Lorentz-tail engineering toward over 10-year data retention with minimum loss in ferroelectric HZO

Abstract

As the annual volume of data production exceeds tens of zettabytes, there is increasing interest in developing non-volatile materials for next-generation memory technologies. Among them, HfO₂-based fluorite-structured ferroelectrics have emerged as leading candidates due to their ability to maintain ferroelectric properties even at thicknesses below 10 nm and their compatibility with conventional complementary metal–oxide–semiconductor (CMOS) processes. However, the inherently large depolarisation field induced by the ultra-thin film nature makes it challenging to achieve the over 10-year data retention required for practical memory applications. In this study, we identify that retention degradation originates from the tail region of the polarisation switching distribution and demonstrate that Lorentz-tail engineering can substantially enhance retention performance. Accelerated retention tests show that the engineered ferroelectric HZO retains over 93% of its polarisation after a projected 10 years, thus contributing to the advancement of HfO₂-based ferroelectrics for memory device applications.

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New concepts

While conventional studies have focused on process-level optimizations to mitigate fatigue in ferroelectric HZO, retention degradation caused by partial polarisation reverse switching remains largely unaddressed. This work introduces a novel device-level programming strategy—Lorentz-Tail Engineering—that selectively pre-reverses the unstable polarisation components responsible for long-term retention loss. By identifying the intrinsic Lorentz-tail effect within the intermediate switching states, and counteracting it via a two-step pulse scheme, this study presents a fundamentally new approach to achieving >10-year reliable retention in ferroelectric tunnel devices. This concept offers a practical and scalable pathway to unlock the full potential of HZO-based ferroelectrics for future non-volatile memory applications.

Introduction

As conventional memory technologies approach their scaling limits, the collapse of Moore's law has intensified¹ the demand for new memory solutions, drawing significant attention to materials with non-volatile properties for emerging memory applications.^2,3 Among various candidates, HfO₂-based ferroelectrics with a fluorite structure have garnered particular interest because they can be integrated into conventional complementary metal–oxide–semiconductor (CMOS) processes and maintain intrinsic remanent polarisation even at sub-10 nm thicknesses, offering substantial advantages for further scaling.^4,5 Consequently, extensive research efforts have been devoted to applying these ferroelectrics in memory devices such as ferroelectric random access memory (FeRAM),^6,7 ferroelectric tunnel junctions (FTJ),^8,9 and ferroelectric field-effect transistors (FeFET).^10,11

The retention characteristic—fundamental requirements for memory devices applicable to the semiconductor industry—is typically evaluated based on retention tests over 10 years. However, most previous studies on HfO₂-based fluorite-structure ferroelectrics have evaluated 10-year retention characteristics by extrapolating early-stage data with minimal initial loss, making the results unreliable.^12–18 Moreover, even extrapolated data often fail to demonstrate retention performance exceeding 90%. The primary factors contributing to the degradation of ferroelectric HZO retention characteristics are fatigue effects and polarisation reverse switching. Among these, fatigue refers to the partial loss of polarisation properties, whereas polarisation reverse switching involves the reversal of oriented polarisation into the opposite direction. The fatigue effect can be mitigated by controlling device fabrication conditions, and numerous studies have reported related approaches. The fatigue effect can be mitigated by controlling device fabrication conditions, and numerous studies have reported related approaches.^19–23 However, strategies to overcome partial polarisation reverse switching—which significantly contributes to retention degradation in polycrystalline ferroelectric HZO²⁴—have not been extensively explored. Since this phenomenon is difficult to address through process-based modifications, a new programming approach at the device operation level is critically required to enable the widespread application of ferroelectric materials in memory devices by improving retention characteristics.

In this study, we investigate the switching behaviour of ferroelectric HZO and demonstrate that excellent retention characteristics can be achieved through Lorentz-tail engineering. By analysing the intermediate-state polarisation switching characteristics of ferroelectric HZO, we identify that the degradation in retention characteristics originates from the Lorentz-tail—an intrinsic feature of the Lorentz distribution—within the switching behaviour. Based on this understanding, a Lorentz-tail engineering based on a two-step pulse programming method is proposed, where the Lorentz-tail is selectively reversed in advance. Finally, accelerated retention tests based on the Arrhenius acceleration model are conducted at 85 °C to evaluate over 10-year retention characteristics.

Experimental section

Device fabrication

HZO ferroelectric thin films were grown on a TiN/SiO₂/Si substrate by PEALD at 180 °C. For enhanced reliability, a remote plasma method was adopted, where plasma discharge and deposition take place in a separate chamber, unlike the direct plasma method that exposes the substrate to plasma directly.²⁵ They were deposited using tetrakis (ethylmethylamido) hafnium(IV) and tetrakis (ethylmethylamido) zirconium(IV) with O₂ as the oxidant. HfO₂ and ZrO₂ were alternately deposited to prepare HZO with each ratio. The top TiN electrode was deposited via RF magnetron sputtering in Ar and N₂ atmospheres using a circular-patterned hard mask (r = 100 µm). Subsequently, the initial amorphous HZO thin films were crystallised in a N₂ atmosphere at each temperature and time to stabilise the ferroelectric o-phase.

Electrical measurements

Electrical measurements were performed using a parameter analyser (4200A-SCS, Keithley) with a 4225-PMU.

Scanning transmission electron microscopy (STEM) measurements

Cross-sectional STEM imaging was performed using a JEM-2100F (JEOL) with a STEM Cs corrector, following FIB processing with a Quanta 3D FEG (FEI).

Results and discussion

Ferroelectric HZO exhibits non-volatile polarisation properties due to the structural asymmetry between Hf/Zr atoms and oxygen atoms.^26–28Fig. 1a illustrates the orthorhombic (o-) phase with Pca₂1, the structural origin of HZO ferroelectricity. An external electric field enables physical displacement switching of oxygen atoms between two energetically favourable and stable polarisation states (P_down and P_up). However, as shown in Fig. 1b, typical ferroelectric HZO fails to retain polarisation for over 10 years, and previous studies claiming over 10-year data retention are largely based on extrapolations from early-stage measurements with minimal initial loss, making their reliability questionable. As presented in Fig. S1, such data loss can significantly compromise the reliability of ferroelectric HZO in memory device applications, and the resulting variability may lead to misinterpretation of readout results. Prior to the analysis of polarisation reverse switching, we fabricated 27 metal–ferroelectric–metal (MFM) structure TiN/H_xZ_1−xO₂/TiN devices—by varying the composition, thickness, and annealing time—to obtain high-performance ferroelectric HZO devices that account for both the fatigue effect and the manifestation of ferroelectricity. Detailed fabrication conditions are provided in Table S1. Fig. 1c presents the pulsed J–V curves after cycling for nine H_0.5Z_0.5O₂ devices, which exhibited the most stable electrical characteristics among the three compositions. The endurance against electrical stress, the ferroelectric properties of the fabricated devices, and optimised woken-up condition are evaluated in Fig. S2, S3, and S4, respectively. Among them, the 5 nm-thick H_0.5Z_0.5O₂ device (hereafter referred to as the “ferroelectric HZO device”) annealed at 600 °C for 60 s and subjected to 10⁵ cycles of electrical on/off stress at 2.5 V was identified as the most promising. Fig. 1d and its inset present the STEM and corresponding FFT images used to confirm the ferroelectricity of the device, showing the actual HZO thickness of approximately 5 nm and the extracted d-spacing values. Fig. S5 presents a full view of the TiN/HZO/TiN structure as well as grazing incidence X-ray diffraction (GI-XRD) results that provide additional phase information. The measured d-spacings of 2.64 Å, 2.99 Å, and 3.04 Å correspond to the (200)_o²⁹ or (110)_t,³⁰ (111)_o,^30,31 and (111)_o^29,32 planes, respectively, confirming the clear presence of the ferroelectric o-phase. Fig. 1e shows the pulsed J–V and P–V curves of the optimised ferroelectric HZO device obtained through PUND measurements. The PUND measurement procedure and derivation process are described in detail in Fig. S6, and all subsequent experiments were performed using the woken-up ferroelectric HZO device.

Fig. 1 Schematic illustration of the ferroelectric structure, its electrical and structural characteristics, and the associated retention degradation issues. (a) Schematic illustration of the ferroelectric orthorhombic (o-) phase (space group Pca2₁). Red and blue spheres indicate oxygen atoms contributing to polarisation, whereas grey spheres represent non-polarisation-contributing oxygen atoms. Black spheres denote Hf and Zr atoms. (b) Retention characteristics of ferroelectric HZO pose a critical challenge to its viability for memory applications. (c) Pulsed J–V curves measured after 10⁷ cycles at 2.5 V for nine 5 : 5 HZO devices fabricated under different thickness and annealing time conditions. (d) Cross-sectional STEM image and FFT image of 5 nm-thick H_0.5Z_0.5O₂ device annealed at 600 °C for 60 s. Labelled Miller indices and phase information analysed based on the d-spacing extracted along the coloured translucent line. (e) Pulsed J–V curve obtained by PUND measurements and P–V curve derived from the pulsed J–V curve.

Polarisation reverse switching refers to the reversal of the oriented polarisation to the opposite direction during data retention, even in the absence of an additional external electric field. This behaviour can be attributed to the Lorentz tail of the Lorentz distribution in the nucleation-limited switching (NLS) model,^33,34 which effectively describes the switching characteristics of HfO₂-based ferroelectrics. Theoretically, the switching dynamics are also described by a Lorentz function governed by the nucleation probability,²⁷ and this description is generally valid unless extremely small electrodes are employed.³⁵ A more detailed explanation of the Lorentz tail is provided in Fig. S7a. The Lorentz-tail refers to the non-ideal distribution of low coercive voltages deviating from the centre (peak) of the Lorentz distribution. As shown in Fig. S7b, such Lorentz-tails are associated with low energy barriers for switching to the opposite polarisation, making them highly susceptible to reverse switching under various influences such as depolarisation fields³⁶ and temperature. This type of degradation is difficult to mitigate through process-level control. To enable the practical application of ferroelectrics in memory devices, a universal approach to controlling the Lorentz-tail at the device operation level is critically needed, which in turn necessitates a clear understanding of polarisation switching behaviour.

Fig. 2a illustrates the PU sequence of intermediate-state PUND measurements used to analyse polarisation switching behaviour, consisting of cycling, monitoring, a fixed pre-pulse, and P and U pulses. The intermediate-state PUND measurements were performed using two different amplitude increment methods for the triangular pulses: width-fixed and slope-fixed methods. The detailed sequences and measurement conditions for each method are provided in Fig. S8. Fig. 2b shows the pulsed J–V curves for the 140 monitoring pulses applied during the width-fixed method, indicating that the device state remained stable. The pulsed J–V curves obtained from a total of 280 monitoring pulses for both the width-fixed and slope-fixed methods are shown in Fig. S9, and nearly identical P–V curves were observed across the monitoring pulses. The consistency of the measured P–V curves indicate that the ferroelectricity remained unchanged throughout the measurements, validating the reliability of the analysis. Fig. 2c and d show the representative case of J–V curve obtained from the PU measurement with a –1.5 V_fix pre-pulse under the width-fixed condition, and the corresponding P–V curve derived by integrating the current density. The complete results for the width-fixed and slope-fixed methods are presented in Fig. S10 and S11, respectively. Notably, for both the width-fixed and slope-fixed methods, all P–V curves obtained with different fixed pre-pulses exhibited the same shape trends as the reference curve measured at the largest amplitude (±1.5 V). This consistency implies that, under different memory windows defined by the fixed pre-pulses, the polarisation switching behaviour follows a specific rule.

Fig. 2 Analysis of polarisation switching behaviour using intermediate-state PUND measurements under fixed pulse width conditions. (a) Pulse sequence for the intermediate-state PUND measurement, including on/off cycling, poling pulse, monitoring pulse, pre-pulse, P pulse, and U pulse, applied in the indicated order. (b) Pulsed J–V curve measured from a total of 140 monitoring pulses applied under the fixed-width condition. (c) Pulsed J–V curve obtained by subtracting the transient current density of the U pulse from that of the P pulse, and (d) corresponding P–V curve derived from it.

To analyse the observed switching behaviour, the polarisation values (P_r) obtained from the intermediate-state PUND measurements were fitted to a Lorentz function. Fig. 3a presents the extracted +P_r values from the PU measurements under five different fixed pre-pulse conditions, obtained using the width-fixed method. The complete results are provided in Fig. S12a–d. To fit the data to the Lorentz function, the P_r values were normalised to a range between 0 and 1, and the complete results are provided in Fig. S12e–h. The Lorentz function used for the fitting is given below:³⁷

where P is the normalised P_r value, A is the height of the Lorentz distribution, V_average is the average switching voltage (centre of Lorentz distribution), and ω is the half width at half maximum (HWHM) of the Lorentz distribution. Fig. 3b shows the normalised P_r data fitted with a Lorentz function. The high coefficient of determination (R² > 0.99) indicates an excellent fit, demonstrating that the observed polarisation switching behaviour can be well described by a Lorentz distribution. The complete fitting results are provided in Fig. S12i–l. Fig. 3c shows the Lorentz distribution extracted from the Lorentz fit, where a distinct Lorentz-tail is observed, and the switching distribution is found to exhibit a nearly identical shape. The complete results are provided in Fig. S13. To gain further insight into the polarisation switching behaviour, each parameter obtained from the Lorentz function fitting was additionally analysed and presented in Fig. S14. It was found that the parameters V_average and A changed consistently in accordance with the magnitude of each memory window. This indicates that, under each memory window defined by the fixed pre-pulse, polarisation switching is induced in a consistent ratio relative to the window magnitude.³⁸ This explanation is validated by Fig. 3d, where the five P_r data curves—rescaled to a common range from 0 to 1—almost perfectly overlap. A detailed explanation and the complete results are provided in Fig. S15.

Fig. 3 Analysis of polarisation switching behaviour under fixed pulse width conditions based on the Lorentz function, and schematic diagrams of polarisation switching behaviour. (a) P_r data obtained from intermediate-state PUND measurements. (b) Normalised P_r data within the 0–1 range and the fitted curve based on the Lorentz function. (c) Lorentz distribution extracted by fitting the P_r data to the Lorentz function. (d) Normalised P_r data rescaled to a common range from 0 to 1. (e) Schematic diagram providing intuitive insight into polarisation switching behaviour.

Fig. 3e presents a simplified schematic illustrating the polarisation switching behaviour described above. Initially, when negative (blue) and positive (red) poling pulses are applied—capable of fully aligning the polarisation upward and downward, respectively. The resulting polarisation switching distributions induced by the applied poling pulses for positive and negative voltages are shown in the first panel. Subsequently, when a pulse of opposite polarity is applied, a portion of the initially formed hatched pattern in the first panel is switched, resulting in the formation of the respective hatched patterns as shown in the second panel. Assuming the pulse amplitude is V_average, the amount of switched polarisation is 50%, and the switching distribution exhibits the same shape trend as that of the fully oriented state. Next, the final panel illustrates the polarisation switching distribution after the application of a positive pulse with an amplitude of V_average. In the upper panel, where a pulse of the same polarity was previously applied, minimal or no additional switching occurs. However, in the lower panel, the newly applied pulse has an opposite polarity to the previous one, inducing additional polarisation switching. Since the pulse amplitude is assumed to be the V_average, 50% of the red hatched pattern is switched, forming the corresponding blue hatched pattern, as marked by the orange dotted circle. By applying this rule, the expected P_r loss caused by the Lorentz-tail can be precisely pre-empted in advance through intentional reverse switching.

As previously analysed, deliberately shaping the polarisation switching distribution—termed ‘Lorentz-tail engineering’—has theoretical potential to improve retention characteristics by preventing P_r loss induced by the Lorentz-tail. To verify this, measurements were performed using both the conventional programming method and the newly proposed two-step programming method. The measurement sequence is illustrated in Fig. 4a. Both the general and two-step programming methods follow the same sequence; the only distinction lies in the application of an additional pulse (fixed pre-pulse) immediately following the P (or N) pulse in the two-step method. Fig. 4b shows the polarisation switching distributions resulting from the P pulse applied in the general-method-based retention test. The upper and lower panels respectively correspond to the polarisation switching distributions that can be induced by positive and negative pulses. Similarly, Fig. 4c shows the polarisation switching distributions formed after the application of the N pulse using the same procedure. The polarisation switching distributions used here are based on the actual experimental data presented in Fig. S13. The retention characteristics of the general method were evaluated at a total of 31 retention times, ranging from 0 s, 20 ns, 50 ns, and so on, up to 100 s, and the results are presented in Fig. 4d. At an initial retention time of 0 s, the P_r values for PU and ND measurements were 17.31 and −16.75 µC cm⁻², respectively. These values gradually decreased over time, reaching 15.61 and –15.42 µC cm⁻² after 100 s. In other words, after 100 s, approximately 90.1% and 92.1% of the initial polarisation was retained for PU and ND, respectively. The retention trends in terms of percentage as a function of time are presented in Fig. S16a. In addition, by extrapolating the results, the expected P_r loss over 10 years was estimated to be approximately 3.1 and 2.1 µC cm⁻² for PU and ND, respectively. This corresponds to an average data loss of approximately 15.3% due to reverse switching over 10 years, and it is expected that long-term retention could deteriorate further if additional contributions from fatigue effects are considered.

Fig. 4 Comparison of polarisation switching distributions at zero retention time and evaluation of retention characteristics measured at room temperature. (a) Pulse sequence for retention measurements. In the 2-step programming method, an additional fixed pulse (indicated by the green dashed line) is applied. (b) and (c) Polarisation switching distributions immediately after the first triangular P pulse (upper panel) and D pulse (lower panel) in PU and ND measurements using the general method. (d) Results of the retention test obtained using the general method. (e) and (f) Engineered polarisation switching distributions immediately after the additional pulse −0.3 and +0.3 V_fix pulse in PU and ND measurements based on the 2-step programming method. (g) Results of the retention test obtained using the 2-step programming method.

Lorentz-tail engineering was performed by using a two-step programming method, in which the Lorentz-tail corresponding to the expected P_r loss over 10 years, predicted from the general method, is pre-switched in advance. To reverse-switch the polarisation losses observed in the PU and ND measurements—3.1 µC cm⁻² and 2.1 µC cm⁻², respectively—the pulse amplitude was set to ∓0.3 V_fix. Fig. 4e and f show the resulting polarisation switching distributions after applying the P (upper panel) and D (lower panel) pulses, each followed by an additional ∓0.3 V_fix pulse. The Lorentz-tail was effectively reverse-switched, and an equivalent amount of polarisation was formed to the opposite switching distribution. Notably, the newly formed forward Lorentz-tail of polarisation switching distribution, may serve as an effective reservoir to compensate for P_r loss during data retention. The retention characteristics with Lorentz-tail engineering applied via the 2-step programming method are presented in Fig. 4g. At an initial retention time of 0 s, the P_r values for PU and ND measurements were 14.22 and −14.73 µC cm⁻², respectively, which are lower by 3.1 and 2.1 µC cm⁻² compared to those obtained by the general method at 0 s. This result confirms that Lorentz-tail engineering was successfully performed, as the initial P_r reduction closely matches the previously predicted P_r loss expected over 10 years for the general method. Furthermore, it was observed that the P_r values exhibited minimal change over time. After 100 s retention, the P_r value for results of PU measurement slightly decreased by 0.06 µC cm⁻² to 14.16 µC cm⁻², while that for results of ND measurement slightly increased by 0.18 µC cm⁻² to −14.91 µC cm⁻². That is, the results of PU measurement showed approximately 99.6% data retention, whereas the results of ND measurement exhibited approximately 101.2%, exceeding full retention. This behaviour is attributed to the forward Lorentz-tail generated by the two-step pulse, which compensates for P_r loss during retention, as previously explained. The retention trends as a function of time are presented in Fig. S16b in terms of percentage retention. Furthermore, device-to-device uniformity was evaluated, confirming that Lorentz-tail engineering can be consistently implemented, as shown in Fig. S17.

To evaluate whether excellent 10-year data retention could be achieved without extrapolation through Lorentz-tail engineering based on the two-step programming method, an accelerated retention test was performed at 85 °C. At high temperatures, retention degradation is accelerated by thermal activation, and the retention time can be estimated by applying an Arrhenius-based acceleration model as follows:^39–41

where, t₁ is the expected retention time at room temperature, t₂ is the measured retention time at high temperature, T₁ is the room temperature (25 °C), T₂ is the measurement temperature (85 °C), E_a is the activation energy, and κ is the Boltzmann constant (∼8.617 × 10⁻⁵ eV K⁻¹). The activation energy E_a was set to 1.0 eV, based on previous studies.^42,43 According to the Arrhenius-based acceleration model, 10 years of data retention at room temperature can be equivalently represented by maintaining retention for 462 000 s at 85 °C. Therefore, retention tests were performed across 42 time points, ranging from 0 ns, 20 ns, 50 ns, and so on, up to 500 000 s (5 days, 18 hours, and 53 minutes, 20 seconds), and the results were converted to room-temperature equivalents based on the Arrhenius model, as shown in Fig. 5a. The results indicate that after 10.8 years of retention time, the P_r losses for the results of PU and ND measurement were 0.94 µC cm⁻² and 0.86 µC cm⁻², respectively. These correspond to data losses of approximately 6.70% and 6.27%, respectively, and the percentage data retention is presented in Fig. 5b. Furthermore, both PU and ND measurements exhibited retention characteristics exceeding 100% at 1.1 years, during which over 98.7% of the data was maintained. These results demonstrate that excellent long-term data retention—93.30% for PU and 93.73% for ND—was successfully achieved 10.8 years without extrapolation, while retention loss of less than 1% throughout the one-year evaluation period. This result highlights the effectiveness of Lorentz-tail engineering in achieving reliable memory performance. An additional consideration is that the two-step programming method for Lorentz-tail engineering inevitably requires an extra pulse, which may increase both write energy and write latency. In our proposed sequence, the write latency increases by approximately 20%. Given that ferroelectric switching inherently operates at nanosecond timescales and Lorentz-tail engineering involves only partial polarisation switching, the overhead can be readily absorbed in practical device operation. As for energy consumption, Fig. S18 shows that the write energy increases by only ∼3%, owing to the use of relatively low-amplitude and short-duration pulses for Lorentz-tail engineering. Therefore, despite this minor trade-off, Lorentz-tail engineering can be broadly applied to general-purpose ferroelectric applications, beyond specific structures or process-dependent characterisation, and offers a substantial improvement in retention characteristics.

Fig. 5 Accelerated retention test conducted at 85 °C based on an Arrhenius-based acceleration model to evaluate 10-year data retention. (a) Retained P_r values and (b) the corresponding data retention percentages, expressed as equivalent retention time to room temperature based on the Arrhenius acceleration model. The yellow dotted line indicates 90% data retention relative to the initial state, and the black dotted line represents the equivalent of 10 years of retention at room temperature, as determined by the Arrhenius-based acceleration model.

Conclusions

In this study, Lorentz-tail engineering was applied to improve the retention characteristics of ferroelectric HZO devices, and retention tests were conducted over a period corresponding to more than 10 years. The polarisation switching behaviour was analysed through intermediate-state PUND measurements, which verified that the Lorentz-tail can be precisely controlled. The two-step programming method was employed to pre-emptively reverse-switch the corresponding polarisation through Lorentz-tail engineering. The accelerated retention test demonstrated excellent data retention characteristics, maintaining over 93% without extrapolation for more than 10 years. Notably, an extremely stable retention was achieved with no data loss observed at 1.1 years. These findings indicate that Lorentz-tail engineering can significantly enhance the retention characteristics of ferroelectric HZO, suggesting its strong potential for application in the memory semiconductor industry.

Author contributions

W. K. and S. A. conceived the project. W. K. fabricated devices, conducted electrical measurements. W. K. contributed to the characteristic analysis. W. K. wrote the manuscript. All authors discussed and contributed to the refinement of the manuscript.

Conflicts of interest

There are no conflicts to declare.

Data availability

The datasets supporting this article are included within the article and the supplementary information (SI). Supplementary information is available. The Supplementary Information includes supporting data, figures, and analysis that complement the results discussed in the main manuscript. See DOI: https://doi.org/10.1039/d5mh01981h.

Additional data are available from the corresponding author upon reasonable request.

Acknowledgements

This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (RS-2025-24523758). This study was also supported by research funds from Tech University of Korea (2025).

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