Reversible modulation of critical electric fields for a field-induced ferroelectric effect with field-cycling in ZrO₂ thin films

Abstract

This study investigates the effects of field-cycling on the critical electric fields (E_t→PO and E_PO→t) of the field-induced ferroelectric (FFE) effect in atomic layer deposited ZrO₂ thin films, focusing on their reversibility and temperature dependence. High-field cycling decreases these critical fields, whereas subsequent lower-field cycling effectively rejuvenates them, challenging the previous report of their irreversibility. Elevated temperature experiments reveal that higher temperature increases the lower limit of E_t→PO reduction, corroborating the thermodynamic predictions of the Landau–Ginzburg–Devonshire (LGD) theory. The rejuvenation effect is also more pronounced at higher temperatures, further corroborating the LGD theory. This study highlights that these reversible transitions between polar and non-polar phases with high- and low-field cycling are a universal phenomenon in fluorite-structured materials, not limited to ferroelectric materials. These findings provide new insights into the field-cycling and temperature-dependent behavior of FFE thin films.

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1. Introduction

Since the first discovery of ferroelectric (FE) properties in fluorite-structured doped HfO₂-based thin films,¹ numerous studies have focused on the Hf_1−xZr_xO₂ (HZO) solid solution for their low crystallization temperature (350–550 °C) and tunable properties across a wide composition range (Hf : Zr ratio).^2–11 Depending on the Zr content (x-value), HZO thin films display dielectric (DE) (x = 0), FE (x = 0.5), and field-induced ferroelectric (FFE) (x > 0.7) behaviors, which correspond to monoclinic (m-phase, space group: P2₁/c), polar orthorhombic (PO-phase, space group: Pca2₁), and tetragonal (t-phase, space group: P4₂/nmc) phases, respectively.^5,10,12–19 Compared to the extensively studied FE properties, the FFE properties have been relatively less explored.

The FFE characteristic indicates the temporary transition of the non-polar, centrosymmetric t-phase to the PO-phase by applying a sufficiently large electric field, which transitions back to the t-phase upon removal of the electric field.^8,20 It has been unclear whether the field-induced phase transition occurs between the t-phase and PO-phase.²¹ However, Lombardo et al. reported direct evidence for such a transition using high-resolution transmission electron microscopy (HRTEM) imaging with in situ biasing, observing the reversible atomic arrangements in ZrO₂ thin films.²² Lomenzo et al. used in situ band-excitation piezoresponse force microscopy (BE-PFM) imaging to track changes in localized piezoresponses, directly observing the reversible formation and disappearance of polar states in FFE ZrO₂ and Hf_0.13Zr_0.87O₂ thin films.²³ The reversible field-induced phase transition is attributed to the sufficiently small free energy difference between the t- and PO-phases, with the applied electric field decreasing the free energy of the PO-phase while the free energy of the t-phase remains constant.^8,20 Therefore, FFE Zr-rich HZO or ZrO₂ thin films display antiferroelectric (AFE)-like double hysteresis loops in the polarization–electric field (P–E) curves.^8,20,24 Specifically, they display linear DE behavior at low fields, but above a specific field, a forward switching current peak appears due to the t- to PO-phase transition. When the field is decreased to zero, a reverse switching current peak from the PO- to the t-phase transition is observed.^8,20

It should be noted that many prior studies refer to t-phase dominant ZrO₂, which exhibits FFE characteristics, as AFE. However, according to Kittel's theory suggested in 1951, AFE refers to a state where antiparallel aligned dipoles within a unit cell are energetically more stable than a homogeneously aligned dipole state.^21,25 In the case of the FFE, where a reversible transition occurs between the non-polar t-phase and the polar PO-phase, no antiparallel aligned dipoles exist when the electric field is removed.^21,26 Instead, the dipoles are absent for the non-polar t-phase, thus not meeting the definition of AFE.^21,26 This study differentiates the AFE and FFE and refers to ZrO₂ as FFE. The relevant schematic figure distinguishing FFE and AFE is presented in Fig. S1 (ESI†).

In HZO thin films, the coercive fields (E_c) for FE switching are crucial parameters.¹¹ Similarly, in ZrO₂ thin films, the critical parameters are the critical electric fields for FFE forward switching from the t- to the PO-phase (E_t→PO) and reverse switching from the PO- to the t-phase (E_PO→t). Tasneem et al. experimentally demonstrated that E_t→PO and E_PO→t follow the Janovec–Kay–Dunn-like scaling law in ZrO₂ films of varying thicknesses, with a −2/3 power dependence on crystallite size.²⁷ Ye et al. predicted from density functional theory calculations that the E_t→PO change is influenced by grain size.²⁸ However, research on these parameters remains limited. Furthermore, previous studies on the FE HZO films noted that E_c may exhibit a distribution rather than a single value due to polycrystalline characteristics and surface-energy-dependent polymorphisms.^29,30 In contrast, research considering the distribution of E_t→PO and E_PO→t is rare.

To utilize fluorite-structured materials in memory or energy applications, achieving stable characteristics during repeated electrical stimuli, known as field-cycling, is crucial.^6,31,32 Field-cycling properties of FFE thin films have been less scrutinized than their FE counterparts. Field-cycling of fluorite-structured FFE films has been shown to lower E_t→PO.^6,20,33,34 Several studies speculated that defects such as oxygen vacancies act as pinning centers in the pristine state, hindering the nucleation of the PO-phase from the t-phase, thereby increasing the E_t→PO.^6,34 When a sufficiently high electric field is applied during cycling, defect activation, de-pinning, and redistribution may occur, lowering the E_t→PO.^6,34 However, these speculations lack supporting evidence. Other studies use the first-order transition theory, the Landau–Ginzburg–Devonshire (LGD) model, to thermodynamically interpret this effect as a change in transition temperature, as discussed in detail later.^13,20,33,35 However, the exact mechanism remains uncertain. Moreover, past studies have regarded the reduction of E_t→PO as irreversible.^6,20,33

Therefore, this work investigated the field-cycling characteristics of 9.4-nm-thick atomic layer deposited ZrO₂ thin films to determine the reversibility of the critical electric fields. Interestingly, high-field cycling decreased the critical electric fields, while subsequent low-field cycling rejuvenated them, challenging the previously held notion of their irreversibility. Elevated temperature increased the lower limit of E_t→PO reduction, supporting the thermodynamic predictions of the first-order transition theory. Additionally, the rejuvenation effect was more pronounced at higher temperatures, consistent with the LGD model.

2. Results and discussion

2.1. Field-cycling characteristics in the pristine state

Fig. 1(a) shows the background-subtracted grazing-angle incidence X-ray diffraction (GIXRD) pattern of the 9.4-nm-thick ZrO₂ film, revealing tetragonal (111) and (002) peaks at ∼30.6° and ∼35.6°, respectively, indicating the well-crystallized structure.^7,36,37Fig. 1(b) shows the dielectric permittivity–electric field (k–E) curves, showing a double butterfly shape typical of FFE films.²⁴ The k values in the maximum electric field region (∼34–37) coincide well with previously reported values for the t-phase.^20,36,38

Fig. 1 (a) Background-subtracted GIXRD pattern and the (b) k–E curve of the 9.4 nm ZrO₂ film. Ideal (c) I–E and (d) P–E curves of FFE films. (e) I–E and (f) P–E curves of the actual 9.4 nm ZrO₂ film.

Fig. 1(c) and (d) show the schematic diagram for the transient current–electric field (I–E) and P–E curves of ideal FFE films, with the t- and PO-phase transitions occurring at a single electric field, respectively. In this case, the forward and reverse switching peaks in the I–E curve do not show broadening, and the P–E curve exhibits a sharp increase and decrease with an infinite slope at E_t→PO and E_PO→t, respectively. Fig. 1(e) and (f) show the I–E and P–E curves of the ZrO₂ film, where the forward and reverse switching peaks are broadened, resulting in finite FFE slopes in the P–E curves. Previous studies generally define E_t→PO and E_PO→t as single values,^27,28 but these parameters exhibit a distribution within the film. As the applied field increases, film regions with higher E_t→PO values sequentially contribute to the FFE switching, broadening the forward and reverse switching peaks. Thus, the point where the P–E curve's slope starts to increase sharply (∼2.8–2.9 MV cm⁻¹) should be considered the minimum value of the E_t→PO distribution, marking the onset electric field for the FFE effect rather than a single E_t→PO. In the experimental ZrO₂ films, non-uniform crystallite size, oxygen vacancy distribution across the film, and polycrystalline nature may cause the distribution of E_t→PO and E_PO→t values.^27,29,39

Field-cycling tests were conducted using pulses shown in Fig. 2(a). Initially, a bipolar triangular pulse of 4.5 MV cm⁻¹ at 1 kHz was applied to obtain the pristine P–E curve. Subsequently, field-cycling tests were performed with bipolar triangular pulses between 1.5–4 MV cm⁻¹ at 100 kHz. Between field-cycling sequences, a bipolar triangular pulse of 4.5 MV cm⁻¹ was applied to examine changes in the P–E curve.

Fig. 2 (a) The schematic diagram of the pulse sequences for the field-cycling test. P–E curve changes with field-cycling at bipolar pulse magnitudes of (b) 1.5 MV cm⁻¹, (c) 2.0 MV cm⁻¹, (d) 2.5 MV cm⁻¹, (e) 3.0 MV cm⁻¹, (f) 3.5 MV cm⁻¹, and (g) 4.0 MV cm⁻¹.

Fig. 2(b)–(g) show the P–E curve changes after cycling with the field-cycling pulse magnitudes of 1.5, 2.0, 2.5, 3.0, 3.5, and 4.0 MV cm⁻¹, respectively. Cycling was performed up to 10⁸ cycles, except for the 4.0 MV cm⁻¹ case, where it was limited to 10⁷ cycles due to increased leakage. For 1.5, 2.0, and 2.5 MV cm⁻¹ cases (Fig. 2(b)–(d)), which have lower cycling pulse magnitudes than the pristine E_t→PO minimum value (∼2.8–2.9 MV cm⁻¹), no FFE switching occurred during the cycling, resulting in minimal changes in the P–E curves. In contrast, for cycling pulses higher than ∼2.8–2.9 MV cm⁻¹ (Fig. 2(e)–(g)), the changes in the P–E curves became more pronounced with increasing field magnitudes. In the 4 MV cm⁻¹ cycling case (Fig. 2(g)), the FFE onset electric field decreased with cycling, consistent with previous reports.^6,20,34 The increased saturated polarization (P_s) is attributed to the leakage under high cycling stress.²⁰ Notably, cycling with 3.0 and 3.5 MV cm⁻¹ pulses (Fig. 2(e) and (f), respectively) showed the appearance of a humped region, indicating a split in the FFE onset field into two distinct parts.

I–E curves were carefully examined for the cycling cases where noticeable changes occurred to understand this phenomenon in detail. The I–E curves correspond to the differential of the P–E curves, showing a peak at the abrupt P–E curve changes, facilitating the identification of the changes. Fig. 3(a)–(c) shows the I–E curve changes after cycling with pulse magnitudes of 3.0, 3.5, and 4.0 MV cm⁻¹, respectively, corresponding to the Fig. 2(e)–(g) cases. Since the P–E and I–E curves of ZrO₂ showed nearly symmetrical behavior at both bias polarities, only the positive bias region is presented for clarity. In the pristine state, the forward and reverse switching peaks are located at ∼2.8–4.5 MV cm⁻¹ and ∼1.2–3 MV cm⁻¹, indicating the E_t→PO and E_PO→t distribution, respectively. The E_t→PO distribution may extend beyond 4.5 MV cm⁻¹ but cannot be detected with a measurement pulse of 4.5 MV cm⁻¹.

Fig. 3 I–E curve changes with field-cycling at (a) 3.0 MV cm⁻¹, (b) 3.5 MV cm⁻¹, and (c) 4.0 MV cm⁻¹. (d) Comparison of I–E curves after 10⁷ cycles.

In Fig. 3(a), cycling at 3.0 MV cm⁻¹ causes only a minor portion of the forward and reverse switching peaks to split and shift to lower fields. When the cycling field is increased to 3.5 MV cm⁻¹ (Fig. 3(b)), a major portion of the switching peaks shifts to lower fields. At 4.0 MV cm⁻¹ (Fig. 3(c)), most switching peaks shift from their original positions, with only the lowered forward and reverse switching peaks visible. The increased leakage between 4.0–4.5 MV cm⁻¹ after cycling is attributed to leakage contributions rather than FFE switching.²⁰ The splitting of the switching peaks for the 3.0 and 3.5 MV cm⁻¹ cases resulted in two separate FFE onset points in Fig. 2(e) and (f), while only one lowered FFE onset is observed for the 4.0 MV cm⁻¹ case in Fig. 2(g).

Fig. 3(d) compares the I–E curves of the pristine state and those after 10⁷ cycles at 3.0, 3.5, and 4.0 MV cm⁻¹. It is confirmed that the portion of lowered switching peaks increases with the higher magnitude of the cycling fields while those remaining unchanged decrease. To summarize, no FFE effect occurs during cycling when a field below the minimum E_t→PO value (2.8–2.9 MV cm⁻¹) is applied. Applying a field slightly above the minimum (3.0 MV cm⁻¹) initiates FFE switching in a minor portion of the film during cycling. As the applied field increases, the FFE switching portion gradually increases. Repeated cycling reduces the E_t→PO and E_PO→t values of the switching portions, whereas the non-switching portions remain unchanged. The underlying reasons for these reductions are discussed in Section 2.2.

The lowered switching peaks also exhibit broadened shapes, indicating that E_t→PO and E_PO→t maintain distributions even after the reduction. Notably, the centers of the forward switching peaks shift from 3.9 to 2.2 MV cm⁻¹ (Δ1.7 MV cm⁻¹, grey dashed lines), whereas the centers of the reverse switching peaks shift from 1.75 to 0.85 MV cm⁻¹ (Δ0.9 MV cm⁻¹, green dashed lines), showing a significantly smaller shift. This results in a more distinct splitting for the forward switching peaks than the reverse switching peaks. This tendency is consistently observed in subsequent results. Therefore, in subsequent discussions, the forward switching peaks and E_t→PO are focused on for clarity, while the reverse switching peaks exhibit similar trends.

Section 2.3 examine the rejuvenation of forward-switching peaks with high-field cycling (3.5 MV cm⁻¹) followed by lower-field cycling. Hence, the 3.5 MV cm⁻¹ cycling case is examined in more detail. Fig. 4 shows the changes in the forward switching peaks at a cycling field of 3.5 MV cm⁻¹ up to 5 × 10⁹ cycles (it took ∼14 hours to test). Fig. S2 in the ESI† shows the full I–E curves. As previously observed, a significant portion of the forward switching peaks shift to lower fields with cycling. With increasing the number of cycles to 10⁵, 10⁶, and 10⁷, the lowered peaks gradually shift toward the lower field direction, with the minimum of the E_t→PO distribution decreasing to ∼1.9, ∼1.7, and ∼1.5 MV cm⁻¹, respectively. Interestingly, no further shift occurred beyond this point, while only increased leakage current was observed with further cycling. This result indicated a lower limit (∼1.5 MV cm⁻¹) to which E_t→PO can be reduced.

Fig. 4 Forward switching peak changes with field-cycling at 3.5 MV cm⁻¹ for 5 × 10⁹ cycles.

2.2. Critical electric field change interpretations based on the first-order phase transition theory

This section discusses the underlying reasons for the reduction in E_t→PO. Many experimental studies reported the lowering of E_t→PO in fluorite-structured FFE films with cycling,^6,20,33–35 where several studies attributed the E_t→PO lowering to defect redistribution and de-pinning.^6,34 However, these suggestions lack supporting proof. Also, E_t→PO lowering should be irreversible according to this perspective.^6,34

Other studies utilize the first-order phase transition theory, the LGD model, to explain the transitions between the t- and PO-phases.^13,20,33,35Eqn (1) represents the relationship between internal energy (U) and polarization (P), while eqn (2) does the relationship between electric field (E) and polarization (P) in the LGD model

E = α₀{T − T₀}P + βP³ + γP⁵ (2)

where α₀, β and γ are the Landau coefficients. The first-order phase transition model includes four transition temperatures: T₀ (Curie–Weiss temperature), T_c (Curie temperature), T₁ (polar phase limiting temperature), and T₂ (field-induced polar phase limiting temperature).³⁵ It was reported that the transition temperatures of HfO₂- or ZrO₂-based thin films may change with Hf : Zr ratio, film thickness, crystallite size, oxygen vacancy, and field-cycling.^20,33,35T₁ is the temperature above which the local energy minima of the polar phase disappear, making it metastable. Hence, the transition from the non-polar to the polar phase occurs only when an electric field above a certain value (E_t→PO in this work case) is applied. Above T₂, the transition to the polar phase cannot occur even with an external electric field. Thus, the FFE double hysteresis loop observed in the ZrO₂ film indicated that the film meets the T₁ < T (operating temperature) < T₂ condition.²⁰ The LGD model was extensively applied in previous studies to interpret the AFE or FFE characteristics of fluorite-structured thin films in the T₁ < T < T₂ regime, confirming feasible agreement between thermodynamic predictions and experimental results.^20,26,33,40 Further explanations of other LGD model parameters and details on the calculations and assumptions can be found in previous studies.^20,33,35,41

Fig. 5(a) and (b) show the changes in the schematic U–P and P–E curves measured at a fixed temperature (T) when the T₁ varied. As the T₁ increases (or decreases), α₀(T − T₀) in eqn (1) decreases (or increases), altering the shape of the U–P curves and consequently decreasing (or increasing) the E_t→PO and E_PO→t in the P–E curves. It was reported that the field-cycling decreases the energy difference between the non-polar t-phase and the polar PO-phase.²⁰ This change can increase the T₁ and consequently decrease the E_t→PO.²⁰ Hence, the lower limit of E_t→PO observed in Fig. 4 indicates a decreasing energy difference between the t- and PO-phases with cycling. Previous studies considering first-order phase transition theory also considered the E_t→PO lowering in FFE films irreversible.^20,33 However, it remains unclear whether E_t→PO can only decrease or if it can be increased by decreasing T₁. Cycling experiments to investigate this are presented in Sections 2.3.

Fig. 5 The schematic diagram of the (a) U–P and (b) P–E curves with various T₁ in a fixed temperature and diagram of the (c) U–P and (d) P–E curves with varying temperatures in a fixed T₁, based on the first-order phase transition theory.

Fig. 5(c) and (d) schematically shows how the U–P and P–E curves change when T varies with a given T₁. As T increases (or decreases), α₀(T − T₀) in eqn (1) increases (or decreases), altering the shape of the U–P curves and consequently increasing (or decreasing) E_t→PO and E_PO→t in the P–E curves theoretically. Relevant experiments with changing temperatures are conducted in Section 2.4.

Several previous studies modified the LGD model by incorporating Kittel's AFE theory to better account for polar and antipolar order parameters.^25,42,43 These modifications lead to a Landau–Kittel model, effectively simulating AFE characteristics.^42,43 However, in the case of FFE ZrO₂, the lack of antiparallel dipoles without an electric field makes it inconsistent with the definition of AFE.^21,26 Future research could benefit from further refining the LGD model to precisely simulate the FFE characteristic, which is beyond the scope of this work.

2.3. Rejuvenation and reversible transition of critical electric fields

Previous studies on FE HfO₂-based materials reported that high-field and low-field cycling induces reversible transitions between the polar PO-phase and the non-polar antipolar orthorhombic phase (AO-phase, space group: Pbca).³² To investigate whether a similar reversible transition occurs between the polar PO-phase and the non-polar t-phase in FFE ZrO₂ films, the ZrO₂ film was tested with initial cycling at a high electric field (3.5 MV cm⁻¹) followed by cycling at relatively lower electric fields (1.5, 2.0, 2.5, and 3.0 MV cm⁻¹).

Fig. 6(a) shows the forward switching peak changes after cycling at 3.5 MV cm⁻¹ for 10⁵ cycles (dotted black), followed by 10⁹ cycles at 1.5 (red), 2.0 (blue), 2.5 (pink), and 3.0 (brown) MV cm⁻¹, respectively. Fig. S3(a)–(d) in the ESI† shows the full I–E curves. After cycling at 3.5 MV cm⁻¹ for 10⁵ cycles (upper part of Fig. 6(a)), the lowered switching peak is distributed between ∼1.9–3.3 MV cm⁻¹, indicating the reduced E_t→PO distribution. The lower limit of E_t→PO (∼1.5 MV cm⁻¹, discussed in Fig. 4) has not been reached due to insufficient cycles. Thus, additional cycling may further decrease the E_t→PO, as in Fig. 6(b) (dotted black line) discussed later. The cycling field magnitude applied during subsequent low-field cycling is denoted as E^l_cycle and represented by green dashed lines in Fig. 6. In Fig. 6(a), for E^l_cycle = 1.5 and 2.0 MV cm⁻¹, most of the switching peak portions (1.9–3.3 MV cm⁻¹) are distributed at fields higher than E^l_cycle (E^l_cycle < E_t→PO). In contrast, for E^l_cycle = 2.5 and 3.0 MV cm⁻¹, certain peak portions are observed at fields lower than E^l_cycle (E^l_cycle > E_t→PO), while others remain at fields higher than E^l_cycle (E^l_cycle < E_t→PO). In the 2.5 MV cm⁻¹ and 3.0 MV cm⁻¹ cases, the latter has a more significant portion.

Fig. 6 Forward switching peak changes with (a) cycling at 3.5 MV cm⁻¹ for 10⁵ cycles, followed by cycling at 1.5/2.0/2.5/3.0 MV cm⁻¹ for 10⁹ cycles, and (b) cycling at 3.5 MV cm⁻¹ for 10⁷ cycles, followed by cycling at 1.5/2.0/2.5/3.0 MV cm⁻¹ for 10⁸ cycles.

When E^l_cycle > E_t→PO, the switching peaks shift toward the lower field direction, further lowering E_t→PO until they reach the lower limit of 1.5 MV cm⁻¹, indicated by the red dashed boxes in the third and fourth panel of Fig. 6(a) where E^l_cycle = 2.5 and 3.0 MV cm⁻¹. Conversely, when E^l_cycle < E_t→PO, the switching peaks shift toward the higher electric field direction (for example, yellow dot-edged box in the second panel of Fig. 6(a), where E^l_cycle = 1.5 MV cm⁻¹), indicating E_t→PO rejuvenation. These results contrast with previous studies suggesting cycling only lowers E_t→PO irreversibly.^6,20,33,34 Instead, the change in E_t→PO with cycling depends on the relative magnitudes of E^l_cycle and E_t→PO. Applying a cycling field higher than E_t→PO (E^l_cycle > E_t→PO) decreases the energy difference between the t- and PO-phases, decreasing E_t→PO until the lower limit of energy difference is reached. This change is consistent with the increasing T₁. In contrast, lower cycling fields (E^l_cycle < E_t→PO) rejuvenate the reduced energy difference, increasing E_t→PO and decreasing T₁.

Additionally, the switching peaks located at much higher fields than E^l_cycle (above 3.5 MV cm⁻¹) remain unchanged and exhibit minimal shift during the cycling (pink boxes in Fig. 6(a)), indicating that its E_t→PO ≫ E^l_cycle. This tendency suggests that the rejuvenation effect diminishes as the difference between E_t→PO and E^l_cycle increases. While the rejuvenation process can restore the reduced energy difference between the t- and PO-phases, it likely cannot increase this energy difference beyond the pristine state.

Similar cycling tests are conducted in Fig. 6(b), but with initial 3.5 MV cm⁻¹ cycling increased from 10⁵ to 10⁷ cycles to reach the E_t→PO lower limit (∼1.5 MV cm⁻¹) as discussed in Fig. 4. Subsequent lower-field cycling is reduced from 10⁹ to 10⁸ cycles to shorten the cycling time for convenience. Fig. S3(e)–(h) in the ESI† shows the full I–E curves. Different from the Fig. 6(a) case, the forward switching peak is further lowered (upper part of Fig. 6(b)), distributed between ∼1.5–3.3 MV cm⁻¹. For E^l_cycle = 1.5 MV cm⁻¹, all the lowered switching peak portions (1.5–3.3 MV cm⁻¹) are distributed at fields higher than E^l_cycle (E^l_cycle < E_t→PO, yellow dot-edged boxes). For E^l_cycle = 2.0, 2.5, and 3.0 MV cm⁻¹, both E^l_cycle < E_t→PO (yellow dot-edged boxes) and E^l_cycle > E_t→PO (red dash-edged boxes) portions are present, with the proportion of E^l_cycle > E_t→PO increasing as E^l_cycle increases. As in Fig. 6(a), the E^l_cycle < E_t→PO portions rejuvenate, and the E^l_cycle ≪ E_t→PO portions show minimal shifts. However, unlike in Fig. 6(a), the E^l_cycle > E_t→PO portions do not shift toward the lower field direction since the E_t→PO already reached the lower limit of 1.5 MV cm⁻¹ with the 3.5 MV cm⁻¹ cycling.

Several studies attributed the lowering of E_t→PO to irreversible defect redistribution and de-pinning.^6,34 However, according to this model, applying lower-field cycling after higher-field cycling should result in either (1) no further changes due to sufficient defect redistribution and de-pinning in the previous step or (2) further lowering of E_t→PO due to the activation of previously inactive defects during high-field cycling, leading to additional E_t→PO reductions even at lower fields. Therefore, the observed rejuvenation of E_t→PO contradicts this defect chemistry model, which is further supported by the high-temperature measurement results in Sections 2–4. However, this does not rule out the possibility that more intricate defect chemistry influences the reversible changes in E_t→PO, as discussed later.

The observed reversible transitions resemble the previously reported reversible transitions between the AO- and PO-phases in FE HZO films.³² Similar to the FFE ZrO₂ case, the non-polar AO-phase HZO was considered more thermodynamically stable than the polar PO-phase HZO at the pristine state in the U-P curves.³² The critical field needed to stabilize the PO-phase over the AO-phase was calculated as E₀. When the effective cycling field applied to the FE layer (E_eff) is greater than E₀ (E_eff > E₀), the AO-phase transitions to the PO-phase, similar to the E^l_cycle > E_t→PO in this work. Conversely, when E_eff < E₀, the PO-phase transitions back to the AO-phase, similar to the E^l_cycle < E_t→PO in this work.³² These similar results suggest that the reversible transitions between polar and non-polar phases with high- and low-field cycling are a universal phenomenon in fluorite-structured materials, not limited to FE HZO materials.

These results suggest that the T₁ of FFE ZrO₂ can be reversibly increased (or decreased) by high-field (or low-field) cycling. Cycling may induce intricate reversible structural or chemical changes, which in turn affect T₁. However, directly observing these changes in cycled capacitors is generally challenging.⁴⁴ Previous studies identified structural phase changes before and after cycling in fluorite-structured HfO₂- or ZrO₂-based films by XRD,^44–48 TEM,²² scanning TEM (STEM),^31,32 Raman spectroscopy,⁴⁹ and Fourier transform infrared spectroscopy.⁵⁰ However, changes were typically detectable only when significant wake-up (or fatigue) effects occurred, with a substantial increase (or decrease) in double remnant polarization (2P_r). In contrast, minimal wake-up effects in cycled FFE films resulted in no noticeable structural changes.⁵¹ Fig. S4 and S5 in the ESI† show the P–E and k–E curve changes in the pristine, cycled (3.5 MV cm⁻¹), and rejuvenated states. Regardless of the cycling state, the 2P_r and k values exhibited minimal changes, indicating that the t-phase remained predominantly stable after the field-cycling without significant phase transition.^31,47,50 Similarly, Fig. S6 in the ESI† shows minimal changes in the GIXRD patterns for the pristine, cycled (3.5 MV cm⁻¹), and rejuvenated states, consistent with the observations in Fig. S4 and S5 (ESI†). Thus, structural evidence is difficult to capture from the post-cycling states, and in situ biasing techniques may be required, as the phase changes only occur during the application and removal of the electric field in FFE ZrO₂ films.^8,20,22,23

Detecting direct defect changes in cycled capacitors is even more challenging, with only a few studies reporting feasible results. Zheng et al. used high-angle annular dark-field STEM (HAADF-STEM) and electron energy loss spectra (EELS) to demonstrate that oxygen vacancy formation in cycled Hf_0.5Zr_0.5O₂ films may vary depending on the polar axis orientation in different localized regions.⁵² Chen et al. directly observed oxygen vacancy migration in woken-up and fatigued Hf_0.5Zr_0.5O₂ films using differential phase contrast-STEM (DPC-STEM) and energy dispersive spectroscopy (EDS), correlating the defect redistribution to the built-in bias changes.⁵³ However, these chemical changes were only detected with significant wake-up or fatigue effects and were observed ex situ rather than during the bias application.^52,53 Nukala et al. used in situ integrated differential phase contrast-STEM (iDPC-STEM) imaging to observe the reversible oxygen migration in La_0.67Sr_0.33MnO₃/Hf_0.5Zr_0.5O₂ thin films at millisecond time scales, correlating it with the reversible phase transitions.⁵⁴ However, this technology is limited in availability. Therefore, past studies infer defect changes indirectly by monitoring the leakage current variations or performing measurements at elevated temperatures.^31,32 Fig. S7 in the ESI† examines changes in leakage current density for the pristine, cycled (3.5 MV cm⁻¹), and rejuvenated states. However, no reversible changes were observed, with only minimal or irreversible changes detected. The inability to observe reversible structural or chemical changes in Fig. S6 and S7 (ESI†) may be due to the limitations of the measurement techniques. Thus, these results do not exclude the possibility that cycling induces structural or chemical changes that affect T₁. Therefore, future research should focus on directly correlating the structural and chemical changes with the LGD model transition temperature variations, using in situ biasing techniques, which are beyond the scope of this study.

Next, cycling tests were conducted to confirm the reversible nature of E_t→PO lowering and rejuvenation, and Fig. 7(a)–(c) shows the result. Fig. S8(a)–(d) in the ESI† shows the full I–E curves. All experiments involved continuous cycling on a single capacitor. Fig. 7(a) shows the forward switching peak changes after sequential cycling steps: (step 1) 3.5 MV cm⁻¹, 10⁷ cycles (red) → (step 2) 2.0 MV cm⁻¹, 10⁸ cycles (blue) → (step 3) 3.5 MV cm⁻¹, 10⁷ cycles (pink) → (step 4) 2.5 MV cm⁻¹, 10⁸ cycles (green) → (step 5) 3.5 MV cm⁻¹, 10⁷ cycles (brown). The original I–E curve (black dotted curve) shows a single peak centered at 3.5–4 MV cm⁻¹. In step 1, the high-field cycling at 3.5 MV cm⁻¹ shifts the portion of the original peak lower than 3.5 MV cm⁻¹ toward the lower field direction and forms a strong peak centered at 2.0–2.5 MV cm⁻¹ (red line curve). In step 2, the low-field cycling at 2.0 MV cm⁻¹ rejuvenated peaks at E_t→PO > 2.0 MV cm⁻¹ (blue line curve). Reapplying high-field cycling (3.5 MV cm⁻¹) in step 3 lowered the rejuvenated peaks to the previous position (pink line curve). In step 4, low-field cycling (2.5 MV cm⁻¹) rejuvenated peaks at E_t→PO > 2.5 MV cm⁻¹, lowered again with the high-field cycling in step 5. Notably, the rejuvenation of the lower field-shifted peak (by the 3.5 MV cm⁻¹ cycling) occurs only for the E_t→PO > E^l_cycle portions.

Fig. 7 (a) Sequential forward switching peak changes after cycling at (1) 3.5 MV cm⁻¹, 10⁷ cycles (red) → (2) 2.0 MV cm⁻¹, 10⁸ cycles (blue) → (3) 3.5 MV cm⁻¹, 10⁷ cycles (pink) → (4) 2.5 MV cm⁻¹, 10⁸ cycles (green) → (5) 3.5 MV cm⁻¹, 10⁷ cycles (brown). (b) Sequential forward switching peak changes after cycling at (1) 3.5 MV cm⁻¹, 10⁷ cycles (red) → (2) 2.5 MV cm⁻¹, 10⁷ cycles (blue) → (3) 2.0 MV cm⁻¹, 10⁸ cycles (pink) → (4) 2.5 MV cm⁻¹, 10⁷ cycles (green) → (5) 3.0 MV cm⁻¹, 10⁸ cycles (brown). (c) Sequential forward switching peak changes after alternating cycling of 3.5 MV cm⁻¹ for 10⁷ cycles and 2.5 MV cm⁻¹ for 10⁸ cycles, repeated five times.

Fig. 7(b) shows the test results similar to Fig. 7(a) but sequential rejuvenation with different rejuvenating E^l_cycle. It reveals the switching peak changes after sequential cycling steps: (step 1) 3.5 MV cm⁻¹, 10⁷ cycles (red) → (step 2) 2.5 MV cm⁻¹, 10⁷ cycles (blue) → (step 3) 2.0 MV cm⁻¹, 10⁸ cycles (pink) → (step 4) 2.5 MV cm⁻¹, 10⁷ cycles (green) → (step 5) 3.0 MV cm⁻¹, 10⁸ cycles (brown). Step 1 results in a similar change in the pristine state to the one in Fig. 7(a). In step 2, 2.5 MV cm⁻¹ of rejuvenation E^l_cycle rejuvenates peaks at E_t→PO > 2.5 MV cm⁻¹. In step 3, an even lower-field cycling at 2.0 MV cm⁻¹ of rejuvenation E^l_cycle further rejuvenates peaks at 2.0 MV cm⁻¹ < E_t→PO < 2.5 MV cm⁻¹, which were not rejuvenated in the previous step, merging with the previously rejuvenated peaks. In step 4, cycling at a slightly higher field of 2.5 MV cm⁻¹ lowers only the peaks below this field, and in step 5, cycling at a field of 3.0 MV cm⁻¹ lowers additional peaks, merging with those lowered in the previous step. These results further confirm the reversible switching peak lowering and rejuvenation, dependent on the cycling field magnitudes.

Cycling tests are conducted with alternating cycles of 3.5 MV cm⁻¹, 10⁷ cycles → 2.5 MV cm⁻¹, 10⁸ cycles, repeated five times to address whether these reversible processes remain consistent with repeated cycles. Fig. 7(c) shows the forward switching peak changes after each step. After step 1, as in Fig. 7(a) and (b), low-field cycling at 2.5 MV cm⁻¹ identically rejuvenates the E_t→PO > 2.5 MV cm⁻¹ portions in steps 2, 4, 6, 8, and 10. Likewise, the high-field cycling at 3.5 MV cm⁻¹ uniformly lowers the rejuvenated peaks in steps 3, 5, 7, and 9. These results further confirm the consistency of the reversible peak lowering and rejuvenation with repetitions.

2.4. Cycling at elevated temperature

The effects of elevated measurement temperature on the critical electric fields are evaluated through P–E measurements and cycling tests. Fig. 8(a) shows the pristine P–E curves at 25 °C and 75 °C. With a measurement temperature increase, E_t→PO and E_PO→t slightly increase, resulting in a corresponding decrease in P_s, consistent with previous reports and the LGD theory in Fig. 5(c) and (d).^13,33,35

Fig. 8 (a) P–E curves at 25 °C and 75 °C. I–E curve changes with field-cycling at 3.5 MV cm⁻¹, 10⁸ cycles for (b) 25 °C and (c) 75 °C. (d) Comparison of forward switching peaks after 10⁸ cycles.

Fig. 8(b) and (c) show the I–E curve changes after cycling with pulse magnitudes of 3.5 MV cm⁻¹ at 25 °C and 75 °C, respectively, up to 10⁸ cycles. The triangular measurement pulse magnitude was reduced to 4.0 MV cm⁻¹ to avoid high leakage at elevated temperatures. Cycling could not be conducted above 75 °C due to significant leakage. In Fig. 8(b), cycling at 25 °C shows both forward and reverse switching peaks shifting gradually toward the lower field direction, consistent with the results above. However, in Fig. 8(c), cycling at 75 °C shows peak shifting toward the lower field direction up to 10⁶ cycles but no further decrease beyond that point, only showing increases in leakage contributions. Fig. 8(d) compares the forward switching peaks after 10⁸ cycles at 25 °C (red) and 75 °C (blue). The 25 °C and 75 °C cases show an E_t→PO lower limit of ∼1.5 and ∼1.7 MV cm⁻¹, respectively.

It was extensively reported that defect activation, de-trapping, and diffusion/drift are accelerated at elevated temperatures in fluorite-structured HfO₂ or ZrO₂-based materials.³¹ If the E_t→PO lowering with cycling was due to defect redistribution and de-pinning, cycling at 75 °C should cause a more pronounced peak shift compared to 25 °C, inconsistent with these hypotheses. Conversely, the LGD theory predictions in Fig. 5(c) and (d) corroborate with the experimental results, showing an increased lower limit of E_t→PO at 75 °C due to the increased energy difference between the t- and PO-phases, thus validating this interpretation.

Finally, the rejuvenation characteristics at different measurement temperatures were investigated. High-field cycling at 3.5 MV cm⁻¹ was performed at 25 °C for all cases, followed by lower-field cycling at 2.5 or 2.0 MV cm⁻¹ at 25 °C or 75 °C for comparison to observe the rejuvenation effect at higher temperatures. Fig. 9(a) shows the forward switching peak changes after cycling at 3.5 MV cm⁻¹ for 10⁷ cycles at 25 °C (black or grey dotted lines), followed by cycling at 2.5 MV cm⁻¹ for 10⁸ cycles at 25 °C (upper panel, red line) and 75 °C (lower panel, blue line), respectively. Fig. S9(a) and (b) in the ESI† shows the full I–E curves. 3.5 MV cm⁻¹ cycling at 25 °C resulted in a lower limit of ∼1.5 MV cm⁻¹ as previously discussed. The lower limit remained unchanged when lower-field cycling (2.5 MV cm⁻¹) was performed at 25 °C. However, it increases to ∼1.7 MV cm⁻¹ for the 75 °C case, coinciding with Fig. 8(d). Furthermore, the rejuvenated portion and extent of the shifts are more significant at 75 °C, consistent with Fig. 5(c) and (d). Fig. 9(b) shows the forward switching peak changes after cycling at 3.5 MV cm⁻¹ for 10⁷ cycles at 25 °C (black or grey dotted lines), followed by cycling at 2.0 MV cm⁻¹ for 10⁸ cycles at 25 °C (upper panel, red line) and 75 °C (lower panel, blue line), respectively. Fig. S9(c) and (d) in the ESI† shows the full I–E curves. As in Fig. 9(a), lower-field cycling at 75 °C enhances rejuvenation compared to the 25 °C case. The rejuvenation of E_t→PO is driven by the restored, increased energy difference between the t- and PO-phases. This energy difference increases at higher temperatures, enhancing the rejuvenation effect. These results further support introducing the first-order phase transition theory in interpreting the changes in the FFE critical electric fields. While the temperature-dependent LGD model alone provides a plausible explanation for the changes in critical electric fields at elevated temperatures, structural or chemical changes may also influence the reversible critical electric field changes, as discussed in Sections 2–3. Although these changes were not observed in this study, further research should utilize in situ biasing techniques to acquire direct evidence on how these factors influence the lowering and rejuvenation of critical electric fields at different temperatures.

Fig. 9 Forward switching peak changes after cycling at 3.5 MV cm⁻¹ for 10⁷ cycles at 25 °C (black or grey dotted lines), followed by cycling at (a) 2.5 MV cm⁻¹ or (b) 2.0 MV cm⁻¹ for 10⁸ cycles at 25 °C (red line) and 75 °C (blue line), respectively.

3. Experimental section

Sample preparation

A 50 nm TiN bottom electrode was deposited on a thermally oxidized SiO₂ (100 nm)/Si substrate via sputtering (ENDURA 5500, Applied Materials). The 9.4-nm-thick ZrO₂ (70 cycles) was deposited via thermal atomic layer deposition at a substrate temperature of 250 °C. Zr[N(CH₃)C₂H₅]₄ and ozone (260 g m⁻³) were used as the Zr and oxygen sources, respectively. Circular Pt (30 nm)/TiN (7 nm) top electrodes (TE) were deposited with metal shadow masks via sputtering (CDS 5000, SNTEK). The electrode areas were precisely measured using an optical microscope. For experiments observing GIXRD before and after cycling, the sample's TE was deposited differently to increase the cycled area relative to the total sample area. A 50 nm TiN TE was deposited using radio-frequency reactive sputtering (SRN 120, Sorona) at 500 W. After TiN deposition, square TEs (area: ∼160 000 μm²), spaced 100 μm apart from each other, were patterned using photolithography and a dry etching process. After the TE deposition, post-metallization annealing was performed at 450 °C for 30 seconds in an N₂ atmosphere to crystallize the films.

Physical and electrical characterization

The thickness of the ZrO₂ film was measured using spectroscopic ellipsometry (SE; M-2000, J. A. Woollam) and X-ray fluorescence spectroscopy (XRF; Quant'X, Thermo SCIENTIFIC). The film crystal structure was analyzed via GIXRD (X’pert Pro, PANalytical, angle of incidence = 0.5°). Capacitance–voltage characteristics were obtained using an impedance analyzer (4194A, HP) at the 10 kHz AC frequency. P–E and I–E curves were obtained via a ferroelectric tester (TF Analyzer 2000) using triangular bipolar pulses at 1 kHz. Field-cycling tests were conducted with triangular bipolar pulses at 100 kHz using the same ferroelectric tester. The leakage current density measurements with cycling were conducted using a semiconductor characterization system (Keithley, 4200A-SCS). The accurate electrode area was estimated via an optical microscope. Measurements at different temperatures (25 °C and 75 °C) were conducted using a hot chuck, with a 30-minute stabilization period at each temperature before measurements to exclude errors from inaccurate temperatures.

4. Conclusions

This study explores the field-cycling characteristics of field-induced ferroelectric ZrO₂ films, highlighting the reversible and temperature-dependent nature of the critical electric fields. High-field cycling lowers these critical fields, and lower-field cycling rejuvenates them. This work provides experimental proof that challenges the previous suggestions that critical electric field lowering is irreversible by demonstrating that these values can be reversibly modulated.^6,20,29 Cycling tests identified lower and upper limits to the extent of lowering and rejuvenating the critical fields, indicating constraints on decreasing and restoring the energy differences between the t- and PO-phases.

Experiments at different measurement temperatures further supported these findings. The higher temperature increased the energy difference between the t- and PO-phases, increasing the lower limit of E_t→PO reduction with cycling and resulting in less pronounced switching peak lowering. Furthermore, rejuvenation effects were more significant at higher temperatures, coinciding with the increased energy differences. These findings are inconsistent with the previous assumptions that irreversible defect redistribution and de-pinning are the primary factors for lowering the critical electric fields with cycling.^6,29 Instead, the results could be feasibly interpreted with the first-order phase transition model based on the Landau–Ginzburg–Devonshire theory, describing the reversible and temperature-dependent behavior of critical electric fields.

These results indicate that the reversible transitions between polar and non-polar phases with higher- and lower-field cycling are not exclusive to ferroelectric materials but extend to the field-induced ferroelectric fluorite-structured materials. This improved understanding of field-cycling behavior in field-induced ferroelectric films could enhance their potential application in memory and energy storage devices. Structural or chemical factors influenced by cycling or elevated temperatures may have intricately affected the critical electric field changes observed in this study, although direct evidence could not be obtained. Thus, further research should focus on comprehensive in situ observations under bias application to acquire further evidence.

Author contributions

J. Shin designed and performed the experiments and wrote the manuscript. D. H. Shin assisted with the device fabrications. K. D. Kim, H. Seo, and K. H. Ye assisted with the data interpretations. J. W. Jeon and S. H. Lee assisted with the elevated temperature measurements. T. K. Kim, H. Paik, H. Song, and J.-H. Choi helped review the manuscript and added comments. C. S. Hwang supervised the whole research and manuscript preparation.

Data availability

The data supporting this article have been included as part of the ESI.† The data that support the findings of this study are available from the corresponding author upon reasonable request.

Conflicts of interest

The authors declare that they have no conflict of interest.

Acknowledgements

This work was supported by the Technology Innovation Program (20017224, Development of new ALD System for the next-generation mass-production memory devices) funded by the Ministry of Trade Industry & Energy (MOTIE, Korea).

Notes and references

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Footnote

† Electronic supplementary information (ESI) available. See DOI: https://doi.org/10.1039/d4tc03024a

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