Programmable ferroelectric rectifier for reliable and efficient neuromorphic crossbar array

Domain: biology
Published: 2026-03-17
Editorial outcome: major_revision

Abstract
The advancement of neuromorphic computing hardware requires energy-efficient operation, scalable device integration, and reliable conduction. These challenges can be effectively addressed by employing functional ferroelectric material as an active layer in memristors, leveraging their electrostatically modulated conduction for reliable switching. In this study, we present memristor devices that achieve a rectifying ratio exceeding 10⁶ and an off-state current below 10⁻¹² A based on epitaxial heterostructures consisting of Pt/Ba Bi FeOS (BBFO)/SrRuO /SrTiO stacks.
0.2 0.8 3 3 3
Substitution of 20% Ba in BiFeO₃ induces a coupled inteRraction between ferroelectric polarization and oxygen vacancy migration, which under pulsed bias governs vacancy transport and ensures reliable memristive synaptic behavior with near-zero nonlinearity and endurance beyond 10⁷ cycles. Owing to the demonstrated linear synaptic performance and strong memristive rectification, a selector-free crossbar array (CBA) was implemented. By mitigating key CBA challenges such as sneak currents and cell-to-cell variability while maintaining high synaptic performance, BBFO provides a robust mateArial platform for CBA-based neuromorphic systems.

Introduction
In the post-Von Neumann era, the development of neuromorphic computing hardware based on artificial neural networks (ANNs) has become a critical focus in advancing next-generation semiconductor technologies. While complementary metal oxide semiconductors (CMOS)-based platforms have played a pivotal role in accelerating artificial intelligence (AI) technologies [1-4], there is an increasing need to overcome their inherent limitations. These limitations primarily arise from high energy consumption and challenges in device scaling. To overcome these bottlenecks, developing more energy-efficient and scaling-compatible alternatives is essential.

Among the candidates to overcome these challe nges, memristors are promising structures that show low operation voltages and fast programming/erase speed. [5] Additionally, multilevel conductance tunability for storing muLlti-bit data has been demonstrated [6, 7], along with high integration density at the sub-2 nm scale, which is compatible with recent CMOS technologies [8-10] . Leveraging these proRperties, artificial synaptic elements in neuromorphic systems have been widely developed using various memristor types by alternating insulator layers such as halide perovskites [11-13], phase change materials [14, 15], or electrochemical oxide materials. [9] These materials have been characterized by their own ionic motions in the nonvolatile manner, showing multi-level resistive change in collaborative conduction mediums within regularly aligned lattice structures. [16-19]

However, this conduction mechanism is often hindered by reliability issues, such as random distribution of ions/vacancies [20], inconsistent device-to-device performance [21], and nonlinear programming behaviors [22] even considering an application of highly crystalline active layer. Furthermore, the ambipolar switching behavior observed in typical memristors renders crossbar array (CBA) fabrication—an ideal memory architecture in in-memory computing (IMC) systems [19]—vulnerable to sneak currents. This leakage undermines cell selectivity [20], leading to degraded CBA programming functionality and increased processing costs [21] due to the need to integrate a selector device with each memory cell. These challenges in recent memristors technologies impede the further advancement of CBA integration. Therefore, it is imperative to explore self-rectifying memristor designs with reliable conduction mechanisms for the practical application of CBAs in neuromorphic computational systems. [23-31]

In this article, we demonstrate the implementation oRf highly rectifying electrical performance with an on/off ratio surpassing 106 using a two-terminal memristor structure composed of Pt/Ba Bi FeO (BBFO)/SrRuO (SRO)/SrTiO (STO) epitaxial heterostructures. By incorporating 20 % Ba into the ferroelectric material BiFeO (BFO), we reveal a dynamic interplay between ferroelectricity and oxygen vacancy migration, enabling rectifying J–V performance and linear synaptic performance.

In the rectifying J–V performance, additional dipole stemming from the oxygen vacancy migration contributes to Schottky- and Ohmic-like conduction at the BBFO/SRO and BBFO/Pt interfaces, respectively. Of course, such alternation is not limited to rectifying memristors; however, in our case, the rectification primarily originates from the coupling between ferroelectric polarization and oxygen vacancy modulation. The homogeneous variation in the migration velocity of oxygen vacancies, governed by the ferroelectric electrostatic field, leads to an enhanced on/off current ratio in the J-V characteristics. Negative dipoles are induced in conjunction with the annihilation of oxygen vacancies by oxygen ion compensation from the SRO side, while positive dipoles arise along with the accumulation of oxygen vacancies near the Pt interface. Variations in oxygen vacancy density in BBFO modify the ferroelectric polarization. The resulting change enables effective modulation of the interface barrier profiles, supporting consistent device behavior and high performance. Beyond its self-rectifying capability, the device shows reliable artificial synaptic behavior, characterized by regular charge migration with near-zero nonlinearity. Furthermore, linearly programmable synaptic responses are achieved through ferroelectric modulation, which retards vacancy migration and prevents fast saturation depending on the voltage pulses. Benefiting from artificial synapses capable of enduring over 10⁷ repeated weight updates, we successfully implement a selector-free CBA consisting Eof 11 × 11 BBFO memristor cells. Our strategy enables the theoretical integration of up to 2.6 × 10⁹ cells within a densely integrated crossbar array architecture, maintaining a 10N% readout margin. These findings suggest that epitaxially grown BBFO films are promisin g memristive materials for ultra-dense neuromorphic computing architectures, enabling robust crossbar integration and reliable synaptic functionality within in-memory systems.

Results
Crossbar array device based on epitaxial ferroelectric materials

Figure 1 shows a comprehensive summary of the characteristics of the CBA based on an epitaxially grown BBFO ferroelectric film. As illustrated in Figure 1a, the CBA consists of a stacked structure of Pt word lines/BBFO/SRO bit lines on a (001) STO substrate. In this configuration, BBFO serves as the active layer of the memristor, while SRO acts as the bottom electrode. According to Supplementary figure 1, the cross-sectional energy dispersive spectroscopy (EDS) image, obtained during transmission electron microscopy (TEM) observation, clearly distinguishes the individual layer, revealing thicknesses of 100 nm and 40 nm for BBFO and SRO, respectively. The CBA comprises 121 memory cells, arranged in an 11 × 11 crossbar matrix, patterned within a 1cm × 1cm STO substrate (Figure 1b). Notably, our CBA demonstrates unidirectional current flow from the top electrode to bottom electrode, enabling selective reading target memristor cells while effectively blocking parasitic current. This asymmetric current flow is consistently observed in every memristor cells, ensuring excellent cell-to-cell uniformity. This device reproducibility can be attributed to sophisticatedly controlled defects across a substrate due to the epitaxial heterostructures.

High-angle annular dark field scanning transmissioRn electron microscopy (STEM-HAADF) imaging was performed to confirm the epitaxial growth of the configured layers (Figure 1c). This image reveals periodically aligned atomic arrangements in BBFO and SRO, with atomic distances of 0.596 nm and 0.618 nm at the A-site (Sr and Ba/Bi atoms) and B-site (Fe, Ru, and Ti atoms) in oxide perovskite structure (ABO ), respectively. Additionally, Supplementary figures 2a and 2b reveal clear atomic differentiation between BBFO and SRO, together with pronounced Ba substitution confirmedA by EDS mapping, indicating that the BBFO film grows uniformly from the interface. Furthermore, Supplementary figure 2c presents a globally measured STEM-HAADF image of the BBFO film, which confirms that the pristine polarization direction is downward. The fast Fourier transform (FFT) images in Supplementary figure 2d further verify the distinct crystallographic character. The electron backscattered diffraction (EBSD) image of Pt/BBFO/SRO device (as shown in Supplementary figure 3) further supports the uniformity of epitaxial BBFO film. Beyond TEM analyses, X-ray diffraction (XRD) measurements were conducted including theta-2theta, phi-scans, and reciprocal space mapping (RSM) (Supplementary figures 4a-4c). Based on these results, we conclude that the BFO and BBFO were grown epitaxially while simultaneously undergoing compressive strain along the in-plane direction. The BBFO possesses greater compressive strain, which is attributed to the larger atomic radius of the substituting Ba compared to Bi. (Supplementary figure 4d) The c-axis expanded structure maintains stability even under high concentrations of barium substitution, and this strained structure effectively suppresses oxygen diffusion, enabling stable resistive modulation. [32-34]

The rectification properties of an individual memristor unit are evident in its memristive J-V curve, which exhibits clockwise current modulation and a high rectifying ratio exceeding 105 between the low resistance state (LRS) and high resistance statSe (HRS) (Figure 1d). Thanks to the significantly suppressed leakage currents in BBFO indRuced by charge canceling provided from SRO oxygen ions, an ultra-low current level (< 10-12 A) in the HRS region is achieved, contributing to the high rectification ratio. Additionally, the interplay between ferroelectricity and oxygen vacancies dynamically modulates the energy barrier at BBFO/SRO and Pt/BBFO junctions. Notably, the velocity of oxygen vacancy migration can be controlled by ferroelectric polarization. Gradually facilitating oxygen vacancy migration, ferroelectricity induces velocity change of oxygen vacancies. ThAis dynamically changed charge migration induces linearly modulated synaptic performance, as illustrated in Figure 1e. In contrast to the typical LTP/LTD curve, represented by the red dotted line in Figure 1e, our linearly modulated curves originate from the coupling effect between oxygen vacancies and ferroelectricity. A detailed explanation will be provided in Figure 3d. As a result of this phenomenon, we obtain highly linear long-term potentiation/depression (LTP/LTD) performances across 39 memristor devices (Figure 1f). Using these reliable memristor devices, CBA fabrication is implemented. As shown in Figure 1g, a clear letter B pattern was obtained by applying a multiply–accumulated (MAC) operation at the S 3 column in the cell matrix. This obvious text image is primarily attributed to the uniform conductance modulation across all memristor cells, ensuring consistent conductance gap achieved by voltage pulses ranging from 10 to 100 (Figure 1h).

Self-rectifying electrical performances

The rectification mechanism of BBFO was investigated by analyzing its electrical performance. Using a unit memristor composed of Pt/BBFO/SRO shown in Figure 2a, we conducted multiple J-V measurements. Interestingly, the J-V characteristics (Figure 2b) exhibited robust endurance, maintaining a high rectifying ratio exceeding 105 for over 100 consecutive cycles. This high rectification cannot be achieved if the applied voltage sweep is either below or beyond ±5 V (Supplementary figure 5). For voltage ranges lower than ±5V (Supplementary figure 5a), the LRS current level is significantly reduced compared to that of Figure 2b. Furthermore, for voltage ranges exceeding ±5 V, the HRS current is more increased than that of Figure 2b, leading to a decrease in rectifying ratio (Supplementary figure 5b). These findings highlight that a precise voltage range of ±5 V is critical to achieving optimal seElf-rectification in BBFO memristors. Supplementary figure 6 shows that the BBFO device can exhibit filamentary-type behavior, but only after electroforming under a high positiveN bias of +28 V. In contrast, the BBFO memristor investigated in the present study operates in a forming-free manner within a voltage window below ±5 V. The comparison indicates that oxygen vacancies can participate in the BBFO device operation mechanism, yet their contribution is manifested as interface-modulated resistive switching rather than localized filament formation.

The endurance of ferroelectricity in BBFO was assessed through polarization endurance measurements, applying a voltage sequence from 0 V to 5 V, returning to 0 V, stepping to −5 V, and returning to 0 V (Supplementary Figure 7a). Even after 108 cycles, the remnant polarization (P) exhibited minimal degradation, demonstrating excellent ferroelectricity stability. The P r r during the polarization endurance test was changed from 55.7 μ Ccm-2, 47.7 μ Ccm-2 (Supplementary figures 7b-7c) to 41.8 μCcm-2 (Figure 2c) after measuring the most initial stage, 104 cycles, and 108 cycles, respectively. The STEM-HAADF image in the inset of Figure 2c further confirms the robust downward polarization of BBFO. We performed out-of-plane piezoelectric force microscopy (PFM) under an applied voltage of ± 10 V to investigate the polarization characteristics (Supplementary figures 8a-8d). A clear double-window pattern was observed in both phase and amplitude PFM images, confirming the strong piezoresponse by ±10 V. The opposite phase under reverse voltage polarity was distinctly differentiated, while protrusion in the phase signal was evident at the outer window region under +10 V application (Supplementary figure 8e).

Additionally, we conducted X-ray photoelectron spectroscopy (XPS) analysis to quantify the oxygen vacancy (V ) concentration in BBFO (Supplementary Sfigures 9a-9c). The results revealed O that oxygen vacancies in BBFO originate from Ba–O boRnding. The XPS peak observed at 531 eV, ascribed to Ba–O–Ba bonding, is related to the Ba 3d signal observed at 779.5 eV. [35] The Ba-O-V bond, characterized by a binding energy of 778.5 eV, indicates that oxygen vacancies can O be generated by Ba substitution within the lattice. These results suggest that barium alloying may serve as an effective method for generating oxygen vacancies, providing a more controllable approach to vacancy incorporation than that arising from unstable Bi bonding. Based on our XPS results, the oxygen vAacancy ratios in BFO and BBFO were calculated to be 6% and 8%, respectively (Supplementary figure 9b). These results suggest that Ba incorporation increases the concentration of mobile oxygen vacancies, potentially contributing to the resistive switching mechanism in the BBFO film. Based on the depth profile of the BBFO/SRO/STO heterostructures (Supplementary figure 9d), it can be further confirmed that Ba and Bi are uniformly alloyed in BBFO at a ratio of 1:4.

A band diagram illustrating electron flow under different applied voltages was constructed to investigate the electrical rectification mechanism. The bandgap and band alignment information used for band diagram illustration were obtained from ultraviolet photoelectron spectroscopy (UPS) and UV-visible spectroscopy (Supplementary figures 10a, 10b). The switching process follows 4 sequential steps, corresponding to the 4 processes denoted in Figure 2d. [5] 1) At the initial stage, a negative voltage (on Pt electrode) drives oxygen vacancies toward the Pt/BBFO interface, inducing the upward band bending. 2) When the negative voltage reaches close to -5 V, oxygen vacancies are migrated toward the BBFO/Pt interface, leading to sharp upward band bending. The accumulation of oxygen vacancies within BBFO may enhance the effectiveness of positive dipoles by coupling with the intrinsic dipoles. Such dipolar interactions could reinforce the ferroelectric response, potentially leading to an increased upward polEarization magnitude. This correlation where the migrated oxygen vacancies increase magnitude of upward polarization mainly contributes to the Ohmic-like conduction at BBNFO/Pt interface, despite the sharp upward energy barrier at Pt/BBFO. Supplementary figures 11a-11c also enforces the Ohmic conduction behavior at Pt/BBFO induced by the accumulation of oxygen vacancies, by showing opposite rectifying behavior when applying ground to the SRO electrode. The minimized hysteresis observed in Supplementary figure 11c, where SRO electrodes capable of supplying oxygen ions are used for both the top and bottom contacts, indirectly suggests that oxygen vacancy migration contributes to the device mechanism. Furthermore, the Schottky emission fitting in Supplementary figure 12 reveals that the effective barrier height differs between the LRS and HRS, indicating that resistance switching involves changes in oxygen vacancy distribution or polarization state. A significant barrier reduction occurs during the transition from HRS to LRS under negative voltage sweep. 3) Upon applying a positive voltage, oxygen vacancies begin to deplete at the BBFO/Pt interface. At this step, additional oxygen ions from the SRO electrode neutralize the charges of migrating oxygen vacancies, resulting in a depletion region near the BBFO/SRO interface. Even with sufficient electron supply from SRO, the interface barrier height of 0.77 eV between BBFO and SRO is large enough to block electron transport unless oxygen vacancies are present to significantly narrow the barrier width. 4) As the positive voltage increases to +5 V, the polarization switches downward, and the resulting vacancy-depleted region helps maintain stable rectification by suppressing leakage pathways. The enhanced oxygen ion flow further expands this depletion region within the BBFO layer, leading to a flatter band structure compared to earlier steps. The resulting charge deficiency within BBFO may also contribute to internal negative dipole formation. Consequently, the increased downward polarization facilitates Schottky conduction during J–V sweeping. XPS analysis in Supplementary figure 13 waEs conducted after removing the top electrodes of devices in both LRS and HRS states. In the LRS state, oxygen vacancy accumulation toward the top side (attributed to barium dopingN) was observed. Supplementary figure 14 presents the extracted activation energy required for device operation, showing an Arrhenius fitting result of approximately 0.4 eV. Supplementary figure 15 compares the effective oxygen-vacancy diffusion coefficients by extracting the activation energy in the same manner for the undoped BFO device. The results are 5×10−21 m2 s−1 for BFO and 9×10−22 m2 s−1 for BBFO at room temperature, indicating the robustness of BBFO, which does not permit higher leakage currents than BFO over the investigated temperature range. [32]

Supplementary figure 16 where the negative voltage of -5 V for the upward poling leads to higher on/off current ratio gives further persuasion that the asymmetrically high current magnitude in the negative voltage range. Supplementary Note 1 explains much detailed self-rectifying electrical behaviors induced by ferroelectricity-oxygen vacancy interaction.

Notably, the high rectification can be proven even under various voltage sweep velocity, voltage range, and ambient temperature (Supplementary figure 17). Additionally, the maintained rectification ratio and direction, even when using different TE materials including Ag, Ti, and Au further supports that the observed asymmetric electrical conduction cannot be explained by metal ion diffusion or Schottky diode effect, but rather to the intrinsic conduction mechanism of the BBFO material (Supplementary figure 18). Furthermore, deep-level transient spectroscopy (DLTS) measurements (Figure 2e, Supplementary figures 19a-19b, Supplementary Note 2) revealed trap density (𝑛 ) can be shown as 4.75 × 1017 cm-3 when assuming effective density of states in 𝑇 conduction band (𝑁 ) as 1019 cm-3. [36] Based on the DLTS parameters summarized in 𝑐 Supplementary Table 1, the results also revealed the preEsence of a shallow trap state located approximately 0.074 eV below the conduction bandP edge. This energy level is consistent with donor-like traps and is likely associated with oNxygen vacancies acting as shallow donors in the BBFO matrix. Figure 2f presents a schemati c energy band diagram reflecting the presence of these shallow trap states.

Electronic-structure calculations based on spin-polarized density functional theory (DFT) were carried out for Bi₁₋ₓBaₓFeO₃ with x = 0, ≈ 0.18, and ≈ 0.30, and the density of states (DOS) was quantitatively analyzed in an energy window around the Fermi level (Supplementary figure 20). In that near-𝐸 region, more than 90% of the states originate from Fe–O networks, whereas the 𝐹 Ba-projected contribution remains below ~1% and does not form a distinct Ba-centered peak inside the gap, indicating that Ba substitution stabilizes the A-site environment without introducing deep electronic traps and provides an electronically clean ferroelectric matrix within which shallow oxygen-vacancy donors identified by DLTS can modulate conduction. The effect of Ba substitution on rectification behavior was explored by measuring memristive J-V characteristics across various Ba concentrations, ranging from 5% to 30% (Supplementary figures 21a-21f). Notably, a high rectifying ratio exceeding 105 was only observed S when the Ba concentration was 20 %. Ba substitution induces a lattice expansion and optimiEzes the oxygen-vacancy concentration, thereby mitigating leakage currents and strengthening the diode-like rectifying behavior. [37] In compositions with Ba content deviating from 20 % , suppression of ferroelectric polarization or an increase in oxygen vacancies reduces the rec tifying ratio and can even lead to switchable rectifying characteristics. [38] The overall trend indicates that 20 % Ba substitution provides the most suitable composition for fabricating selector-free CBA. Contribution of oxygen vacancy migration to the switching mechanism was indirectly supported by current relaxation behavior under external bias (Supplementary figure 22) and varying ambient temperatures (Supplementary figure 23).

Such rectifying behavior was reduced with decreasing BBFO thickness, as shown in Supplementary figures 24a, 24b. This observation suggests that the enhanced diode effect originates from the expansion of ferroelectric domains, which contributes to improved rectification.

Rectifying electrical performances are consistently observed through memristive J-V measurements conducted on 25 devices comprehensively over 50 cycles, as shown in Supplementary figure 25. Considering the high device-to-device (D2D) and cycle-to-cycle (C2C) reproducibility observed across 25 memristors, where the rectifying ratio in all graphs exceeds 105, BBFO can be considered as a promising memristor material candidate for selector-free CBA integration.

Artificial synapse performances

The synaptic capability of the BBFO memristor was evaluated through an analog DC voltage sweep from -4.5 V to 4.5 V (Figure 3a). The data show that the LRS current level is significantly higher than the HRS level, with a gradual increase in conductance observed in both potentiation and depression regions. This consistent conductance modulation in the BBFO memristor is also evident in its long-term potentiation/depression (LTP/LTD) performance (Figure 3b). Notably, the BBFO memristor exhibits much better linearity compared to the BFO memristor in which the nonlinearity values for LTP/LTD are 5.1/5.0 for BFO memristor and 0.152/0.303 for BBFO memristor, respectively. The detailed method for nonlinearity fitting is explained in Supplementary Note 3. The linearity of the BBFO memristor arises from the homogeneous migration of oxygen vacancies, facilitated by the coupling between oxygen vacancy dynamics and ferroelectric conduction, which effectively prevents prematuEre saturation. The fact that the oxygen vacancy can be played as a conduction medium in this study can be evidenced by the change of oxygen concentration in BBFO in XPS depth pNrofiling (Supplementary figures 26a-26b). When applying LTP and LTD voltage pulses, the sharp and gradual decrease in oxygen concentration at Pt/BBFO interface and at throughout BBFO layer can be observed. These observations suggest that the memristive reset characteristics and LTD behavior are primarily governed by a reduction in mobile charge carriers associated with the decrease in oxygen vacancies. During the LTP measurements, the polarization direction remains unchanged due to the insufficient magnitude of the programming voltage, which is lower than the coercive voltage (V ) in the P-E curve of c Pt/BBFO/SRO structure (Supplementary figure 6b). However, the migration of oxygen vacancies locally affects the dipole arrangement within BBFO, influencing their velocity. Then, the conductance can be homogeneously controlled across the BBFO energy barrier along with the control of depletion width induced by oxygen vacancy migration (Supplementary figure 27a). Conversely, during the LTD measurements, oxygen vacancies migrate away from the Pt electrode. While the polarization direction remains unchanged still due to the small voltage magnitude lower than V , oxygen vacancies begin to be insufficient due to the additional providing of oxygen ions oc from SRO (Supplementary figure 27b). Contrary to the LTP mechanism, in the case of LTD, the linearity can be explained by the regularly annihilated mobile charges. Considering the results in Supplementary figure 28a showing that the nonlinear behaviors in LTP/LTD induced by the voltage magnitude for the BBFO poling is more degraded as high voltage pulses applied, the assumption that the dipole arrangements by the small voltage pulses within ± 2V homogeneously change the velocity of oxygen vacancy migration can be persuaded. Also, the fact that the current magnitude in the negative voltage range is higher than that in the positive voltage range considering Figure 2b well corresponds with the higher coEnductance value after negative poling voltage, as shown in Supplementary figure 28b.

Spike timing dependent plasticity (STDP) measurements reveal a pronounced expansion of the dynamic range for pulse time differences of less than a few milliseconds, as shown in Supplementary figure 29a. The pronounced dynamic range expansion indicates that oxygen vacancy migration induced by Ba alloying effectively captures the temporal correlations between distinct voltage pulses applied at both electrodes on a fast timescale. The mean decay times, fitted for LTD and LTP, are 12.21 ms and 11.49 ms, respectively, while the mean weight change rates are calculated as 148.2% and 145.8% for LTD and LTP, respectively. Paired-pulse facilitation (PPF) measurements (Supplementary figure 29b) indicate that reducing the interval between pulses applied to the device results in a nonlinear enhancement of the dynamic range, allowing sufficient modulation on a timescale of tens to hundreds of microseconds. The PPF ratio was calculated as [ 𝐴2−𝐴1]×100%. [39] Spike number dependent plasticity (SNDP) characteristics, shown in 𝐴1 Supplementary figure 30a, illustrate the effects of a 200 μs pulse train. Despite the limited migration time of oxygen vacancies, high linearity and symmetry are maintained. Spike width dependent plasticity (SWDP) and spike voltage dependent plasticity (SVDP) measurements, displayed in Figure 3c and Supplementary figure 30b, demonstrate robust conductance change behaviors, even when the input pulse waveform is varied. Increasing the duration of the input voltage segment affords more time for oxygen vacancies arising from Ba bonding to migrate, thereby inducing conductance modulation over a relatively broader dynamic range. The dynamic range remained comparable between pulse durations of 200 μs and 300 μs, while pulse durations of 400 μs and 500 μs appeared to lead to a noticeable increase. Furthermore, Supplementary figure 30c illustrates spike width–voltage-dependent plasticEity (SWVDP), where conductance modulation is examined as a function of pulse duratiPon and voltage magnitude, ranging from 1.3 V to 2.2 V. In the case of SWVDP applied byN 1.3 V voltage pulses, prolonged pulsing cannot sustain conductance modulation with showi ng a conductance saturation when the time duration of voltage pulse was 1.5 ms. In contrast, at 2.2 V, increasing the pulse duration up to 3 ms resulted in uniform resistance modulation. These results suggest that optimizing the timescale can mitigate saturation effects caused by a stronger electric field driving oxygen vacancy migration.

To determine whether oxygen vacancy migration drives conductance modulation in the BBFO synaptic device, ultrafast pulses were applied, and the corresponding device response was analyzed. As shown in Supplementary figures 31a, 31b, 100 uniform LTP/LTD pulses of 20 ns and 500 ns were applied. A read voltage of 0.1 V was applied between the writing pulses to track conductance states. The dynamic range was significantly smaller at sub-microsecond scales compared to hundreds of microseconds. These findings indicate that oxygen vacancies migrate insufficiently below a few microseconds, resulting in minimal resistance change. Considering the polarization switching response time of BBFO, the conductance modulation observed in our synaptic device suggests that oxygen vacancy migration is the dominant mechanism rather than multilevel polarization switching. This robust conduction mechanism by oxygen vacancy migration is also supported by long-term retention measurement, which shows stable conductance level by the time above 5000 seconds (Supplementary figure 32).

As illustrated in Figure 3d, the linearity of BBFO and BFO memristor can be compared based on ferroelectric domain schematics as a function of the number of applied voltage pulses. In the case of BFO memristor, oxygen vacancies are dramatically accumulated due to the strong electrostatic field from pristine ferroelectricity. In contrast, BBSFO contains an optimal density of oxygen vacancies in which oxygen vacancy ratio amoRng possible oxygen sites is 7.82 %. This oxygen vacancy ratio isn’t high enough to impede ferroelectricity, so the oxygen vacancy can be migrated in the opposite way with maintaining ferroelectricity conditions. At the initial step of voltage pulse application, the oxygen vacancies may be diffused toward the Pt/BBFO interface. As voltage pulses are continuously applied, the initial slow migration of oxygen vacancies can be further accelerated by the electric fields arising from surrounding local dipoles. This process mitigates the initial Asaturation of vacancy migration, thereby contributing to the linear programming of artificial synapse. The correlation between oxygen vacancy dynamics and ferroelectricity governs both the rectifying J–V characteristics and linear synaptic programming. This interplay is bidirectional, with oxygen vacancy accumulation affecting ferroelectric polarization and, conversely, dipole reorientation influencing vacancy migration. Together, these coupled mechanisms represent key considerations in the design of selector-free CBA materials for reliable neuromorphic hardware.

Relationship between oxygen vacancy migration and ferroelectricity

The influence of oxygen vacancies on ferroelectric behavior has been extensively studied. [40-44] In BBFO, Ba substitution induces oxygen vacancies, but vacancy concentration alone is insufficient for linear resistance modulation. We propose that BBFO's intrinsic ferroelectricity facilitates vacancy migration via internal dipolar fields, enabling the observed linear synaptic behavior. To examine this, we assumed that (1) dipole alignment responds dynamically to vacancy migration, and (2) mobile oxygen vacancies interact electrostatically with surrounding local dipoles, modulating the migration barrier. As illustrated in Supplementary figures 2a-2c, Bi and Ba share the A-site position, supporting the view that vacancy formation and dipole generation are complementary. We examined their interplay by analyzing (E1) vacancy migration relative to dipole displacement, and (2) polarization response with respect to the degree of vacancy migration. The results support a second-order mechanism in BNBFO, in which polarization and oxygen vacancy migration act as coupled internal variables, and device operation arises from their interdependent dynamics rather than from a single dominant process. [45-47]. In contrast, single-process-dominated behavior, as commonly observed in interface-type and filamentary-type switching, leads to progressive insensitivity and saturation of conductance modulation due to the accumulation of responses under repeated stimuli. This coupled evolution of ferroelectric polarization and oxygen vacancy migration gives rise to the second-order switching mechanism, as depicted in Supplementary figure 33.

First, the dipole response under varying degrees of potentiation and depression was assessed using positive-up-negative-down (PUND) measurements at 4 kHz triangular 8 V pulses. As shown in Supplementary figures 34a, 34b, the polarization response decreased after LTP and recovered during LTD. This behavior can be attributed to two effects: (1) vacancy migration toward the Pt electrode reduces electric field strength, weakening dipole switching response; and (2) redistribution toward the SRO side allows oxygen compensation, restoring polarization response. This interpretation is supported by the J–V characteristics, while the minimal variation in leakage current during U and D pulses confirms that the transient current changes originate from reversible dipole activity governed by oxygen vacancy distribution, rather than increased leakage.

Second, we investigated the influence of local dipole states on vacancy migration using two pulse schemes: short triangular pulses (<5 µs) for dipole alignment and longer rectangular pulses (~200 µs) for vacancy modulation. Four poling-response conditions were tested following vacancy initialization. As shown in Supplementary figure 35, strongSer negative poling (−5 V to −7 V) facilitated vacancy migration and increased conductRance, while positive poling suppressed modulation. Devices subjected to stronger prior negative poling exhibited lower resistance under the same +5 V bias, indicating that residual dipolar fields persist and continue to influence vacancy transport. These findings underscore the role of dipole realignment in regulating vacancy dynamics during synaptic operation.

Finally, we examined dRynamic interactions between migrating oxygen vacancies and adjacent local dipoles during synaptic programming. In LTP and LTD operations involving repeated unipolar pulses, both vacancy migration and gradual dipole alignment are expected. To investigate these effects, we similarly applied separate dipole-control and vacancy-control pulses under incrementally increasing poling voltages (+5 V to +9 V). Each time the dipole state was changed, we performed five LTD learning steps, followed by a single LTP pulse, and observed the resulting resistance changes. Supplementary figure 36 shows the voltage schemes and LTP current responses. The current baseline during LTP pulsing decreased progressively with gradually increasing dipole alignment. In contrast, when strong poling was applied first and then reduced in same direction, resistance changes were minimal. These results imply that the dynamically changing dipole environment contributes to the uniform migration of oxygen vacancies by controlling the energy barrier for vacancy migration, which in turn aids linear resistance modulation. This coupled mechanism between dipoles and vacancies may be critical for reliable synaptic programming with repeated unidirectional pulses (see Supplementary figures 37-39). A detailed investigation of the measurement methodology and the underlying mechanisms is provided in Supplementary Notes 4 and 5.

From our measurements, two key conclusions can be drawnS: (1) Ba-induced oxygen vacancies affect dipole alignment, and (2) vacancy migration is mRodulated by the extent of dipole ordering. Supplementary figure 40 illustrates this coupling during synaptic operation. Under a ferroelectric polarization environment, the velocity of oxygen vacancies varies with the number of applied voltage pulses. Although the pulse amplitude remains below V , repeated subthreshold pulses c (±2 V) can gradually tilt the dipole configuration, which in turn promotes the otherwise delayed migration of oxygen vacancies. During programming, vacancies dynamically interact with local dipoles near Ba/Bi caAtions, modifying the polarization state. While the vacancy-control pulses alone are insufficient to induce complete polarization switching, the progressive dipole alignment compensates for the delayed vacancy migration, thereby preventing early saturation. These dynamics differ slightly between LTP and LTD processes. In LTP, migration is initially hindered by oppositely oriented dipoles but becomes facilitated as polarization aligns and the internal field increases. In LTD, vacancy annihilation near the SRO interface and dipole recovery suppresses initial migration and reduces the risk of saturation over successive cycles. Such dynamic coupling prevents premature saturation and enables linear modulation of resistance, indicating the presence of a second-order feedback mechanism between dipole orientation and vacancy distribution.

Endurable synaptic weight update

The BBFO memristor demonstrates robust synaptic performance across various input pulse waveforms, ensuring stable characteristics over extended cycling. This durability is crucial for achieving durable resistance modulation in forming free memristive synapse devices at the chip scale. Cycle endurance measurements, shown in Figure 4a, were conducted by applying 400 potentiation and 400 depression pulses, each with a voltage pulse duration of 200 μs. Even after 10 million pulses, the conductance modulation remained stableS without any electrical degradation across all cycling (Supplementary figure 41). These endRurable performances may be attributed to non-scattering charge modulation due to epitaxially grown-BBFO and to the reproducible interactive effect between ferroelectricity and oxygen vacancies.

The robustness of the BBFO synaptic device under high-temperature conditions is presented in Supplementary figures 42a, 42b. The potential influence of heat generation during device operation on reliability was examined through cycle endurance measurements at 473 K, with a voltage time duration of 200 μs and 400 voltage pulses applied for LTP/LTD measurements. These results confirm stable performance even after 10 million pulsesS. However, at elevated temperatures, conductance modulation became more nonlinear andR asymmetric, possibly due to enhanced thermal activation of oxygen vacancy migration leading to earlier saturation (Supplementary figure 42c). These findings further support oxygIen vacancy migration as the primary mechanism governing resistance modulation in BBFO synaptic devices.

The quantitative comparisonI of rectification and state-update endurance for the BBFO memristor, benchmarked against artificial synaptic devices based on organic compounds, halide perovskites, 2D materials, binary oxides, and complex oxides, is graphically illustrated in Figure 4b. This analysis is derived from the broader comparative study presented in Supplementary Table 2, which compiles performance metrics from previous studies. [12, 15, 39, 48-63] Expected performance metrics for BBFO synaptic devices in CBAs designed for deep learning accelerators are depicted in Figure 4c. In BFO, ferroelectric polarization acts as the major conduction medium, making conduction modulation difficult to be linear. As a result, the training accuracy is significantly lower than the numerical computation results. This discrepancy suggests difficulties in precisely regulating feedback mechanisms needed to compensate for nonlinear and asymmetric resistance modulation, including pulse train characteristics (e.g., pulse count and voltage magnitude). In contrast, simulations of a MAC accelerator using BBFO devices result in closer alignment with numerical outcomes due to more consistent and linear conductance modulation. These findings suggest that BBFO thin films can support effective learning when integrated into chip-scale neuromorphic hardware. Simulations of CNN-based computations further indicate broad applicability in neural networks requiring MAC operations. Neural network architectures and learning outcomes are illustrated in Supplementary figures 43–45 and Supplementary Table 3.

Implementation of selector-free crossbar arrays using Bi SBa FeO
0.8 0.2 3

We demonstrated the feasibility of implementing high-rectification synaptic devices using epitaxially grown ferroelectric BBFO single thNin films. A CBA system aligned with the device structure was fabricated to verify the pr actical applicability of this approach. A schematic representation of the 11 × 11 CBA deLveloped in this study is provided in Figure 5a, highlighting its structural organization and kIey functional components. The width of each line pattern was designed to match the 50 μm × 50 μm square area of the characterized device. If each cell in the CBA maintains rectification and linear conductance modulation, it would be possible to develop a neuromorphic computing system that is robust against external interference. For bit-line integration, we etched an SRO (001) thin film to form the bitlines while carefully controlling the (001) surface to ensure that BBFO could still grow epitaxially following the orientation of SRO. Elemental distribution and crystalline quality of BBFO films grown on etched SRO bitlines are examined using EDS and EBSD, as shown in Supplementary figures 46a, 46b. The EDS elemental mapping clearly distinguishes the SRO line pattern, confirming its distinct separation. Additionally, the EBSD analysis indicates that BBFO continues to grow as an epitaxial single-phase thin film, maintaining its (001) orientation, guided by the line patterned SRO seed and surrounding STO (001) substrate. Supplementary figures 47a-47f provides the etched SRO information including etching images and J-V curves to show electrical isolation from another adjacent SRO line. This huge resistance between the two adjacent SRO electrodes (3.3 GΩ) alludes that the SRO bitline design prevents unintended conductive paths toward neighboring cells. Despite ex-situ deposition, BBFO maintains epitaxial growth even after etching the SRO into a line pattern, as demonstrated in Supplementary figure 48a. The OM images after depositing BBFO at overall substrate (Supplementary figures 48b-48d) further validate the structural integrity of SRO bitlines and BBFO film.

As shown in Figure 5b, we patterned the top wordline Pt electrodes to construct an 11 × 11 CBA. Elemental differentiation of the CBA, confirmed by EDS mapping, is globally presented in Supplementary figure 49. Using this CBA structure, we can successfully suppress the unwanted parasitic current path during the potentiation and depression process (Figure 5c) within a full substrate. Thanks to these self-rectifying performances using the uniform BBFO film, LTP and LTD characteristics acAross all 121 cells in the 11 × 11 CBA demonstrate highly linear conductance modulation with minimal variation (Figure 5d). Supplementary figure 50 quantitatively presents statistical information on the LTP/LTD characteristics of each cell within the 11 × 11 CBA, including the 95% confidence intervals and deviations. J-V characteristics of individual cells in the CBA are also shown in Figure 5e and Supplementary figure 51, highlighting D2D uniformity and operational stability. The results reveal a uniform memory window exceeding two orders of magnitude and a rectification ratio exceeding six orders of magnitude across the entire array. The use of non-identical LTP/LTD voltages originates from differences in the effective electric field required for comparable resistance modulation, arising from the asymmetric device configuration, including work-function mismatch, remanent polarization, and the resulting built-in electric field. Consequently, different voltage amplitudes are required for LTP and LTD. Consistent with this mechanism, although the dot-patterned cells in Figure 1f require different absolute voltages, the same positive-to-negative voltage ratio produces comparable synaptic behavior, confirming the validity of the proposed device mechanism in the CBA architecture. The high rectification ensures reliable readout during synaptic weight modulation and retention, reinforcing the stability of the CBA. Additionally, the uniformity of individual cells suggests the potential for scaling the array to larger sizes.

A comparative analysis of read margin performance between CBAs composed of BFO and BBFO is shown in Figure 5f, demonstrating the advantages of BBFO in maintaining stable and distinguishable conductance states. Within the circuit’s error tolerance range, the BBFO CBA exhibits a size scalability over 15,000 times greater than the conventional BFO-based array, making it highly promising for integrated neuromorphic systems. This high read margin is attributed that Ba alloying enables optimizing CBA integration, including leakage current suppression, controllable vacancy migration under strong ferroelectricity conditions. The influence of the rectification ratio of self-rectifying memristors on CBA operation and the calculation method are detailed in Supplementary Note 6. Our BBFO memristor allows a maximum array size accommodating 260G cells under tEhe 10% readout margin criterion. As shown in Figure 5g, experimental validation confirms the feasibility of text programming in the BBFO CBA, demonstrating that stored states cNan be erased and retrained with different images. The high rectification enables that voltage application during array-level measurements did not significantly affect device operation. The applied voltage selectively potentiated target cells, enabling the learning of text and image patterns. Additionally, the array could be successfully reset by applying a depression pulse sequence equal in number to the previously applied potentiation pulses due to the linear and symmetric potentiation and depression characteristics. The ability to train on various types of data aligns with the earlier DNN and CNN simulation results, which is likely due to the high rectification and the capability for linear, symmetric resistance modulation.

Operational principles of the CBA, emphasizing the advantages of selectively programming individual cells, are detailed in Supplementary figures 52a-52e. In circuitry perspectives, sneak paths correspond to leakage currents through neighboring cells, forming an equivalent circuit model. Since at least one reverse-biased BBFO memristor exists within each sneak path, the high rectification of BBFO effectively suppresses leakage currents, ensuring that only the intended data is programmed into the array.

Methods
Fabrication of Bi Ba FeO ceramic targets
1-x x 3
Pure BiFeO and Ba doped BiFeO ceramic targets were prepared using conventional solid-state 3 3 reaction method. Bi Ba FeO (x = 0, 0.05, 0.1, 0.15, 0.2, 0.25, 0.3) weighed following 1-x x 3 stoichiometric amounts of Bi O (99.99%, High Purity Chemicals), BaCO (99.95%, Alfa Aesar), 2 3 3 and Fe O (99.9%, High Purity Chemicals) and thoroughly mixed using ball milling for 24 hours. 2 3 The mixed powders were subsequently calcined at 800 °C foSr 5 hours and hand ground with a E mortar and pestle. The synthesized powders were pressed into pellets and subsequently sintered. R The temperature was maintained at 700°C for 30 minutes, then gradually increased to 800°C over P 30 minutes, followed by sintering at 800°C for 12 hours.

Growth of epitaxial Bi Ba FeO /SrLRuO thin films
1-x x 3 3
The epitaxial Bi Ba FeO /STrRuO (x = 0, 0.05, 0.1, 0.15, 0.2) thin films were deposited on (001) 1-x x 3 3 SrTiO single crystal substrate (Crystal, Gmbh) through pulsed laser deposition (PLD) using KrF 3 A 248 nm excimer laser (COHERENT, COMPEX PRO 205F). The film thickness of BFO and SRO were 100 and 40 nm, respectively. Under an oxygen partial pressure of 100 mTorr, the SRO thin film was first deposited with a laser with 3 Hz repetition, 2.0 Jcm−2 energy density at 680 °C, whereas the pure BiFeO and Ba doped BiFeO thin films were deposited under an oxygen partial 3 3 pressure of 200 mTorr, with a laser of 10 Hz repetition, 2.0 Jcm−2 energy density at 670 °C. The target-to-substrate distance of 50 mm was employed for all layers. The deposited film was cooled at a rate of 30°C per minute under an oxygen pressure of 50 Torr. The Pt TEs were deposited using E-beam evaporator (SRN-200, SORONA). The size of Pt TEs was 50×50 𝜇𝑚2, and these TE patterns could be realized using chromium shadow mask. For CBA fabrication, we patterned and wet-etched the SRO thin film into bit lines using a standard lithography process. For selective etching of the SRO layer, an aqueous 0.4 mol/L sodium metaperiodate (NaIO₄) solution was prepared and sonicated for 30 min to ensure complete dissolution. The SRO film patterned with photoresist was then immersed in the solution for 30 s to remove the exposed SRO. After stripping the photoresist, the BFO layer was subsequently deposited ex-situ under the conditions described above. followed by the patterning of the top cross-line electrodes using the lift-off process.

Material Characterizations

The crystal structure of BBFO/SRO film was investigated by theta-2theta XRD (Bruker, D8 Discover), XRC, phi-scan, and RSM (PANalytNical, Xpert Pro) with Cu K𝛼 radiation (𝜆 = 1.5418 Å). XRD PDF card numbers for BBFO, SR O, and STO were 04-019-6114, 01-072-5834, and 00-005-0634, respectively. OM image ofL the device was obtained from an optical microscopy (Leica Microsystems CNS GmbH, DMI4000 M LED). Out-of-plane Piezoresponse force microscope (PFM) measurements were performed using a Bruker Dimension Icon. The Pt/Ir coated tip (SCM- PIT V2) with a spring constant (k) of ∼3 N m−1 and a resonant frequency of ∼75 kHz was employed. In contact mode, an AC voltage at 25 kHz was applied between the conductive probe and grounded sample. This frequency is well below the resonance frequency of the cantilever and contact resonance of the tip–sample system to avoid artificial amplification of the signal. Cross-sectional STEM images in low magnitude and HAADF version were obtained (Themis Z, ThermoFisher) after focusing ion beam (FIB) sampling (SMI3050Sem SII Nanotechnology). UPS measurements were obtained using a ThermoFisher Scientific NEXSA G2 XPS system calibrated with Au standards. X-ray photoelectron spectroscopy (Thermo Scientific, ESCALAB 250Xi) was utilized to verify the Co oxidation state and depth profile. All spectral peaks were calibrated using the carbon 1s peak as a reference.

Electrical Characterizations

Consecutive memristive J–V curves, analog sweep curves, and cell-to-cell variability were obtained using a 4-tip probe station (MSTECH, Agilent 4156C). DC voltage sweeps were applied to the top electrode while the bottom electrode was grounded. TheS J–V sweeps were performed in S a dual-sweep manner, from 0 to -5 V and from 0 to 5 V, with a sweep velocity of 0.2 Vs⁻¹. The E R SRO electrode was kept at ground potential during the measurements. Analog sweeps were P conducted by applying 15 consecutive sweeps fNrom 0 to -4.5 V, followed by 15 sweeps from 0 to I 4.5 V at the same sweep velocity. The P-E c urve and the polarization endurance was characterized E by a 4-tip probe station (Keithley, L4200A-SCS) equipped with a polarization measurement C program (RADIANT TechnologIies. InC., Precision LC Ferroelectric Tester). Synaptic electrical T characteristics, including Rmulti-level retention and endurance, were measured using a 4-tip probe A station (Keithley 4200A Semiconductor Analyzer and Keithley 2636A). The probe tip diameter used for all electrical measurements was 30 μm. DLTS measurement was conducted using a Keithley 4200A-SCS equipped with a capacitance measurement unit (CMU) under conditions employed by an oscillation level of 25 mV and a frequency of 10 kHz.

Computational details

All the spin-polarized density functional theory (DFT) calculations were performed using the Vienna Ab initio Simulation Package (VASP) program with the projector augmented wave method for the core region and a plane-wave kinetic energy cutoff of 400 eV. The generalized gradient approximation (GGA), in the form of Perdew-Burke-Ernzerhof (PBE), was used for the exchange-correlation potentials. A 4x4x1 Gamma-centered Monkhorst-pack sampled k-point grid was employed to sample the reciprocal space. The atoms are free to move in all directions until the convergence of energy and residual atomic force on each atom was less than 1x10-4 eV and 0.01 eV/Å , respectively.

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "This manuscript by Kim et al. presents a comprehensive and compelling study on a Ba-doped BiFeO3 (BBFO) ferroelectric memristor for neuromorphic crossbar arrays (CBAs). The work is impressive in its scope, spanning from epitaxial material growth and detailed physical characterization to the demonstration of reliable synaptic plasticity and the successful implementation of a functional, selector-free 11×11 crossbar array. The central claim of a synergistic interaction between ferroelectric polarization and oxygen vacancy migration to achieve high rectification (>105) and linear synaptic update is significant and well-supported by a substantial dataset. The potential impact on neuromorphic hardware is high, as it directly addresses critical challenges of sneak currents and device variability. However, the manuscript, in its current form, requires major revisions to improve clarity, strengthen the mechanistic evidence, and provide a more balanced discussion before it can be considered for publication. The following points should be addressed.\n1. The interplay between ferroelectricity and oxygen vacancies is the core of this work, but its description is often convoluted and sometimes appears self-contradictory. A more lucid, step-by-step model is needed. For instance, the roles of \"dipoles\" from vacancies versus ferroelectric polarization should be explicitly differentiated and their coupling mechanism (electrostatic, strain, etc.) more clearly hypothesized.\n2. The manuscript initially suggests a homogeneous mechanism but later (Supplementary Fig. 5c) mentions \"typical filamentary resistive switching behavior after electroforming.\" This creates confusion. The authors must clarify the nature of the conductive path. Is it a localized filament or a uniform interface-modulated barrier? Additional analysis (e.g., area-dependent measurements) or a revised discussion reconciling these observations is necessary.\n3. While the linearity of potentiation/depression is highlighted and nonlinearity factors are provided, the methodology for this fitting is buried in a supplementary note. The key parameters (e.g., the number of devices used for the 0.152/0.303 nonlinearity values in Fig. 3b, the fitting model) should be clearly stated in the main text or figure caption to allow for a critical assessment of this crucial claim.\n4. The excellent uniformity across the 11×11 array is a key result. However, the data in Figures 1f, 1h, and 5d would be significantly strengthened by providing standard deviations or confidence intervals for the conductance states and LTP/LTD curves, rather than just showing overlapping traces. A quantitative measure of device-to-device (D2D) and cycle-to-cycle (C2C) variability for the entire array is essential.\n5. The rationale for using different voltage amplitudes for LTP/LTD (e.g., -1.6 V/+1.0 V in Fig. 1f, -2.4 V/+1.5 V in Fig. 5d) and for the CBA operation is not explained. The authors should justify these choices, especially in relation to the coercive voltage and the need for asymmetric programming, and discuss how this impacts energy consumption and circuit design.\n6. The concept of a second-order mechanism coupling polarization and vacancies is intriguing but underdeveloped. The description in the section \"Relationship between oxygen vacancy migration and ferroelectricity\" is dense and difficult to follow. A clearer schematic or a more pedagogical explanation of this feedback loop and how it precisely enables linear updates would greatly enhance the manuscript's impact.\n7. Figure 4b is a good start, but the comparison with other technologies would be more informative if key metrics like switching speed, energy consumption per spike, and retention were also included in a table (perhaps in Supplementary Information). This would provide a more holistic view of where BBFO stands in the competitive landscape.\n8. The manuscript focuses on the successes but lacks a critical discussion of limitations. For example, the use of an epitaxial SrTiO3 substrate and SrRuO3 bottom electrode poses significant challenges for large-scale, back-end-of-line (BEOL) integration with silicon CMOS. The high forming voltage (>25 V) is also a practical concern. A paragraph acknowledging these challenges and outlining a path forward is necessary.\n9. Several figures (e.g., Fig. 2d, 3d) are overly complex and could be simplified. The quality of some schematic illustrations (e.g., Fig. 5c) should be improved for professional presentation. The manuscript would benefit from a thorough proofreading to correct minor grammatical errors and improve sentence flow.\n10. The data in Supplementary Fig. 21 convincingly shows that 20% Ba is optimal. The manuscript should provide a deeper physical explanation for why this specific concentration yields the best performance, linking it to the optimal balance between oxygen vacancy concentration and the stability of ferroelectricity.\n11. The abstract could be slightly refined to more immediately state the key achievement (e.g., \"We demonstrate a memristor... that achieves a rectifying ratio >106 and linear synaptic updates via a coupled ferroelectricity-vacancy mechanism\").\n12. In the Methods section, more details on the patterning and etching processes for the SRO bitlines and Pt wordlines would be beneficial for reproducibility.\n13. Please ensure all acronyms are defined upon first use (e.g., MAC in Fig. 1g should be spelled out).\n14. The manuscript lacks comprehensive review on recent works. Please refer:\nhttps://www.nature.com/articles/s41467-025-60970-4\nhttps://www.nature.com/articles/s41928-024-01318-6\nhttps://pubs.acs.org/doi/10.1021/acs.nanolett.4c04385\nhttps://pubs.aip.org/apl/article/125/13/133501/3314036/Self-rectifying-memristors-with-high-rectification\nhttps://link.aps.org/doi/10.1103/PhysRevApplied.22.064003", "reviewer_2": "This is an interesting work with excellent performances of the self-rectifying ferroelectric tunnel junction by cleverly combining conductance modulation by both polarization of ferroelectrics and oxygen vacancies. The authors report extremely reliable operation of the synaptic device even beyond 10 M cycles with a rectifying ratio higher than 106. The reviewer believes that this work deserves publication in Nature Communications, but it requires modifications as shown below.\n1. The authors used current instead of current density in several current-voltage curves. However, using current density should be better for readers. Especially, for the case of ferroelectric tunnel junctions, low on current density is a critical technical issue. So, please use current density and add some discussion on the current density observed in this study.\n2. In figure 1e and related text, the authors argue that they could achieve highly linear potentiation/depression by combining the polarization and oxygen vacancies. However, the reason for this mechanism is not clear for the reviewer. From the reviewer’s knowledge, for both cases the non-linear potentiation/depression like red dashed curve in figure 1e is frequently observed. Please add more details with adequate references for the suggested mechanism.\n3. The absolute dynamics range is not clear from figure 1f. Add also raw conductance values in figure 1f. The authors can simple use the right y-axis for showing the raw conductance values.", "reviewer_3": "I co-reviewed this manuscript with one of the reviewers who provided the listed reports. This is part of the Nature Communications initiative to facilitate training in peer review and to provide appropriate recognition for Early Career Researchers who co-review manuscripts.", "reviewer_4": "The manuscript reports the fabrication of memristors based on20 % Ba into BFO within a Pt/BBFO/SRO structure. The performance of the device is governed by the interplayed between ferroelectric polarization and oxygen vacancies inside the materials. In addition, authors also realized the 11 × 11 array to demonstrate the learning capability. However, the current manuscript still contains several issues that require further clarification, additional experimental evidences, and a strengthened discussion.\n1. In this work, the authors fabricate the device structure of Pt/Ba0.2Bi0.8FeO3 (BBFO)/SrRuO3 (SRO)/SrTiO3 (STO) epitaxial heterostructures. As the interface between Ba0.2Bi0.8FeO3 (BBFO) and SrRuO3 (SRO) plays important role in the performance, I wonder whether it is possible to present the transmission electron microcopy image at the interface.\n2. The authors claim that \"rectifying I–V performance stems from oxygen vacancy migration contributes to Schottky- and Ohmic-like conduction\". It is widely accepted that the memristor behavior is also attributed from conductive filaments. Please provide more evidence and discussion on the origin of rectifying I–V performance.\n3. In reference Phys. Rev. Lett. 98, 146403 (2007), the authors present the study of oxygen vacancies diffusion coefficient. I suggest the authors to further quantitively investigate the movement of these oxygen vacancies based on the similar methods.\n4. By incorporating 20 % Ba into BFO within a Pt/BBFO/SRO structure, the device presents promising memristive behavior, I suggest the authors to further show the density function theory result on the interaction of doped Ba in BFO layers.\n5. The authors claims the 11 × 11 array exhibited negligible D2D variability, please provide more results and discussion on the uniformity."}, "author_response": "We appreciated all reviewers for dedicating their time and providing constructive comments on our manuscript, and we revised the main text and Supplementary Information accordingly. In the point-by-point responses below, the original reviewer comments are shown in black, and our replies are indicated in blue. Revisions to the main text and Supplementary Information are highlighted in yellow. Excerpts taken from the manuscript and Supplementary Information are presented using the original font size and are enclosed in boxes to minimize any inconvenience during reading.\nOne by one Response to Reviewers’ comments:\nReviewer #1 (Remarks to the Author):\nThis manuscript by Kim et al presents a comprehensive and compelling study on a Ba-doped BiFeO3 (BBFO) ferroelectric memristor for neuromorphic crossbar arrays (CBAs). The work is impressive in its scope, spanning from epitaxial material growth and detailed physical characterization to the demonstration of reliable synaptic plasticity and the successful implementation of a functional, selector-free 11 × 11 crossbar array. The central claim of a synergistic interaction between ferroelectric polarization and oxygen vacancy migration to achieve high rectification (>105) and linear synaptic update is significant and well-supported by a substantial dataset. The potential impact on neuromorphic hardware is high, as it directly addresses critical challenges of sneak currents and device variability. However, the manuscript, in its current form, requires major revisions to improve clarity, strengthen the mechanistic evidence, and provide a more balanced discussion before it can be considered for publication. The following points should be addressed.\nResponse: We appreciated the referee’s positive assessment of the significance of our work. Point-by-point responses to the individual comments are provided below.\n1. The interplay between ferroelectricity and oxygen vacancies is the core of this work, but its description is often convoluted and sometimes appears self-contradictory. A more lucid, step-by-step model is needed. For instance, the roles of \"dipoles\" from vacancies versus ferroelectric polarization should be explicitly differentiated and their coupling mechanism (electrostatic, strain, etc.) more clearly hypothesized.\nAnswer: Thank you for your valuable comment. As shown in Figure 2d, the role of oxygen vacancies as polarization dipoles is clearly supported. We did not explicitly distinguish between oxygen vacancy-induced dipoles and intrinsic ferroelectric polarization because these two mechanisms are strongly coupled. Without the electrostatic interaction from the ferroelectric layer, the oxygen vacancy dipoles would merely act as leakage paths. Therefore, the two sources of polarization cannot be separated in their physical manifestation. However, their coupling mechanisms should indeed be treated at distinct. In terms of electrostatic modulation, this mechanism is explained in Figure 2d. However, for the strain effect, we have incorporated the quantitative analysis of the lattice expansion using the Bragg Law. Specifically, we calculated the degree of lattice strain induced by Ba substitution. Furthermore, we have added a detailed discussion on how this strain influences the stability of resistive modulation by suppressing oxygen vacancy diffusion. This information is now presented on pages 6 and 7 of the revised manuscript.\n in page 6.\nBeyond TEM analyses, X-ray diffraction (XRD) measurements were conducted including theta-2theta, phi-scans, and reciprocal space mapping (RSM) (Supplementary Figs. 4a-c). Based on these results, we conclude that the BFO and BBFO were grown epitaxially while simultaneously undergoing compressive strain along the in-plane direction. The BBFO possesses greater compressive strain, which is attributed to the larger atomic radius of the substituting Ba compared to Bi. (Supplementary Fig. 4d) The compressively strained oxide perovskite exhibits increased formation and migration energies for oxygen vacancies, where the oxygen vacancy diffusion is a critical factor that causes the decay of resistive states in memristors. [1,2] The c-axis expanded structure maintains stability even under high concentrations of barium substitution, and this strained structure effectively suppresses oxygen diffusion, enabling stable resistive modulation. [3]\n[1] Nian, Y., et al., Evidence for an oxygen diffusion model for the electric pulse induced resistance change effect in transition-metal oxides. Physical review letters, 2007. 98(14): p. 146403.\n[2] Yang, Q., et al., Strain effects on formation and migration energies of oxygen vacancy in perovskite ferroelectrics: A first-principles study. Journal of Applied Physics, 2013. 113(18).\n[3] Xiang, X., et al., Manipulating the resistive switching in epitaxial SrCoO2.5 thin-film-based memristors by strain engineering. ACS Applied Electronic Materials, 2022. 4(6): p. 2729-2738.\n2. The manuscript initially suggests a homogeneous mechanism but later (Supplementary Fig. 5c) mentions \"typical filamentary resistive switching behavior after electroforming.\" This creates confusion. The authors must clarify the nature of the conductive path. Is it a localized filament or a uniform interface-modulated barrier? Additional analysis (e.g., area-dependent measurements) or a revised discussion reconciling these observations is necessary.\nAnswer: We appreciated the insightful question. The BBFO memristor in the manuscript operates without electroforming. To assess whether a vacancy-controlled mechanism can emerge only under extreme bias and to demonstrate the presence of an oxygen-vacancy population sufficient to enable the combined effects of ferroelectric polarization and vacancy transport, a high-field stress test was performed.\nIf oxygen vacancies did not participate, an epitaxial film with a very low vacancy concentration would be expected to show ohmic behavior after breakdown under a strong electric field. In contrast, application of tens of V induced a soft breakdown, and subsequent sweeps exhibited oxygen vacancy filament-type on/off switching. The observation indicates that oxygen vacancies are present in the BBFO layer; however, the proposed device mechanism does not rely on filament formation, as standard operation remains within approximately ±5 V and is governed by interface barrier modulation.\n in Supplementary Figure 5\nSupplementary Figure 5. Memristive J–V curves of the BBFO device under different voltage ranges. a) Offset of the curves swept from 1 V to 5 V. b) Offset of the curves swept from 5 V to 8 V. In all cases, measurements were conducted sequentially in the order of negative voltage, 0 V, positive voltage, and back to 0 V.\n in Supplementary Figure 6\nSupplementary Figure 6. Filamentary ReRAM operation. When a high voltage of approximately +28 V is applied, a soft breakdown occurs, inducing filamentary resistive switching behavior in subsequent voltage sweeps. This observation suggests that the BBFO thin film contains oxygen vacancies that can contribute to device operation. Although the BBFO device exhibits forming-less behavior, this result implies that a moderate amount of oxygen vacancies is present within the BBFO layer, enabling the memristive operation.\n in page 9\nSupplementary Fig. 6 shows that the BBFO device can exhibit filamentary-type behavior, but only after electroforming under a high positive bias of +28 V. In contrast, the BBFO memristor investigated in the present study operates in a forming-free manner within a voltage window below ±5 V. The comparison indicates that oxygen vacancies can participate in the BBFO device operation mechanism, yet their contribution is manifested as interface-modulated resistive switching rather than localized filament formation.\n3. While the linearity of potentiation/depression is highlighted and nonlinearity factors are provided, the methodology for this fitting is buried in a supplementary note. The key parameters (e.g., the number of devices used for the 0.152/0.303 nonlinearity values in Fig. 3b, the fitting model) should be clearly stated in the main text or figure caption to allow for a critical assessment of this crucial claim.\nAnswer: Thank you for your fruitful comment. We have added the nonlinearity values for LTP/LTD (vpo/vde) in Figure 3b as well as in the caption of Figure 3b. The corresponding values can be also found on page 15 of the main manuscript. Please find the revised section below Figure 3.\n in Figure 3.\nFigure 3. Artificial synapse performances using BBFO memristor a) Analog DC sweeping measurement showing synaptic potentiation and depression over 15 cycles. The inset presents a magnified view of the positive voltage region to highlight the depression characteristics. b) Potentiation/depression characteristics measured by 100 pulse number using BFO and BBFO memristors. The applied programming voltages were -1.6 V/+1.0 V, respectively, with a read voltage of +0.2 V. The pulse duration was 200 s. The nonlinearity at LTP and LTD (vpo and vde) was denoted in Figure 2b, as 0.152 and 0.303, respectively. c) SWDP characteristics. The voltage amplitudes of the pulses for synaptic weight potentiation and depression are -1.7 V and +1.1 V, respectively. d) Illustration of linearity mechanism in the case of BBFO and BFO memristor. The inset image depicts the oxygen vacancy migration influenced by dipole arrangement in the BBFO.\n4. The excellent uniformity across the 11×11 array is a key result. However, the data in Figures 1f, 1h, and 5d would be significantly strengthened by providing standard deviations or confidence intervals for the conductance states and LTP/LTD curves, rather than just showing overlapping traces. A quantitative measure of device-to-device (D2D) and cycle-to-cycle (C2C) variability for the entire array is essential.\nAnswer: We appreciated the insightful question. To quantitatively reflect the statistical information of the multilevel states that underpin the synaptic device characteristics, we have revised the manuscript to include the following supplementary materials.\nSupplementary Figure 50. Statistical analysis of LTP/LTD characteristics for each cell in the 11 × 11 CBA. a) Ninety-five percent confidence intervals for 100 conductance states under LTP and LTD operation in the synaptic device. b) Conductance evolution as a function of potentiation number, represented with error bars.\n in page 26.\nThanks to these self-rectifying performances using the uniform BBFO film, LTP and LTD characteristics across all 121 cells in the 11 × 11 CBA demonstrate highly linear conductance modulation with minimal variation (Figure 5d). Supplementary Fig. 50 quantitatively presents statistical information on the LTP/LTD characteristics of each cell within the 11 × 11 CBA, including the 95% confidence intervals and deviations. J-V characteristics of individual cells in the CBA are also shown in Figure 5e and Supplementary Fig. 51, highlighting D2D uniformity and operational stability.\n5. The rationale for using different voltage amplitudes for LTP/LTD (e.g., -1.6 V/+1.0 V in Fig. 1f, -2.4 V/+1.5 V in Fig. 5d) and for the CBA operation is not explained. The authors should justify these choices, especially in relation to the coercive voltage and the need for asymmetric programming, and discuss how this impacts energy consumption and circuit design.\nAnswer: Thank you for the thoughtful question. In a vertical memristor, using dissimilar electrodes naturally leads to an equilibrium band profile that is not perfectly symmetric, due to the difference in their work functions. In addition, internal field compensation caused by the remanent polarization and possible accumulation of oxygen vacancies can make the required voltage amplitudes for device operation—particularly during LTP/LTD programming—appear asymmetric. Furthermore, as indicated in the caption of Fig. 1f, the device was fabricated by growing BBFO on a deposited bottom conductive layer and then forming dot-patterned top electrodes. When the same stack is implemented as a crossbar line structure, the operating voltages can differ. This is because the measurement condition in which the bottom electrode is fully deposited and directly contacted with the dot-patterned top electrode is not identical to the condition of a crossbar array in which each cell is addressed through line contacts; these two cases represent different device configurations. Nevertheless, once the appropriate voltage amplitude is optimized for each configuration, comparable performance can be achieved, which confirms that the proposed device mechanism remains valid even when applied to the CBA structure. We acknowledge this difference and have revised the text to discuss its implication for circuit-level design as follows:\n in page 26.\nSupplementary Fig. 50 quantitatively presents statistical information on the LTP/LTD characteristics of each cell within the 11 × 11 CBA, including the 95% confidence intervals and deviations. J-V characteristics of individual cells in the CBA are also shown in Figure 5e and Supplementary Fig. 51, highlighting D2D uniformity and operational stability. The results reveal a uniform memory window exceeding two orders of magnitude and a rectification ratio exceeding six orders of magnitude across the entire array. Although the dot-patterned cells in Figure 1f required a different absolute voltage, using the same positive/negative voltage ratio produced comparable synaptic behavior, confirming that our proposed device mechanism remains valid for the CBA architecture. The high rectification ensures reliable readout during synaptic weight modulation and retention, reinforcing the stability of the CBA. Additionally, the uniformity of individual cells suggests the potential for scaling the array to larger sizes.\n6. The concept of a second-order mechanism coupling polarization and vacancies is intriguing but underdeveloped. The description in the section \"Relationship between oxygen vacancy migration and ferroelectricity\" is dense and difficult to follow. A clearer schematic or a more pedagogical explanation of this feedback loop and how it precisely enables linear updates would greatly enhance the manuscript's impact.\nAnswer: Thank you for your fruitful comment. For elucidating a second-order mechanism, we add a new figure in Supplementary information. In detail, two-step conductance rise can be explained by 1) polarization direction change and 2) oxygen vacancy migration. Using the existing figure in main manuscript (Figure 2d), we newly make another supplementary figure in Supplementary Fig. 30.\nSupplementary Figure 33. Illustration of second-order mechanism. The conductance modulation occurs in two steps: 1) Ferroelectric polarization is induced by voltage pulses, and 2) the homogeneously migrated oxygen vacancies contribute to the linear programming of conductance. Each step of this second-order mechanism is illustrated during the LTP/LTD processes.\n in page 20.\nThe results support a second-order mechanism in BBFO, where polarization and vacancy migration act as coupled internal variables [32-34]. The two variables induced by ferroelectricity and oxygen vacancy migration lead to second-order switching mechanism, as depicted in Supplementary Figs. 33.\n7. Figure 4b is a good start, but the comparison with other technologies would be more informative if key metrics like switching speed, energy consumption per spike, and retention were also included in a table (perhaps in Supplementary Information). This would provide a more holistic view of where BBFO stands in the competitive landscape.\nAnswer: Thank you for the good question. We have already benchmarked our device against various material systems, as summarized in Table 1. Since the switching speed corresponds to the “Time scale” entry, we have included the energy consumption and retention metrics as follows:\n in Supplementary Table 2.\nSupplementary Table 2. Various memristors for artificial synapses with the following properties: linearity/symmetry, rectifying ratio, memory window, LTP/LTD voltage, time scale, Gmax/Gmin (dynamic range), maximum weight updates, fabrication method, high-temperature operation, retention, energy per operation, CBA implementation, experimental CBA size, potential maximum array size.\n[Table omitted for brevity]\n8. The manuscript focuses on the successes but lacks a critical discussion of limitations. For example, the use of an epitaxial SrTiO3 substrate and SrRuO3 bottom electrode poses significant challenges for large-scale, back-end-of-line (BEOL) integration with silicon CMOS. The high forming voltage (>25 V) is also a practical concern. A paragraph acknowledging these challenges and outlining a path forward is necessary.\nAnswer: We appreciated the insightful question. Consistent with Question 2, the device exhibits forming-less behavior and does not require an electroforming step. Accordingly, from the perspective of using SRO electrodes, we have revised the Conclusion to outline future directions for CMOS-compatible BEOL integration, as follows:\n page 29.\nThe 11 × 11 array exhibited negligible D2D variability, with less than 1 % variation in the on/off current ratio among 121 devices, highlighting the potential of BBFO for reliable and uniform neuromorphic hardware implementation. These results indicate that BBFO-based mechanism can underpin practical CBA realization in future IMC systems. As wafer-scale epitaxy and epitaxial transfer continue to mature, the device-operation mechanism has strong potential for practical, large-scale integration in future neuromorphic hardware platforms.\n9. Several figures (e.g., Fig. 2d, 3d) are overly complex and could be simplified. The quality of some schematic illustrations (e.g., Fig. 5c) should be improved for professional presentation. The manuscript would benefit from a thorough proofreading to correct minor grammatical errors and improve sentence flow.\nAnswer: Thank you for the thoughtful question. To help readers more easily understand the mechanism diagrams in Figs. 2d and 3d, we have added a supporting figure as Supplementary Fig. 30 and revised the manuscript accordingly, as noted in our response to Comment 6. In addition, we have refined the circuit schematic in Figure 5c to further improve clarity.\n in Figure 5.\n10. The data in Supplementary Fig. 21 convincingly shows that 20% Ba is optimal. The manuscript should provide a deeper physical explanation for why this specific concentration yields the best performance, linking it to the optimal balance between oxygen vacancy concentration and the stability of ferroelectricity.\nAnswer: Thank you for your valuable comments. We have added further explanations detailing how the enhanced oxygen vacancy concentration induced by Ba doping leads to a reduction in leakage current and strengthens the rectifying behavior. Conversely, we also elucidated the adverse effect of excessive doping, where the resulting decreased stability of ferroelecitricity hinders the rectifying behavior. Corresponding references have been added to support these discussions.\n in page 14.\nThe effect of Ba substitution on rectification behavior was explored by measuring memristive J-V characteristics across various Ba concentrations, ranging from 5% to 30% (Supplementary Figs. 21a-f). Notably, a high rectifying ratio exceeding 105 was only observed when the Ba concentration was 20 %. Ba substitution induces a lattice expansion and optimizes the oxygen-vacancy concentration, thereby mitigating leakage currents and strengthening the diode-like rectifying behavior.[4] In compositions with Ba content deviating from 20 %, suppression of ferroelectric polarization or an increase in oxygen vacancies reduces the rectifying ratio and can even lead to switchable rectifying characteristics.[6] The overall trend indicates that 20 % Ba substitution provides the most suitable composition for fabricating selector-free CBA.\n[4] Lee, D., et al., Polarity control of carrier injection at ferroelectric/metal interfaces for electrically switchable diode and photovoltaic effects. Physical Review B—Condensed Matter and Materials Physics, 2011. 84(12): p. 125305.\n[5] Liang, N., et al., Structure evolution and energy band modulation in Ba-doped BiFeO3 thin films. Journal of Applied Physics, 2024. 135(4).\n11. The abstract could be slightly refined to more immediately state the key achievement (e.g., \"We demonstrate a memristor... that achieves a rectifying ratio >106 and linear synaptic updates via a coupled ferroelectricity-vacancy mechanism\")\nAnswer: We appreciated the constructive comment. To state the key achievement more directly, we revised the sentence to front-load the performance metrics, as follows:\n in page 2.\nIn this study, we present memristor devices that achieve a rectifying ratio exceeding 10⁶ and an off-state current below 10⁻¹² A based on epitaxial heterostructures consisting of Pt/Ba0.2Bi0.8FeO3 (BBFO)/SrRuO3/SrTiO3 stacks. Substitution of 20% Ba in BiFeO₃ induces a unique interaction between ferroelectric polarization and oxygen vacancy migration, which under pulsed bias governs vacancy transport and ensures reliable memristive synaptic behavior with near-zero nonlinearity and endurance beyond 10⁷ cycles.\n12. In the Methods section, more details on the patterning and etching processes for the SRO bitlines and Pt wordlines would be beneficial for reproducibility.\nAnswer: Thank you for the constructive comment. We have revised the manuscript to provide a more detailed description of the crossbar array fabrication process, ensuring that the experiments can be readily reproduced by other researchers.\n in page 31.\nFor CBA fabrication, we patterned and wet-etched the SRO thin film into bit lines using a standard lithography process. For selective etching of the SRO layer, an aqueous 0.4 mol/L sodium metaperiodate (NaIO₄) solution was prepared and sonicated for 30 min to ensure complete dissolution. The SRO film patterned with photoresist was then immersed in the solution for 30 s to remove the exposed SRO. After stripping the photoresist, the BFO layer was subsequently deposited ex-situ under the conditions described above. followed by the patterning of the top cross-line electrodes using the lift-off process.\n13. Please ensure all acronyms are defined upon first use (e.g., MAC in Fig. 1g should be spelled out).\nAnswer: Thank you for the valuable comment. We have revised Figure 1g to ensure that all abbreviations are clearly defined, as shown below.\n in Figure 1.\nFigure 1. Comprehensive summary of this study.\n14. The manuscript lacks comprehensive review on recent works. Please refer:\nhttps://www.nature.com/articles/s41467-025-60970-4\nhttps://www.nature.com/articles/s41928-024-01318-6\nhttps://pubs.acs.org/doi/10.1021/acs.nanolett.4c04385\nhttps://pubs.aip.org/apl/article/125/13/133501/3314036/Self-rectifying-memristors-with-high-rectification\nhttps://link.aps.org/doi/10.1103/PhysRevApplied.22.064003\nAnswer: Thank you for the helpful comment. We have improved the section by adding relevant references as suggested, to more clearly present the current progress, as shown below:\n in page 4.\nTherefore, it is imperative to explore self-rectifying memristor designs with reliable conduction mechanisms for the practical application of CBAs in neuromorphic computational systems. [22-28]\nReviewer #2 (Remarks to the Author):\nThis is an interesting work with excellent performances of the self-rectifying ferroelectric tunnel junction by cleverly combining conductance modulation by both polarization of ferroelectrics and oxygen vacancies. The authors report extremely reliable operation of the synaptic device even beyond 10 M cycles with a rectifying ratio higher than 106. The reviewer believes that this work deserves publication in Nature Communications, but it requires modifications as shown below.\nResponse: We appreciated the referee’s positive evaluation of the significance and impact of our study. In the following, we provide detailed point-by-point replies to each comment raised by the referee.\n1. The authors used current instead of current density in several current-voltage curves. However, using current density should be better for readers. Especially, for the case of ferroelectric tunnel junctions, low on current density is a critical technical issue. So, please use current density and add some discussion on the current density observed in this study.\nAnswer: Thank you for the valuable comment. We have reconstructed the figure based on current density representation as suggested.\n in Figure 1.\nFigure 1. Comprehensive summary of this study. a) Schematic illustration of the CBA structure. b) OM image of the CBA sample and SEM image of CBA memristor cells. The scale bars for the device image and OM image are 4 and 100 mm, respectively. Two parallel memristor cells are shown, highlighting the target and parasitic current paths. The parasitic current path is blocked by the rectifying current in BBFO. c) STEM-HAADF image of the BBFO/SRO interface. The scale bar is 2 nm. d) Memristive J-V characteristics measured under a bias range of −5 V to +5 V with the SRO electrode grounded. e) Schematic representation of the LTP and LTD behaviors governed by ferroelectric polarization and oxygen vacancies in BBFO. f) Cell-to-cell variation in LTP and LTD characteristics evaluated using dot-patterned electrode-devices configured with 39 individual cells. The applied voltage pulses for LTP and LTD measurement were -1.6 V/+1.0 V, with a read voltage of 0.2 V and a pulse duration of 200 s, g) Conductance mapping image displaying the letter “B” in the selector-free CBA, with the blocked sneak path at S column illustrated alongside the text image. h) Conductance mapping of individual memristor cells in the 11 x 11 CBA, ranging from 1.98 nS to 10.8 nS, as the number of applied voltage pulses varied from 10 to 100 in increments of 10.\n in Figure 2b.\nFigure 2. Self-rectifying electrical performance. a) Schematic of a unit memristor composed of Pt/BBFO/SRO. The inset shows a STEM-HAADF image of BBFO, with downward arrows indicating the pristine polarization direction. The scale bar is 200pm. b) Repetitive J-V cycling measurements using the BBFO memristor, demonstrating stable operation over 100 cycles. The applied voltage was swept from -5 V to 5 V. c) Polarization (P) – voltage (V) hysteresis curve measured at 100 kHz for the Pt/BBFO/SRO device. d) Evolution of band diagrams illustrating the 4 steps of current transport mechanisms corresponding to the I-V characteristics in Figure 2b. Green circles represent oxygen vacancies, and the arrows in the BBFO band indicate the polarization direction. e) Calculated values as a function of temperature based on Table S1 and the following equation, confirming the presence of a donor-like shallow trap state at approximately 0.074 eV. f) Energy–density of states diagram constructed based on the band energy analysis.\n in Figure 5e.\nFigure 5. Implementation of the 11×11 BBFO selector-free crossbar array. a) Schematic of the selector-free BBFO CBA. b) Optical microscope image of the fabricated CBA. The scale bar is 200 µm. c) The sneak current blocking mechanism of self-rectifying memristors during CBA operation. Red-colored devices represent reverse-biased elements, blue-colored devices indicate forward-biased elements, and white-colored devices correspond to target cells. d) LTP/LTD characteristics of individual CBA cells, with applied pulses of -2.4 V and +1.5 V, respectively. In all cases, the read voltage was +0.2 V, and the pulse duration was 200 µs. e) J-V measurement results for individual cells within the CBA. f) Read margin comparison of selector-free CBAs based on BBFO and BFO. The blue line represents BBFO, while the red line corresponds to BFO. g) Learning demonstration results using the 11×11 BBFO CBA.\n in Figure S5.\nSupplementary Figure 5. Memristive J–V curves of the BBFO device under different voltage ranges. a) Offset of the curves swept from 1 V to 5 V. b) Offset of the curves swept from 5 V to 8 V. In all cases, measurements were conducted sequentially in the order of negative voltage, 0 V, positive voltage, and back to 0 V.\n in Figure S11.\nSupplementary Figure 11. Comparison of BBFO device J-V characteristics according to electrode structure. The device structures are a) Pt / BBFO / SRO, b) SRO / BBFO /Pt, and c) SRO/ BBFO/ SRO, respectively. Notably, when both the top and bottom electrodes are made oxygen-permeable, hysteresis caused by oxygen vacancy formation and migration is suppressed in both directions.\n in Figure S16.\nSupplementary Figure 16. J-V characteristics after ferroelectric poling. a) Comparison of read voltage sweep responses after poling with opposite polarities. Poling was performed with a short pulse of 100 ms. The voltage sweep was −0.2 V → 0 V → 0.2 V. b) J-V characteristics under different voltage sweep sequences. The voltage was swept in the order of +5 V → -5 V → -5V → +5 V → -5V, confirming reversible resistance switching between the LRS and HRS states.\n in Figure S17.\nSupplementary Figure 17. Comparison of J–V characteristics under different measurement conditions. a) Voltage sweep from 0 V → −3 V → 0 V with varying sweep rates. b) Voltage sweep from 0 V → −5 V → 0 V → 5 V → 0 V. c) Voltage sweep from 0 V → −5 V → 0 V → 5 V → 0 V under different temperatures.\n in Figure S18.\nSupplementary Figure 18. J–V characteristics depending on the top electrode material. a) Ag (50 nm) / BBFO (100 nm) / SRO (40 nm) device. b) Ti (50 nm) / BBFO (100 nm) / SRO (40 nm) device. c) Au (50 nm) / BBFO (100 nm) / SRO (40 nm) device. All configurations exhibit self-rectifying behavior. The resistance state is reset under positive voltage sweep.\n in Figure S21.\nSupplementary Figure 21. J–V characteristics of BBFO memristors with varying Ba concentrations. 30% doped BBFO exhibited volatile behavior, while 25%, 15%, 10%, and 5% doped BBFOs showed insufficient rectification and a low memory window.\n in Figure S24\nSupplementary Figure 24. a) Comparison of J–V characteristics and b) maximum rectification ratios of BBFO films with varying thicknesses.\n in Figure S25\nSupplementary Figure 25. Device-to-device and cycle-to-cycle variation in J–V measurements. The dot-patterned device exhibited uniform switching behavior over multiple cycles across more than 25 cells.\n in Figure S51\nSupplementary Figure 51. D2D J-V measurements variation in 11 × 11 CBA cells. Every cell exhibited uniform self-rectifying memristive behavior.\n2. In figure 1e and related text, the authors argue that they could achieve highly linear potentiation/depression by combining the polarization and oxygen vacancies. However, the reason for this mechanism is not clear for the reviewer. From the reviewer’s knowledge, for both cases the non-linear potentiation/depression like red dashed curve in figure 1e is frequently observed. Please add more details with adequate references for the suggested mechanism.\nAnswer: Thank you for your fruitful comment. This point has already been addressed on page 14 of the main manuscript. As shown in Figure 3d, the saturated programming behavior commonly observed in conventional memristive synapses arise from the sudden accumulation of oxygen vacancies induced by ferroelectric polarization. In our study, this accumulation is mitigated by optimizing the oxygen vacancy concentration. Since the origin of the LTP/LTD: curves are already discussed on page 18, we will add one clarifying sentence in the section corresponding to Figure 1e.\n in page 7.\nNotably, the velocity of oxygen vacancy migration can be controlled by ferroelectric polarization. Gradually facilitating oxygen vacancy migration, ferroelectricity induces velocity change of oxygen vacancies. This dynamically changed charge migration induces linearly modulated synaptic performance, as illustrated in Figure 1e. In contrast to the typical LTP/LTD curve, represented by the red dotted line in Figure 1e, our linearly modulated curves originate from the coupling effect between oxygen vacancies and ferroelectricity. A detailed explanation will be provided in Figure 3d.\n3. The absolute dynamics range is not clear from figure 1f. Add also raw conductance values in figure 1f. The authors can simple use the right y-axis for showing the raw conductance values.\nAnswer: Thank you for the valuable comment. We have revised the manuscript accordingly to explicitly present the raw conductivity values, as suggested.\n in Figure 1.\nFigure 1. Comprehensive summary of this study.\nReviewer #3 (Remarks to the Author):\nI co-reviewed this manuscript with one of the reviewers who provided the listed reports. This is part of the Nature Communications initiative to facilitate training in peer review and to provide appropriate recognition for Early Career Researchers who co-review manuscripts.\nResponse: We sincerely appreciate the referee’s positive and encouraging comments on our work. The constructive feedback greatly assisted us in refining the manuscript and improving the clarity of the presentation. We are grateful for the time and effort the referee devoted to the evaluation of our study.\nReviewer #4 (Remarks to the Author):\nThe manuscript reports the fabrication of memristors based on 20 % Ba into BFO within a Pt/BBFO/SRO structure. The performance of the device is governed by the interplayed between ferroelectric polarization and oxygen vacancies inside the materials. In addition, authors also realized the 11 × 11 array to demonstrate the learning capability. However, the current manuscript still contains several issues that require further clarification, additional experimental evidences, and a strengthened discussion.\nResponse: We appreciated the referee’s positive assessment of the significance of our study. Detailed point-by-point replies to each comment are provided below.\n1. In this work, the authors fabricate the device structure of Pt/Ba0.2Bi0.8FeO3 (BBFO)/SrRuO3 (SRO)/SrTiO3 (STO) epitaxial heterostructures. As the interface between Ba0.2Bi0.8FeO3 (BBFO) and SrRuO3 (SRO) plays important role in the performance, I wonder whether it is possible to present the transmission electron microcopy image at the interface.\nAnswer: Thank you for the insightful comment. As you noted, the interface between the two epitaxially grown films plays an important role in determining device behavior, including oxygen-ion supply. Therefore, careful observation of this interface is crucial. Figures 1c, S2a, and S2b clearly present this interfacial structure, while Figure S2d confirms that all films are well grown in a single-crystalline form, showing uniformly aligned A-site ion displacements within BBFO domains. We have obtained a clear TEM image of the interface based on these findings. As shown in Figure S2a, the distinct atomic-resolution EDS mapping requires long-term electron beam exposure, which demonstrates that the interface is well aligned epitaxially without additional defects. Moreover, the Ba elemental mapping in Figure S2b enables a correlation between the interfacial image and the device mechanism. The progression of Ba substitution from the interface indicates that vacancy-related effects can be induced not only in the bulk but also near the interface. We have accordingly added a discussion on the interfacial TEM images as follows.\n in page 6.\nHigh-angle annular dark field scanning transmission electron microscopy (STEM-HAADF) imaging was performed to confirm the epitaxial growth of the configured layers (Figure 1c). This image reveals periodically aligned atomic arrangements in BBFO and SRO, with atomic distances of 0.596 nm and 0.618 nm at the A-site (Sr and Ba/Bi atoms) and B-site (Fe, Ru, and Ti atoms) in oxide perovskite structure (ABO3), respectively. Additionally, Supplementary Figs. 2a and b reveal clear atomic differentiation between BBFO and SRO, together with pronounced Ba substitution confirmed by EDS mapping, indicating that the BBFO film grows uniformly from the bottom interface. Furthermore, Supplementary Fig. 2c presents a globally measured STEM-HAADF image of the BBFO film, which confirms that the pristine polarization direction is downward. The fast Fourier transform (FFT) images in Supplementary Fig. 2d further verify the distinct crystallographic character. The electron backscattered diffraction (EBSD) image of Pt/BBFO/SRO device (as shown in Supplementary Fig. 3) further supports the uniformity of epitaxial BBFO film.\n2. The authors claim that \"rectifying I–V performance stems from oxygen vacancy migration contributes to Schottky- and Ohmic-like conduction\". It is widely accepted that the memristor behavior is also attributed from conductive filaments. Please provide more evidence and discussion on the origin of rectifying I–V performance.\nAnswer: Thank you for your fruitful comment. We agree that the Schottky- and Ohmic-like conduction is prevalent in many memristors, not just confined to the rectifying memristor. So, we add some sentences in page 4 to support the rectification of our work.\n in page 4.\nIn the rectifying J–V performance, additional dipole stemming from the oxygen vacancy migration contributes to Schottky- and Ohmic-like conduction at the BBFO/SRO and BBFO/Pt interfaces, respectively. Of course, such alternation is not limited to rectifying memristors; however, in our case, the rectification primarily originates from the coupling between ferroelectric polarization and oxygen vacancy modulation. The homogeneous variation in the migration velocity of oxygen vacancies, governed by the ferroelectric electrostatic field, leads to an enhanced on/off current ratio in the J-V characteristics.\n3. In reference Phys. Rev. Lett. 98, 146403 (2007), the authors present the study of oxygen vacancies diffusion coefficient. I suggest the authors to further quantitively investigate the movement of these oxygen vacancies based on the similar methods.\nAnswer: Thank you for recommending a highly suitable paper. We have verified the oxygen vacancy diffusion equation using the referenced paper and have incorporated content detailing how strain control suppresses the migration energy, thereby inhibiting the time-dependent decay of the resistive state.\n in page 12.\nSupplementary Fig. 14 presents the extracted activation energy required for device operation, showing an Arrhenius fitting result of approximately 0.4 eV. Supplementary Fig. 15 compares the effective oxygen-vacancy diffusion coefficients by extracting the activation energy in the same manner for the undoped BFO device. The results are for BFO and for BBFO at room temperature, indicating the robustness of BBFO, which does not permit higher leakage currents than BFO over the investigated temperature range. [2]\n[2] Nian, Y., et al., Evidence for an oxygen diffusion model for the electric pulse induced resistance change effect in transition-metal oxides. Physical review letters, 2007. 98(14): p. 146403.\n4. By incorporating 20 % Ba into BFO within a Pt/BBFO/SRO structure, the device presents promising memristive behavior, I suggest the authors to further show the density function theory result on the interaction of doped Ba in BFO layers.\nAnswer: We appreciated the reviewer’s comment regarding the role of Ba concentration in shaping the balance between ferroelectric switching and vacancy-mediated conduction. All compositions are based on a ferroelectric BiFeO₃ matrix. However, the relative contribution of leakage and oxygen-vacancy transport differs markedly with Ba content. Devices based on undoped BiFeO₃ (x = 0) retain ferroelectricity but suffer from Bi volatility and significant leakage, which imply a relatively high density of oxygen vacancies and defect-assisted conduction paths. As a result, memristive behavior is dominated by leakage and vacancy motion, leading to limited rectification and nonlinear, saturating synaptic weight updates despite the presence of ferroelectric polarization. In contrast, Bi0.8Ba0.2FeO3 (x ≈ 0.2) exhibits strong rectifying behavior together with gradual and nearly linear conductance modulation under pulsed operation. Deep-level transient spectroscopy (in Figure 2e, 2f) reveals a shallow donor level at ~0.074 eV below the conduction band with a trap density on the order of 10¹⁷–10¹⁸ cm⁻³, which is consistent with oxygen-vacancy-related donors that are mobile under synaptic pulse conditions but not abundant enough to suppress the ferroelectric order.\nTo provide quantitative evidence, we performed density-of-states (DOS) calculations for BaxBi1-xFeO3. Because the observed memristive behavior cannot be explained by vacancy migration alone, the DOS evolution provides quantitative support that ferroelectric–vacancy coupling governs conductance modulation. Taken together, the findings indicate that ~20% Ba substitution establishes an energetically favorable regime for linear conductance modulation. Spin-polarized DFT calculations for stoichiometric Bi1-xBaxFeO3 indicate that Ba substitution around x ≈ 0.2 preserves Fe–O-dominated band edges and does not introduce pronounced deep states inside the gap, providing an electronically clean ferroelectric background. The combined experimental and theoretical results support a picture in which ferroelectric polarization and shallow oxygen-vacancy redistribution are effectively coupled near x ≈ 0.2, yielding progressive depletion-width modulation and highly linear synaptic weight updates. For higher Ba content (x ≈ 0.30), the memristor characteristics evolve toward an almost ideal ferroelectric-diode I–V curve (as shown in Supplementary Figure 21), while synaptic conductance changes become more abrupt and saturating. Together with the reduced low-energy DOS obtained from DFT and the absence of a significant shallow-level response in DLTS, such behavior suggests that oxygen-vacancy contributions are strongly suppressed at x ≈ 0.30 and that conductance modulation is governed predominantly by pure ferroelectric barrier switching. Consequently, an intermediate Ba concentration around 20% represents a regime in which a stabilized ferroelectric Fe–O matrix coexists with a moderate population of shallow oxygen vacancies, enabling rectifying memristive behavior and linear synaptic plasticity that cannot be achieved in either undoped or heavily Ba-doped compositions.\nSupplementary Fig. 20 | Density of states (DOS) calculation results of BaxBi1-xFeO3 (x = 0–30%).\n in page 33\nComputational details: All the spin-polarized density functional theory (DFT) calculations were performed using the Vienna Ab initio Simulation Package (VASP) program with the projector augmented wave method for the core region and a plane-wave kinetic energy cutoff of 400 eV. The generalized gradient approximation (GGA), in the form of Perdew-Burke-Ernzerhof (PBE), was used for the exchange-correlation potentials. A 4x4x1 Gamma-centered Monkhorst-pack sampled k-point grid was employed to sample the reciprocal space. The atoms are free to move in all directions until the convergence of energy and residual atomic force on each atom was less than 1x10-4 eV and 0.01 eV/Å, respectively.\n in page 14.\nElectronic-structure calculations based on spin-polarized density functional theory (DFT) were carried out for Bi1-xBaxFeO3 with x = 0, ≈ 0.18, and ≈ 0.30, and the density of states (DOS) was quantitatively analyzed in an energy window around the Fermi level (Supplementary Fig. S20). In that near-EF region, more than 90% of the states originate from Fe–O networks, whereas the Ba-projected contribution remains below ~1% and does not form a distinct Ba-centered peak inside the gap, indicating that Ba substitution stabilizes the A-site environment without introducing deep electronic traps and provides an electronically clean ferroelectric matrix within which shallow oxygen-vacancy donors identified by DLTS can modulate conduction. The effect of Ba substitution on rectification behavior was explored by measuring memristive J-V characteristics across various Ba concentrations, ranging from 5% to 30% (Supplementary Figs. 21a-f). Notably, a high rectifying ratio exceeding 105 was only observed when the Ba concentration was 20 %. This indicates that the Ba substitution with 20 % represents the most optimal composition for fabricating selector-free CBA.\n5. The authors claims the 11 × 11 array exhibited negligible D2D variability, please provide more results and discussion on the uniformity.\nAnswer: Thank you for your fruitful comment. We already show the D2D variability in Supplementary Fig. S46. As shown in Supplementary Fig. S46, there is little variation in on/off ratio. We revised page 28 in the main manuscript.\n in page 29.\nThe 11 × 11 array exhibited negligible D2D variability, with less than 1 % variation in the on/off current ratio among 121 devices, highlighting the potential of BBFO for reliable and uniform neuromorphic hardware implementation.\nSupplementary Figure 46. D2D J-V measurements variation in 11 × 11 CBA cells. Every cell exhibited uniform self-rectifying memristive behavior."}, {"round": 2, "reviewer_comments": {"reviewer_1": "The authors have made substantial efforts to address the previous concerns, significantly improving the clarity, mechanistic explanation, and data presentation. The revised manuscript is much stronger, with enhanced discussion on the coupling mechanism, statistical validation, and device uniformity. The addition of DFT results and diffusion analysis further strengthens the scientific rigor. Overall, the manuscript is nearly ready for publication.\n1. While the authors have introduced the concept of a “second-order mechanism” to describe the interplay between ferroelectric polarization and oxygen vacancy migration, the terminology remains somewhat nonstandard and could benefit from a brief contextual or literature-based definition. A short sentence comparing it to other known memristive models (e.g., first-order filamentary or interface-type switching) would help readers better appreciate its significance.\n2. Although the authors explain the rationale behind the asymmetric LTP/LTD voltages, the description is somewhat dispersed across the text. Consider consolidating this explanation in one dedicated paragraph within the main text or Methods section to improve readability and avoid redundancy.\n3. In the new version, the review requires to be much more comprehensive. There are some latest references:\nhttps://doi.org/10.1016/j.device.2025.100988\nhttps://doi.org/10.1063/5.0283706", "reviewer_2": "Thank you for providing a sufficiently detailed explanation that fully addresses this reviewer’s suggestions. The reviewer has no further questions regarding the authors’ responses and has no objection to the manuscript being published in its current revised form in Nature Communications.", "reviewer_3": "I co-reviewed this manuscript with one of the reviewers who provided the listed reports. This is part of the Nature Communications initiative to facilitate training in peer review and to provide appropriate recognition for Early Career Researchers who co-review manuscripts.", "reviewer_4": "The authors have addressed the issues. I recommend the publication of the manuscript in current form."}, "author_response": "Response: We are grateful to all reviewers for their time and constructive feedback on the manuscript. The main text and Supplementary Information have been revised accordingly. In the point-by-point response provided below, reviewer comments are shown in black, while our responses are indicated in blue. All revisions made to the main text and Supplementary Information are highlighted in yellow. Extracted text from the manuscript and Supplementary Information is presented in the original font size and enclosed in boxes to facilitate readability.\nPoint by point Response to Reviewers’ comments:\nReviewer #1 (Remarks to the Author):\nThe authors have made substantial efforts to address the previous concerns, significantly improving the clarity, mechanistic explanation, and data presentation. The revised manuscript is much stronger, with enhanced discussion on the coupling mechanism, statistical validation, and device uniformity. The addition of DFT results and diffusion analysis further strengthens the scientific rigor. Overall, the manuscript is nearly ready for publication.\nResponse: We are grateful for the referee’s positive evaluation of the significance of the present work. Detailed, point-by-point responses to each comment are provided below.\n1. While the authors have introduced the concept of a “second-order mechanism” to describe the interplay between ferroelectric polarization and oxygen vacancy migration, the terminology remains somewhat nonstandard and could benefit from a brief contextual or literature-based definition. A short sentence comparing it to other known memristive models (e.g., first-order filamentary or interface-type switching) would help readers better appreciate its significance.\nAnswer: We appreciate the reviewer’s insightful comment. To clarify the meaning of the term “second-order mechanism,” we have expanded the discussion in the device-mechanism section to explicitly describe the physical factors. In addition, the revised text discusses whether the observed vacancy behavior is more consistent with filamentary-type or interface-type memristive switching.\n in page 20.\nWe examined their interplay by analyzing (1) vacancy migration relative to dipole displacement, and (2) polarization response with respect to the degree of vacancy migration. The results support a second-order mechanism in BBFO, where polarization and vacancy migration act as coupled internal variables in which polarization and oxygen vacancy migration act as coupled internal variables, and device operation arises from their interdependent dynamics rather than from a single dominant process. [43-45] In contrast, single-process-dominated behavior, as commonly observed in interface-type and filamentary-type switching, leads to progressive insensitivity and saturation of conductance modulation due to the accumulation of responses under repeated stimuli. The two variables induced by ferroelectricity and oxygen vacancy migration lead to This coupled evolution of ferroelectric polarization and oxygen vacancy migration gives rise to the second-order switching mechanism, as depicted in Supplementary Figs. 33.\n2. Although the authors explain the rationale behind the asymmetric LTP/LTD voltages, the description is somewhat dispersed across the text. Consider consolidating this explanation in one dedicated paragraph within the main text or Methods section to improve readability and avoid redundancy.\nAnswer: We appreciate the reviewer’s constructive comment. The proposed BBFO device simultaneously satisfies high rectification, nonvolatile memory functionality, and linear, symmetric synaptic resistance modulation. The physical mechanisms responsible for each of these performance metrics must therefore be mutually consistent, and we have described the origin of the device behavior in a step-by-step manner throughout the manuscript. These explanations include the rectification mechanism discussed in Supporting Note 1, the operating mechanism of the I–V characteristics described on page 10, and the synaptic device mechanisms presented in Supporting Notes 4 and 5 as well as Supporting Figs. 27, 33, and 40.\nHowever, as correctly pointed out by the reviewer, the discussion specifically addressing the use of different voltage amplitudes for LTP and LTD programming was not sufficiently consolidated. As a result, the explanation may appear fragmented, potentially requiring readers to interpret multiple mechanisms simultaneously. To address this issue, we have revised the manuscript to clearly explain the physical origin of the non-identical LTP/LTD voltages. Furthermore, we confirmed that the proposed mechanism consistently applies to both single devices and array-integrated cells, thereby strengthening the overall interpretation..\n in page 24.\nThe use of non-identical LTP/LTD voltages originates from differences in the effective electric field required for comparable resistance modulation, arising from the asymmetric device configuration, including work-function mismatch, remanent polarization, and the resulting built-in electric field. Consequently, different voltage amplitudes are required for LTP and LTD. Consistent with this mechanism, although the dot-patterned cells in Figure 1f require different absolute voltages, the same positive-to-negative voltage ratio produces comparable synaptic behavior, confirming the validity of the proposed device mechanism in the CBA architecture.\n3. In the new version, the review requires to be much more comprehensive. There are some latest references:\nhttps://doi.org/10.1016/j.device.2025.100988\nhttps://doi.org/10.1063/5.0283706\nAnswer: We thank the reviewer for this important comment. The suggested studies have been added to the reference list in the revised manuscript and cited where appropriate to improve the completeness and contextual coverage of the review.\n in page 4.\nTherefore, it is imperative to explore self-rectifying memristor designs with reliable conduction mechanisms for the practical application of CBAs in neuromorphic computational systems. [23-31]\n29. Zhang, G., et al., Self-rectifying memristors with high rectification ratio and dynamic linearity for in-memory computing. Applied Physics Letters, 2024. 125(13).\n30. Zhang, G., et al., Stochastic self-rectifying memristor crossbar array as physical unclonable function for authentication and tamper-evident image security. Device, 2025.\n in Supplementary Note 1.\nAchieving diode-like characteristics in memristor devices is a key strategy for suppressing leakage current pathways during 1R-crossbar array (CBA) operation. [1-3] Various mechanisms have been reported to induce rectification, depending on the polarity of the applied electric field along the out-of-plane direction of the thin film. [4] A common approach involves PN junction-like doping effect through ion migration.\n2. Fan, X., et al., Superior rectification self-rectifying memristors with self-recovery capabilities enabled by GaOx/InOx heterostructures. Applied Physics Letters, 2025. 127(19).\n3. Zhang, G., et al., Stochastic self-rectifying memristor crossbar array as physical unclonable function for authentication and tamper-evident image security. Device, 2025.\nReviewer #2 (Remarks to the Author):\nThank you for providing a sufficiently detailed explanation that fully addresses this reviewer’s suggestions. The reviewer has no further questions regarding the authors’ responses and has no objection to the manuscript being published in its current revised form in Nature Communications.\nResponse: We appreciate the reviewer’s insightful comment.\nReviewer #3 (Remarks to the Author):\nI co-reviewed this manuscript with one of the reviewers who provided the listed reports. This is part of the Nature Communications initiative to facilitate training in peer review and to provide appropriate recognition for Early Career Researchers who co-review manuscripts.\nResponse: We appreciate the reviewer’s constructive comment.\nReviewer #4 (Remarks to the Author):\nThe authors have addressed the issues. I recommend the publication of the manuscript in current form.\nResponse: We appreciate the reviewer’s valuable observation."}, {"round": 3, "reviewer_comments": {"reviewer_1": "The authors have addressed all of my concerns so I endorse its publication in current form."}, "author_response": "Response: We appreciate the reviewer’s insightful comment."}]

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