Electrostatic Gating of Ionic Conductance through Heterogeneous van der Waals Nanopores

Abstract

Nanofluidic ionic transistors typically require gate voltages above 1 V and operate only at submillimolar ionic strengths, limiting their biocompatible applications. We demonstrate ionic transistors consisting of single sub-10 nm nanopores drilled in van der Waals (vdW) heterostructures with internal gate electrodes made of few-layer graphene. These devices deliver up to 10-fold current modulation at gate voltages as low as 0.3 V in 10 mM KCl, and ∼2-fold modulation at near-physiological 100 mM KCl. Baseline conductance with no gate shows surface-charge-dominated transport below 100 mM KCl, consistent with negatively charged hBN walls and ∼5 nm opening of the pores. The surface charge and the electrochemical asymmetry introduced by the three-electrode configuration govern the device’s behavior: negative gate voltage (V _G) enriches ionic concentrations and enhances current, whereas positive V _G induces a local depletion zone that suppresses transport. The current modulation by V _G is dependent on the polarity of the transmembrane potential and leads to ion current rectification. Molecular dynamics simulations of a nanopore in a hBN–graphene–hBN stack reveal confinement and surface charge-dependent suppression of the relative permittivity of interfacial water. Continuum modeling with radially varying interfacial water permittivity reproduces the asymmetric I–V characteristics and explains how the embedded gate sculpts local potential and ion concentrations. By enabling sub-0.5 V control of ionic transport at up to 100 mM salt concentrations, these devices address a key need in nanofluidics to create low-power ionic circuits and biosensing.

Ion transport at the nanoscale exhibits phenomena not observed in microstructures due to the large surface-to-volume ratio of nanopores and nanochannels that makes the transport extremely sensitive to the electrochemical properties of the pore walls. − Changing the polarity and magnitude of surface charges tunes ion selectivity and conductance of the structures. Introducing surface charge patterns can break the electrochemical symmetry of nanopores, leading to rectification and diode-like characteristics of the transmembrane current, − behavior observed in many biological channels in a cell membrane.

The field of nanofluidics has also been inspired by gating achieved in electronic solid-state devices, specifically the ability to control ionic current by integration of electrically addressable gates. , If we could electrically, on demand, change the local electric potential in the pore, we could create ionic equivalents of electronic devices and connect them into circuits to achieve logic gates and ionic amplifiers. −

An ionic transistor modulates ion current by means of an electrically addressable electrode, and several examples of such systems have already been reported in the literature. Sub-10 nm in diameter nanopore field-effect transistors, fabricated using electron beam lithography and atomic layer deposition, provided gating in KCl concentrations of 1 mM and lower. At a gate voltage of −1 V and at 0.1 mM KCl, the transmembrane ion current was enhanced by a factor of up to 10. Similarly, 20 nm thick nanofluidic channels with two independent gates functioned as reconfigurable ionic diodes at mM concentrations of KCl and gate voltages of ∼1 V, while larger nanofluidic channels required gate voltages of tens of V to achieve ion current modulation. Ionic ambipolar transistors were reported as well, where carbon nanotubes templated into alumina were biased by an integrated gate. The smallest opening of the carbon nanotubes was 5 nm in diameter. When gate voltages of −1 and +1 V were applied to the membrane, two conductance states were obtained with an on–off ratio of up to 16,000 in 0.1 mM KCl. Another type of ionic transistor utilized atomic-scale channels in graphene oxide with an interlayer spacing of ∼0.45 nm. Applying gate voltage to the material changed the energy barrier for ion intercalation into the channel and enabled the transport for negative gate voltages exceeding −0.8 V, while blocking the transport for positive gate voltages.

Ionic transistors based on channels with an opening significantly larger than the Debye screening length were reported, as well. A voltage of 1 V at a gate placed on top of a membrane with a 300 nm pore increased surface charge density on the pore walls and ion selectivity, without significantly influencing the pore conductance. Even larger-scale ionic transistors were prepared based on microchannels and ion exchange membranes, offering high on–off ratios at the cost of high gate potentials of a few volts.

Nearly all ionic transistors reported thus far required gate voltages of at least 1 V to achieve significant modulations of ion current, and gating was observed in KCl concentrations of ∼1 mM or lower. Reducing the magnitude of the gate voltage while being able to modulate the ionic current at physiological salt concentrations of 100 mM is, however, important for future applications in ionic circuits, biocompatible devices, and biosensing. Low gate voltages would also mitigate energy requirements for operation, minimize undesired electrochemical reactions, and are expected to increase the longevity of the nanopore systems.

van der Waals (vdW) materials, such as graphite or hexagonal boron nitride and others, offer a unique host for nanopore-based devices. − Because of their layered structure, vdW materials can be stacked to form heterogeneous membranes − with atomically sharp interfaces between materials that exhibit vastly different properties. In principle, this enables the design of electric fields within a nanopore on the nanoscale, which is difficult to achieve with conventional nanofabrication techniques. Moreover, the single-crystal nature of vdW materials departs strongly from the amorphous or granular nature of the typical substrates used in solid-state nanopores.

Here, we utilize the properties of vdW films and report the design and performance of atomically precise ionic transistors that function at high salt concentrations, operate at gate voltages as low as 0.3 V, and offer modulation factors of up to 10× in 10 mM KCl. Our ionic transistor consists of a ∼5 nm diameter nanopore drilled in a vdW heterostructure comprising two layers of hBN encapsulating an internal graphene layer that acts as the gate electrode. As we and others have shown, transport properties of pores with aspect ratios significantly larger than 1 are much more sensitive to the properties of the pore walls than short pores whose conductance is mostly determined by the region at the pore entrance. − The thickness of the hBN layers was therefore tuned to ensure that the ionic transistor nanopores had an aspect ratio of at least 3.5. The multilayer hBN and graphene in our devices are therefore in contrast to single-layer hBN, graphene, and MoS₂ films used for single-molecule detection. ,,− The sub-10 nm opening diameter and large aspect ratio, as well as proximity of the gate electrode to the solution of our nanopores, enabled gating of ion currents in physiological conditions and sub-0.5 V gate voltages.

Results and Discussion

A scheme of the ionic transistor we designed is shown in Figure a,b. The vdW heterostructure consists of a sequential stack of hBN, few-layer graphene, and another hBN, which are assembled following a dry transfer technique. The final stack is transferred onto a TEM grid containing a 200 nm thick SiN _x membrane with a 5 μm diameter pore (Norcada Industrial Company), Figure c. Gold electrodes were attached to the graphene gate using electron beam lithography and metal evaporation following a liftoff process (see the Methods section for details). To avoid direct exposure to the solution, the metallic contacts were passivated by a 170 nm thick layer of SiO₂ deposited using plasma-enhanced chemical vapor deposition. A window on the SiO₂ layer was subsequently etched to expose the vdW membrane while leaving the electrodes protected. A nanopore was drilled into the vdW membrane with a focused electron beam in a transmission electron microscope (TEM) (Figure d). , This protocol allowed us to consistently fabricate sub-10 nm in diameter nanopore transistors within the vdW membranes.

1.

Nanopore ionic transistor in heterogeneous stacks of van der Waals (vdW) materials with an internal graphene gate electrode. (a) Cross-section schematic of the assembled stack of graphene and two layers of hBN. (b) Measurement circuit consisting of two independent voltages: source–drain, V _SD, and gate–drain, V _G. (c) Optical image of the assembled stack. (d) Transmission electron microscope (TEM) image of the nanopore drilled by electron beam (Device A). (e) Ionic conductance, G, versus KCl concentration for the nanopore shown in (d) at pH = 6. G_σ and G₀ are the fits of the experimental data with eq when considering −2.3 mC/m² and zero effective surface charge of the pore walls, respectively. For this sample, the top and bottom hBN layer thicknesses were 16.7 and 13.7 nm, respectively, and the middle graphene layer was 1 nm thick.

To characterize the conductance of the ionic transistor under gating, we measured the samples in KCl solutions at concentrations between 1 mM and 1 M. A custom electrolytic cell with an incorporated PCB board allowed us to establish an electrical connection to the graphene gate electrode (see Supporting Information Section 1). The measurements entailed application of two independent voltages: the source–drain voltage, V _SD, which drives the ions through the nanopore, and the gate voltage, V _G, which modulates the local ion concentration in the nanopore (Figure b).

Conductance Measurements without Gating Reveal Surface-Charge-Dominated Transport through vdW Nanopores

Nanopores prepared in the vdW heterostructures were first characterized without any gate modulation. Under the application of only V _SD, we observed that vdW nanopores behaved similarly to other nanopore systems (Figure e). Namely, the nanopore conductance followed a linear dependence on the salt concentration until a threshold concentration of 100 mM KCl, and leveled off at lower concentrations. Due to the effective screening of surface charge at 1 M KCl, , we used the conductance at this concentration to calculate the pore diameter. In the calculations, we assumed that the pore was cylindrical in shape with length L = 31.4 nm (determined by AFM measurements of the stack), and filled with a solution whose conductivity was equal to the bulk conductivity of 1 M KCl, i.e., 10 S/m. For device A shown in Figure , the electrochemically measured diameter was ∼4 nm, which is in good agreement with the 6 nm diameter measured by TEM. The small discrepancy between these two values might stem from the possible double-conical shape of pores drilled in TEM, as shown before for nanopores in silicon nitride films. ,

The plateauing of conductance at ∼100 mM KCl stems from the sub-10 nm opening and the presence of negative surface charges on hBN, shown before to enhance ionic transport by adding surface conductance. , Once the thickness of the screening length approaches the pore radius, the ionic transport of the system is dominated by the surface conductance, i.e., the number of ions in the pore is determined by the surface charge density, not the bulk salt concentration. The magnitude of the residual conductance at low concentrations can be used to determine the effective surface charge density of the pore walls, σ, using eq . ,

$$G=\left(\frac{\pi d^2}{4L}\right)[({\mu }_{\mathrm{K}}+{\mu }_{\mathrm{Cl}})n_{\mathrm{KCl}}\mathrm{e}+{\mu }_{\mathrm{K}}\frac{4\sigma }{d}]$$ 1

where d and L are pore diameter and length, respectively, and μ_K and μ_Cl are the mobilities of the potassium and chloride ions, respectively.

At pH 6, the surface charge density obtained from Figure e is −2.3 mC/m², which falls within the wide range of previously reported values for surface charge density of hBN surface and hBN nanopores of −1.2 and −250 mC/m². − Note that the leveling off of the currents already in a high concentration of 100 mM KCl (Figure e) supports the nanoscopic opening of the pore as well as the dominant role of the internal surface charges for the properties of ionic transport. We measured similar behavior in other vdW nanopores (Figure S2) and calculated surface charge densities in the same order of magnitude.

The presence of negative surface charges on the edges of the hBN nanopore was further verified by conductance measurements of a nanopore prepared in an hBN flake as a function of solution pH (see the Supporting Information, Section 2). As the solution becomes more acidic, the residual conductance at low concentrations decreases, indicating a lower effective negative surface charge. These observations are in agreement with recent studies that revealed adsorption of OH^– groups as the primary source of the effective surface charge on hBN. The lower availability of OH^– groups with lower pH reduces the surface charge and, consequently, reduces the conductance at low salt concentrations.

vdW Ionic Transistors Gate Ion Current with sub-0.5 V Gate Voltages

After completing test experiments with nanopores in the hBN–graphene–hBN stacks without electrodes, we performed electrochemical measurements of devices containing nanofabricated contacts (Figure a,b and Table S1). We expected the transmembrane current, I _D, to be gated with V _G significantly lower than 1 V, as shown before with graphene nanopore transistors whose opening was diminished by the presence of nanobubbles.

2.

Performance of vdW ionic transistors with gate voltage. (a) Optical image of Device B (Table S1) with layer thicknesses of 30, 2.5, and 6 nm for the top hBN, graphene, and bottom hBN, respectively, leading to a total membrane thickness of 38.5 nm. (b) TEM image of the 5 nm in diameter nanopore in Device B. (c) Drain current, I _D, vs source–drain voltage, V _SD, curves at different gate voltages, V _G, in 10 mM KCl for Device B. The results show that the ionic current through the nanopore is modulated by V _G, such that I _D increases (decreases) for negative (positive) V _G in comparison with the V _G = 0 V case. The ion current modulation is larger for positive V _SD values. (d) Plot of ion currents from panel (c) versus V _G reveals that for V _SD = 0.5 V, there is a ∼10 times modulation of the current for the V _G range measured (0.3 to −0.2 V). (e) Local conductance (G’) as a function of V _G, where G’ = ΔI _D/ΔV _SD, was calculated in the range of V _SD from 0.2 to 0.4 V. The local conductance also undergoes 10 times modulation in the same range of applied gate voltages. (f), (g), (h), and (i) show schemes of local ionic concentrations for the most representative cases: (f) V _SD = 0 and V _G = 0, (g) V _SD > 0, V _G < 0, (h) V _SD < 0, V _G < 0, (i) V _SD > 0, V _G > 0. Red and blue circles represent positive and negative ions, respectively.

Figure c,d shows results for device B, which was subjected to source–drain voltage, V _SD, from −0.5 to 0.5 V, and gate voltage, V _G, from −0.2 to +0.3 V. The I _D vs V _SD curves in Figure c reveal an enhancement of the transmembrane current for negative V _G. The current gating is significant for both positive and negative V _SD, but with larger modulation for positive biases, leading to ion current rectification. Figure d plots I _D as a function of V _G for a series of V _SD and reveals that at V _SD = 0.5 V, we observe a 10-fold modulation of the ionic current magnitude in the range of the applied gate voltages. To quantify the gating, we have also calculated the differential conductance (G’ = ΔI _D/ΔV _SD) for the positive V_SD values and confirmed the 10-fold enhancement of I _D current as V _G changes from −0.2 to +0.3 V (Figure e). Note that in the three-electrode configuration, the device rectifies the current such that the currents for positive V _SD are higher than the currents for negative V _SD. The asymmetry in the I _D vs V _SD curves is present even for V _G = 0, which points to the intrinsic asymmetry of the system introduced by the gate and negative charges on hBN, discussed below. Nanopores drilled in hBN-only films, as well as stacks of hBN–graphene–hBN with graphene floating, produced mostly symmetric I _D–V _SD relationships (Figure S2).

The observation of the strong current enhancement for negative V _G was observed in two additional independently fabricated stacks and nanopores with a diameter of ∼5 nm (See Supporting Information Section 3). We verified that the effect of gating occurred in devices with symmetric thicknesses of the hBN layers, as well as devices where the two hBN layers significantly differed in their thickness. These results confirmed that a graphite gate whose thickness does not exceed a few nm and, in some devices, constitutes only 1/10th of the entire stack thickness can effectively modulate the transmembrane current. Table S1 in Section 3 of the Supporting Information summarizes geometrical and electrochemical properties of devices used in this study. The devices exhibit the following reproducible behavior. V_G < 0 at positive V _SD leads to enhancement of I _SD of at least a factor of 2, and gating effects are larger for V _SD > 0 than for V _SD < 0. The devices we present, however, differ by the degree of ion current modulation, with device B showing the largest modulation and device D the weakest. We believe the variability of the degree of current gating with V _G could stem from differences in the pore geometry that could be introduced by the process of drilling with an electron beam through large-aspect-ratio stacks.

To understand the behavior of our ionic transistors, namely, enhancement (suppression) of I _SD for negative (positive) gate voltages, we considered a simple electrostatic model of the nanopore and 3 electrode configuration. Based on the voltage gating observed in the experiments and cation selectivity of the nanopores, we analyzed the influence of both V _SD and V _G on local electric potential and ionic concentrations in the pore and proposed the mechanism of current modulation (Figure f–i). We begin with the analysis of the system when V _SD and V _G are zero (Figure f). In this case, ionic concentrations in the pore are entirely dominated by the presence of surface charges on the pore walls, as in Figure e. The concentration of cations is enhanced in comparison to what one would expect if the pore were filled with a bulk solution, thereby increasing the pore conductance. The configuration in Figure f is our starting point to consider three cases with different arrangements of V _SD and V _G: (i) V _G < 0 and V _SD > 0 (Figure g), (ii) V _G < 0 and V _SD < 0 (Figure h), and (iii) V _G > 0 for both polarities of V _SD (Figure i).

Figure g shows the schematic of the electric potential and local cation concentration for V _G < 0 and V _SD > 0. Application of negative gate voltages will increase the K⁺ concentration near the gate beyond the enhancement that results from the presence of negative surface charges on hBN, hence leading to higher conductance. It is important to note that in this three-electrode device, applying positive or negative V _SD produces different electric potential (and ionic concentration) profiles in the pore due to the asymmetry of the source-to-gate, V _SG, and drain-to-gate, V _DG, potential differences. For example, when V _G = −0.2 V and V _SD = 0.5 V (Figure g), V _SG is 0.7 V, and V _DG is 0.2 V, both enhancing the cation concentration that already exists due to the surface charge. On the other hand, when V _SD < 0, e.g., V _SD = −0.5 V, V _SG = −0.3 V, and the majority carriers (cations) are driven into the pore only from the drain side with V _DG = 0.2 V, and exit through the source side. This results in a smaller relative increase in K⁺ ion concentration and conductance when compared to V _G = −0.2 V and V _SD = 0.5 V. Due to the clear differences in the nanopore ionic concentrations for the same V _G but opposite polarities of V _SD and the stronger enhancement of K⁺ concentration for positive V _SD, the current modulation will also be more significant for positive V _SD values. Thus, the simple schemes of ionic concentrations for negative V _G with positive (Figure g) or negative V _SD (Figure h) provide an intuitive explanation for the asymmetry observed in the experimental I _D vs V _SD curves (Figure c). A similar reasoning also explains the presence of rectification observed for a V _G = 0 V. When V _SD > 0, cations enter the pore from the source side with V _SG = V _SD, e.g., 0.5 V, leading to locally enhanced ionic concentrations in the pore. In contrast, for V _SD < 0, cations enter the device from the drain side with V _DG = 0 V, which limits their arrival rate and lowers ionic concentration and current.

Finally, a positive V _G (Figure i) will repel K⁺ ions away from the center of the device and create an ionic bipolar junction with two antiparallel ionic diodes. , For both polarities of V _SD, one of the diode junctions remains reverse-biased, leading to an overall reduced concentration of ions in the nanopore, and, consequently, reduced transmembrane current. The experimental I _D vs V _SD characteristics become more symmetric for more positive V _G, which points to the dominant role of the gate in ionic depletion and, consequently, similar ionic concentrations for both positive and negative V _SD voltages.

The device shown in Figure remained operational for ∼2 months, which we attribute to the low gate voltages applied during the measurements. Our three-electrode setup also allowed us to quantify the leakage gate currents, whose detailed analysis is included in the Supporting Information file (Section 4). The measurements confirmed that the leakage current does not influence our transmembrane currents such that V _G modulates ionic concentrations in the pore but does not contribute to I _D.

The salt concentration is a critical parameter that determines the magnitude of electrostatic modulation in nanofluidic systems. ,, In general, lower salt concentrations allow electrostatic interactions within the nanopore to dominate the conductance, whereas at high salt concentrations, the bulk properties of the solution control the transport behavior. Therefore, it is important to determine the concentration range at which the gating effect is attainable in our devices. To accomplish this, we characterized the gating properties of device C (Figure a, b) by recording I _D vs V _SD curves for different gate voltages at KCl concentrations ranging from 1 mM to 1 M (See Supporting Information, Section 3). From these I _D–V _SD curves, we determined the local differential conductance of the nanopore for positive V _SD values (from 0.3 to 0.6 V), where the gating effects are the strongest (see Supporting Information, Figure S3), and plotted it as a function of the KCl concentration and V _G. Figure a shows that the gating effects are more significant at lower KCl concentrations. In addition, for all concentrations probed, the conductance increases with the magnitude of negative V _G and decreases for more positive V _G relative to the V _G = 0 case. To further quantify the conductance gating with V _G, at each KCl concentration, we calculated the modulation ratio G’_max/G’_min (Figure b), defined as the conductance at V _G = −0.3 V divided by that at V _G = 0.3 V. The analysis in Figure b confirms that the current modulation becomes stronger as salt concentration decreases. The gating is already significant at 100 mM KCl, with a modulation ratio of 1.8 ± 0.1, and it continues to increase for lower concentrations, reaching a maximum of 4.3 ± 0.4 at 1 mM KCl for this device. At 1 M KCl, the modulation ratio of 1.3 ± 0.2 is the closest to 1 (no modulation).

3.

Gating of ion current in vdW ionic transistors as a function of salt concentration. (a) Local differential conductance as a function of salt concentration for Device C (Table S1). The local conductance was calculated for the V _SD range from 0.3 to 0.6 V, where the modulation effects are the strongest. The inset shows a TEM image of the nanopore. Device C consisted of two 11 nm thick hBN layers and a 3.5 nm thick layer of graphene in the middle of the sandwich structure. (b) Conductance ratio G’ (V _G = −0.3 V)/ G’(V _G = 0.3 V) for each KCl concentration. This ratio is used to quantify the dependence of the conductance modulation on the ionic concentration.

Continuum Modeling of vdW Ionic Transistors Reveals Significant Modulation of Ionic Concentrations with V _G

To understand the gating effects in the vdW ionic transistor, we simulated the system using the Poisson–Nernst–Planck equations solved using the COMSOL Multiphysics package. We began the modeling with a system containing the same thickness of the two hBN layers to confirm that the three-electrode setup with graphene leads to electrochemical asymmetry of our devices. Two 15 nm thick hBN layers were modeled considering the physical properties of the material, such as dielectric constant and a surface charge density of −10 mC/m² (Figures S6 and S8). The relative permittivity of the solution was assumed to be the lowest at the surface, in accordance with recent experimental and molecular dynamics simulations with hBN and other surfaces. , Specifically, a piecewise relationship of the permittivity in the radial direction was assumed such that the magnitude of 2 was set at the 0.472 nm closest to the pore wall (corresponding to the first interfacial water layer), a value of 11 was used for the next 0.315 nm (the second interfacial layer), and a value 80 elsewhere in the middle of the pore (Figure S7). A 3 nm graphene layer was declared as an electrode, as shown in Figure a.

4.

COMSOL MultiPhysics finite element model of ionic concentrations and electric potential in a 5 nm in diameter vdW ionic transistor in 10 mM KCl as the bulk electrolyte. (a) The system consisted of two 15 nm thick layers of hBN and a 3 nm graphene layer. The surface charge density on all hBN surfaces was set at −10 mC/m². V _SD is the voltage applied across the nanopore, and V _G is the gate voltage at the graphene. (b) Profiles of ionic concentrations and (c) electric potential along the pore axis for different V _G with V _SD = 0.5 V. The profiles in (b) and (c) were averaged over the pore cross-section, as indicated in panel (a). (d, e) Current–voltage curves obtained from the model in 10 mM and 100 mM KCl, respectively. The modeling shown as a dashed green line (panels b–e) was obtained when the graphene region was changed to hBN and the applied gate voltage V _G was disabled. All results were obtained with radially varying relative permittivity of the water inside the pore. The permittivity was set to a piecewise function of the radial coordinate (instead of the value of 80 used everywhere else for water) with magnitude of 2 for the 0.472 nm closest to the pore wall (the first interfacial water layer), a value of 11 for the next 0.315 nm (the second interfacial layer), and a value 80 elsewhere in the middle of the pore (Figures S6, S7).

Figure b shows profiles of radially averaged ionic concentrations for V _SD = 0.5 V and a range of V _G between −0.3 and +0.3 V obtained from the COMSOL model. The model confirmed the predictions for gate voltage-dependent ionic concentrations in the pore that were schematically analyzed in Figure . For negative V _G and positive V _SD, the concentration of K⁺ ions is enhanced in the whole volume of the pore, reaching the highest values at the gate region, while the concentration of Cl^– is depleted in accordance with the expected cation selectivity of the system. ,−

As predicted by the schemes in Figure , the voltage configuration with V _SD = −0.5 V and V _G = −0.3 V leads to a weaker enhancement of K⁺ ion concentration inside the pore compared to V _SD = 0.5 V, and therefore, weaker current modulation (see Figures b and S9, S10). Even though potassium concentration is enhanced above the bulk value at V _G < 0 for both V _SD = −0.5 V and V _SD = 0.5 V cases, at V _SD = −0.5 V, potassium ions assume the lowest concentrations in the gate region, even lower than in the configuration without any gate (“no graphene”), Figure S9. This counterintuitive finding can be understood through the effect of concentration polarization ,− due to the ion selectivity of the gate and hBN regions. This leads to the formation of a depletion zone not only at the drain side (right-hand side in Figure a, where K⁺ ions enter the pore in this case) but also at the gate, since K⁺ ions are then sourced from the gate region to pass toward the source. This conclusion is also supported by the profile of electric potential in Figure S9b for V _SD = −0.5 V that reveals formation of a barrier at the gate, even at negative gate voltages. Figures b and S9 showing ionic concentrations for both polarities of V _SD confirm our qualitative explanation of ion current rectification observed even at V _G = 0, which stems from the higher ionic concentrations at V _SD = 0.5 V compared to V _SD = −0.5 V.

The modeling also provided a direct insight into what happens when a positive gate is applied. In accordance with our intuition based on a similar system of a bipolar junction, , V _G > 0 forms a depletion zone whose extent is voltage dependent and limits the transmembrane current. For V _SD = 0.5 V and V _G = 0.3 V, the concentration of potassium ions remains above the bulk value in the whole pore volume, but is the lowest in a zone that extends from the axial position of ∼ −5 to + ∼10 nm (Figure ). For the configuration of V _SD = −0.5 V and V _G = +0.3 V, on the other hand, due to the larger potential difference between source and gate, V _SG = −0.8 V, potassium ions are depleted below the bulk concentration in a gate region, at the axial positions between −10 and 5 nm (Figure S9b for 10 mM KCl). These results underscore the intrinsic asymmetry of the three-electrode system.

The distribution of the electric potential along the pore axis for a range of gate voltages is shown in Figure c. The results revealed that V _G significantly influenced the local electric potential in the pore, leading to the formation of a well (barrier) for potassium ions at V _G < 0 (V _G > 0) for V _SD = 0.5 V. The presence of the graphene layer and surface charges on hBN are responsible for the broken electrochemical symmetry of the system observed as rectification of ion current and gating that depend on the polarity of V _SD. The calculated current–voltage curves in Figure d,e qualitatively agree with the experimental data and predict enhancement (decrease) of the current for negative (positive) gate voltages.

The model in Figure considered a device with the same thickness of the two hBN layers, which allowed us to confirm that the asymmetry in I _D–V _SD curves we observe, as well as V _SD polarity-dependent gating, is inherent to our devices. The devices we prepared, however, comprised hBN layers that were not always identical in length, and the individual thicknesses of hBN varied between ∼10 nm and 30 nm (Table S1). In the next step, we therefore considered how the device’s overall length, location, and thickness of the graphene layer, as well as pore diameter, influence gating. Figure S11 shows the modulation of I _D current with gate voltage expressed as a ratio of I _D at V _SD = 0.5 V, calculated for V _G = −0.3 and 0.3 V for different parameters. The modeling revealed that for the conditions probed in our experiments, changing relative thicknesses of the top and bottom hBN layers resulted in relatively weak changes of the current gating, suggesting a robustness of the design. Due to variations in the pore geometries caused by the nanofabrication process, this weak trend would be difficult to observe experimentally. The gating is predicted to be stronger for a thicker graphene layer that will enhance or deplete ionic concentration over a larger part of the pore volume. On the other hand, increasing pore opening will weaken current modulations. The model also predicted that the gating is robust in a wide range of surface charge densities on hBN.

It is important to note that the quantitative agreement of the continuum model with the experimental data was significantly improved by introducing the diminished relative permittivity of the solution next to the pore walls. Figure S12 shows results from the same model but with the solution permittivity set to 80 in the whole pore volume. When homogeneous, bulk permittivity was assumed, the modulation of ion concentrations reached unphysically high values, and the gating at positive V _G predicted a nearly complete switching off of the currents, which was not observed in experiments. We also confirmed that as long as the first interfacial layer had a relative permittivity of 2, changing the relative permittivity of the inner layer or the thickness of the interfacial layers(s) with reduced permittivity did not significantly affect local ionic concentrations (Figure S13).

Molecular Dynamics Simulations Support the Reduced Relative Permittivity of Water in the Ionic Transistors and the Interdependence of Water and Ionic Distributions

To reinforce COMSOL assumptions and predictions, and to gain additional molecular-level insight into the gating mechanism, we performed classical molecular dynamics (MD) simulations using empirical force fields on a smaller, representative model of the vdW ionic transistor. Figure a shows snapshots of the simulation setup, which included prescribed surface charge densities on the hBN layers, a source–drain electric field equivalent to +0.5 V applied across the pore, and partial charges applied to the graphene sheets to impose positive and negative gate potentials. The model consisted of a 1 nm diameter nanopore drilled through an hBN–graphene–hBN stack connecting two water reservoirs containing 100 mM KCl with a 75 Å long nanopore (Figure a). Further details of the simulations can be found in the Methods section.

5.

Classical molecular dynamics simulations of a 1 nm-diameter nanopore drilled through an hBN–graphene–hBN stack in 100 mM KCl electrolyte, serving as a reduced model of the experimental system. (a) Top-down view of the system and a snapshot of the nanopore, illustrating the applied source–drain electric field and the water bisector vector used to define molecular orientation. A schematic illustration indicates the definition of cos­(θ) relative to the pore axis. (b) Top: system snapshot divided into regions to guide the eye in visualizing changes in water orientation along the pore. Bottom: mean ⟨cos­(θ)⟩ as a function of z position. (c) Ion frequency distributions along the nanopore over 200 ns for simulations with positive and negative graphene surface charges.

Figure b shows how water orientation within the pore responds to the applied gate potential through the combined effects of surface charging, the source–drain electric field, and confinement. Water dipole orientations are defined by the angle between the molecular bisector, weighted toward the hydrogen atoms, and the source–drain field along the positive z direction, such that alignment toward a negatively charged surface corresponds to hydrogens pointing toward the interface (as shown in Figure a). As shown in Figure b, in the absence of surface charges on the pore walls, water molecules preferentially orient radially within the nanopore. Introducing partial charges on the hBN sheets, while leaving the graphene uncharged and applying no source–drain field, alters the preferred water orientation to align with the nanopore axis throughout the pore, except in the graphene region where no surface charge is present. Under a negative gate potential, water dipoles align parallel to the pore axis below the pore midpoint and antiparallel above it, revealing a clear spatial asymmetry in orientation. This behavior arises from the superposition of the axial source–drain field and the local electrostatic fields generated by the negatively charged graphene surfaces, which reverse sign across the pore midpoint and drive a corresponding flip in the preferred water dipole orientation. In contrast, under a positive gate field (positive partial charges on the graphene sheets), water in both the hBN and graphene regions predominantly aligns parallel to the source–drain field, reflecting the dominance of the axial driving field over surface electrostatics. Here, perpendicular alignment is confined to the first hBN–graphene interface, where strong local fields and interfacial polarization locally outweigh the axial field. Figure S14 shows the water orientation angle probability distributions for each defined region across the different partial charge scenarios.

Overall, partial surface charges on the nanosheets drive water molecules to align along the pore axis through the combined action of confinement and gate-induced electric fields. This axial alignment suppresses dipole fluctuations perpendicular to the confining surfaces, which are the primary contributors to polarization in that direction. Within the fluctuation framework of dielectric response, this reduction in transverse dipolar fluctuations directly leads to a lowered out-of-plane permittivity. At the same time, dipole alignment along the pore axis enhances polarization in the axial direction, resulting in a strongly anisotropic dielectric response. This behavior reflects the transition from isotropic bulk-like polarization to a confined regime where interfacial fields and geometric constraints restrict rotational freedom and reorient dipoles, consistent with prior studies of nanoconfined water near charged and atomically smooth interfaces. , For example, Underwood and Bourg’s molecular dynamics simulations of water confined in charged Na smectite nanopores reported a large, anisotropic reduction in the dielectric constant under confinement, consistent with our results, indicating that confinement aligns water molecules along the pore axis, suppresses radial dipole fluctuations, and reduces the out-of-plane dielectric response. This microscopic behavior supports the reduced relative permittivity assigned to nanoscale confined water along the confinement direction, as assumed in the COMSOL simulations. The observed water ordering is a local interfacial effect and is therefore expected to persist near the surface for larger pore widths. However, increased electrostatic screening in wider pores would reduce the spatial extent of this ordering and its impact on the pore interior. Additionally, increasing the number of layers of 2D hBN sheets primarily extends the spatial region over which interfacial fields and water ordering persist, rather than altering the underlying dielectric mechanism. In our ∼1 nm pore, this interfacial region spans the full confinement length, so additional layers would mainly increase the extent of the ordered region.

Figure c presents the ion (K⁺, Cl^–) distributions within the pore as a function of position for positive and negative surface charging applied to the graphene sheet. Here, the reported frequency reflects both the number of ions and their residence time within each spatial bin. Under a negative graphene surface charge, K⁺ ions preferentially accumulated near the graphene region and in the adjacent hBN region, whereas Cl^– ions were effectively excluded from the pore, consistent with the strongly negative electrostatic environment arising from negatively charged graphene and hBN surfaces. In contrast, applying a positive graphene surface charge substantially altered the ionic organization: K⁺ ions remained the dominant species but shifted toward the hBN region, and Cl^– ions entered the pore and preferentially accumulated near the graphene/hBN interface. Notably, this accumulation coincides with the region where water molecules exhibit a perpendicular orientational ordering, suggesting a possible strong coupling between interfacial water structure and ion localization. The ion distributions agree well with the COMSOL concentration profiles for the 100 mM KCl model, indicating that the COMSOL simulations capture the relevant microscopic physics. Ultimately, the MD simulations demonstrate that surface charges in the hBN–graphene–hBN stack strongly couple water structure and dynamics to ion localization, underscoring the central role of water-mediated effects in governing ion transport through nanopores.

Conclusions

In summary, we demonstrate ionic transistors based on van der Waals hBN–graphene–hBN stacks that deliver strong, reversible modulation of the ionic current at low voltages, and at salt concentrations up to 100 mM KCl. Modulations of 10-fold and 2-fold were measured at 10 mM and 100 mM KCl, respectively, at V _G as low as 0.3 V. The three-electrode system exhibits an intrinsically broken symmetry of the electrochemical potential where the effects of gate voltage, V _G, depend on the polarity and magnitude of the source–drain voltage. This asymmetry is consistent with a negatively charged, high aspect ratio hBN pore combined with an internal few-nanometer gate whose polarity sets the local ion density: negative V _G increases K⁺ concentration and enhances the current, while positive V _G induces local ionic depletion and suppresses the transmembrane conductance. This mechanism is further elucidated by a continuum model based on the coupled Poisson–Nernst–Planck equations that reproduces the asymmetric I _D–V _SD curves and reveals how gate polarity sculpts local ion profiles. Molecular dynamics simulations demonstrate that water-mediated effects play a central role in governing ion transport through nanopores and support a reduced effective permittivity for the confined water. These findings translate into practical design rules linking pore geometry, surface charge, salt concentration, water-mediated effects, and gate bias, enabling the preparation of low-power ionic circuits that operate at physiological ionic strength.

Methods

Device Assembly

The devices were fabricated on SiN _x /Si TEM grids with a 50 × 50 μm large and 200 nm thick SiN _x membrane and a single 5 μm diameter pore (Norcada, Inc.). All of the graphene and hBN layers were mechanically exfoliated from bulk crystals, resulting in a random distribution of flakes of different thicknesses. Flakes of desired thickness and uniformity were prescreened by optical microscopy and atomic force microscopy measurements. The stacks were fabricated by the dry transfer method using stamps made of a polycarbonate (PC) film on top of a polydimethylsiloxane (PDMS) dome on a glass slide. Electron Beam Lithography (EBL) was used to write the patterns of the fine contacts using a layer of poly­(methyl methacrylate) (PMMA) resist. For this purpose, PMMA 950 A5 was spun for 2 min at 2800 rpm. The EBL patterns were written at 1.6 nA with 30 kV excitation and then developed for 3 to 4 min in a cold mixture of 3:1 isopropyl alcohol (IPA)/water. After writing and developing the patterns, reactive ion etching (RIE) was used to expose the graphene with the following parameters: a flow of 10 standard cubic centimeters per minute (SCCM) of SF₆, 2 SCCM of O₂, and 30W of radio frequency power, at 100 mTorr for 30 s. As the next step, 2 nm of Cr and 100 nm of Au were deposited in an electron beam evaporator system at the rate of 1 Å/s. Liftoff was performed by soaking the sample in acetone for 1 to 2 h and agitating with a pipet. For the large contacts, on the other hand, a prepatterned polyamide shadow mask was placed on the sample, and a second Cr and Au evaporation was carried out to deposit the contacts. To passivate the metallic contacts, a 170 nm layer of SiO₂ was deposited by PECVD at 250 °C. A commercial glass etcher was subsequently used to expose the outer ends of the metallic contacts. After that, a window opening was patterned on PMMA using EBL in the micropore zone of the sample, followed by wet etching a window in the SiO₂ using BOE 6:1 for a few minutes, exposing the stack only in the etched region. Finally, a single nanopore was drilled using a JEOL 2100f Transmission Electron Microscope with an accelerating voltage of 200 kV and 0.5 nA probe current. , Drilling occurred by narrowing the beam and dwelling it on a single point on the surface for ∼2 min. After drilling, the opening diameters of the nanopores were measured from TEM micrographs.

Device Electrochemical Measurement

The devices were measured at room temperature in a PDMS electrolytic cell adapted to incorporate a custom flexible polyimide PCB board that allowed us to establish an electrical connection with the devices (Supporting Information, Section 1). Two small carbon tape squares cut with a microknife (Fine Science Tools) were placed on the PCB center contacts to ensure a strong electrical connection to the chip contacts. Two 50 μm thick PDMS (Nacalai USA, Inc.) laser cut (Epilog Fusion M2 Laser Cutter) rectangular o-rings with a center opening of 200 μm diameter were placed over the center opening of the PCB to ensure a good fluidic seal between the chip and the electrolytic cell channel. The current into the drain was measured with a Keithley 6487 picoammeter that simultaneously sourced the source–drain voltage. The source and drain were the fluidic reservoirs of the electrolytic cell, and two Ag/AgCl electrodes were used for the electrochemical measurements. The gate voltage was applied with a Keithley 2450 SMU that also measured the gate current using SMA connections with the PCB. The grounds of these two Keithleys were connected. All devices were first probed in a two-electrode setup with source–drain voltage, and the gate voltage floating. We began the measurements in 1 M KCl with 50% ethanol/50% deionized water (Milli-Q IQ 7000), because highly concentrated solutions and the presence of ethanol facilitate wetting of nanopores. Wetting was determined by comparing the experimentally measured conductance with the expected conductance based on the pore diameter as measured by TEM, as well as the stability of the ion current signal. Once the measurements in 1 M KCl 50% ethanol/50% water were successful, recordings with 100% water and lower KCl concentrations were performed in 2 and 3-electrode configurations. Current–voltage curves were recorded using custom written Labview programs. All current values are averages of at least three consecutive voltage sweeps, with error bars calculated as the standard deviation of the measurements. pH of KCl solutions was adjusted with 0.1 M HCl or NaOH. Control measurements of a stack with a nanopore when it was not wet were performed at low gate voltages of ∼0.1 V to confirm the I _D remained at the pA level. In addition, an hBN flake, only before and after drilling a nanopore, was subjected to transmembrane potentials up to 1.5 V to confirm the lack of significant defect-mediated current pathways.

COMSOL Simulations

Models were developed to investigate ionic transport through single nanopores with an inner gating region. Two-dimensional axisymmetric geometries were constructed and solved in COMSOL Multiphysics using the coupled Poisson–Nernst–Planck equations. Including the Navier–Stokes equations had a negligible impact on the results, and the effects of fluid flow were therefore omitted. Details of the model are included in the Supporting Information.

Molecular Dynamics Simulation

Classical MD simulations were carried out with the LAMMPS simulation package. The system was solvated using the SPC/E water model, with O–H bonds constrained using the SHAKE algorithm. Force-field parameters for hBN were taken from Won and Aluru, while graphene and ion interactions were modeled using the OPLS-AA force field. The model consisted of a 1 nm diameter nanopore drilled through an hBN–graphene–hBN stack connecting two water reservoirs containing 100 mM KCl. The system’s dimension is 37.6 Å × 39.6 Å × 197.35 Å. The stack comprises eight hBN layers on each side of a three-layer graphene stack. A source–drain electric field equivalent to +0.5 V was applied in the Z direction defined to the region of the nanopore (with a length of 75 Å), and additional gate fields of ±0.3 V were applied to the graphene sheets. To impose positive and negative gate fields, partial charges of +0.01 and −0.01e, respectively, were assigned to each atom in the graphene sheet, following prior work. In addition, an extra −0.01e charge per atom was applied to the hBN layer to reproduce a negatively charged hBN surface, consistent with experimental observations and COMSOL modeling. Long-range electrostatics were treated using the particle–particle–particle–mesh (PPPM) method. After energy minimization, the system was equilibrated in the NPT ensemble using a Berendsen barostat. Production simulations of 200 ns were then performed in the NVT ensemble with a Nose–Hoover thermostat, maintaining the temperature at 298.15 K.

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acsnano.6c03174.

• Additional experimental results and modeling of ionic transistors based on heterogeneous stacks of vdW materials and details of the experimental setup (PDF)

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A.H.B.-A. and M.S. contributed equally to this work.

The authors declare no competing financial interest.