Cross-sectional STEM-HAADF image from a 9-nm-thick HZO sample. (D) STEM-HAADF image observed along STO [100] (the STO substrate is not shown in the images), revealing an interfacial T-phase layer of HZO^[29]. SAED: Selected-area electron diffraction; STEM-HAADF: scanning transmission electron microscopy-high angle annular dark-field; HZO: Hf_0.5Zr_0.5O₂; STO: SrTiO₃.

A systematic investigation for the strain-induced stabilization of the R-phase was carried out by Nukala et al.^[79]. This work indicates that compressive strain has a critical effect on stabilizing the (111)-oriented R-phase, which could be achieved by growing HZO films on a hexagonal (0001)-oriented substrate, e.g., gallium nitride (GaN) buffered Si. To understand the origin of this R-phase, Zhang et al.^[158] investigated the evolution of structure and ferroelectricity with film thickness and in-plane compressive strain using DFT calculations. According to the calculations, a large stain of ~5% is necessary to maintain the polarization, which is comparable with the experimental one. In addition, a short and long Hf-O bonding order is along the out-of-plane direction in (111)-oriented R-phase under an in-plane compressive strain, which is considered as the origin of the polarization. Thickness is another key factor in stabilizing this FE phase. Although the R-phase has higher bulk energy than other polar phases, it could be stabilized in nanoscale thin films, according to the DFT results. From the results mentioned earlier^[29], the R-phase is a FE phase that is responsible for the high polarization in HZO films and can be stabilized with compressive strain and thickness effect.

It can be concluded that the phase formation (orthorhombic or rhombohedral) in epitaxial HZO films depends on various factors, including the epitaxial strain and interfacial chemistry. The underlying mechanisms and accurate control for epitaxial phase require further exploration in future works.

Epitaxial HfO₂ films on silicon

Lee et al.^[163] reported that (001)-oriented Y-doped HfO₂ films were epitaxially grown on (001)Si with YSZ as the buffer layer. The O-phase Pca2₁ with the out-of-plane direction of [001]/[010] is illustrated by X-ray θ-2θ scans and no other secondary phase is observed. A P_r of up to 20 μC·cm^-2 is achieved in obtained films, with the retention performance comparable with that of polycrystalline Pb(Zr_xTi_1-x)O₃ (x = 0.24-0.68). Lyu et al.^[70] integrated a HZO/LSMO film on Si(001) substrate using STO as the buffer layer. The 10-nm-thick HZO film has a high P_rof 34 μC·cm^-2 and the HZO capacitors show a ten-year retention time and a high endurance up to 10⁹ electric cycles. Rhombohedral single-phase HfZrO₄ could also be grown on a GaN(0001)/Si(111) substrate using the PLD method. A single crystalline phase characteristic is evidenced by reflection high-energy electron diffraction patterns, and the epitaxial relationship of HZO/GaN films/substrate at the same azimuthal angles of [10$$\bar 1$$0] and [11$$\bar 2$$0] is also clarified. Oxygen columns are imaged using the STEM-iDPC techniques, by which a R-phase is identified^[164].

Comparison of FE properties between polycrystalline and epitaxial HfO₂ films

In polycrystalline HfO₂ films, the FE O-phase coexists with non-FE T-, M- and C-phases. Therefore, the reduction of P_r is induced by the generation of non-polar phases from polar phases. Under an electric field, the non-polar phases transform to a polar phase, resulting in a higher P_r value, known as the wake-up effect^[118]. In addition, oxygen vacancies accumulate along grain boundaries during the electric cycling loading, leading to large remanent leakage current and retention loss, known as device fatigue^[25]. Epitaxial methods are used to obtain HfO₂ films with a single O-phase, reducing the fraction of non-polar phases and grain boundaries that are detrimental for device performance. Therefore, improvements in remanent polarization, wake-up stage, and fatigue are expected in epitaxial films, as shown in Table 3^{[19,29,35,45,47,48,69,125,131,165-167]}.

For HfO₂ epitaxial films, the highest polarization value is 34 μC·cm^-2 in (111)-oriented rhombohedral Hf_0.5Zr_0.5O₂ films^[29] on a (001)LSMO/(001)STO substrate with a E_c up to 5 MV·cm^-1 or (111)-oriented orthorhombic Hf_0.5Zr_0.5O₂ films^[133] on a (001)LSMO/(001)SrTiO₃/(001)Si substrate with a E_c up to 3 MV·cm^-1. In both films, the wake-up effect is negligible. In addition, as-fabricated capacitors using epitaxial HZO films have a retention time longer than ten years and good endurance against fatigue up to 10¹¹ cycles^[133]. These properties are better than their polycrystalline counterparts. The performance of both epitaxial and polycrystalline HfO₂ films with similar preparation parameters are shown in Table 3. Although a similar remanent polarization of 34.6 μC·cm^-2 is reported for polycrystalline TiN/Hf_0.42Zr_0.58O₂/Ge using an atomic oxygen deposition method, its E_c is only 1.8 MV·cm^-1 and its endurance cycle is only 10⁵. As we expected before, a well-oriented single crystalline phase (Pca2₁ or R3m) could be obtained in epitaxial films, leading to a high remanent polarization and a longer endurance without a wake-up effect. However, fatigue in epitaxial films is still severe compared with conventional perovskite FEs and related fundamental research is currently absent. In polycrystalline films, the wake-up effect and the fatigue are attributed to the coupling effect of phase evolution, defect redistribution and charge injection during electric cycling, which is too complicated to understand the evolution mechanism. For epitaxial films, the absence of the wake-up effect and grain boundaries could simplify the conditions for fatigue investigation.

Up to now, epitaxial HfO₂ films are less investigated than their polycrystalline counterparts. It is much more difficult to grow epitaxial films with a single phase and certain orientations than polycrystalline films because of the requirements of lattice matching between a film and its substrate. The first epitaxial HfO₂ film was reported in 2015, based on an ITO coated YSZ substrate and a PLD method. In addition, polycrystalline HfO₂ films are mainly based on the ALD technique that is a mature fabrication method, while the epitaxial HfO₂ is mainly prepared by PLD that is relatively less popular at present. However, the excellent FE performance has been demonstrated within epitaxial HfO₂ films. At present, epitaxial films have been to the research core, more investigations will be carried for optimizing FE performance and proposing fundamental mechanisms related to phase stability and fatigue behavior.