Thickness effect on the ferroelectric properties of La-doped HfO2 epitaxial films down to 4.5 nm

Epitaxial La:HfO2 films of less than 7 nm have a high remanent polarization of about 30 μC cm−2, and show slight wake-up, endurance of at least 1010 cycles and retention of more than 10 years, with both latter properties measured at the same poling voltage.


Introduction
The existence of a ferroelectric phase in Si-doped HfO2 films was first reported in 2011 by Böscke et al.. 1 In the following years, ferroelectricity was observed in HfO2 films doped with other chemical elements, including Al, Ga, Co, Mg, Zr, In, Er, Y, Nd, Sm, Gd, La, Sr and Ba. 2 The dopant content required to stabilize the ferroelectric phase depends on the atom. For example, in Si, Al or Y doped films the optimal doping content is less than 10 at% and the optimal doping content windows are narrow. Instead, for Zr doped films the optimal window is centered around 50 at% and it is wide. 2 Naturally, the remanent polarization (Pr) also depends on the doping atom and content. Theoretical 3 and experimental 4 studies have shown that Pr is higher when HfO2 is doped with atoms having a large ionic radius such as Y, La or Sr.
Among the large radius dopant atoms studied, La has enabled excellent ferroelectric properties. [5][6][7][8][9] Kosadaev et al. 6 reported La-doped HfO2 films with Pr above 13 µC cm -2 and very high endurance (limited by fatigue) of up to 10 10 cycles. Schroeder et al. 7 reported very high Pr above 27 µC cm -2 and moderately high endurance of 10 7 cycles, without fatigue and with low wake-up effect. Schenk et al. 10 concluded that the high polarization of polycrystalline La:HfO2 films is due to the strong orientation of the [001] polar axis towards the normal in these films. However, La:HfO2 films with very high polarization do not show good endurance, 7 as often occur in HfO2 films doped with other dopants due to the endurance -polarization dilemma. 11 Doping Hf0.5Zr0.5O2 (HZO) films with La was effective to enhance endurance without diminishing the polarization. 12,13 Further optimization of La:HfO2 films could perhaps allow the desired combination of high polarization and high endurance. On the other hand, ferroelectricity with Pr around 9 µC cm -2 was reported in La:HfO2 films up to 1 µm thick. 8 In contrast, to our knowledge, the ferroelectric properties of La:HfO2 films thinner than 10 nm have not been reported.
Recently, the ferroelectric phase was stabilized in epitaxial La-doped HfO2 films. 14 Films of thickness t = 8, 12 and 16 nm were grown on different oxide monocrystalline substrates buffered with La0.67Sr0.33MnO3 (LSMO) electrodes. The t = 12 nm film on (001)-oriented SrTiO3 (STO) exhibited the best properties, with Pr = 16 µC cm -2 and endurance (limited by fatigue) of 10 7 cycles, while the high leakage of the thinner film (t = 8 nm) did not allow the measurement of the ferroelectric properties. We report here on (111)-oriented epitaxial La:HfO2 films with thicknesses ranging from 4.5 to 17.5 nm and showing excellent ferroelectric properties, including polarization, endurance and retention, which have not yet been achieved in polycrystalline or epitaxial La:HfO2 films. Epitaxial films, enabling better control of microstructure and crystal orientation, can help to better understand the properties of ferroelectric HfO2. [15][16][17][18][19][20][21] We show that films with 6.9 nm thick, deposited on LSMO/STO(001), have a high Pr up to around 30 µC cm -2 with endurance greater than 10 10 cycles. Robust ferroelectricity is preserved in 4.5 nm films, with Pr above 25 µC cm -2 , endurance of 10 9 cycles. We also show that epitaxial La:HfO2 films on buffered Si(001) wafers exhibit excellent ferroelectric properties: a film of t = 6.9 nm has Pr above 32 µC cm -2 , endurance of more than 5×10 9 cycles. All films show good extrapolated retention beyond 10 years.

Experimental
La:HfO2 films and bottom LSMO electrodes were grown in a single process by pulsed laser deposition using a KrF excimer laser. Sintered Hf0.98La0.02O2-x and La0.67Sr0.33MnO3 ceramics were used as targets. The LSMO electrodes were deposited at a substrate temperature Ts = 700 °C, an oxygen pressure of 0.1 mbar and a laser frequency of 5 Hz. The growth parameters for La:HfO2 films were 2 Hz of laser frequency, Ts = 800 °C and oxygen pressure of 0.1 mbar. A series of La:HfO2 films of thickness t = 4.5, 6.9, 9.2 and 17.5 nm were grown on the LSMO electrodes (t = 25 nm) in a single process. STO(001) and STO buffered Si(001) were used as substrates in each deposition process. The STO buffer layers were grown ex-situ by molecular beam epitaxy. 22,23 Circular platinum top electrodes of 20 μm in diameter and 20 nm in thickness, were deposited ex-situ by sputtering on the La:HfO2 films through stencil masks for electrical measurements. Platinum top electrodes of 14 μm in diameter were additionally deposited on the t = 4.5 nm film on Si(001) to reduce leakage effect on the measurement of polarization loops.
The crystal structure was characterized by X-ray diffraction (XRD) with Cu Kα radiation, using a Siemens D5000 and a Bruker D8-Discover diffractometers equipped with a point detector, and a Bruker D8-Advance diffractometer equipped with a 2D detector. The surface topography was studied by atomic force microscopy (AFM) using a Keysight 5100 in dynamic mode.
Ferroelectric polarization loops, leakage current, endurance and retention were measured at room temperature, using an AixACCT TFAnalyser2000 platform, and connecting the LSMO bottom electrode to the ground and biasing the top Pt contact. Ferroelectric polarization loops were obtained in dynamic leakage current compensation (DLCC) mode with a frequency of 1 kHz. 24,25 Endurance was evaluated using bipolar square pulses, and after cycling, the memory window was extracted by DLCC. Retention was measured poling the sample using triangular pulse of 0.25 ms and determining the Pr from the first polarization curve of the polarization loop measured at 1kHz using the positive-up negative-down protocol after a delay time. Leakage current has been measured with integration time of 2s and averaging data collected with increasing and deacresing voltage. Capacitance (C) loops were measured using an impedance analyzer (HP4192LF, Agilent Co.) operated with an excitation voltage of 0.3V at 20 kHz. Relative dielectric permittivity (εr)-voltage loops were extracted from capacitance values using the C = ε0εrA/t relation, where A is the electrode area and t is the film thickness.  (001), which causes tensile stress in the films when cooled after growth. 26,27 The do-(111) parameters of equivalent La-doped (1 at%) Hf0.5Zr0.49O2 films 13 are also shown in Fig. 1c. The substrate and thickness dependencies are coincident, but the do-(111) parameters of the La:HfO2 films are slightly expanded. The inplane lattice distance along  and HfO2 [1][2][3][4][5][6][7][8][9][10] parameters of the t = 4.5, 6.9 and 9.2 nm films on STO(001) were determined by reciprocal space maps (Fig. S2, ESI †). The lattice distances are similar in the three films, and close to the estimated values in relaxed undoped HfO2. 28 Therefore, the thinner film shows a slight expansion of the out-of-plane parameter while the in-plane parameters are basically relaxed.  29,30 The AFM topographic images (Fig. 2) of the La:HfO2 films on STO(001) show extremely flat surfaces. The morphology of terraces and steps presented by the STO substrates 31 is replicated in the deposited LSMO and La:HfO2 films. The terraces in the films are well-visible, and the root mean square roughness, calculated in 5 µm × 5 µm areas, is 2.8 Å in the t = 17.5 nm film and less than 2 Å in the thinner films.

Results
The ferroelectric polarization loops of the La:HfO2 films on STO(001), measured using a high maximum applied field, are shown in Fig. 3a. The maximum electric field applied to measure the loops was lower in the thicker films, since the coercive Please do not adjust margins Please do not adjust margins electric field EC and the breakdown electric field decreases with the thickness. The two thinner films have a very high polarization, with Pr around 26 and 32 µC cm -2 in the t = 4.5 nm and t = 6.9 nm films, respectively. The polarization is less with increasing thickness, with Pr around 10 µC cm -2 in the t = 17.5 nm film. The t = 6.9 nm La:HfO2 film on Si(001) has the largest Pr around 32 µC cm -2 (Fig. 3b). Note that the round shape of the loops near the maximum applied electric field is a signature of residual leakage contribution, which results in a possible overestimation of the remanent polarization within 2 µC cm -2 . 32 All the loops shown in Fig. 3 have been collected at the largest applied electric field before breakdown, at saturation and after cycling the sample 10 times to avoid the wake-up effect discussed as follows and obtain comparable results. The dependencies of Pr with the thickness of the La:HfO2 films on STO(001) and Si(001) are represented in Fig. 3c. Both series exhibit a similar thickness dependence, with maximum Pr in the t = 6.9 nm films. The Pr of the La:HfO2 films ranges from 10 to 30 µC cm -2 on STO(001), and from 12 to 32.5 µC cm -2 on Si(001). We reported a similar Pr dependence for HZO 33 and La-doped HZO 13 films on STO(001). In contrast, epitaxial HZO 34 and Ladoped HZO 13 films on Si(001) did not exhibit a peak and films thinner than 5 nm had the highest Pr. The dependence of the coercive electric field with thickness is shown in Fig. 3d. The EC of the films on both STO(001) and Si(001) decreases linearly     with the thickness (in logarithmic scale), with slope about 0.5. Thus, it follows the EC  t -2/3 dependence usual in high-quality ferroelectric perovskite films [35][36][37] and epitaxial HfO2-based films 13,15,33,34 , but scarcely observed in polycrystalline HfO2based films. 38 The films exhibit a small wake-up effect, basically observed only in the first cycle and when the applied maximum voltage was lower than the used to obtain fully saturated loops (Fig. 4). The wake-up is evidenced by a double peak in the currentvoltage curves, causing a slight shrinkage in the polarization loop. Redistribution of oxygen vacancies or phase transitions induced by electric field have been proposed as wake-up mechanisms. 11 The wake-up effect in our epitaxial films is more pronounced if the maximum applied electric field is reduced (Fig. S3, ESI †). The minimal wake-up effects is in sharp contrast with the persistent wake-up effects commonly observed in polycrystalline La:HfO2 films, [5][6][7] were explained by the displacement of oxygen vacancies that induce the transformation from the monoclinic phase to the orthorhombic phase. 7 However, the wake-up effect is usually null in epitaxial doped HfO2 films, even in epitaxial HZO films on STO(001) that have a significant amount of monoclinic phase. See the recent review of Fina and Sánchez 15 for a description of the wake-up effects in epitaxial HfO2 films and the differences with polycrystalline HfO2 films. Some specific properties of epitaxial films can be responsible of the generally negligible wake-up effect compared to polycrystalline films: i) use of electrodes (LSMO and Pt) more stable against oxidation, ii) less amount of defects in optimized epitaxial films, and iii) semi-coherent interface between the bottom electrode and the epitaxial HfO2 film. The fact that the here reported La:HfO2 films show more pronounced wake-up effect can be related to the larger number of defects compared with Zr doped films as a consequence of the larger dopant radii. In the case of epitaxial La:HfO2 films on Si(001), the wake-up effect is similar and also limited to a few cycles (Fig. S4, ESI †). Note also that the residual leakage contribution, signalled by a current increase near the maximum applied voltage and more prominent in thinner films, also reduces while cycling. This is in agreement with the oxygen vacancies redistribution upon cycling scenario proposed in polycrystalline films, although here the effects are minimal, indicating that the oxygen vacancies amount is smaller in epitaxial films.
The leakage current curves of the films on STO(001) are shown in Fig. 5a. The leakage of the t = 4.5 nm film (3x10 -6 A cm -2 at 1 MV cm -1 ) is moderately low considering the ultra-low thickness. The leakage of the thicker film, t = 17.5 nm, ranges from around 5x10 -8 A cm -2 at low field up to about 4x10 -7 A cm -2 at 2 MV cm -1 . The t = 6.9 nm film is highly insulating, with leakage well below 10 -8 A cm -2 at low field and less than 5x10 -8 A cm -2 at 1 MV cm -1 . Therefore, the t = 6.9 nm film combines a very high Pr about 30 µC cm -2 and very low conductivity. The films on buffered Si(001) are more leaky, and only the t = 17.5 nm film exhibit low leakage of less than 10 -7 A cm -2 at 1 MV cm -1 (Fig. S5, ESI †). The dielectric permittivity loops of the films on STO(001), Fig. 5b, vary greatly with the thickness of the films. The loop corresponding to the t = 4.5 nm film has a well-defined butterfly shape. The hysteresis reduces with thickness increasing, and it is barely appreciated in the t = 17.5 nm film. The value of the dielectric constant also depends on the thickness. The permittivity at high electric field is 30 in the t = 4.5 and 6.9 nm films, and it is reduced to 28 in the t = 9.2 nm film and to 24.5 in the t = 17.5 nm film. The decrease of the dielectric constant is in agreement with the observation by XRD of an increase of the monoclinic phase fraction with thickness, and with the reported dependencies of the permittivity of other doped HfO2 films on the ratio between orthorhombic and monoclinic phase. 34,[39][40][41]   The endurance of the films on STO(001) is shown in Fig. 6 ad. The polarization of the t = 4.5 nm film (Fig. 6a), cycled by electric pulses of amplitude 6.7 MV cm -1 , increases from 2Pr = 19.5 µC cm -2 in the pristine state to 24.5 µC cm -2 after a few (less than ten) cycles, evidencing the small wake-up effect described above. With additional cycles the capacitor is fatigued and 2Pr decreases to 18.8 µC cm -2 after 10 5 cycles and then more abruptly to 6 µC cm -2 after 10 9 cycles. The loss of polarization is, in average, about 75% after eight magnitudes. The t = 6.9 nm film exhibits similar behavior when cycled at 5.8 MV cm -1 , being 2Pr = 2.8 µC cm -2 after 10 10 cycles (Fig. 6b). The polarization was higher for applied pulses of 6.5 MV cm -1 , and 2Pr was 4 µC cm -2 when the measurement was stopped after 10 10 cycles. A higher cycling electric field, 7.2 MV cm -1 , causes a larger switchable polarization, but the capacitor undergoes hard breakdown after 10 9 cycles (open blue triangle in Fig. 6b). Representative polarization loops of the t = 6.9 nm film, measured applying several maximum electric fields and number of cycles, are shown in Fig. S6, ESI †. The endurance of the t = 9.2 nm (Fig. 6c) is similar, while it is highly degraded in the t = 17.5 nm film (Fig.  6d). This degradation is because hard breakdown occurs at lower field as the film is thicker, which limits the applied field that can be applied. Breakdown occurs through conductive filaments formed after enough high electrical stress. 42 Ionic conduction though incoherent boundaries between monoclinic and orthorhombic grains, more abundant in thicker films, can be a relevant contribution. 43 Thus, there is not direct relation with the thickness dependence of the current leakage (Fig. 5). It has been observed a similar degradation of endurance with thickness in other epitaxial 13,34 and polycrystalline 44 doped-HfO2 films.
Li et al., reported endurance up to 10 7 cycles in epitaxial Ladoped (5.5 cat%) HfO2 films. 14 The endurance was limited by fatigue, and they found that the loss of polarization was much more severe when the electrical stress was lower (lower pulse amplitude or shorter pulse width) and also when the interval between pulses was longer. It was argued that the high density of charged domain walls in incompletely switched capacitors could be pinned and then cause fatigue. In the case of polycrystalline doped HfO2 films, increased fatigue with decreasing electric field has been reported, [45][46][47] as well as with increasing cycling frequency. 46 Schroeder and coworkers 46 proposed that the faster degradation of polarization by cycling with pulses of lower amplitude or higher frequency was caused by the less saturated switching in these cases (the frequency effect was due to the fact that the coercive field increases with the frequency). The fatigue mechanism suggested by Schroeder and coworkers 46 considered that oxygen vacancies migrate during each cycle from switchable regions to non-switchable regions, creating local fields. The intensity of the local field strength would increase with cycling until the domains of the initially switchable regions would be pinned. On the other hand, Starschich et al. 48 observed that hard breakdown occurred earlier, as the cycling frequency was lower, and they assumed that this was due to the suppression of generation of oxygen vacancies at high frequency. In our epitaxial films, the amplitude of the electric field has a critical effect on the junction breakdown if it is too high. However, the amplitude of the electric field has no impact on the fatigue (Fig. S7, ESI †). It determines the fraction of ferroelectric domains that are switched and thus influences the polarization, but not the reduction of the normalized polarization with the number of cycles. On the other hand, the endurance of our films is also degraded by a lower cycling frequency, which causes here more fatigue or even breakdown (Fig. S8, ESI †). Note that low frequency measurements we performed implied long period pulses. Using the data shown in Fig. S7 as example, a capacitor cycled N times by bipolar pulses of 3V at 10 kHz is poled for a time 100 longer than another cycled at 1 MHz. Therefore, the degradation effects induced by the applied field scale exponentially with frequency decrease (longer pulse duration and longer time between pulses), as expected in the defects redistribution in the bulk of the device. 49 Besides, longer pulse   also promotes the migration of free carriers towards domain walls, thus inducing severer pinning effect. 45 The retention of the films on STO(001) is shown in Fig. 7, where the remanent polarization is plotted as a function of the delay time after poling (td). Each film was poled at the same electric field used in the endurance measurements (Fig. 6), and for positive (blue squares) and negative (red circles) poling fields. The experimental data are fitted (blue and red dashed lines) to the rational dependence Pr = P0 · td −n . 50 The vertical black dashed line corresponds to a time of 10 years. The extrapolated data indicate that the four films retain a high fraction of the initial polarization. The memory window (2Pr) extrapolated to 10 years of the thicker film, which has a high amount of paraelectric monoclinic phase, is 54% of the initial value. The percentage of the initial memory window of the thinnest film, t = 4.5 nm, is 53% despite the expected high depolarization fields. The t = 6.9 and 9.2 nm films maintain 69 and 63% of the initial memory window. Therefore, all films exhibit excellent retention after being poling with the same electric field used to determine the endurance properties. The retention of more than 10 years is accompanied of endurance of at least 10 9 cycles in the t = 4.5 nm film and 10 10 cycles in the t = 6.9 nm. The equivalent t = 6.9 nm film on Si(001) also exhibits endurance of at least 5x10 9 cycles and retention of more than 10 years (Fig. S9, ESI †).

Conclusions
In summary, the orthorhombic phase of HfO2 has been epitaxially stabilized in La-doped films. The films present majority of orthorhombic phase, (111)-oriented, with increased fraction of monoclinic phase in films thicker than 10 nm. The robust ferroelectric properties of La-doped HfO2 are preserved in films even as thin as 4.5 nm. The films exhibit minimal wakeup, basically limited to the first cycle. Films with thickness less than 7 nm show a remanent polarization of about 30 µC cm -2 , endurance of 10 10 cycles, and retention of more than 10 years. These excellent properties are achieved in films epitaxially grown on either SrTiO3(001) or buffered Si(001) substrates.

Conflicts of interest
There are no conflicts to declare.