Origin of the Intrinsic Ferroelectricity of HfO2 from Ab Initio Molecular

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C: Physical Processes in Nanomaterials and Nanostructures

Origin of the Intrinsic Ferroelectricity of HfO from Ab Initio Molecular Dynamics 2

Pan Fan, Yuke Zhang, Qiong Yang, Jie Jiang, Limei Jiang, Min Liao, and Yichun Zhou J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.9b04106 • Publication Date (Web): 12 Aug 2019 Downloaded from pubs.acs.org on August 13, 2019

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The Journal of Physical Chemistry

Origin of the Intrinsic Ferroelectricity of HfO2 from ab initio Molecular Dynamics P. Fan,†, §Y. K. Zhang,†, § Q. Yang,*, † J. Jiang,† L. M. Jiang,† M. Liao,† and Y. C. Zhou*, † †

Key Laboratory of Low Dimensional Materials and Application Technology, Ministry of

Education, School of Materials Science and Engineering, Xiangtan University, Xiangtan, Hunan 411105, China

ABSTRACT HfO2-based ferroelectric film has shown great potential for the application of ferroelectric memory due to its great advantages as compared to the traditional ferroelectrics. However, the origin of the ferroelectricity of the HfO2-based ferroelectric film is still under debate. In this work, by performing the ab initial molecular dynamics calculation, the phase stability and the polarization switching behavior of HfO2 were systematically studied to illuminate the intrinsic origin its ferroelectricity. Results show that, under different in-plane constraints and room temperature, the out-of-plane polarized orthorhombic ferroelectric phase Pca21 is always the metastable phase of HfO2. As driven by the out-of-plane electric field, HfO2 exhibits linear dielectric behavior or antiferroelectric behavior with the ferroelectric-tetragonal-ferroelectric

phase

transformation

under

the

in-plane

compression. While with the tensile strain condition, the non-ferroelectric HfO2 could be transformed to be the out-of-plane polarized orthorhombic ferroelectric phase, which shows good ferroelectricity under the periodic electric field. The triggered phase transformation and ferroelectricity as modulated by the epitaxial constraint as found in this work were verified by the recent experiment and should be intrinsic origin of the ferroelectricity of the HfO2-based films.

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1. INTRODUCTION Since the ferroelectricity was found in Si-doped hafnium oxide (HfO2) thin film, the HfO2-based ferroelectric film has aroused tremendous interests.1 The HfO2-based film has been considered as the most promising candidate of ferroelectric films for the application of high-density information memory due to its good ferroelectricity in thin film with the thickness under 10 nm and its excellent compatibility with the silicon-based complementary-metal-oxide-semiconductor (CMOS) technology.2-5 Despite enormous experimental and theoretical researches have been done on the HfO2-based ferroelectric film, the origin of its ferroelectricity has not been well understood yet, which may hinder the improvement of the electrical properties and the technology consistency of this new-type of ferroelectric film. The controversial origin of ferroelectricity for the HfO2-based film stems from the competition between the possible ferroelectric and non-ferroelectric phases.6 Though many polar phases, such as the orthorhombic phases with space groups of Pca21 and Pmn217 and the rhombohedral phase with R3m space group,8 were thought to be the possible origins of the ferroelectricity of HfO2-based thin films, the orthorhombic phase with space group of Pca21 is most widely recognized to be responsible for its ferroelectricity up to now.9-11 However, the most accepted orthorhombic ferroelectric phase (f-phase) Pca21 (the same for the other possible polar phases) is unstable compared with the non-polar orthorhombic (such as oI-phase Pbca) and monoclinic (P21/c) phases (m-phase) in the relative energy based on the theoretical calculations.12-13 From the observation of phase distribution of the HfO2-based ferroelectric film, the orthorhombic Pca21 phase was often found to be coexisting with the other phases, especially the monoclinic phase (P21/c).6, 14 And there is a series of complex phase transformations from the tetragonal phase (t-phase, P42/nmc) or monoclinic phase (P21/c) to the orthorhombic phase (Pca21), and then to the monoclinic phase (P21/c), while the film undergoing “wake-up” and fatigue processes.14-16 The stress condition induced by the clamping effect of the substrate was considered to be an essential factor to stabilize the ferroelectric phase of HfO2-based film.17-19 2


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The HfO2 film also exhibits good ferroelectricity even without doping.20 However, specific mechanism of the stress effect on the ferroelectricity of the HfO2-based film has not been well illuminated yet, since the separate strain affect was found to be not sufficient to make the ferroelectric phase more stable than the other competitive phases, e.g. P21/c, from the density functional theory (DFT) calculations.12, 21 And only the non-polar phases are found in the pressure-temperature equilibrium phase diagram from the minima hopping method, which are used to search for the low-energy structures.7 However, the hydrostatic pressure is not easy to be introduced into the general film materials. This stimulated us to study the phase diagram within the in-plane constraint induced by the epitaxial growth in this work. Based on the comparison between the experimental and theoretical results, we think that the metastable phases may also play important roles in the ferroelectricity of HfO2-based ferroelectric film, besides the equilibrium phases. To elucidate the phase stability of HfO2-based ferroelectric films under different in-plane strain and temperature conditions, the phase diagram of HfO2 was explored by the annealing simulation based on the ab initio molecular dynamics (AIMD). In addition, the structural and polarization responses of HfO2 under the motivation of external electrical field were studied to clarify the possible roles of the metastable phases in the ferroelectricity of HfO2-based film. Results show that the ferroelectric phase (f-phase, Pca21) only appears in the strain-temperature equilibrium phase diagram with the polarization direction in the constrained plane. However, in the tensely strained area, the metastable f-phase with the out-of-plane polarization, which exhibits good ferroelectric hysteresis loop under the periodic electric field, could be responsible for the origin of ferroelectricity of HfO2. Our results are meaningful for the understanding of the ferroelectricity of the HfO2-based ferroelectric film.

2. COMPUTATIONAL DETAILS In this work, all the simulations were carried out by employing the Born-Oppenheimer molecular dynamics methods with Gaussian and plane waves, which are implemented in Quickstep module of the CP2K package.22 We used the 3



generalized

gradient

approximation

(GGA)

of

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PBEsol

to

describe

the

exchange-correlation potential.23 The core electrons of each atom were described by the pseudopotentials of Goedecker, Teter and Hutter (GTH).24 The Kohn-Sham orbitals were expanded in a Double-Zeta Split Valence plus Polarization Gaussian-type basis set, and the plane wave representation was truncated with a cutoff of 750 Ry. The Brillouin zone was sampled with the Γ point. The time-step of the integration

of

the

dynamic

equations

was

set

to

be

1

fs.

The constant temperature of the sysmtem was achieved by using the Nose-Hoover the rmostat.25-26 The 2×2×2 supercells with 96 atoms were adopted for the calculation of each HfO2 phase. The lattice parameters of the HfO2 unit cells of each phase optimized under 0 K and stress-free condition are given in Table 1, which are in good agreement with the experiments. The total energies of Pbca (half unit cell), Pca21, P42/nmc and Fm3m HfO2 per unit cell (12 atoms) are 0.14, 0.47, 0.50 and 1.00 eV, respectively, relative to that of P21/c HfO2. Table 1. Lattice constants of HfO2 unit cells with the unit in Å Space Phase

Previous Experiments

Groups

Monoclinic

P21/c

This work Calculation

a=5.0727

a=5.1328

a=5.07

b=5.14

b=5.19

b=5.12

c=5.29 a=5.01 Orthorhombic

Pbca

c= 5.30 29, a

b=5.06

b=4.96

c=5.23 a=5.23 Orthorhombic

Pca21

a=5.23

b=5.00

Tetragonal

Fm3m P42/nmc

a=5.08

31

a=5.06

32

c=5.20

c= 5.25 a=4.95 b=5.01

c= 5.16 30

c= 5.05 Cubic

a=4.92

28

21

c= 5.18 a=5.25

b=5.04

b=5.03

c=5.06

c= 5.07

a=5.06

28

a=5.01

a=5.06

28

a=5.01

c=5.20

c=5.15

a. Half of the lattice a of Pbca was used in this paper for the convenience of comparison.

Firstly, we examined the phase transition sequence of HfO2 with increasing the temperature or hydrostatic pressure, separately, by starting with the monoclinic P21/c 4


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phase optimized under the room temperature and atmospheric pressure. When heating, the temperature was increased from room temperature to 3300 K with the heating rate of 6.25×1014 K/s (The whole system was fully relaxed to equilibrium state within 3000 fs at each temperature condition and the temperature step is 200 K), under standard atmospheric pressure within the NPT ensemble. When loading, the hydrostatic pressure was increased from 2 GPa to 62 GPa with an interval of 4 GPa at room temperature within the NPT ensemble. The phase transition sequence was examined by observing the changes of lattice parameters and atomic structures during the heating and loading processes (Since the lattice parameters of one phase may vary under different applied conditions, to further confirm the phase of the obtained MD equilibrium structure, we reconstructed many atomic structures of HfO2 phases from the known experimental data within the visualization software and the MD equilibrium structures were carefully compared with the known experimental atomic configurations) as shown in Part 3.1. Then we studied the equilibrium phase diagram of HfO2 by simulating the annealing processes of HfO2 under the fixed hydrostatic pressure

or

in-plane

constraint,

respectively.

To

explore

the

hydrostatic

pressure-temperature phase diagram, the P21/c HfO2 was heated from room temperature to 2300 K and then cooled down to room temperature at cooling rate of 9.09×1014 K/s (The temperature step is 200 K, and the relaxation time at each temperature is 2000 fs to reach the equilibrium state), with the hydrostatic pressure fixed to be 0-30 GPa (with the interval of 5GPa), respectively (NPT ensemble). Then the similar heating and cooling procedures were applied to the HfO2 with different in-plane constraints by relaxing the out-of-plane lattice to stress free to obtain the in-plane strain-temperature phase diagram. Here, the angles β of the supercells were fixed to be 99.82o (β of optimized P21/c) and 90o to keep the monoclinic and orthorhombic cell, respectively, while relaxing out-of-plane lattices. The results of equilibrium phase diagram are given in Part 3.2. The ferroelectricity of HfO2 at room temperature with different in-plane constraints was studied by investigating the structural and polarization evolutions of the supercells under the applied electrical field. Since the external electric field was found 5



to be of great importance in the phase transformation of HfO2, we firstly explored the phase transformation of HfO2 by applying a 45 MV/cm activation electric field along the out-of-plane direction within the orthorhombic cells (NVT ensemble). Then an activated phase of HfO2 would be obtained after the removal of activation electrical field and a bias-free stabilization stage (3000 fs). Then the alternating electric fields were applied to the unactivated and activated HfO2 under -1% and 3% equiaxial strains (by taking the lattice constants of short axes of optimized P42/nmc phase as the strain-free case), respectively, and the structural and polarization evolutions of HfO2 were analyzed to study the ferroelectricity of HfO2. Here, the triangular-wave periodic electric fields with each stage width of 200 fs (200 MD steps) and the electric field step between the two adjacent stages of 2.1 MV/cm were utilized to model the alternating electric field. The polarization of the HfO2 was calculated with the Bonn effective charge method, which is described by the following formular:33  1 1     1 1 P  (  Z corner,i rcorner,i   Z edge,i redge,i   Z face,i rface,i   Z in ,i rin ,i ) (1) V 8 4 2 Where, Z corner,i , Zedge,i , Z face,i and Zin ,i are Born effective charges of the ith atoms located at the corner, on the edge, on the face and inside of the supercell,

    respectively. And rcorner,i , redge,i , rface,i and rin,i are the coordinates of the corresponding atoms. The Bonn effective charges Zzz of Hf and O in the t-phase of HfO2, as calculated to be 5 and -2.5 e, respectively, which are consistent with the previous calculation results,34 were adopted to calculate the polarization magnitude in this work. The spontaneous polarization of stress-free Pca21 HfO2 as calculated with this method is 54 µC/cm2, which is in accordance with the former calculation and experiments.7, 10, 35-36 The results of the structural and polarization responses under the applied electrical field are shown in Part 3.3.

3. RESULTS AND DISCUSSION 3.1. Phase transition sequence of HfO2 under the increasing temperature or hydrostatic pressure. In order to clarify the phase transformation sequence of stress-free HfO2 under the heating process, we increased the temperature of HfO2 6


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from 300 K to 3300 K under the standard atmospheric pressure and the structural evolution of HfO2 during the heating process was investigated. From the variations of angles and lattice constants of HfO2 unit cell as shown in Fig. 1(a) and 1(b), as well as the symmetries of atomic structures, it can be found that the m-phase would transform to t-phase and then to cubic phase (c-phase, Fm3m) at 1900 K and 2600 K, respectively, which are consistent with the experimental results.37 Then the phase transformation of HfO2 under room temperature and increasing hydrostatic pressure from 2GPa to 62 GPa was studied. From the structural analysis as shown in Fig. 1(c) and 1(d), the m-phase (P21/c) and orthorhombic oI-phase (Pbca) are stable below and above 26 GPa, respectively. This result is also in good agreement with the observation of experiments.38 When the pressure was increased to 50 GPa, Pbca phase is found to transform to the a orthorhombic phase Pbcm. It was found that the HfO2 would transform to Pnma phase under the high pressure in the experiments and previous theoretical calculation.7, 38 It could be the insufficient structural relaxation under room temperature and increasing pressure, which leads to the disagreement of high pressure phase transformations in the present calculation and the experiments. Then, we compared the total energies of the P21/c, Pbca, Pbcm and Pnma phases under the whole pressure range. And it is found that the P21/c is the most stable phase when the pressure is below 18 GPa, Pbca is the most stable phase when the pressure is between 18 and 50 GPa, and Pnma is the most stable phase with the pressure higher than 50 GPa. Therefore, the structural evolution of HfO2 under different pressure conditions from the total energy calculation are replotted in Fig. 1(e) and 1(f). In the following, we studied the phase diagram of HfO2 based on the AIMD annealing simulation which would provide sufficient structural relaxation.

7



Figure 1. Phase transformation of HfO2 under increasing hydrostatic pressure and temperature, respectively. (a) and (b) show the angles and the lattice parameters of unit cell under increasing temperature and stress free condition. (c) and (d) are the angles and the lattice parameters of cell under increasing hydrostatic pressure and room temperature. (e) and (f) are the angles and the lattice parameters of the cell from the total energy calculation under room temperature and different pressures. Inserts show the atomic structures of each phase. The cyan and red circles represent Hf and O atoms, respectively.

3.2. Stress-temperature equilibrium phase diagram of HfO2 under hydrostatic pressure or in-plane constraint. To elucidate the phase stability of HfO2 under different stress and temperature conditions, the stress-temperature equilibrium phase 8


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diagram of HfO2 was studied in this work. Firstly, we studied the equilibrium phase diagram of HfO2 under the varying hydrostatic pressure and temperature by simulating the annealing process of HfO2 from 2300 K to room temperature. The equilibrium phases of HfO2 under different pressures were summarized into the phase diagram as shown in Fig. 2. From Fig. 2, under the hydrostatic pressure of 0 GPa, the HfO2 undergoes a phase transformation from t-phase (P42/nmc) to m-phase (P21/c) when the temperature drops down to 1800 K, which means that the m-phase would be dominative at room temperature under the stress-free condition. When the hydrostatic pressure was increased to 5 GPa, the t-phase would transform to f-phase (Pca21) at 1000 K. When the hydrostatic pressure was 10 or 15 GPa, the t-phase was the most stable phase during the annealing process. And the orthorhombic oI-phase (Pbca) was most stable in the considered temperature range under the hydrostatic pressure of 20-30 GPa. Y. Al-Khatatbeh et al. has studied the phase transformation of HfO2 by imposing the high temperature laser heating under high pressure, and found that oI-phase was stable under the hydrostatic pressure between 20 GPa and 36 GPa.38 The distribution of oI-phase in our results is well consistent with their experimental results. From the phase diagram, it can be seen that the ferroelectric phase (Pca21) would exist in a small pressure and temperature range. However, since the hydrostatic pressure is difficult to be introduced into the film during the film growth procedure, it is necessary to clarify the phase stability of HfO2 under the in-plane stress condition as induced by the epitaxial growth of film materials.

9



Figure 2. Equilibrium phase diagram of HfO2 under varying hydrostatic pressure and temperature. The inserts show the atomic structures of HfO2 within different phases, respectively.

To explore the phase stability of HfO2 with the in-plane constraints induced by the lattice misfit between the film and substrate in the epitaxial growth, the equilibrium phase diagram of HfO2 with different in-plane strains was studied. Here, we did the similar annealing simulation as abovementioned by fixing the different in-plane constraints of the supercells. The in-plane strains are ranging -2% to 2% by varying the two in-plane lattice constants (Lattice 1 and Lattice 2) as shown is Fig. 3. The out-of-plane lattice constants (Lattice 3) of the supercells were relaxed to be stress free with keeping the orthorhombic and monoclinic shapes of the supercells, respectively. The final equilibrium phase diagram was established by extracting the more stable phase obtained in the monoclinic and orthorhombic cells under the same in-plane constraint and temperature conditions. Fig. 3(a) and 3(b) give the equilibrium phase diagram of HfO2 under room temperature within the orthorhombic and monoclinic cells, respectively. From Fig. 3(a), it can be seen that the f-phase (Pca21) was the dominant phase in the considered strain range. However, this f-phase would not contribute to the polarization along the normal direction of the film, because the crystallographic b- and c-axes of this Pca21 HfO2 (polarization direction is along the c axis) are in the constrained plane. Therefore, we denote this f-phase with fbc-phase. 10


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And this naming rule is applied in the following part of this paper. While in the monoclinic supercell, the equilibrium phase is mab-phase (with the crystallographic aand b-axes of P21/c in the constrained plane) at room temperature in the whole considered strain range. Then the total energies of the equilibrium phases within the orthorhombic and monoclinic supercells at room temperature were compared as shown in Fig. 3(c). From Fig. 3(c), the in-plane polarized fbc-phase (Pca21) is more stable than the mab-phase (P21/c) in the compressively strained area, while the mab-phase is more stable in the tensely strained area. Finally, we can obtain the equilibrium phase diagram of HfO2 as shown in Fig. 3(d) from the energy comparison. It can be seen that, the out-of-plane polarized fab-phase does not appear in the equilibrium phase diagram, which means that the strain effect, separately, can not make the out-of-plane polarized fab-phase to be the most stable phase. The phase stability of HfO2 under 3% and 4% equiaxial tensile strain as denoted by the extension of the red dashed diagonal line in Fig. 3(a) was also studied with the results shown in Part 3.3.

11



Figure 3. In-plane strain phase diagrams of HfO2 at room temperature (300 K). (a) and (b) are the phase diagrams of HfO2 in orthorhombic and monoclinic cells, respectively. Inserts of (a) and (b) show the cell shapes. (c) gives the distribution of the relative energy (Ediff, in the unit of eV) between the HfO2 in the orthorhombic cells and monoclinic cells, by defining the Ediff as Eo – Em, where Eo and Em are the total energy of orthorhombic cells and monoclinic cells, respectively. The black line in (c) denotes the strains for Ediff =0. (d) is the final equilibrium phase diagram of HfO2 at room temperature.

3.3. The structural and polarization responses of HfO2 under the applied electric field. Since the ferroelectricity can exist even in the dopant-free HfO2 in the experiments,20 then we studied the phase transformation and polarization response of HfO2 under the external electrical field. In order to study the possible phase transformation of HfO2 driven by the poling electric field as the case in the experiments,39 a constant activation electric field of 45 MV/cm was applied on the HfO2 along the out-of-plane direction. For the consideration of computational cost, only the stable phases of HfO2 in the orthorhombic cells with Lattice 1= Lattice 2, as denoted by the red dashed diagonal line in Fig. 3(a), were chosen as the typical representatives. And the considered in-plane strain range is from -2% to 4%. After the removal of poling electric field, a series of stable phase structures of HfO2 can be obtained. The relative stability of the phase structures of HfO2 before and after the electrical field activation was analyzed in Fig. 4(a). It can be seen that, when the in-plane strain is ranging from -2% to 1%, the in-plane polarized fbc-phase would be transformed into the tab-phase (with the a- and b-axes of P42/nmc along the constrained plane), though the new tab-phase is energetically less stable. The phase transformation of HfO2 under the strain range from -2% to 1% driven by the activation electric field is shown in Fig. 4(c) and 4(d). When the same poling electric field was applied on the in-plane polarized fbc-phase under 2% tensile strain, the atomic structure would restore to the original fbc-phase after the removal of electric field. When the tensile strain is equal to 3% and 4%, the fac and mab are the most stable phases of HfO2 in orthorhombic and monoclinic cells, respectively, with the relative energy between these two phases can be seen from Fig. 4(a). However, the in-plane polarized fac-phase could be transformed into the out-of-plane polarized fab-phase by applying the activation electric field, as shown in Fig. 4(e) and 4(f). And the energies of fab- and 12


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fac-phases are very similar under this strain range. This electric-field-driven transformation was confirmed by the recent experimental results of T. Shimizu et al.39 They found that the polarization direction of the Y-doped HfO2 (YHO) film epitaxially grown on yttria-stabilized zirconia (YSZ) substrate tends to be in the in-plane direction and this in-plane polarization direction of the as-grown orthorhombic ferroelectric phase would be mediated to be along the out-of-plane direction through the ferroelastic domain switching by applying an electric field. And the (YHO) film exhibits a good ferroelectricity after the electric field poling. From the experimental lattice constants along b- and c-axes of Pca21 HfO2, the strain caused by the ferroelectric domain switching is only 1%, which is the same magnitude of that for BaTiO3. It should be pointed out that the lattice mismatch between YSZ and t-phase of HfO2 is about 3%, which is consistent with strain range for the activated fab-phase in this work. Since the static density-functional-theory (DFT) calculation is a more widely accepted way to study the relative stability of the different phases, we calculated the relative energies of HfO2 in different phases by employing the DFT method under 0 K within the VASP code40 to further confirm the phase stability of the HfO2 as given in Fig. 4(a). The exchange-correlation effects were described by using the GGA PBEsol functional.23 The same equiaxial in-plane strains as in the Fig. 4(a) were applied on the HfO2 by considering the different orientations. The total energies of the t-, f- and m-phases, which appear in Fig. 4(a), are given in Fig. 4(b). From the relative energies in Fig. 4(b), fbc-phase and mab-phase are the most stable phase configurations in the compressively and tensely strained area, respectively, which is in agreement with the in-plane strain equilibrium phase diagram in Fig. 3. If we only focus on the f-phase of HfO2, the relative stability of fbc- and fac-phases under different strains can be the reason for the equilibrium phases from the annealing simulation (before activation) in the orthorhombic cell as shown in Fig. 4(a). And the energy of fab-phase is similar but higher as compared with that of fac-phase under tensile strain. And in the compressive strain area, the tab-phase is more stable than the fab-phase, which is the reason for the activated t-phase in Fig. 4(a). 13



Figure 4. Phase transformation driven by the poling electric field. (a) shows the energy difference of HfO2 before and after the electric field activation as compared with that of monoclinic phase under varying equiaxial in-plane strain. (b) shows the total energies of t-, f- and m-phase of HfO2 with different orientations under varying equiaxial in-plane strain. (c) and (d) show the atomic structures of HfO2 under -2%~1% in-plane strain before and after the electric-field-driven phase transformation, respectively. (e) and (f) show the atomic structures of HfO2 under 3%~4% in-plane tensile strain before and after the electric-field-driven phase transformation, respectively.

The dynamic evolutions of phase structure and polarization of HfO2 were simulated by applying the periodic triangular-wave electric field on the orthorhombic supercells along the out-of-plane direction to understand the ferroelectricity of HfO2. Here, the HfO2 before and after the electric field activation with the -1% and 3% in-plane strain conditions were taken as the pristine structures in the simulation. Fig. 5(a) shows the polarization and structure variations of the unactivated equilibrium phase of HfO2 14


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(fbc-phase) under -1% compressive strain. It can be seen that the polarization varies linearly with the electric field and the maximum polarization magnitude is about 20 µC/cm2 neglecting the polarization variation induced by the thermal fluctuations. And the phase structure is always unchanged even under the maximum electric field of 23.1 MV/cm. While for the activated tab-phase under -1% compressive strain, also no phase transformation was observed and the polarization varies linearly when the maximum of the periodic electric field is less than 12.6 MV/cm. However, as the maximum of the periodic electric field was increased to 23.1 MV/cm, a hysteresis loop of polarization appeared. From Fig. 5(b), when we firstly increased electric field from 0 to 23.1 MV/cm, the tab-phase remains unchanged. However, the tab-phase transformed into fab-phase with a sudden increase of polarization magnitude when we began to decrease the positive electric field. This delay of phase transformation originates from the high change rate of electric field in the MD simulation, which would suppress the full relaxation of the atomic structures on each electric field stage. During the decreasing of electric field from positive to zero, the fab-phase remains well with linear part of the polarization gradually being removed. As the negative electric field increases, the HfO2 undergoes a fup→tab→fdown phase transformation series, with the polarization switched from positive to negative. This variation of phase structures corresponds well with the antiferroelectric phase transition observed in the experiments.41 And the polarization response also consists with the double hysteresis loop, which is the typical characteristic of the polarization switching behavior of the antiferroelectrics, if excluding the effects of the high change rate of external electric field in the simulation. Then the polarization behavior of HfO2 under 3% tensile strain was studied. As shown in Fig. 5(c) and 5(d), the fac- and fab-phases before and after the electric field activation were both chosen to be the pristine structures, respectively. From Fig. 5 (c), when the 12.6 MV/cm positive electric field was applied on the in-plane polarized fac-phase, the polarization varies linearly and no phase transformation was observed. Actually, it was found that, the fac-phase can be transformed into fab-phase after being activated by a constant electric field of 15 MV/cm. This indicates that the in-plane 15



polarized fac-phase is easier to be activated to be the out-of-plane polarized fab-phase under the tensile strain. When the periodic electric field with was imposed on the activated fab-phase under 3% tensile strain, the polarization variation exhibits a typical ferroelectric hysteresis loop. From Fig. 5(d), when the negative electric field was increasingly applied on the positive polarized fab-phase, the ferroelectric phase and polarization magnitude remain well firstly. The ferroelectric polarization would be reversed when the negative electric field reaches the coercive field of about 10 MV/cm, which is two to several times larger than the experimental results due to the higher change rate of electric field here.39, 42 When the negative electric field decrease and the positive electric field increase, the HfO2 undergoes contrary structural and polarization variations. We further estimated the relative dielectric constants of facand fab-phases under 3% tensile strain from the linear parts of polarization-electric field loops as marked by the blue dashed lines in Fig. 5(c) and 5(d). It was found that the relative dielectric constants of the fac- and fab-phases are 22 and 27, respectively, which are in close agreement with the observed dielectric constants of YHO film before and after electric-field poling.39

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Figure 5. Structural and polarization responses of HfO2 under the periodic electric field. (a), (b), (c) and (d) are hysteresis loops of HfO2 with biaxial strain of -1% and +3% before and after the electric field activation, respectively. The blue arrows denote the direction of the polarization hysteresis loops. The inserts of (a), (b), (c) and (d) show the atomic structures of HfO2 during the polarization switching.

For comparison, the polarization behavior of HfO2 under the non-equiaxial in-plane strain was also studied. Here, the strains of 4% and 0% along the two in-plane axes, respectively, were applied on HfO2, which would make the in-plane lattice constants equal to the in-plane lattice constants of stress-free fab-phase (see Table 1 for details). From the annealing simulation, the out-of-plane polarized fab-phase and the mab-phase were the most stable phases in the orthorhombic and monoclinic supercells, respectively. And the mab-phase is also the equilibrium phase with the energy lower than the fab-phase under this strain condition. Then the same periodic electric field was applied on the fab-phase in the orthorhombic cell, as shown in Fig. 6(a), to study the polarization behavior. From the varying polarization and phase structure given in Fig. 6(b), it can be seen that the ferroelectric polarization is switchable with a ferroelectric hysteresis loop similar to that of HfO2 under the 3% equiaxial in-plane 17



strain, as given in Fig. 5(d).

Figure 6. (a) The pristine atomic structure of HfO2 under (4%, 0%) biaxial strain. (b) The ferroelectric hysteresis loop and the corresponding structural evolution HfO2 under the non-equiaxial in-plane strain condition.

The calculated results of the structural and polarization evolutions under different strain and the electric field conditions in present work could shed some light on the intrinsic origin of ferroelectricity of HfO2 and the related materials. It can be seen that, the in-plane polarized orthorhombic phase is the equilibrium phase of HfO2, which would exhibit a linear dielectric behavior under the applied electric field along the out-of-plane direction. However, after the activation by a large poling electric field, the compressively-strained HfO2 would be transformed into a non-polar tetragonal phase. This tetragonal phase shows an antiferroelectric behavior with a ferroelectric-tetragonal-ferroelectric phase transformation under the driven of periodic electric field. While, under the tensile strain condition, the monoclinic phase is equilibrium phase of HfO2. However, with the special symmetry constraint, the orthorhombic phases could exist as the metastable phases in the materials. This symmetry constraint may originate from the poling of the external electric field, the build-in electric field from the dopants and the defects, as well as the clamping and electrochemical effects from the substrate. As calculated in this work, the in-plane polarized orthorhombic ferroelectric phase is a little bit more stable than the out-of-plane polarized ferroelectric phase under the tensile strain condition. The in-plane polarized ferroelectric phase shows a linear dielectric behavior under the 18


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out-of-plane electric field, which is similar to the monoclinic phase. However, after being poled by a small out-of-plane electric field, the in-plane polarized ferroelectric phase can be transformed into the out-of-plane polarized ferroelectric phase, which would show good ferroelectricity under the periodic electric filed. This polarization switching behavior originates from the activated metastable ferroelectric phase is in good agreement with the experiments for the epitaxial HfO2-based thin film grown on the YSZ substrate39 and could be origin of the ferroelectricity of HfO2-based thin films. Since the ferroelectric orthorhombic phase is metastable as compared with the monoclinic phase of HfO2, the orthorhombic phase could transform into the monoclinic phase when the symmetry constraint was destroyed by specific factors, such as the arising of the unfavorable defects and the rotation of crystal grains. This would cause the fatigue phenomenon to the ferroelectricity of the HfO2-based films. Therefore, this might be the reason for the “fragile” ferroelectricity of HfO2-based films as found in the experiments.6 As only the crystal orientation of (001) was taken in consideration in this work, the newly discovered (111)-oriented rhombohedral ferroelectric phase, which would exist in the HfO2-based thin film epitaxially grown on a substrate with larger lattice constants

(such as the Hf0.5Zr0.5O2 thin film grown

on LSMO (001)-oriented La0.7Sr0.3MnO3/SrTiO3 substrate8) doesn’t appear in all the considered conditions.

4. CONCLUSION In summary, a systematic ab initio molecular dynamics study was performed to elucidate the origin of the ferroelectricity of HfO2-based thin film in this work. In order to study phase stability of HfO2, we simulated the annealing process of HfO2 under different in-plane constraints and finally an equilibrium phase diagram was established. From the results, the orthorhombic ferroelectric phase only appears in the equilibrium phase diagram with the polarization direction in the compressively constrained plane at room temperature. And the out-of-plane polarized ferroelectric phase is the metastable phase, as compared with the more stable monoclinic phase. By 19



simulating the phase transformation and the polarization evolution of HfO2 driven by the external electric field, it was found that HfO2 shows linear dielectric or antiferroelectric properties under the compressive strain condition. While with the in-plane tensile strain, the non-ferroelectric HfO2 could be triggered to be the out-of-plane polarized orthorhombic ferroelectric phase after poled by a small out-of-plane electric field. This activated metastable ferroelectric phase shows good ferroelectricity under the periodic electric field, which indicates that the metastable ferroelectric phase as modulated by proper epitaxial constraint should be the intrinsic origin of the ferroelectricity of HfO2-based thin films. And the triggered ferroelectricity as found in this work was also confirmed in the recent experiments on the ferroelectricity of HfO2-based thin film as mediated by ferroelastic domain switching. We hope this work could be helpful for the understanding of the ferroelectricity of the HfO2-based thin film and could give some guidance for its epitaxial growth.

■ AUTHOR INFORMATION Corresponding Author *E-mail: [email protected] *E-mail: [email protected] ORCID Q. Yang: 0000-0002-3235-1986 J. Jiang: 0000-0002-1540-4281 Author Contributions §

P.F. and Y.K.Z. contributed equally to this work.

Notes The authors declare no competing financial interest. ■ ACKNOWLEDGEMENTS The authors are grateful to Prof. E. Y. Tsymbal and V. Alexandrov for fruitful discussions. This work was financially supported by National Natural Science Foundation of China (Grant Numbers: 11502224, 61504115 and 51702273) and 20


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Natural Science Foundation of Hunan Province, China (Grant Number: 2017JJ3289) and Research Foundation of Education Bureau of Hunan Province, China (Grant Number: 18B056). Part of the computation described in this research was carried out on the ScGrid, Computer Network Information Center of Chinese Academy of Sciences.

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Origin of the Intrinsic Ferroelectricity of HfO2 from Ab Initio Molecular

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