Single symmetric nanopores in ultrathin crystalline ferroelectric BiFeO_3 as polarization-switchable ionic diodes

Domain: physics
Published: 2026-01-08
Editorial outcome: major_revision

Abstract
Artificial ionic diodes, inspired by biological ion channels, are typically realized by creating asymmetries in pore geometry or surface charge. Ferroelectric polarization, arising from the spontaneous alignment of electric dipoles within materials, provides an alternative strategy to achieve directional ion transport without additional geometry modification or surface functionalization. This work demonstrates that ultrathin freestanding ferroelectric crystalline bismuth ferrite symmetric-type single-nanopore membranes, with a thickness down to 30 nm, exhibit rectified ion currents driven by naturally spontaneous polarization. These nanopores exhibit reversible polarization switching with hysteretic ion current rectification in response to external pH stimuli, offering additional tunability in emulating the functions of biological ion channels. Furthermore, significant osmotic power generation is observed, enabled by current amplification through directional ion transport. These findings highlight the potential of utilizing ultrathin ferroelectric oxide membrane materials as ionic diodes with directional preferences and switchable polarizations for developing ionic circuits, mimicking biological membranes, and facilitating osmotic power conversion.

Introduction
Biological ion channels are specialized proteins embedded within cell membranes that regulate the passage of ions, such as protons, potassium, sodium, calcium, and chloride ions, across the membranes1,2. These ion channels are essential for various physiological processes in living organisms, helping to maintain the electrochemical gradient and ionic balance3,4. Some ion channels demonstrate directional preferences analogously to electronic semiconductor p-n junctions, functioning as ionic diodes5,6. For instance, inward-rectifying potassium channels facilitate the flow of K+ into the cell, whereas other specific ion channels preferentially transport in the opposite direction7,8. Inspired by these natural functions, artificial ionic diodes are designed and fabricated asymmetrically using materials and techniques to enable selective filtering and rectifying capability2,9,10. These artificial ionic diodes, with directional transport preferences, serve as foundational building blocks in the development of ionic circuits and emulating biological membranes11.

The presence of asymmetry plays a pivotal role in enabling directional ion transport in ionic diodes, typically accomplished through the introduction of geometric or surface charge asymmetry12–15. Geometric asymmetry with one end narrower than the other induces directional ion flow16,17. Various shapes encompassing conical, funnel, and bullet geometries have been designed to tailor the degree of rectification12,15,18. On the other hand, surface charge asymmetry, including polarity or density, is induced by charge gradients along the channel, leading to an electrostatic potential difference19. This asymmetry is typically achieved through the modification of surface functional groups on membranes or the use of heterostructured membrane architectures19–22. In particular, single nanopores have been extensively studied to explore nanofluidic ion transport in confined nanospaces, aiming to fundamentally replicate the specialized ion transport observed in biological ion channels11,23. Polymer-based materials, such as polyethylene terephthalate and polyimide, are typically employed to fabricate single-nanopore ionic diodes, which demonstrate directional ion transport behaviors24–27. However, the membranes in these artificial ionic diodes have thicknesses often of micrometers, which are much thicker than the only a few nanometers of natural cell membranes. For more accurately emulating the functional characteristics of biological ion channels, the development of ultrathin single-nanopore membranes with directional ion transport is crucial and remains a significant challenge28–30.

Ferroelectric polarization, arising from the spontaneous alignment of electric dipoles within materials31, presents a compelling alternative strategy for constructing ionic diodes with directional ion transport and rectification. This intrinsic polarization alignment naturally generates an asymmetric surface charge distribution, offering a viable approach for achieving directional ion transport within an ultrathin membrane and eliminating the need for asymmetric geometric design or additional surface functionalization. The epitaxial growth of ferroelectric oxide thin films has garnered significant attention over the past decades, particularly due to the surge of interest in multiferroics, which possess coexisting ferroic orders32,33. These materials show great promise for nonvolatile components, exhibiting robust room-temperature ferroelectricity even in ultrathin films just a few unit cells thick34,35. Furthermore, recent developments in ultrathin freestanding ferroelectric oxide thin films, enabled by the use of a water-soluble sacrificial layer in epitaxial structures, have led to the realization of crack-free membranes extending up to several millimeters34,36,37. These breakthroughs in ultrathin freestanding thin films shed light on the development of innovative ionic diodes based on ultrathin single-nanopore ferroelectric membranes (FEMs).

This work demonstrates a freestanding single-crystalline FEM made of bismuth ferrite (BiFeO3, BFO), with an ultrathin thickness down to 30 nm, functioning as a single-nanopore ionic diode. By employing state-of-the-art nanofabrication techniques, a single “symmetric-type” BFO nanopore with pore dimensions of only a few nanometers is fabricated to exhibit distinction current rectification (ICR) behavior driven by the spontaneous polarization of the freestanding FEM. In addition, the single-nanopore BFO FEM exhibits hysteresis-like switchable rectification behavior under external pH regulation, establishing the membrane as a stimuli-adaptive system and offering additional control for mimicking biological functions. The single-nanopore BFO FEM ionic diodes also exhibit efficient osmotic power harvesting, benefiting from the significant current amplification of directional ion transport. These findings indicate that ultrathin ferroelectric oxide single-nanopore membranes offer a robust and controllable platform for investigating directional ion transport at the nanoscale, driven by intrinsic spontaneous polarization. Incorporating ferroelectric systems opens an avenue for artificial nanomembranes to more faithfully emulate the fundamental transport characteristics of biological membranes.

Results
Ultrathin ferroelectric single-nanopore membrane
Given that well-regulated spontaneous polarization offers a promising route to controllable directional ion transport, high-quality single-crystalline FEMs with precise polarization control are essential. To this end, (001)-oriented BFO thin films were epitaxially grown on SrTiO3 (STO) single crystal substrates, buffered with Sr3Al2O6 (SAO) sacrificial layer (Step I, Fig. 1a). Here, BFO thin films with varying thicknesses of 30, 80, and 110 nm were prepared. The water-soluble SAO layer acted as a sacrificial layer, allowing the BFO layer to be released as a freestanding membrane without additional support (Step II). Following the release process of the freestanding membrane, the BFO thin film was transferred onto the target substrate for subsequent device fabrication and ionic transport measurements. Freestanding BFO single nanopores were prepared by initially employing a helium ion beam to drill an opening in the SiNx window, creating a hole with dimensions of approximately 100 nm × 200 nm (Step III, Supplementary Fig. 1). The BFO membranes were then transferred onto the SiNx window opening using a polymer-free transfer method (Supplementary Fig. 2)37. The resulting freestanding membranes preserved an uncontaminated surface, which is crucial for ensuring the functionality of ionic channels. Subsequently, single nanopores with various diameters were drilled into the BFO FEMs using an electron beam with TEM irradiation (Step IV).

The X-ray diffraction (XRD) L-scan (upper panel) and phi-scan (lower panel) of the freestanding BFO, presented in Fig. 1b, show (00L) reflections with no impurity peaks along the out-of-plane (OP) direction, and a distinct four-fold symmetry in the in-plane direction. These results confirm the high-quality single-crystalline nature of the BFO FEM. The high-resolution TEM image and selected-area electron diffraction (SAED) pattern (inset) shown in Fig. 1c confirm the preservation of the single-crystalline lattice structure in the BFO FEM after the freestanding process. The spontaneous ferroelectricity in BFO originates from the lone pair electrons and the displacement of the Bi3+ from their centrosymmetric positions relative to the distorted FeO6 octahedra, resulting in a large net polarization along the OP direction38,39. To verify the ferroelectricity of the freestanding BFO, scanning probe microscopy characterizations were performed. Fig. 1d presents the hysteresis loop of the BFO FEM, obtained through piezoresponse force microscopy (PFM). The result shows typical switchable ferroelectric behavior, as evidenced by a butterfly-shaped piezoresponse amplitude and 180° phase switching in response to the applied voltage. The switchable polarization enables the modulation of positively and negatively charged surface distributions, thereby allowing reversible control of surface potential, as further demonstrated by Kelvin probe force microscopy (KPFM) (Supplementary Fig. 4). Figure 1e presents the TEM image of a BFO single nanopore, featuring an effective diameter of 5 nm within a 30-nm-thick BFO FEM, which was produced using the aforementioned nanofabrication technique. Additionally, BFO single-nanopore FEMs with effective diameters of 3 nm and 9 nm were also fabricated, as shown in Supplementary Fig. 3.

Asymmetric ion transport in asymmetric-type nanopore
The ion transport characteristics of the single-nanopore BFO FEMs were investigated using a two-compartment electrochemical cell, as shown in Fig. 2a. Potassium chloride (KCl) was used as the electrolyte for all measurements due to the comparable mobilities and hydration radii of K⁺ and Cl− ions40. Prior to nanopore drilling, the integrity of the BFO FEM was verified by its near-zero, voltage-independent current response (Supplementary Fig. 5), confirming that the freestanding BFO FEM effectively blocks ion transport. Figure 2b presents the current–voltage (I–V) curves of 30-nm-thick BFO single nanopores with diameters of 3, 5, and 9 nm. For comparison, a single nanopore fabricated in a SiNx membrane with a similar thickness and a pore size of 3 nm was also created using the same nanofabrication process. The symmetric-type BFO nanopores exhibit non-linear asymmetric voltage-dependent ion transport behavior with a preferential transport direction, which is a characteristic feature of ICR observed in ionic diodes. The ICR ratio, which quantifies the degree of rectification, is defined as the ratio of current magnitudes at ±1V (see “Methods” section). These 30-nm-thick BFO single nanopore FEMs, with pore sizes ranging from 3 to 9 nm, exhibit increasing ionic currents with increasing pore sizes. Their corresponding ICR ratios remain relatively consistent with values of 4.2 for 3 nm, 4.1 for 5 nm, and 4.3 for 9 nm at an electrolyte concentration of 10-3 M. As the pore size is further increased to 15 nm, the ionic current continues to rise, whereas the ICR ratio exhibits a slight decrease (Supplementary Fig. 6). This decline is attributed to the diminished influence of surface-governed effects in larger pores41. The pronounced rectification in single-pore BFO FEMs is primarily attributed to the asymmetric surface charge induced by ferroelectric polarization. In contrast, the symmetric-type SiNx nanopore, which lacks ferroelectricity, displays the expected linear and symmetric I–V response, as shown in the inset of Fig. 2b. In addition to pore size, the influence of membrane thickness on the ion transport behavior of single-nanopore BFO FEMs was examined by controlling the growth thickness of the membranes. Ferroelectric BFO nanopores with increased thicknesses of 80 and 110 nm exhibit enhanced ICR ratios of 7.8 and 13.7, respectively (Supplementary Fig. 7). These results indicate that, despite their symmetric-type geometry, the ferroelectric polarization in ultrathin single-nanopore BFO FEMs can effectively induce directional ion transport through the spontaneous alignment of electric dipoles, even at a thickness of only 30 nm. Typically, creating asymmetry in nanopore membranes is accomplished through methods such as asymmetric geometric fabrication, additional surface functionalization, or heterostructural architectures (see Supplementary Table 1). By contrast, the spontaneous ferroelectric polarization in single-nanopore FEMs provides a fundamentally distinct and inherently more straightforward approach to establishing asymmetry for directional ion transport, without the need for additional fabrication or modification techniques.

We then examined the dependence of ionic conductance on electrolyte concentrations in a single-nanopore BFO FEM with a pore size of 9 nm and a thickness of 30 nm (Fig. 2c and Supplementary Fig. 8). As shown, the BFO nanopore exhibits a deviation from linear bulk behavior at low electrolyte concentrations, which is a typical signature of nanofluidic behavior42,43. As the salt concentration decreases, the electric double layer overlap becomes significant, and thus, the surface conductance, influenced by the surface charges on the pore walls, dominates the overall conductance behavior9,44. Furthermore, Fig. 2d demonstrates the stable operation of the single nanopore BFO FEM, highlighting its robustness as a potential ionic diode component, attributed to the inherent stability of metal oxides.

Polarization-switchable directional ion transport
In biological ion channels, activities, such as protonation or ion selectivity, are strongly influenced by the surrounding pH environment45. Similarly, the surface charge characteristics of artificial ion membranes, including charge density and polarity, can be modulated by the environmental pH, thereby affecting ion transport behavior23. Understanding the rectification responses of ionic diodes under varying pH conditions enables enhanced control of nanopore membranes for mimicking biological functionalities. In particular, the surface termination of metal oxides follows a general equilibrium expressed as

M-OH + H+ ⇌ M-OH2+ and M-OH ⇌ M-O- + H+ (1)

where M represents the metal element46. The equilibrium shifts to the right as pH increases and to the left as pH decreases, depending on the degree of hydroxyl dissociation when the metal oxide surface is in contact with an aqueous solution. By harnessing the pH-dependent surface termination chemistry of BFO thin films at the solid-liquid interface, polarization-switchable rectification behavior in response to environmental pH changes is demonstrated. This endows the membrane with pH-responsive adaptability and offers an additional level of control for emulating a biological ion channel. Fig. 3a shows the I–V characteristics of a 9-nm BFO single pore with a thickness of 30 nm measured at pH values of 11, 6, and 3. The I–V curves show current amplification at positive voltages and current suppression at negative voltages at pH 11 and 6. By contrast, the behavior reverses at pH 3, showing current amplification at negative voltages and suppression at positive voltages. The corresponding rectification ratios are 4.3 and 3.4 for pH 11 and 6, while a negative ratio of -3.2 is observed for pH 3. This shift from a positive to a negative ICR ratio indicates that the directional ionic transport behavior is responsive to environmental pH levels. The ferroelectric polarization directions of the BFO FEMs after exposure to the electrolytes with pH values of 11, 6, and 3 were examined through PFM. The resulting OP PFM phase images reveal a strong correlation between the polarization direction and the observed ionic rectification behavior, as indicated by the sign of the ICR ratio. As shown in Fig. 3b, upward polarization (Pup) for the BFO FEMs corresponds to positive ICR ratios at pH 11 and 6, while the downward polarization (Pdown) gives rise to a negative ratio at pH 3. Nevertheless, for a thicker BFO FEM with a thickness of 110 nm, the unchanged upward polarization direction leads to the consistently positive ICR ratios after exposure to electrolytes at pH 11 and 3 with no inversion observed (Supplementary Fig. 9). This underscores the critical role of polarization direction in governing directional ion transport in single-nanopore BFO FEMs, as reversing the polarization results in a corresponding inversion of the ICR.

The polarization reversal in the 30-nm-thick BFO FEM is primarily driven by pH-varied surface termination of the metal oxide as the H⁺/OH⁻ concentration in aqueous solution changes. Initially, under alkaline conditions (pH 11), the surface is dominated by M–O- bonds, resulting in a negatively charged termination that generates an upward electric field aligned with the original upward polarization of the as-grown BFO FEM. At the neutral condition (pH 6), which is close to the point of zero charge for the BFO FEM surface47, the resulting weak electric field does not alter the polarization direction. In contrast, at acidic conditions (pH 3), the surface becomes enriched with M–OH2+ groups, creating a positively charged termination and a downward electric field that opposes the original polarization, thereby causing the polarization to switch direction. When H+ and OH- interact with O and Fe on the BFO surface, they form M–O–H bonds, leading to upward and downward displacements of Fe ions from their original positions48. This behavior is further supported by the X-ray photoelectron spectroscopy (XPS) result (Supplementary Fig. 10), which shows a significant increase in M–O–H surface species during the switching process as the environmental pH changes, indicating a strong interplay between the surface electrostatics and ionic interactions. However, when the BFO FEM thickness is increased to 110 nm, the electric field generated by surface termination becomes insufficient compared to the 30-nm-thick membrane despite having a similar surface charge density. These findings indicate that the polarization-switchable ion transport in response to pH stimuli is a distinct characteristic of the ultrathin single-nanopore BFO FEM, mimicking the behavior of biological ion channels.

Building on the polarization-switchable directional ionic transport behavior of the ultrathin single-nanopore BFO FEM in various pH environments, we performed ion selectivity measurements as shown in Fig. 3c. Ion selectivity is assessed under a significant concentration gradient across the membrane, which allows for the evaluation of its selective ion transport characteristics and surface charge properties14. One side of the BFO FEM is in contact with 1 M KCl, while the opposite side is in contact with 10⁻⁵ M KCl. The contribution from the highly diluted side is considered negligible, enabling estimation of the individual ionic currents from K⁺ and Cl− by reversing the electrolyte configuration. At pH levels of 11 and 6, the BFO single nanopore exhibits cation-selective transport, with the K⁺ current being the dominant contribution. In contrast, at pH 3, the membrane shifts toward anion selectivity, where the Cl− current exceeds that of the cations. This switch in ion selectivity underscores the dynamic pH-responsive surface behavior of the BFO FEM for its ionic transport properties, which is closely linked to alterations in ferroelectric polarizations. Furthermore, the inversion of the ICR is quantitatively modeled using theoretical simulations based on the multi-ion Poisson–Nernst–Planck and Navier–Stokes (PNP-NS) model49, which incorporates surface chemical reactions on the pore wall, all ion species, and the effects of electroosmotic flow (see Methods). In the BFO nanopore model, the surface charge distribution is set to align with the direction of polarization, as illustrated in Fig. 3d and Supplementary Fig. 11. The simulated I–V curves, along with the corresponding ion concentration distributions, reproduce the observed ICR inversion with ion accumulation and depletion under opposite voltage polarities (Fig. 3e and Supplementary Fig. 11). It is worth noting that a discrepancy exists between the values of experimental and simulated ionic currents, arising from deviations in simulated parameters (e.g., induced surface charge density, nanopore dielectric constant, and surface site densities of functional groups) from the actual system. Nevertheless, the simulations qualitatively explain the experimental observations of rectification inversion under different polarization directions, thereby supporting the proposed polarization-switchable rectification.

Hysteresis-like rectification behavior
In addition to the switchable polarity of ionic transport behavior by adjusting H⁺ or OH⁻ concentrations near the BFO surface, the ultrathin 30-nm-thick BFO single nanopore exhibits an intriguing reversible ICR response to the changes in pH conditions. Fig. 4a, b show the evolution of the I–V curves to reflect ionic diode transport characteristics during pH cycling. A forward sweep was performed from pH 11 to pH 3, followed by a reverse sweep from pH 3 back to pH 11. We observed that an initially positive ICR ratio reverses to negative when exposed to acidic aqueous solutions, and subsequently returns to a positive value when re-exposed to basic aqueous solutions. However, the ICR ratio as a function of varying pH exhibits hysteresis-like behavior between the forward and reverse sweeps. Figure 4c summarizes the ICR ratios of the single-nanopore BFO FEMs during both sweeping directions under various pH values, revealing distinct rectification states at each pH value. For example, there are two sweep-dependent rectification states at pH 6, which are a positive ICR ratio of 3.4 during the forward sweep (also see the inset of Fig. 4a), and a negative ratio of −2.4 during the reverse sweep (also see the inset of Fig. 4b). The corresponding OP PFM phase images in Fig. 4c confirm upward and downward polarizations associated with the two distinct ICR states. This hysteresis-like rectification closely resembles the polarization hysteresis loop of the BFO FEM obtained from PFM measurements, as presented in Fig. 1d and Supplementary Fig. 12. The hysteresis in ferroelectric materials arises from a polarization response that depends on the history of the applied electric field, where polarization switching occurs only when the coercive field is exceeded. Because the directional ion transport in single-nanopore BFO FEMs is primarily governed by ferroelectric polarization, the resulting ICR ratio exhibits a hysteretic response under cyclic pH sweeps, mirroring the ferroelectric switching mechanism. These findings highlight that the rectified ion transport in single-nanopore BFO FEMs is predominantly controlled by ferroelectric polarization, with the ultrathin BFO nanopore functioning as a pH-regulated, polarization-switchable ionic diode capable of reversible switching.

Ferroelectric single nanopores for osmotic power harvesting
Ionic diodes enable directional ion transport, allowing unidirectional current flow, preventing backflow, and reducing Joule heating-induced energy dissipation, thereby improving the efficiency of osmotic power conversion under salinity gradients50. The concentration gradients ranging from 10-fold to 1000-fold were introduced into the system to measure the osmotic power generation performance based on the ultrathin ferroelectric BFO single nanopore FEM as schematically shown in Fig. 5a. By measuring the I–V response of a BFO single nanopore with a thickness of 30 nm and pore size of 9 nm in a concentration gradient system (Supplementary Figs. 13−15 and Supplementary Table 2), we can determine the short-circuit current (Isc) at zero external bias and the osmotic potential derived from the open-circuit voltage (Voc) as shown in Fig. 5b. The pure osmosis-driven osmotic voltage (Vosm) and osmotic current (Iosm) are extracted from the voltage and current axis intercepts, respectively, after subtracting the inherent redox voltages (Vred) generated at the electrode-electrolyte interfaces due to concentration imbalances. Both Vosm and Iosm rise with increasing concentration gradient ratios. The Vosm follows an approximately linear trend, while the Iosm exhibits exponential growth with the concentration gradient, as shown in Fig. 5c, d. As a result, the BFO single nanopore demonstrates a high osmotic power (Posm, where Posm = 1/4 × Iosm × Vosm), as compared with those previously reported single-pore membranes (Supplementary Table 3). This superior osmotic power performance stems from the significant enhancement in the Iosm, enabled by the directional ion transport of the single-nanopore BFO FEM, which effectively amplifies ionic current despite its relatively lower surface charge density compared to state-of-the-art single-nanopore membranes (see Supplementary Figs. 16 and 17 for more details)12,42,44.

In a practical application, the BFO nanopore ionic diode was connected in series with an external electrical resistor to simulate power delivery to a load. Fig. 5e, f show the actual output current (Iout) and output power (Pout) as functions of load resistance (Rload) for the 9-nm BFO nanopore under a concentration gradient of 1000. With increasing Rload, Iout decreases, while the output power, Pout = Iout^2 × Rload, reaches a local maximum when the load resistance matches the internal resistance of the nanopore9,40. Under these conditions, the BFO single nanopore produces a promising peak output power of 13.1 nW at a Rload of 1 MΩ. These results highlight the effectiveness of ferroelectric oxide membranes for energy harvesting, attributed to their unique polarization-induced directional ion transport behavior. In addition, the influence of surface charge on ion transport is known to become more significant as the pore diameter decreases. We evaluated the osmotic power generation performance of the 3-nm BFO nanopore and observed a higher osmotic voltage, which can be attributed to the enhanced electric double layer overlap at smaller pore sizes. However, the reduced pore size also led to a lower osmotic current, thereby limiting the overall power output. Because optimal osmotic power generation requires both high voltage and current, the 9-nm BFO pore, providing a superior osmotic current along with a sufficient voltage, achieves high power performance (also see Supplementary Fig. 18 for details).

In summary, we have demonstrated a polarization-switchable single-nanopore ionic diode fabricated from ultrathin freestanding ferroelectric BFO membranes. These BFO single symmetric-type nanopores enable directional ion transport due to their intrinsically asymmetrical surface charge arising from ferroelectric polarization. By harnessing the functionality of the pH-responsive surface termination of metal oxides, the ultrathin single-pore BFO FEM exhibits polarization-switchable and hysteresis-like reversible ionic rectification transport. Furthermore, a nanowatt-scale osmotic power is generated through a single BFO nanopore, benefiting from the amplification of directional ion currents. These artificial ionic diodes achieve exceptional directional ionic transport at nanometer-scale thicknesses without relying on traditional asymmetric geometry or surface functionalization. Such ultrathin ferroelectric metal oxide single-nanopore membranes act as promising foundational ionic components for future advancement in mimicking the functions of biological cell membranes for developing related ionic circuits and facilitating osmotic power conversion.

Methods
PLD growth
Single-crystalline freestanding BFO films were fabricated using a two-step process. First, epitaxial layers of SAO and BFO were deposited sequentially on STO single-crystal substrates via pulsed laser deposition (PLD), where the SAO layer served as an epitaxial sacrificial layer. The deposition of SAO was carried out at 740°C under an oxygen pressure of 40 mTorr, while BFO was deposited at 700°C under a higher oxygen pressure of 100 mTorr. Following the deposition, the samples were cooled to room temperature in an oxygen atmosphere maintained at 600 Torr to minimize oxygen vacancies.

Materials characterizations
High-resolution XRD L-scan measurement of the freestanding BFO membranes was performed using a synchrotron-based 6+2-circle diffractometer. The measurements utilized a photon energy of 10 keV and a beam size of 0.8 × 0.8 mm². These experiments were conducted at beamlines TPS-09A, TLS-13A1, and TLS-17B at the National Synchrotron Radiation Research Center (NSRRC), Taiwan. The L-scan and RSM measurements were acquired with an integration time of 2 s per data point and were presented in reciprocal lattice units (r.l.u.), normalized to the bulk lattice constant of BFO (1 r.l.u. = 2π/aBFO).

To examine the lattice structure of the freestanding BFO membranes, plane-view TEM images and diffraction patterns were acquired using a JEOL JEM-2100F transmission electron microscope equipped with a spherical aberration (Cs) corrector in STEM mode. These measurements were conducted at the Core Facility Center of National Cheng Kung University, Taiwan.

The PFM, KPFM, and AFM images of BFO were acquired using a commercial scanning probe system (Innova, Bruker; NanoDrive software, version 8.02). The PFM signal was collected in contact mode using the Pt/Ir-coated conductive Si tips (OSCM-PIT, Olympus) with a spring constant of 1–5 Nm−1, driven by an AC voltage amplitude of 1 V. In KPFM, the same conductive tip was used to measure the surface potential. After the first topographic scan, the tip was lifted 100 nm above the surface for the potential measurement. The AFM image was acquired in tapping mode using Si tips (OLTESPA, Olympus) with a spring constant of 0.5–4.4 Nm−1 and frequency at 60–100 kHz. The XPS spectra were acquired using the ULVAC PHI 5000 Versa Probe system equipped with an Al Kα monochromatic X-ray source. The zeta potentials of BFO thin film were measured using a streaming potential-based zeta potential analyzer (SurPASS 3, Anton Paar) in 10-2 M KCl.

Nanopore fabrication
To release the freestanding BFO membranes, the SAO sacrificial layer was selectively etched using deionized water, enabling the detachment of the BFO layer from the underlying STO substrate37. The combination of the mild etching condition and the strong mechanical robustness of the BFO membrane allows it to remain intact with a lateral size on the millimeter scale. The pre-fabricated SiNx aperture is intentionally fabricated at the center of the Si chip, the size of which is 1 cm, making it easy to handle. The floating BFO membrane can then be gently scooped up with the aperture chip, enabling the millimeter-sized BFO membrane to cover the central region of the SiNx aperture chip. The specifications of the SiNx substrate (Norcada, Canada) are as follows: a chip frame size of 10 mm by 10 mm, Si thickness of 200 μm, SiNx membrane thickness of 30 nm, and a membrane area of 50 μm by 50 μm. The SiNx hole was drilled using a helium ion beam microscope (ZEISS ORION NanoFab) with an acceleration voltage of 30 kV, beam current of 20 pA, spacing of 0.5 nm, dwell time of 1 μs for a total duration of 200 s. The secondary electron image of the drilled SiNx hole was also acquired. After the transfer, a BFO single nanopore was drilled using TEM (JEOL JEM-ARM300F2) equipped with double spherical aberration correctors. For comparison, a SiNx nanopore was also fabricated directly on the SiNx membrane using TEM drilling.

Electrical measurement
All electrical measurements were conducted using a customized setup consisting of two PMMA reservoirs and holed PDMS buffer layers to sandwich the nanopore samples securely. Electrodes were prepared by electroplating silver wires (2 mm in diameter and 70 mm in length) in a 0.1 M KCl solution (without adjusting pH) at 2 V against a graphite rod, which served as the counter electrode, for 15 min. In the measurements, the electrode in the left reservoir, positioned at the rear side of the nanopore sample, served as the reference electrode, while the electrode in the right reservoir, located at the front side, functioned as the working electrode. The pH values of the KCl electrolytes were measured and adjusted beforehand using a pH meter (6177 M, Jenco). A Keithley 6487 source meter is used to apply voltage and record current. The measurement was controlled using the LabVIEW program (NI LabVIEW 2019). A variable resistor (RS-200W, IET Labs) with resistance ranging from 0 to 108 Ω is used for real output performances. To minimize electromagnetic interference, the measurement setup is enclosed in a Faraday cage (Ivium Technologies) with a common ground with all the measurement equipment.

ICR ratio
The ICR ratio in this work is defined as the ratio of current magnitudes measured at ±1V, and is expressed as follows:

ICR ratio = |I(1V)| / |I(-1V)| if |I(1V)| ≥ |I(-1V)|
ICR ratio = -|I(-1V)| / |I(1V)| if |I(1V)| ≤ |I(-1V)| (2)

The sign of the ICR ratio value indicates the rectification direction observed.

Theoretical simulation
The influence of pH on the ion transport behaviors of a single cylindrical BFO nanopore was also investigated through numerical simulation (COMSOL Multiphysics, version 4.3a). The multi-ion Poisson–Nernst–Planck (PNP) and Navier–Stokes (NS) equations were adopted to describe the ion transport behaviors. The electrical potential is expressed by the Poisson equation:

-εf ∇^2ϕ = ρe = F Σ z_j C_j (3)

where ϕ is the electric potential, ρe is the electric charge density of the electrolyte, and C_j, z_j are the concentration and valence of the j-th ion (j = 1 for K+, j = 2 for Cl−, j = 3 for H+, and j = 4 for OH−), respectively.

The ion transport is expressed by the Nernst-Planck equation:

∇·J_j = ∇·(uC_j - D_j ∇C_j - (F z_j D_j / RT) C_j ∇ϕ) j=1,2,3,4 (4)

where J_j, R, and D_j are the flux and diffusion coefficient of the j-th ion species, respectively; T is the absolute temperature, respectively; u is the fluid velocity.

The flow field is described by the continuity and Navier–Stokes equations:

-∇p + μ∇^2u - ρe ∇ϕ = 0 (5)

∇·u = 0 (6)

where p and μ are the hydrodynamic pressure and the fluid viscosity, respectively. Since the Reynolds numbers in the system are very small, the inertial terms in the Navier–Stokes equation can be neglected.

Subsequently, the calculation of the ionic current involves integrating the total ionic flux over the cross-sectional area, which can be expressed as follows:

I = F Σ z_j ∫ |J_j| · n dS (7)

where S and n represent the cross-sectional area and unit outer normal vector, respectively.

We assumed the following boundary conditions to solve the above governing Eq. (1). We used the cylindrical coordinate system (r, z) with the origin at the center of the nanopore to describe a cylindrical nanopore with length (L=30 nm) and radius (R=3 nm) connecting two big reservoirs. The symmetric boundary condition was specified along the axis of the nanopore. (2) The reservoirs at both ends were sufficiently large, ensuring that the ion concentrations remained unaffected by the charged channel or the reservoir on the opposite side, allowing both ends to maintain the bulk concentration value (C_j = C_j0). (3) To determine the potential across the system, the electrical potential at the reservoir boundary on the upper side was set to the applied bias voltage (ϕ = V_app), while the electrical potential at the reservoir boundary on the opposite side was set to ground (ϕ = 0). (4) The walls of the BFO region were also ion-impermeable (n·J_j = 0) and nonslip, with a surface charge density (σ). (7) We set an induced surface charge density (σ_p = 1 C m−2) to describe the extra effect of the pH value. In pH 11, surface charge density was set to (σ - σ_p) at the BFO region boundary near the bias voltage, and surface charge density was set to (σ + σ_p) at the BFO region boundary near the grounded. In pH 3, the opposite surface charge density was applied. (8) Since the dielectric material of the membrane wall, when in contact with an aqueous solution, exhibited a charge-regulated nature. Its surface charge density (σ) could be determined by the following deprotonation/protonation reactions with equilibrium constants K_A and K_B:

MOH ⇌ MO- + H+ and MOH + H+ ⇌ MOH2+ (8)

In the above reactions, 10^-pK_A = Γ_MO- [H+] / Γ_MOH and 10^-pK_B = Γ_MOH2+ / (Γ_MOH [H+]), where Γ_MO-, Γ_MOH, and Γ_MOH2+ are the surface site concentrations of MO-, MOH, and MOH2+, respectively. The total number of site density of dissociable MOH molecules on the membrane wall surface was Γ_total = Γ_MOH + Γ_MO- + Γ_MOH2+. The surface charge density of the membrane wall was expressed as:

σ = -F (Γ_MO- - Γ_MOH2+) = -F Γ_total (10^-pK_A / ([H+] + 10^-pK_A) - 10^-pK_B [H+] / (1 + 10^-pK_B [H+])) (9)

For the BFO, we assumed the parameters Γ_total, pK_A, and pK_B were 0.1 nm−2, 5, and -2, respectively.

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "This study presents a new method to control migration of ions by utilizing the intrinsic ferroelectric polarization of ultrathin freestanding single-crystalline BiFeO₃ membranes with single nano-pore and demonstrate a polarization-switchable ionic diode. The pH-switchable rectification and osmotic power generation is very interesting. However, the current experimental evidence is inadequate to conclusively support the primary claims. Here are some major concerns.\n1, The manuscript provides PFM phase images to indicate the polarization state of freestanding BiFeO3. This is a very local characterization of domain. How about the spontaneous and remnant polarization characterized by P-E hysteresis loops? Especially in 30 nm BiFeO3. Usually, its polarization depends on films thickness. Dose thickness-dependent polarization influences the thickness-dependent ion transport behavior? What about the resistivity or I-V characteristic of pure BiFeO3 membrane, is it insulating of semiconducting?\n2, Usually, ultrathin freestanding films have defects like pinholes or cracks if not well prepared. Here, the quality of freestanding BiFeO3 membranes is not well demonstrated. It does not rule out defects elsewhere or potential damage during the transfer and drilling processes. Surface morphology characterized by AFM and SEM is necessary.\n3, Supplementary Fig. 5 is a control test. Which film is used here? Is it true for all the film thickness.\n4, The pH-dependent ICR inversion (Fig. 3a) and hysteresis-like rectification behavior (Fig. 4c) is the critical findings of this work. How many devices has been measured? What about the reproducibility? The error-bar is missing in Fig.4c.", "reviewer_2": "The manuscript titled \"Single symmetric nanopores in ultrathin crystalline ferroelectric BiFeO3 membranes as polarization-switchable ionic diodes\" introduces an ultrathin, freestanding ferroelectric crystalline BiFeO3 (BFO) membrane with a \"symmetric\" single nanopore. This system is claimed to achieve directional ion transport, driven by its natural spontaneous polarization, without requiring additional geometric modifications or surface functionalization. The proposed applications include ionic diodes for developing ionic circuits and enhancing osmotic energy conversion. The authors report that the fabricated artificial ionic diode achieves remarkable directional ion transport at the nanoscale, a feat traditionally reliant on asymmetric geometries or surface modifications.\nOverall, the testing and characterization presented are comprehensive, and the manuscript is well-written. However, upon a thorough review of the work, I find that several key claims are not adequately addressed. Therefore, this reviewer holds reservations about the suitability of this work for publication in Nature Communications. The specific points are as follows:\n1. Regarding Fig. 2b, the rectification property is attributed to the asymmetric surface charge induced by ferroelectric polarization. Generally, the influence of surface charge on ion transport becomes stronger as the pore diameter decreases. Consequently, would pores with diameters smaller than 3 nm exhibit superior rectification characteristics? The authors should comment on this possibility.\n2.In Supplementary Table 2 of the Supporting Information (SI), how were the Eredox values obtained? Were these values measured experimentally, or were they calculated directly from ionic activity coefficients? Please clarify the methodology.\n3.The reported voltage of 193 mV in Supplementary Fig. 13 is indeed significant. To allow for a more robust comparison with existing literature, could the authors perform I-V curve measurements under a 0.01 M / 0.5 M KCl concentration gradient? A vast amount of comparative data on ion selectivity is available for these specific conditions.\n4.In Supplementary Fig. 14, it is observed that the I-V curves transition from a linear to a more curved shape as the concentration gradient increases. The authors should provide a more detailed explanation for this transition from ohmic to rectifying behavior.\n5.In Fig. 5b of the main text, the measured Eredox is nearly twice the value of Eosm. This observation suggests a relatively poor ion selectivity of the BFO membrane. While the short-circuit current (Isc) is also important for osmotic power generation, the low selectivity is a critical issue that needs to be addressed.\n6.Have the authors measured the I-V curves under a 0.01 M / 0.5 M KCl gradient at different pH values, specifically pH 3, 7, and 11? Such experiments would enable a direct comparison of the membrane's ion selectivity under acidic, neutral, and alkaline conditions. Osmotic power performance under neutral conditions (pH 7) is of greater general and practical relevance, yet it is noted that the majority of the I-V curves and osmotic power data in this manuscript were collected at pH 11.", "reviewer_3": "The paper reports polarization-switchable ionic diodes using ultrathin crystalline ferroelectric BiFeO3 nanopore membranes with symmetric nanopores. It is truly worth noting that the fabricated BiFeO3 nanopore membranes achieve unidirectional ion transport using a symmetric nanopore shape with no asymmetric nanopore shape (conical, bullet shape etc.) and surface functionalization (silane coupling, polyelectrolyte modification) differing from conventional thin film ionic diodes. Moreover, reversible polarization switching with hysteretic ion current rectification characteristics, which reflects external pH conditions, is intriguing and is a new concept conventional polarization switching by using external large electric fields. The paper covers scientific fundamentals of a new class of ferroelectric ultrathin ionics diodes and their applications, including osmotic power conversion. To my best knowledge, the synthesized ferroelectric BiFeO3 nanopore membrane is one of the thinnest ionic diodes (~30 nm), except for the realistic biological membranes and theoretical calculations, expecting true artificial biological membranes. The approach presented in the manuscript is quite intriguing from the viewpoint of fundamentals on ultrahin ionic diodes and true applications for nanofluidics, energy conversion, and neuromorphic materials. A topic in the manuscript has garnered significant interest among researchers recently. As a reviewer, I believe this topic in the manuscript is suitable for the journal “Nature Communications”; however, some points need clarification before publication. Listed below are my concerns and comments that should be addressed in the revised manuscript.\nComments\n(1) In Figure 3, the authors explain that the switching of ICR characteristics by electrolyte pH is derived from ferroelectric polarization inversion associated with protonation/deprotonation equilibrium of the oxide surface by using PFM and KPFM. Although PFM and KPFM measurements provide us with the overall polarization and potential difference of the films, there is a lack of the actual surface potential formed by ferroelectric polarization under the different pH conditions. Could the authors estimate the surface potentials under each pH condition (ex., surface zeta potential measurement)? Further, are the electric fields formed by the pH change large enough to invert the ferroelectric polarization?\n(2) The authors accessed the inversion mechanism of ionic current rectification properties using the finite element method calculations (Figure 3d and e). The results seem to explain the overall trend; however, the ionic current calculated from the integration of the total ion flux is much smaller than that of the experimental data. Could the authors explain the gap between the experimental data and the theoretical calculations?\n(3) In all the transmembrane ion transport measurements, are the pH conditions symmetric for both reservoirs? Do the asymmetric pH or ionic strength conditions affect the overall ferroelectric polarization and ion current rectification properties?\n(4) In Figure 4, the authors displayed significantly intriguing ion rectification characteristics with hysteresis. However, such hysterical behavior possibly includes time-dependent changes in the surface potentials of the EFM films. Could the authors provide the detailed information about the time scales of exposure to the electrolyte solution? Is that enough to reach equilibrium? The time-dependent (nonsteady state) finite element calculations might help to understand such phenomena.\n(5) About the comparison of ICR performance to the literatures, it should be included in the detailed measurement conditions such as pH and ionic strength for fair comparison and to avoid positive misleading (Table S1).\n(6) Could the authors provide the size dimensions of the custom-made experimental setup for ionic diode measurements? In such a sandwich cell, the effective contact area of the electrolyte solution possibly affects the sample fabrication yield due to the high surface tension of the water."}, "author_response": "Response letter for “Single symmetric nanopores in ultrathin crystalline\nferroelectric BiFeO membranes as polarization-switchable ionic diodes”\nReviewer#1:\nComments:\nThis study presents a new method to control migration of ions by utilizing the intrinsic\nferroelectric polarization of ultrathin freestanding single-crystalline BiFeO₃ membranes with\nsingle nano-pore and demonstrate a polarization-switchable ionic diode. The pH-switchable\nrectification and osmotic power generation is very interesting. However, the current\nexperimental evidence is inadequate to conclusively support the primary claims. Here are some\nmajor concerns.\n1. The manuscript provides PFM phase images to indicate the polarization state of freestanding\nBiFeO . This is a very local characterization of domain. How about the spontaneous and\n3\nremnant polarization characterized by P-E hysteresis loops? Especially in 30 nm BiFeO .\ninfluences the thickness-dependent ion transport behavior? What about the resistivity or I-V\ncharacteristic of pure BiFeO membrane, is it insulating of semiconducting?\nWe thank the referee for the insightful questions. As noted, the PFM phase images provide\nlocal information on the ferroelectric domain configuration in freestanding BFO. To further\nvalidate the macroscopic ferroelectricity, we conducted P–E hysteresis loop measurements on\nBFO capacitors with various thicknesses (~30, 50, 80, and 105 nm). As shown in Figure R1,\nall devices exhibit well-defined, saturated hysteresis loops at 20 kHz, confirming robust\nferroelectric switching behavior. Notably, spontaneous and remnant polarizations remain\nrelatively consistent across the measured thickness range from 30 nm to 105 nm. Although\npolarization in ferroelectric thin films is often influenced by factors such as strain,\ndepolarization fields, or size effects, these influences typically become more significant in films\nbelow ~10 nm or under strong epitaxial constraints.1,2 Thus, based on these data, the\nmacroscopic P–E measurements with pronounced hysteresis loops indicate that the BFO thin\nfilms exhibit high-quality ferroelectric properties down to a thickness of 30 nm, as adopted in\nour work.\nFigure R1. Thickness-dependent P-E measurements of BFO films with varying thicknesses.\nNevertheless, it is worth mentioning that the BFO ionic diodes in this work were\nperformed with the freestanding dimensions of 100 nm by 200 nm, as shown in Figure R2.\nThus, the ferroelectric behavior at the microscopic scale is also of critical importance; we\nfurther investigated the local ferroelectric properties as follows.\nFigure R2. Schematic illustration and SEM image of the freestanding area (100 nm by 200 nm)\nfor the BFO membranes.\nPFM-based characterizations serve as a critical tool for confirming the presence and\nstability of ferroelectricity in local regions. To further elucidate this, we performed thickness-\ndependent PFM hysteresis loop measurements and employed an advanced PFM-based\ntechnique—contact Kelvin Probe Force Microscopy (cKPFM). This method enables the\ndecoupling of true ferroelectric switching from electrostatic or non-linear charge effects. In\ncKPFM, the sample is written using a series of stepwise DC biases (V ), and the PFM\nwrite\nresponse is subsequently read at multiple DC voltages (V ). The resulting shifts and shapes\nread\nof the response curves offer quantitative insight into polarization dynamics and local charge\nbehavior.3 As shown in Figure R3, both the PFM hysteresis loops and cKPFM measurements\nconfirm that robust and stable ferroelectricity is preserved in freestanding BFO membranes\nacross a wide range of thicknesses. These findings support the result of the sustained local\npolarization states, which plays a major role in influencing the ion transport behaviors of\ndevices.\nFigure R3. Thickness-dependent (a) hysteresis loops of piezoresponse amplitude, phase, and\n(b) cKPFM measurements for BFO membranes with varying thicknesses.\nRegarding the electrical transport properties of the pure BFO membrane, we conducted\nconductive atomic force microscopy (c-AFM) measurements, which are well-suited for\nprobing transport behavior at the nanometer scale—comparable to the ion channel\ndimensions—to investigate the resistivity and assess whether the intrinsic BFO behaves as an\ninsulator or a semiconductor (Figure R4a). Although the measured I-V characteristics exhibit a\nshape reminiscent of a semiconductor, the extremely low conduction currents observed indicate\nthat, under our experimental conditions with a very low oxygen vacancy concentration, the\npristine BFO membrane can be regarded as a semiconductor with extremely low conductivity.\nSpecifically, pore-free BFO membranes exhibit ion conduction currents of tens of picoamperes\n(Figure R4a), approximately three orders of magnitude lower than the currents measured in\nBFO nanopores immersed in electrolyte. This substantial difference demonstrates that the\nintrinsic BFO membrane has a much lower conductivity compared to the ion conduction\npathway formed by the single-nanopore. Furthermore, the negligible ionic current in BFO\nmembranes without nanopores confirms that the observed conduction enhancement is mainly\nresulting from the presence of nanopores (Figure R4b). These findings reinforce the conclusion\nthat the BFO membrane has extremely low conductivity, with nanopores serving as the\ndominant channels for ionic conduction.\nFigure R4. (a) The conduction current of the BFO membranes as measured by c-AFM,\nshowing semiconducting behavior. (b) Ionic current of the 30-nm-thick BFO membrane with\nand without a nanopore, highlighting the contribution of ions passing through the nanopore.\nReferences:\n1. Rault, J. E. et al. Thickness-dependent polarization of strained BiFeO films with constant\n3\ntetragonality. Phys. Rev. Lett. 109, 267601 (2012).\n2. Ren, J., Tang, S., Guo, C., Wang, J. & Huang, H. Surface effect of thickness-dependent\npolarization and domain evolution in BiFeO epitaxial ultrathin films. ACS Appl. Mater.\n3. Balke, N. et al. Differentiating ferroelectric and nonferroelectric electromechanical effects\nwith scanning probe microscopy. ACS Nano 9, 6484–6492 (2015).\n2. Usually, ultrathin freestanding films have defects like pinholes or cracks if not well prepared.\nHere, the quality of freestanding BiFeO membranes is not well demonstrated. It does not rule\n3\nout defects elsewhere or potential damage during the transfer and drilling processes. Surface\nmorphology characterized by AFM and SEM is necessary.\nAnswer:\nWe thank the reviewer for raising this important point. As mentioned above, the BFO ionic\ndiodes in this work were performed with the freestanding dimensions of 100 nm by 200 nm, as\nshown in Figure R2. We examined the morphology of the BFO membrane using atomic force\nmicroscopy (AFM), scanning an area of approximately 25 µm by 25 µm to fully cover the\nfreestanding region. As shown in Figure R5a, the surface was uniform without observable\npinholes, and the height profile revealed a roughness of less than 1 nm. In addition, as\nmentioned above, a BFO membrane without a nanopore exhibits an ion conduction current of\nseveral picoamperes, which is approximately three orders of magnitude lower than that\nmeasured in a BFO membrane with a 3 nm nanopore immersed in electrolyte. This result\nindicates that the ionic current is highly sensitive to the presence of a pinhole or crack.\nTo further confirm the structural integrity of the BFO membrane after transfer onto the\nhole substrate, we conducted a leakage current test in the measurement cell prior to electron\nbeam drilling. As shown in Figure R5b, the as-transferred BFO membrane without a nanopore\nexhibited negligible ionic current, whereas a 3 nm nanopore displayed an ionic current three\norders of magnitude higher. If a pinhole or crack had formed during fabrication, the ionic\ncurrent would have been comparable (or even larger) to that of the nanopore case. These results,\ntherefore, confirm the absence of pinholes and cracks within the freestanding region. Similar\ncurrent responses were also observed for the 80- and 110-nm-thick BFO membranes, as shown\nin Figures R6b and c.\nFigure R5. (a) AFM image and height profile of BFO membrane showing a uniform surface\nwithout observable pinholes and cracks. (b) Leakage current measurement of the BFO\nmembrane in 10⁻³ M KCl at pH 11. Ionic current of the 30-nm-thick BFO membrane with\nand without a nanopore, highlighting the contribution of ions passing through the nanopore.\n3. Supplementary Fig. 5 is a control test. Which film is used here? Is it true for all the film\nthickness.\nAnswer:\nThank the reviewer for this comment. In Supplementary Fig. 5, the I-V curve was\nmeasured from a 30-nm-thick BFO membrane and exhibited a negligible ionic current (Figure\nR6a). Similar current responses were also observed for the 80- and 110-nm-thick BFO\nmembranes, as shown in Figure R6b and c, further confirming the high-quality BFO\nmembranes with integrity in the freestanding regions for those samples with different\nthicknesses.\nFigure R6. Leakage current measurements of the (a) 30-nm-, (b) 80-nm-, and (c) 110-nm-thick\nBFO membranes before the nanopore drilling process, showing negligible ionic currents that\nconfirm the structural integrity of the BFO membranes is preserved during the fabrication\nprocess.\n4. The pH-dependent ICR inversion (Fig. 3a) and hysteresis-like rectification behavior (Fig. 4c)\nis the critical findings of this work. How many devices has been measured? What about the\nreproducibility? The error-bar is missing in Fig.4c.\nAnswer:\nThank the reviewer for raising this point. A total of ten devices were measured for the\nhysteresis-like rectification behavior. All devices exhibited consistent hysteresis behavior,\ndemonstrating repeatable ion current rectification in response to environmental pH.\nRepresentative ICR ratio-pH loops from three devices are shown in Figure R7. These results\nconfirm both the robustness of the observed rectification phenomenon and the reproducibility\nof the BFO nanopore fabrication process. The overall statistical data from all devices, including\ndevice-to-device variation, are reflected in the error bars presented in Figure R8.\nFigure R7. ICR ratio-pH loops measured from three individual BFO nanopore devices,\ndemonstrating consistent hysteresis-like rectification behavior across samples.\nFigure R8. ICR ratio-pH hysteresis loop including error bars.\nRevision made:\nFigure 4c has been revised to Figure R8, which includes error bars, in the revised\nmanuscript (page 26).\nReviewer#2:\nComments:\nThe manuscript titled \"Single symmetric nanopores in ultrathin crystalline ferroelectric BiFeO\n3\n(BFO) membranes as polarization-switchable ionic diodes\" introduces an ultrathin,\nfreestanding ferroelectric crystalline BFO membrane with a \"symmetric\" single nanopore. This\nsystem is claimed to achieve directional ion transport, driven by its natural spontaneous\npolarization, without requiring additional geometric modifications or surface functionalization.\nThe proposed applications include ionic diodes for developing ionic circuits and enhancing\nosmotic energy conversion. The authors report that the fabricated artificial ionic diode achieves\nremarkable directional ion transport at the nanoscale, a feat traditionally reliant on asymmetric\ngeometries or surface modifications.\nOverall, the testing and characterization presented are comprehensive, and the manuscript is\nwell-written. However, upon a thorough review of the work, I find that several key claims are\nnot adequately addressed. Therefore, this reviewer holds reservations about the suitability of\nthis work for publication in Nature Communications. The specific points are as follows:\n1. Regarding Fig. 2b, the rectification property is attributed to the asymmetric surface charge\ninduced by ferroelectric polarization. Generally, the influence of surface charge on ion transport\nbecomes stronger as the pore diameter decreases. Consequently, would pores with diameters\nsmaller than 3 nm exhibit superior rectification characteristics? The authors should comment\non this possibility.\nAnswer:\nWe thank the reviewer for this insightful comment. We agree that smaller nanopores, with\nstronger electric double layer overlap, enhance surface charge effects on ion transport and thus\nfavor higher osmotic voltage. However, with our current TEM drilling technique, fabricating\npores smaller than 3 nm in a 30-nm-thick BFO membrane remains technically challenging.\nAchieving such sizes requires a highly focused electron beam, which significantly increases\nthe local energy density and causes extremely rapid drilling, making it difficult to precisely\ncontrol the final pore diameter. Consequently, the smallest nanopores we could reliably\nfabricate in this work were about 3 nm. Nevertheless, we observe a clear effect of pore size on\nsurface charge and ion transport as the pore diameter decreases from 9 nm to 3 nm. As shown\nin Supplementary Figure 18, the 3 nm nanopore exhibits a higher osmotic voltage of 113.5 mV\ncompared with the 9 nm nanopore with an osmotic voltage of 53.2 mV at a concentration\ngradient of 1000, consistent with the reviewer’s comment that the influence of surface charge\non ion transport becomes more pronounced with decreasing pore diameter.\nRevision made:\nThe description of the pore size effect on the osmotic ion transport has been added to the\nrevised manuscript on page 13, and the corresponding figure has been added to the revised\nSupplementary Information on page 23.\n2. In Supplementary Table 2 of the Supporting Information (SI), how were the Eredox values\nobtained? Were these values measured experimentally, or were they calculated directly from\nionic activity coefficients? Please clarify the methodology.\nAnswer:\nThank the reviewer for pointing out this point. The redox voltages (V ) listed in\nredox\nSupplementary Table 2 were experimentally measured, with the corresponding I-V curves\nunder concentration gradients from 10- to 1000-fold shown in Figure R9. In the osmotic\nmeasurement configuration, the measured open-circuit voltage (V ) contains contributions\noc\nfrom both the electrode redox potential (V ) and the osmotic voltage (V ) arising from ion\nredox osm\nselectivity. To isolate V , the contribution from V must be minimized, which can be\nredox osm\nachieved by suppressing ion selectivity in the transport pathway. When the pore size is much\nlarger than twice the electric double layer thickness, ion selectivity becomes negligible and\nbulk ionic transport dominates. Under this condition, the measured V reflects V . In our\noc redox\nstudy, the KCl electrolyte concentration for osmotic power generation ranged from 10⁻³ to 1 M,\ncorresponding to electric double layer thicknesses of 0.3–9.6 nm.4 A hole substrate with a 50\nμm opening—over three orders of magnitude larger than the electric double layer thickness—\nwas used to ensure bulk transport dominance. This large opening effectively eliminates surface\ncharge effects, allowing the intrinsic electrode-to-electrode V across different concentration\nredox\ngradients to be directly extracted from the voltage-axis intercepts. The low concentration was\nfixed at 10-3 M and the high concentration ranged from 10-2 to 1 M, in order to generate the\nconcentration gradients from 10- to 1000-fold.\nFigure R9. (a) Optical microscopy image of the large-hole (50 μm by 50 μm) substrate used\nfor redox voltage measurements. (b) Corresponding I-V curves measured under various KCl\nconcentration gradients. The low concentration was fixed at 10-3 M and the high concentration\nranged from 10-2 to 1 M, in order to generate the concentration gradients from 10- to 1000-fold.\nReferences:\n4. Wang, C. et al. Ultrathin self‐standing covalent organic frameworks toward highly‐\nefficient nanofluidic osmotic energy generator. Adv. Funct. Mater. 32, 2204068 (2022).\nRevision made:\nThe detailed description of methodology for redox voltage measurement and Figure R9,\npresented as Supplementary Figure 14, have been added to the revised Supplementary\nInformation (pages 17 and 18).\n3. The reported voltage of 193 mV in Supplementary Fig. 13 is indeed significant. To allow for\na more robust comparison with existing literature, could the authors perform I-V curve\nmeasurements under a 0.01 M / 0.5 M KCl concentration gradient? A vast amount of\ncomparative data on ion selectivity is available for these specific conditions.\nAnswer:\nThank the reviewer for the comment. The I-V curves of BFO nanopores with pore sizes\nof 9 nm and 3 nm measured under a 0.01 M/0.5 M concentration gradient are provided in Figure\nR10. The corresponding open-circuit voltages (V ) are 118 and 151 mV for 9 and 3 nm BFO\noc\npores, respectively. The higher voltage generated by the 3 nm pore can be attributed to the\nenhanced electric double layer overlap at a smaller pore size. As summarized in Table R1, the\nobserved voltages are comparable to those of previously reported state-of-the-art membranes\nunder the same KCl concentration gradient condition, highlighting the high ion selectivity of\nBFO nanopores. Notably, the thickness of the BFO membranes is only 30 nm, which is several\norders of magnitude thinner than that of reported membranes, indicating the significant effect\nof ferroelectrinc polarization on the corresponding ionic transport.\nFigure R10. The I-V curves of BFO nanopores with pore sizes of (a) 9 nm and (b) 3 nm\nmeasured under a 0.01 M/0.5 M KCl concentration gradient.\nTable R1. Comparison of the V of BFO nanopores with those of previously reported state-\noc\nof-the-art membranes under a 0.01 M/0.5 M KCl concentration gradient.\nMembrane\nMembrane V Reference\noc\nthickness\n118 mV (9 nm)\nThis\nBFO 30 nm\nwork\n151 mV (3 nm)\nNi (OH) @AAO 52.56 μm 85.58 mV 5\n2 2\nSilk nanofibril/AAO 65 μm 93 mV 6\nKCNF/MXene[a] ~2.83 μm ~110 mV 7\nPSS-modified graphene oxide[b] ~2 μm 146 mV 8\nUiO-66-NH /BANM[c] ~20.19 μm 148 mV 9\n[a] KCNF: kelp cellulose nanofibers\n[b] PSS: poly(sodium 4-styrenesulfonate)\n[c] BANM: branched alumina nanochannel membrane\n[d] PDDA: polydiallyl dimethyl ammonium\nReferences:\n5. Zeng, H. et al. Unleashing the power of osmotic energy: metal hydroxide-organic\nframework membranes for efficient conversion. Small 20, 2310811 (2024).\n6. Xin, W. et al. High-performance silk-based hybrid membranes employed for osmotic\nenergy conversion. Nat. Commun. 10, 3876 (2019).\n7. Zhai, R. et al. Kelp nanofiber‐based composite membranes for highly efficient osmotic\nenergy conversion. Adv. Funct. Mater. 34, 2313914 (2023).\n8. Qian, Y. et al. Two-dimensional membranes with highly charged nanochannels for\nosmotic energy conversion. ChemSusChem 15, e202200933 (2022).\n9. Yang, Z.-J., Yeh, L.-H., Peng, Y.-H., Chuang, Y.-P. & Wu, K. C.-W. Enhancing ionic\nselectivity and osmotic energy by using an ultrathin Zr-MOF-based heterogeneous\nmembrane with trilayered continuous porous structure. Angew. Chem. Int. Ed. 63,\ne202408375 (2024).\n10. Ding, L. et al. Bioinspired Ti C T MXene-based ionic diode membrane for high-\n3 2 x\nefficient osmotic energy conversion. Angew. Chem. Int. Ed. 61, e202206152 (2022).\n4. In Supplementary Fig. 14, it is observed that the I-V curves transition from a linear to a more\ncurved shape as the concentration gradient increases. The authors should provide a more\ndetailed explanation for this transition from ohmic to rectifying behavior.\nAnswer:\nThank the reviewer for this comment. At pH 11, the BFO is cation-selective with K+ ions\nserving as the dominant charge carriers. Arising from the intrinsic ferroelectric polarization of\nthe BFO membrane, asymmetric K+ ion currents are observed even in the absence of a\nconcentration gradient (Figure R11a), resulting in a slightly curved (not completely linear) I-V\ncharacteristic. In fact, the I-V curves remain non-linear even at low concentration gradients.\nWhen a concentration gradient is applied, as seen in osmotic power generation, it further\nintroduces an additional external asymmetry into the system.11 The disparity in ionic\navailability between the two sides becomes more significant (Figure R11b), which makes the\ncurved I-V characteristics bend more noticeably.12 Thus, the stronger the concentration gradient,\nthe more curved and asymmetric the I-V response becomes (Figure R11c).\nFigure R11. Schematic illustration of primary K+ ion transport through a cation-selective BFO\nnanopore under opposite voltage polarities (a) without and (b) with concentration gradient. (c)\nOsmotic I-V curves of the BFO nanopore under various KCl concentration gradients at pH 11.\nReferences:\n11. Cheng, L.-J. & Guo, L. J. Nanofluidic diodes. Chem. Soc. Rev. 39, 923-938 (2010).\n12. Lavi, O. & Green, Y. A theoretical characterization of osmotic power generation in\nnanofluidic systems. Commun. Mater. 5, 124 (2024).\n5. In Fig. 5b of the main text, the measured Eredox is nearly twice the value of Eosm. This\nobservation suggests a relatively poor ion selectivity of the BFO membrane. While the short-\ncircuit current (Isc) is also important for osmotic power generation, the low selectivity is a\ncritical issue that needs to be addressed.\nAnswer:\nThank the reviewer for pointing this out. Ion selectivity strongly depends on channel\nlength (related to membrane thickness) and pore size.13 The relatively low ion selectivity of the\nBFO membrane with a pore size of 9 nm arises from its ultrathin thickness of only 30 nm—\nseveral orders of magnitude thinner than conventional polymer-,14,15 AAO-,16,17 and nanosheet-\nbased membranes,18,19 which typically range from several to tens of micrometers.\nIon selectivity can be further improved by reducing the pore size, as smaller nanopores\npromote more substantial overlap of electric double layers. We also investigated a 3-nm BFO\nnanopore, as shown in Supplementary Information. The osmotic voltage (V = V -V )\nosm oc redox\nand osmotic current as a function of concentration gradient for both pores are compared in\nFigure R12. Notably, the 3-nm pore exhibits a significantly higher osmotic voltage of 113.5\nmV under a concentration gradient of 1000, which is comparable or even surpasses the values\nof reported state-of-the-art single-pore membranes (Table R2). However, the smaller pore also\nproduced a lower osmotic current, which limits the achievable power output. Since both\nosmotic voltage and osmotic current are critical for maximizing power generation, the 9-nm\nBFO pore, which offers a balance of high osmotic current and reasonable osmotic voltage, was\nselected to demonstrate high osmotic power in the main text. In the revised version, we have\ncompared the osmotic performances of 3 nm and 9 nm BFO nanopores in the Supplementary\nInformation to address this issue.\nFigure R12. (a) Osmotic voltage and (b) osmotic current of the 3-nm and 9-nm BFO nanopores\nunder concentration gradients. The base concentration is 10-3 M. Error bars represent standard\ndeviation, and dashed curves are for eye guidance of trends.\nTable R2. Comparison of osmotic voltage with previously reported state-of-the-art single-pore\nmembranes in KCl electrolyte under a concentration gradient of 1000 (1 M/0.001 M).\nMembrane I (nA) V (mV) P (pW) Ref.\nosm osm osm\nBFO (9 nm) 52.5 53.2 ~700 This\nwork\nBFO (3 nm) 8.1 113.5 230\nhBN/SiN 0.8 ~85 17 20\nMoS 8.8 62.7 137.9 21\nConical PET 27.5 97 667 23\nPLL-modified conical PET 21 49 257 24\nReferences:\n13. Chu, C.-W., Fauziah, A. R. & Yeh, L.-H. Optimizing membranes for osmotic power\ngeneration. Angew. Chem. Int. Ed. 62, e202303582 (2023).\n14. Zhang, Z. et al. Ultrathin and ion-selective Janus membranes for high-performance\nosmotic energy conversion. J. Am. Chem. Soc. 139, 8905-8914 (2017).\n15. Zhang, Z. et al. Engineered asymmetric heterogeneous membrane: a concentration-\ngradient-driven energy harvesting device. J. Am. Chem. Soc. 137, 14765-14772 (2015).\n16. Zhu, C. et al. Polyoxometalate-based plasmonic electron sponge membrane for\nnanofluidic osmotic energy conversion. Nat. Commun. 15, 4213 (2024).\n17. Chang, J.-N. et al. Plasmonic ion diode membrane (PIDM) for enhanced nanofluidic\nion transport. Angew. Chem. Int. Ed. 64, e202502591 (2025).\n18. Liu, C. et al. Bio-inspired double angstrom-scale confinement in Ti-deficient Ti0.87O2\nnanosheet membranes for ultrahigh-performance osmotic power generation. Angew.\nChem. Int. Ed. 63, e202315947 (2024).\n19. Wang, Q. et al. Efficient solar-osmotic power generation from bioinspired anti-fouling\n2D WS composite membranes. Angew. Chem. Int. Ed. 62, e202302938 (2023).\n2\n20. Yazda, K. et al. High osmotic power generation via nanopore arrays in hybrid hexagonal\nboron nitride/silicon nitride membranes. Nano Lett. 21, 4152-4159 (2021).\n21. Feng, J. et al. Single-layer MoS nanopores as nanopower generators. Nature 536, 197-\n2\n200 (2016).\n22. Laucirica, G. et al. Shape matters: enhanced osmotic energy harvesting in bullet-shaped\nnanochannels. Nano Energy 71, 104612 (2020).\n23. Gao, M., Tsai, P.-C., Su, Y.-S., Peng, P.-H. & Yeh, L.-H. Single mesopores with high\nsurface charges as ultrahigh performance osmotic power generators. Small 16, 2006013\n(2020).\n24. Tsai, P.-C., Su, Y.-S., Gao, M. & Yeh, L.-H. Realization of robust mesoscale ionic\ndiodes for ultrahigh osmotic energy generation at mild neutral pH. J. Mater. Chem. A 9,\n20502-20509 (2021).\n6. Have the authors measured the I-V curves under a 0.01 M / 0.5 M KCl gradient at different\npH values, specifically pH 3, 7, and 11? Such experiments would enable a direct comparison\nof the membrane's ion selectivity under acidic, neutral, and alkaline conditions. Osmotic power\nperformance under neutral conditions (pH 7) is of greater general and practical relevance, yet\nit is noted that the majority of the I-V curves and osmotic power data in this manuscript were\ncollected at pH 11.\nAnswer:\nThank the reviewer for this comment. We measured the osmotic I-V curves at pH 3, 7, and\n11, representing acidic, neutral, and alkaline conditions, to evaluate the pH-dependent\nperformance for the 9-nm and 3-nm BFO nanopores. The curves measured under a 0.01 M/0.5\nM gradient after subtracting the redox voltage contributions (V = V -V ) are shown in\nosm oc redox\nFigure R13. The corresponding osmotic voltage, osmotic current, and calculated transference\nnumber are summarized in Table R3. Among the three conditions, BFO nanopores at pH 11\nexhibit the highest osmotic voltage, osmotic current, and ion selectivity. The performance at\npH 3 is moderate, while that at pH 7 is the lowest. This trend agrees with the ion selectivity\nmeasurement results in Figure 3c of the manuscript. We agree that osmotic power performance\nunder neutral conditions (pH 7) is of broader practical relevance. In the manuscript, however,\nwe highlighted the optimal performance of the BFO nanopore at pH 11 because it exhibited\nhigher power conversion efficiency.\nFigure R13. Osmotic I-V curves of the (a) 9-nm and (b) 3-nm BFO nanopores under a 0.01\nM/0.5 M KCl concentration gradient at pH 3 (acidic), 7 (neutral), and 11 (alkaline). The\ncontribution of the redox voltage has been subtracted.\nTable R3. Summary of osmotic performance of the 9-nm and 3-nm BFO nanopores under a\n0.01 M / 0.5 M KCl concentration gradient at pH 3, 7, and 11.\n9 nm 3 nm\nV I t+/t- V I t+/t-\nosm osm osm osm\npH 3 29 mV 16.7 nA 0.66 61 mV 1.9 nA 0.83\npH 7 24 mV 12.8 nA 0.63 48 mV 1.4 nA 0.76\npH 11 35 mV 29.7 nA 0.69 68 mV 4.3 nA 0.87\nReviewer#3:\nComments:\nThe paper reports polarization-switchable ionic diodes using ultrathin crystalline ferroelectric\nBiFeO nanopore membranes with symmetric nanopores. It is truly worth noting that the\n3\nfabricated BiFeO nanopore membranes achieve unidirectional ion transport using a symmetric\n3\nnanopore shape with no asymmetric nanopore shape (conical, bullet shape etc.) and surface\nfunctionalization (silane coupling, polyelectrolyte modification) differing from conventional\nthin film ionic diodes. Moreover, reversible polarization switching with hysteretic ion current\nrectification characteristics, which reflects external pH conditions, is intriguing and is a new\nconcept conventional polarization switching by using external large electric fields. The paper\ncovers scientific fundamentals of a new class of ferroelectric ultrathin ionics diodes and their\napplications, including osmotic power conversion. To my best knowledge, the synthesized\nferroelectric BiFeO nanopore membrane is one of the thinnest ionic diodes (~30 nm), except\n3\nfor the realistic biological membranes and theoretical calculations, expecting true artificial\nbiological membranes. The approach presented in the manuscript is quite intriguing from the\nviewpoint of fundamentals on ultrathin ionic diodes and true applications for nanofluidics,\nenergy conversion, and neuromorphic materials. A topic in the manuscript has garnered\nsignificant interest among researchers recently. As a reviewer, I believe this topic in the\nmanuscript is suitable for the journal “Nature Communications”; however, some points need\nclarification before publication. Listed below are my concerns and comments that should be\naddressed in the revised manuscript.\n1. In Figure 3, the authors explain that the switching of ICR characteristics by electrolyte pH\nis derived from ferroelectric polarization inversion associated with protonation/deprotonation\nequilibrium of the oxide surface by using PFM and KPFM. Although PFM and KPFM\nmeasurements provide us with the overall polarization and potential difference of the films,\nthere is a lack of the actual surface potential formed by ferroelectric polarization under the\ndifferent pH conditions. Could the authors estimate the surface potentials under each pH\ncondition (ex., surface zeta potential measurement)? Further, are the electric fields formed by\nthe pH change large enough to invert the ferroelectric polarization?\nAnswer:\nThank the reviewer for raising this point. The protonation/deprotonation process of the\nmetal oxide surfaces generally follows the equilibrium expressed as M-OH + ↔ M-OH + H+\n2\n↔ M-O- + 2H+, where M represents the metal element.25 As a result of this surface chemistry,\nwe observed that the BFO membrane exhibits cation selectivity at pH 11 and shifts to anion\nselectivity at pH 3 in the ion selectivity measurement. This qualitatively indicates that the\nequivalent surface potential of the BFO membrane changes from negative to positive as the pH\ndecreases.\nWe agree with the reviewer that the zeta potential can directly reflect the surface potential\nof a BFO membrane in an electrolyte. However, identifying the membrane zeta potential\ntypically requires a “streaming potential” measurement-based apparatus (e.g., SurPASS 3\nElectrokinetic Analyzer, Anton Paar),26 which operates under a relatively high applied pressure\n(typically 300-600 mbar). Such pressure could destroy a freestanding membrane. Therefore, as\nan alternative, we measured the zeta potential of a BFO sample on its as-grown substrate, as\nshown in Figure R14. The results show the increased surface zeta potential value as the pH is\nreduced from 11 to 3, and demonstrate the reversal of the surface charge property of BFO. This\ntrend agrees with the findings from the ion selectivity measurement.\nFigure R14. Zeta potential of BFO thin film on substrate under varying pH conditions.\nThe inversion of the ferroelectric polarization direction was characterized by PFM\nmeasurements. Based on our examinations, the PFM images in Figures 3b and 4c of the\nmanuscript (see Figure R15a) reveal a clear contrast between upward and downward\npolarization after the 30-nm-thick BFO membrane was exposed to electrolytes at varied pH\nvalues. Due to its ultrathin thickness, this phenomenon is attributed to the electric field\nestablished across the BFO membrane. We also fabricated a thicker (110-nm-thick) BFO\nmembrane for comparison. Figure R15b shows that no observable polarization inversion occurs\nafter electrolyte exposure in the thicker membrane. This absence of polarization switching is\nattributed to surface charge accumulation over a similar area in the thicker membrane, which\nmay cause the reduced electric field. These results indicate that the electric field generated by\npH variation is strong enough to invert the ferroelectric polarization direction in a 30-nm-thick\nBFO membrane, highlighting the critical role of ultrathin thickness in enabling such\npolarization switching.\nFigure R15. PFM piezoresponse phase images of the (a) 30-nm- and (b) 110-nm-thick BFO\nmembrane before and after exposure to electrolyte at pH 11 and 3.\nReferences:\n25. Yan, R., Liang, W., Fan, R. & Yang, P. Nanofluidic diodes based on nanotube\nheterojunctions. Nano Lett. 9, 3820-3825 (2009).\n26. Huang, K. T. et al. Zwitterionic gradient double‐network hydrogel membranes with\nsuperior biofouling resistance for sustainable osmotic energy harvesting. Adv. Funct.\nMater. 33, 2211316 (2023).\n2. The authors accessed the inversion mechanism of ionic current rectification properties using\nthe finite element method calculations (Figure 3d and e). The results seem to explain the overall\ntrend; however, the ionic current calculated from the integration of the total ion flux is much\nsmaller than that of the experimental data. Could the authors explain the gap between the\nexperimental data and the theoretical calculations?\nAnswer:\nWe thank the reviewer for the careful review of our manuscript. We agree that there is a\ngap between the experimental data and the simulated data. First, we would like to emphasize\nthat the simulation results presented were intended to provide a “qualitative” interpretation of\nthe experimental observations of rectification inversion under different polarization directions\nin Figure 3a of the manuscript. Nevertheless, the gap between the experimental data and the\ntheoretical calculations may arise from the choice of simulation parameters. For example, as\nwe increase the induced surface charge density (σ ) from 0.1 C m-2 to 1 C m-2, the amplified\n𝑝\ncurrent increases significantly, as shown in Figure R16, bringing the magnitude closer to the\nexperimental values. However, it becomes difficult to obtain convergent data when σ > 1 C\n𝑝\nm-2. Figure R16 also reveals that as σ increases, the qualitative I-V behaviors of the BFO\n𝑝\nnanopore system with rectification inversion under the two considered polarization directions\ncan be clearly seen, similar to the experimental observations. We believe that the current\nsimulation data can be applied to qualitatively explain the underlying physics observed in our\nexperiments. To avoid possible misunderstanding, we revised the simulated I-V curves of\nFigure 3e in the revised manuscript by using σ of 1 C m-2, which yields magnitudes closer\n𝑝\nto the experimental data.\nFigure R16. Simulated I-V curves of the considered BFO nanopore system under various levels\nof induced surface charge densities (σ ).\n𝑝\nRevision made:\nAn explanation of the gap between the experimental data and the simulated data has been\nadded in the revised manuscript (page 10). Figure 3e has been revised by using σ of 1 C m-\n𝑝\n2 in the revised manuscript (page 25). The corresponding supporting simulation data of\nSupplementary Figure 11 has been revised in the revised Supplementary Information (page 14).\n3. In all the transmembrane ion transport measurements, are the pH conditions symmetric for\nboth reservoirs? Do the asymmetric pH or ionic strength conditions affect the overall\nferroelectric polarization and ion current rectification properties?\nAnswer:\nThank the reviewer for this comment. All transmembrane ion transport measurements\nwere conducted under symmetric pH conditions. We also examined the effect of asymmetric\npH environments. Specifically, the BFO membrane was tested with the electrolytes on opposite\nsides at pH 11 and 3. As illustrated in the inset of Figure R17a, the top side is predominantly\nterminated by M-O- groups, while the bottom surface is dominated by M-OH + groups. Under\n2\nthis condition, the upward electric field by surface terminals aligns the ferroelectric polarization\nin the upward direction, consistent with the symmetric pH conditions. The resulting I-V curve\nis shown in Figure R17b with a corresponding ICR ratio of 5.6, which is higher than the values\nobtained under symmetric pH conditions of -3.2 and 4.3 at pH 3 and 11, respectively. This\nenhancement in rectification can be attributed to the increased surface charge contrast between\nthe two sides of the BFO membrane, particularly with opposite charge polarity.\nFigure R17. (a) Schematic illustration of the surface terminal groups and ferroelectric\npolarization direction of BFO under asymmetric pH conditions (pH 11/pH 3). (b) The resulting\nI-V curve of the BFO nanopore measured.\nWhen an asymmetric ionic strength condition (1 M/0.001 M at pH 11) is applied across\nthe BFO membrane, a convex I-V curve with a positive ICR ratio is observed, as shown in\nFigure R18a. The unequal ion strength (that is, a concentration gradient) introduces an\nadditional asymmetry that breaks the spatial symmetry of ion transport, thereby contributing to\nthe rectified effect. With a higher concentration gradient, the rectifying behavior becomes more\npronounced. Accordingly, more strongly curved I-V responses are observed under strongly\nasymmetric ionic strength (larger concentration gradients), as shown in Figure R18b.\nFigure R18. Ion transport behavior of the BFO nanopore measured under asymmetric ionic\nstrength conditions at pH 11. (a) I-V curve measured under 1 M/0.001 M (a concentration\ngradient of 1000). (b) I-V curves measured under increasing concentration gradients\n4. In Figure 4, the authors displayed significantly intriguing ion rectification characteristics\nwith hysteresis. However, such hysterical behavior possibly includes time-dependent changes\nin the surface potentials of the EFM films. Could the authors provide the detailed information\nabout the time scales of exposure to the electrolyte solution? Is that enough to reach equilibrium?\nThe time-dependent (nonsteady state) finite element calculations might help to understand such\nphenomena.\nAnswer:\nWe thank the reviewer for raising this point. As an example, Figure R19 shows a time\nevolution of ion rectification when pH changes from 5 to 3. The I-V characteristics stabilized\ntypically after approximately 8 minutes, suggesting that the system had reached equilibrium.\nAccordingly, in the hysteresis measurements, we applied a waiting period of 10 minutes after\neach pH change to ensure that the system reached equilibrium. Therefore, the ion rectification\ncharacteristics presented in Figure 4 are measured at steady state. Moreover, our simulation\nmodel already incorporates the interfacial chemical reactions on the BFO membrane surface;\nthus, introducing a dynamic process into the model would lead to non-convergence.\nFigure R19. Time evolution of the I-V curves for a BFO nanopore during the pH transition\nfrom 5 to 3, measured at 2-minute intervals.\n5. About the comparison of ICR performance to the literatures, it should be included in the\ndetailed measurement conditions such as pH and ionic strength for fair comparison and to avoid\npositive misleading (Table S1).\nAnswer:\nThank the reviewer for pointing this out. The measurement conditions have been included\nin the revised table, as shown in Table R4 on the following page.\nTable R4. Comparison of ICR performance with recently reported membranes in KCl\nelectrolyte.\nMembrane Creating asymmetry ICR ratio Concentration pH Voltage Ref.\n4.3 (30 nm)\nFerroelectric This\nBFO 7.8 (80 nm) 10-3 M 11 +1 V/-1 V\npolarization work\n13.7 (110 nm)\nWS/MoS Heterostructure 1.6 10-4 M 6 +1 V/-1 V 27\n2 2\nPMMT/MXene [a] Heterostructure 2.4 10-3 M － +1 V/-1 V 28\nZIF-8/UiO-66-\nHeterostructure 3.52 10-1 M ~7 +1 V/-1 V 29\n(COOH)\nGOM/PET [b] Heterostructure 12.3 10-4 M 5.6 +1 V/-1 V 32\nSurface functionalization,\nDAN/AAO [c] 19.3 10-3 M 7 +1 V/-1 V 33\nHeterostructure\nGeometric fabrication,\nNafion/AAO 21.1 10-1 M 4.3 +1 V/-1 V 34\nHeterostructure\nCu-TCPP(Fe)/PAA [d] Heterostructure 33.1 10-3 M 11 +1 V/-1 V 35\nUiO-66-(COOH)2- Geometric fabrication,\n34.7 10-1 M 5.7 +1 V/-1 V 36\nmodified PET Surface functionalization\n[a] PMMT: montmorillonite decorated with photoelectric molecules\n[b] GOM: graphene oxide membrane\n[c] DAN: dendrimer-nanoparticle network\n[d] PAA: porous anodic aluminum\nRevision made:\nSupplementary Table 1 has been replaced with Table R4 in the revised Supplementary\nInformation (page 9).\nReferences:\n27. Jia, P. et al. Harnessing ionic power from equilibrium electrolyte solution via\nphotoinduced active ion transport through van-der-Waals-like heterostructures. Adv.\nMater. 33, 2007529 (2021).\n28. Wang, L. et al. Photo‐induced active ion transport‐assisted efficient ionic power\nharvesting from bioinspired Janus dual‐field heterostructures. Adv. Funct. Mater. 34,\n2314165 (2024).\n29. Li, Z. Q. et al. Janus metal-organic framework membranes boosting the osmotic energy\nharvesting. ACS Appl. Mater. Interfaces 15, 23922-23930 (2023).\n30. Nie, X. et al. Photosynthetic-membrane-like ion translocation in visible-light-\nharvesting nanofluidic channels. Small 20, 2311531 (2024).\n31. Cao, E. & Siwy, Z. S. Heterogeneous nanopore arrays - selective modification of\nnanopores embedded in a membrane. Adv. Mater., 2418987 (2025).\n32. Dong, Y. et al. High-performance osmotic power generators based on the 1D/2D hybrid\nnanochannel system. ACS Appl. Mater. Interfaces 14, 29197-29212 (2022).\n33. Wang, C. et al. Dendrimer-Au nanoparticle network covered alumina membrane for ion\nrectification and enhanced bioanalysis. Nano Lett. 20, 1846-1854 (2020).\n34. Jung, J., Kim, J., Lee, H. S., Kang, I. S. & Choi, K. Multi-asymmetric ion-diode\nmembranes with superior selectivity and zero concentration polarization effect. ACS\nNano 13, 10761-10767 (2019).\n35. Wang, C. et al. Fabrication of bio‐inspired 2D MOFs/PAA hybrid membrane for\nasymmetric ion transport. Adv. Funct. Mater. 30, 1908804 (2019).\n36. Lu, J. et al. Efficient metal ion sieving in rectifying subnanochannels enabled by metal-\norganic frameworks. Nat. Mater. 19, 767-774 (2020).\n6. Could the authors provide the size dimensions of the custom-made experimental setup for\nionic diode measurements? In such a sandwich cell, the effective contact area of the electrolyte\nsolution possibly affects the sample fabrication yield due to the high surface tension of the\nwater.\nAnswer:\nThank the reviewer for this comment. The schematic illustration and dimensions of the\ncustom-made sandwich-type measurement cell are provided in Figure R20. The effective\ncontact area between the electrolyte solution and the BFO sample is determined by the hole\nsize of the PDMS sealing gasket, which is 6 mm in diameter (Figure R20c) for all\nmeasurements conducted in this study.\nFigure R20. Design and dimensions of the custom-made measurement cell. (a) Schematic\nillustration of the custom-made sandwich-type measurement cell. (b) Detailed dimensions of\nthe cell. (c) Photograph of the PDMS sealing gasket, featuring a 6 mm diameter hole that\ndefines the contact area between the electrolyte and the BFO sample."}, {"round": 2, "reviewer_comments": {"reviewer_3": "The revisions have been appropriately addressed, and I recommend the manuscript for publication in \"Nature\nCommunications\" without further revision.\"", "reviewer_4": "I think the authors have well addressed Reviewer 1's comments, and the work is novel and well written. While before publication in Nature Communications, some few points still require further clarification to fully substantiate the claims made in the manuscript.\n1. The main text heavily focuses on the 9 nm pore, while In Supplementary Fig. 3b, the BFO membrane appears to have lost its crystallinity and become amorphous following 9 nm pore drilling via electron beam irradiation. The authors should state this phenomenon.\n2. The manuscript describes a \"polymer-free transfer method.\" However, the Methods section lacks crucial details on how the freestanding BFO membrane is precisely aligned and placed to cover the pre-fabricated SiNx aperture."}, "author_response": "Response letter for “Single symmetric nanopores in ultrathin crystalline\nferroelectric BiFeO membranes as polarization-switchable ionic diodes”\nReviewer #3:\nComments:\nThe revisions have been appropriately addressed, and I recommend the manuscript for\npublication in \"Nature Communications\" without further revision.\"\nAnswer:\nWe sincerely appreciate the reviewer’s positive feedback and are pleased to know that our\nresponses have satisfactorily addressed the concerns.\nReviewer #4:\nComments:\nI think the authors have well addressed Reviewer 1's comments, and the work is novel and well\nwritten. While before publication in Nature Communications, some few points still require\nfurther clarification to fully substantiate the claims made in the manuscript.\n1. The main text heavily focuses on the 9 nm pore, while In Supplementary Fig. 3b, the BFO\nmembrane appears to have lost its crystallinity and become amorphous following 9 nm pore\ndrilling via electron beam irradiation. The authors should state this phenomenon.\nAnswer:\nThank the reviewer for pointing this out. The image of the 9-nm BFO pore in the previous\nSupplementary Fig. 3b did not clearly exhibit the crystallinity characateristics because it was\ncaptured at a lower magnification. Accordingly, we have provided a TEM image of the same\nBFO pore at a higher magnification of 12,000,000, as shown in Figure R1. The lattice fringes\nare clearly visible, confirming that the crystallinity of membrane is preserved after the nanpore\ndrilling process. We have replaced the higher-magnification image in the revised\nSupplementary Information.\nFigure R1. TEM image at high magnification for the 9-nm BFO nanopore.\nRevision made:\nSupplementary Fig. 3b has been replaced by Figure R1 in the revised Supplementary\nInformation (page 3).\n2. The manuscript describes a \"polymer-free transfer method.\" However, the Methods section\nlacks crucial details on how the freestanding BFO membrane is precisely aligned and placed\nto cover the pre-fabricated SiNx aperture.\nAnswer:\nThank the reviewer for this comment. The transfer process begins with the direct etching\nof the sacrificial SAO layer using water, which causes the BFO layer to detach and float on the\nwater surface. The combination of the mild etching condition and the strong mechanical\nrobustness of the BFO membrane allows it to remain intact with a lateral size on the millimeter\nscale. The pre-fabricated SiN aperture is intentionally fabricated at the center of the Si chip,\nx\nthe size of which is 1 cm., making it easy to handle. The floating BFO membrane can then be\ngently scooped up with the aperture chip, enabling the millimeter-sized BFO membrane to\ncover the central region of the aperture chip. In this way, the BFO membrane is transferred\nwithout using polymer support, thereby avoiding the typical polymer contramination that often\noccurs during the transfer process.\nRevision made:\nA more detailed description of the transfer method has been added to the Methods section\nin the revised manuscript (page 15)."}]

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