Improved Ferroelectricity in Cryogenic Phase Transition of Hf0.5Zr0.5O2

Cryogenic transition from metastable tetragonal phase (t-phase) to orthorhombic phase (o-phase) is crucial in achieving the desired ferroelectric characteristics. Observing the reversible transition from anti-ferroelectricity (AFE) to ferroelectricity (FE) in electrical characteristics, the cryogenic phase transition is experimentally analyzed in Hf0.5Zr0.5O2 alloys. Furthermore, the stabilized o-phase formation is more favorable when applying cryogenics to superlattice Hf0.5Zr0.5O2, manifesting a 23% increase in remanent polarization (Pr) at 77K. To theoretically clarify the emergence of phase transition with decreasing temperatures, Landau–Ginzburg–Devonshire theory and first-principle study are combined in this work. Based on the detailed calculation, the increasing relative free energy of the t-phase contributes to lowering the energy barrier when decreasing the temperature, making the convenient transitional pathway from metastable t- to o-phase. This work exhibits the cryogenic phase transition model involving t- and o-phases in Hf0.5Zr0.5O2 and presents a method to boost ferroelectricity for emerging HfO2-based cryo-device.


I. INTRODUCTION
Excellent ferroelectricity demonstrated in the doped-HfO 2 mixtures [1] shed light on emerging non-volatile memories [2], [3], [4] with CMOS compatibility [5]. The evolution toward cryo-CMOS circuits and quantum computing systems may lead to the need of cryogenic non-volatile ferroelectric (Fe) memory [6]. Our recent work demonstrated the Hf x Zr 1−x O 2 could be applied as a high-κ dielectric due to its anti-ferroelectric (AFE) property [7]. To achieve expected strong ferroelectricity, a high proportion of orthorhombic phase (o-phase) is demanded. It was reported that the formation of o-phase results in FE properties in Hf x Zr 1−x O 2 thin films by thermal process [8], [9]. It has been visualized that the metastable o-phase appears in the cooling down stage, heating up to the high crystallization temperature and then cooling to room temperature [10]. The amount of crystalline phases like dielectric (DE) monoclinic phase (m-phase), FE o-phase, and AFE tetragonal phase (t-phase) determine the electrical characterizations of Hf x Zr 1−x O 2 . Hence high [Hf] and high [Zr] layer favor FE o-phase and AFE t-phase [11], respectively. It has been reported that o-phase can be stabilized in a particular thickness by tuning the surface energy effect [12]. In addition, our previous work has discussed the effects of oxygen vacancy concentration [V o ] on phase formation [13]. The amount of [V o ] is used to control FE and AFE characteristics at room temperature in our MFM/MIM heterostructures [13]. High [V o ] leads to alloys and favors the AFE characteristics at room temperature, while low [V o ] leads to superlattices and favors the FE characteristics at room temperature. Furthermore, Hf x Zr 1−x O 2 with superlattice structures have also been concluded in favoring o-phase, while Hf x Zr 1−x O 2 alloys helped the formation of t-phase with relatively high dielectric constant [13]. Due to the overlaps of the peak position in grazing incident Xray diffraction (GIXRD) spectra, the o-phase and t-phase are challenging to be identified in the Hf x Zr 1−x O 2 films. However, the phase transition can be confirmed thanks to the variations in remanent polarization (P r ) values. The density functional theory (DFT) models for interfacial energy calculation were also reported in [14].
The cryogenic phase transition model is introduced in this work to explain the o-phase transition from t-phase during cooling, validated by the experimental results. The phase transition occurs below Curie temperature, which is also fitted by Landau-Ginzburg-Devonshire (LDG) theory. Kinetics is described by the predicted free energies of the m-, o-, and t-phases by the DFT study as well as the barrier energies of phase transition.

II. EXPERIMENTS
The MFM capacitors were fabricated on Si substrates by Pt/TiN/Hf 0.5 Zr 0.5 O 2 /TiN/Pt ( Fig. 1) to investigate the cryogenic transition between t-and o-phase. The bottom sputtered Pt acts as etch-stop and probe layers [15], [16]. The temperature of 250 • C was maintained during the plasmaenhanced atomic layer deposition (PEALD) process. The O 2 exposure times of 5s and 10s were used to form alloy and superlattice structures, respectively [13]. The Hf 0.5 Zr 0.5 O 2 films were made of 5 cycles ZrO 2 and 5 cycles HfO 2 (5 periods, total 10 cycles) ( Fig. 1 (a)) while ZrO 2 as the first layer can achieve the higher 2P r than HfO 2 first [13]. The insitu TiN bottom and top electrodes were deposited through PEALD in the forming gas (50%N 2 + 50%H 2 ). Note that the precursors of ZrO 2 , HfO 2 , and TiN are TDMAZr, TDMAHf, and TDMATi, respectively. After the PEALD process of TiN/Hf 0.5 Zr 0.5 O 2 /TiN/Pt (bottom), the top sputtered Pt passivation layer was deposited to avoid the oxidation on TiN surface and patterned by the lift-off process. The TiN/Hf 0.5 Zr 0.5 O 2 /TiN films were etched till bottom Pt layer via reactive ion etching (RIE). After the above processes for device fabrication, the 450 • C and 400 • C post metallization annealing (PMA) was performed in forming gas (90%N 2 +10%H 2 ) for the crystallization of the O 2 5s and O 2 10s Hf 0.5 Zr 0.5 O 2 thin films, respectively.

III. RESULTS AND DISCUSSION
Good crystallinity of the 6.3nm Hf 0.5 Zr 0.5 O 2 with 5s O 2 exposure is observed by transmission electron microscope (TEM) image ( Fig. 2(a)). The Hf 0.5 Zr 0.5 O 2 film is an alloy with the ZrO 2 -HfO 2 interfacial mixture, as shown in the high-angle annular dark-field (HAADF) image. On the other hand, the 6.7 nm Hf 0.5 Zr 0.5 O 2 with 10s O 2 exposure has high crystallinity in the superlattices with clear ZrO 2 -HfO 2 interfaces, as shown in the dark-bright fringes of HAADF ( Fig. 2(b)). All the following electrical characteristics are measured from pristine samples. The Hf 0.5 Zr 0.5 O 2 with 5s O 2 exposure yielded an AFE P-V loop at 300K ( Fig. 3(a)), indicating the high [V o ] and alloy structure favored t-phase. Since the free energy of t-, m-, and o-phase is related to the temperature, electrical characteristics can transform when the sample is cooling down to cryogenic temperature [17], [18]. The P-V loop exhibits FE property when the temperature is lowered to 220K, as illustrated in Fig. 3(a). Furthermore, continually lowering the temperatures to 150K and 77K, the FE P-V loops maintain their stability and sustain a rise in 2P r values. Afterward, the P-V loop demonstrates a reversible transition from FE to AFE when heating up to 300K after cooling. To validate the trend of transition from AFE to FE during cooling, C-V sweeps were also measured at 300K, 220K, 150K, 77K, and 300K (heating up after cooling) ( Fig. 3(b)). At 300K, t-phase characteristics are consistently demonstrated with 4 peaks in the forward and reverse C-V sweeps [19]. A transition from AFE (4 peaks) to FE (2 peaks) in C-V hysteresis is observed during cooling, coherent with the observation in P-V loops. When the temperature is back to room temperature, the 5s exposure sample shows the AFE P-V loop with 4 peaks in the C-V hysteresis. The reversible transitions from AFE to FE to AFE verify the feasibility that the energy barrier between o-and t-phase can be overcome reversibly. However, to the best of our knowledge, the AFE-FE-AFE transition has not been engineered for applications.
Concerning the observed enhancement of ferroelectricity in low temperatures, we fabricated Hf 0.5 Zr 0.5 O 2 thin film with O 2 exposure 10s to further investigate the t-to o-phase transition for ferroelectric improvement in cryogenic temperatures. Due to o-phase favoring low [V o ] and superlattices, the pristine P-V loop at 300K shows FE characteristics. Furthermore, the stable FE P-V loop and the higher 2P r are obtained at 77K (54 μC/cm 2 ) with 23% improvement (Fig. 4(a)), exhibiting the enhanced o-phase amount from transitioned t-phase. Meanwhile, the coercive voltage (V c ) shows an increment as the temperature decreases [20]. Besides, the C-V hysteresis remain the same with two peaks, indicating ferroelectric dominance during cooling ( Fig. 4(b)) [19]. In accordance with the transition of electrical properties from AFE to FE observed in Fig. 3(a) and (b), the cooling process can be a method of lessening t-phase and increasing o-phase to enhance the ferroelectricity. Meanwhile, the high O 2 exposure time 10s achieves the higher P r value at 77K than our previous work at room temperature [13].
Based on Landau-Ginzburg-Devonshire theory, intrinsic switching is applied to explain the temperature-dependent phase transition [21]. The thermodynamic free energy (G) is an expansion of the polynomial of polarization (P) up to the sixth order, where α represents the reciprocal of the dielectric susceptibility, β and γ are temperature-independent Landau coefficients, and E is electric field. Relying on this approximation, α is linearly relative to temperature. The reversible phase transition between the o-and t-phase takes place below the Curie temperature (T curie ). On this basis, an expansion of the energy polynomial to the fourth order can be simplified and rewritten. Negative α keeps the sign under the Curie temperature and ranges with decreasing temperatures. The electric field across the ferroelectric at the thermal equilibrium state can be calculated by a differential formula (∂G / ∂P = 0) based on Eq. (1) Known as LGD theory, Eq. (2) offers a simplified description of polarization hysteresis with two crucial coefficients related to phase transitions. Supported by the experimental data P r and V c , the intrinsic switching model can be proposed with the coefficients α and β. The value of remanent polarization can be found by setting E = 0, revealing: And, according to the free energy description, following with the Curie-Weiss behavior, the coefficient α: where α 0 is a positive constant. To determinate the coercive field (E c ), the electric field at local extremes need to be analyzed, Applying Eqs. (3) and (5), α 0 and β can be extracted from the experimental data of Hf 0.5 Zr 0.5 O 2 . Considering the gradual transition from AFE to FE spanning between 300K and 220K in Hf 0.5 Zr 0.5 O 2 with 5s O 2 exposure, AFE data are removed from the following LGD analysis [22]. With the steady growth of P r during cooling, an enhancement of ferroelectricity is obtained due to the t-phase transition to o-phase ( Fig. 5(a)). Note that the Curie temperature of Hf 0.5 Zr 0.5 O 2 with 5s O 2 exposure is 622K, obtained by the best fit of the LGD model using our experimental data in Fig. 5. Moreover, the continually enhanced ferroelectricity drives the increase of average coercive voltage (V c ) during cooling (Fig. 5(b)).
Confirming the consideration of LGD theory, the Hf 0.5 Zr 0.5 O 2 with 10s O 2 exposure is performed to further understand the improvement of ferroelectricity by tto o-phase transition. The Curie temperature is 732K by the best fit of the LGD model using our experimental data in Fig. 6, in line with what has been reported for the similar Hf x Zr 1−x O 2 system [18], [23], [24], [25]. Compared the estimated α 0 (1.7E6 VmK −1 C −1 ) from temperaturedependent permittivity (ε r ) in Curie-Weiss law (Eq. (6)), the fitted α 0 (2.7E6 VmK −1 C −1 ) from our data by LGD theory is reasonably close. Note that due to the hysteresis in capacitance-voltage measurement ( Fig. 4 (b)), the dielectric constant is measured at low voltage without hysteresis. Since the fewer [V o ] occurs in the Hf 0.5 Zr 0.5 O 2 with O 2 exposure 10s compared with that in the Hf 0.5 Zr 0.5 O 2 with O 2 exposure 5s, the T curie undergoes an increase [18]. P r also obtains an improvement of 23% from 300K to 77K (Fig. 6(a)). The low energy barrier from t-to o-phase can obtain more o-phase as temperature decreases. Meanwhile, the fitting average V c is also aligned with the linear trend ( Fig. 6(b)), increased by ferroelectric enhancement [26], [27]. Taking advantage of high V c , the cryogenic temperature also effectively compensates the loss of memory window (MW ≈ 2V c ) caused by the thin film [26], [27]. T curie is crucial for the FE ophase formation during the cooling stage. The amount of [V o ] can be reduced in fabrication to seek a higher T curie and to favor more o-phase formation. Although the LGD theory can illustrate the cryogenic phase transition in properties, the intrinsic phase transition mechanism could not be included due to the lack of energy barriers. The kinetic energy barriers between each phase are critical for understanding the physical mechanism in cryogenics from our experimental data. To better comprehend, the relative free energies of t-, o-, and m-phase in Hf 0.5 Zr 0.5 O 2 dependent on temperature are calculated ( Fig. 7(a)). Considering the purpose of ferroelectric enhancement, the Hf 0.5 Zr 0.5 O 2 with 5s O 2 exposure is taken as a reference of theoretical calculation, same as our analyses in LGD fitting. The phase free energy (Eq. (7)) is composed of bulk energy, entropy contribution, and interfacial energy (Eq. (8)) [28], [29].
Here index i represents the phase in Hf 0.5 Zr 0.5 O 2 film which could be m-phase, o-phase, or t-phase. G i , U i , S i , and i are phase free energy, relative bulk energy, entropy, and interfacial energy. For the computational convenience, the relative bulk energy of m-phase is taken as zero. According to the assumption of cylindrical grain grown in Hf 0.5 Zr 0.5 O 2 film, the interfacial energy i is a function of interfacial energy of Hf 0.5 Zr 0.5 O 2 /ILs (σ i ) ( Table 1), estimated radius of grain size according to experimental Hf 0.5 Zr 0.5 O 2 (r ≈ 6nm) [30], thickness of Hf 0.5 Zr 0.5 O 2 (d = 6.3nm),  and crystalline phase/ amorphous Hf 0.5 Zr 0.5 O 2 interfacial energy (δ i ) (Table 1), as shown in Eq. (8). Note that the grain size radius (r ≈ 6nm) is assumed accord to the experimental thickness. The G i , U i , S i , and i are calculated in DFT [28], [29]. The value of i in our calculation is 9.58 eV/nm 3 for m-phase, 8.45 eV/nm 3 for o-phase, and 7.54 eV/nm 3 for t-phase. The t-phase stability decreases with decreasing temperature due to its increasing free energy. Based on DFT, the calculated relative free energy can be translated into the free energy landscape (Fig. 7(b)) intuitively with the reported energy barriers of phase transition ( Table 2). Note that the explanations from LGD theory exclusively describe the second-order phase transition in phenomenology. The relative free energy(G i ) (Eq. (7), depending on bulk energy(U i ), temperature (T), entropy (S i ), and interfacial energy ( i )) of t-phase keeps increasing while that of other two phases maintain almost static during cooling ( Fig. 7(a)). The activation barriers from literatures are listed in Table 2. Due to the much higher energy barrier between t-and m-phase than t-and o-phase (Table 2), t-phase prefers transiting to o-phase instead to m-phase ( Fig. 7(b)) [9], [31], [32], [33], [34]. Taking the capping effect into consideration in our samples, the activation barrier between t-and m-phase has a higher value of 1.2 eV f.u. −1 [33] to 2.14 eV f.u. −1 [34] and suppresses the mphase formation during the cooling step, similar to [35]. With temperature decreasing from 300K to 77K, the relative free energy of t-phase increases from 9.89 eV/nm 3 to 10.19 eV/nm 3 and the barrier between t-and o-phase decreases ( Fig. 7(b)). Therefore, more o-phase is observed at 77K. This mechanism explains the boost of 2Pr viewed in experiments. Furthermore, the lower energy barrier between t-and o-phase (20∼35 meV f.u. −1 [9], [36], [37], [38], [39] in Table 2) creates the convenient path for cryogenic phase transition from t-to o-phase. The reversible transition between AFE and FE confirms the activation barrier between t-and o-phase is compatible with KT (26 meV@300K). Most equilibrium can be reached at the experimental temperature.

IV. CONCLUSION
With 23% improvement of 2P r , a high value of 54 μC/cm 2 at 77K is obtained, clear cryogenic phase transition in Hf 0.5 Zr 0.5 O 2 film is elucidated experimentally and theoretically. The increasing relative free energy of t-phase decreases the energy barrier for transforming into o-phase which results in the boost of o-phase contents in Hf 0.5 Zr 0.5 O 2 film with higher ferroelectricity.