*3.1. Nanofluidic Membrane*

Prior to investigating the electrical performance of the membranes, we sought to analyze the quality of the membrane fabrication process (Figure 1). Individual silicon membranes were first visually inspected to assess integrity. Figure 1A shows a stereomicroscope picture of a single membrane, highlighting the conductive electrode pads at the top right and bottom left edges. The hexagonal arrangemen<sup>t</sup> of microchannels allowed us to maximize packing density without compromising mechanical robustness. By measuring transmembrane nitrogen gas flow and adopting our predictive model for nanofluidic gas transport [45], we obtained an indirect measurement for the size of nanochannels (~300 nm). Sample membranes were further analyzed with SEM imaging. Figure 1B shows the tightly packed nanochannel arranged in arrays of 19 rows and 96 columns with a horizontal pitch of 2 μm and a vertical pitch of 10 μm. No macroscopic defects or pinholes were observed across wafers, which indicated that the fabrication protocol was repeatable.

The analysis of the membrane cross-sections obtained via FIB milling was performed to evaluate the uniformity of layer deposition at different nanofabrication steps. SiO2 growth via thermal oxidation resulted in a highly uniform layer along the whole length of the vertical nanochannels (Figure 1C). Thermal oxidation is a slow process that enables precise control over layer thickness. Thus, it allowed us to accurately and homogeneously reduce the size of nanochannels. The subsequent deposition of poly-Si (Figure 1D) was used to create a gate electrode that coats the whole nanofluidic structure with the objective of maximizing the electrostatic gating performances. Uniform poly-Si deposition through the chemical vapor deposition-based (CVD) process in high-aspect-ratio hollow structures can be challenging. However, our imaging analysis showed that the deposited layer was uniform (Figure 1D), except for a slight increase in thickness at the nanochannel outlet (bottom right). Finally, a thin layer of SiC (Figure 1E) was used to coat the conductive poly-Si and act as an insulating and chemical inert layer. Despite the high-aspect-ratio of the slit nanochannels, the deposition of SiC was also achieved with good uniformity (Figure 1E). Slight material accumulations at the inlet and outlet of nanochannels were expected. While we did not generate these intentionally, we noted that a local restriction at the nanochannel extremities could improve gating performance.

All materials used for the fabrication of the nanofluidic membrane have previously been demonstrated to be biocompatible using ISO 10993 standards by Kotzar et al. [46]. A subset of these materials has also been investigated in vivo in rodents and has shown biocompatibility and low biofouling [47]. Moreover, in our fabrication protocol, silicon carbide completely encapsulates the membrane and, therefore, is the only material exposed to the environment. Silicon carbide was specifically chosen for this encapsulation purpose as it's considered a versatile material for biomedical applications where extended exposure to physiological fluids is needed [48,49]. Additionally, in vivo biocompatibility of SiC was demonstrated by Cogan et al. [50], who subcutaneously implanted SiC discs in New Zealand White rabbit, the histological evaluation showed no chronic inflammatory response, and a capsule thickness comparable to controls was found.

Furthermore, silicon carbide has previously been shown to offer reduced biofouling when compared to other biocompatible materials, such as silicon or silicon dioxide [51]. Although complete protection against protein adsorption could not be achieved [52], we previously showed that biofouling did not negatively affect the function of our devices. Specifically, nanofluidic membranes, similar to the one presented in this study, have been used in-vivo in rats for up to 6 months [53] and in non-human primates for up to 4 months [54] with no alteration of drug release from biofouling or fibrotic tissue encapsulation.

When compared to membrane architectures previously developed in our lab [55–57], this membrane presented a less cumbersome fabrication process, thanks to the direct alignment of nanochannels and microchannels [58,59]. Further, a substantially higher nanochannels density [55,60] was achieved. In contrast with other gated membrane based on porous alumina (AAO) [29], presenting an irregular pore size distribution [28], our structure achieved a monodispersed nanochannel size that could aid in better control of molecular transport. In its current configuration, featuring 278,600 nanochannels, our membrane configuration was designed to achieve high mass transport rates per unit surface area. This is typically preferable in the context of implantable drug delivery application, where miniaturization is a requirement [39]. However, in light of its modular structure, the same fabrication process could be employed to create alternative configurations with a different number of channels for adoption in electrokinetic-enabled molecular manipulation or sorting applications. For these purposes, the large gate electrode surface area might provide increased electrostatic control of fluid molecules as compared to common Polydimethylsiloxane-glass (PDMS-glass) systems [61,62] which feature localized gate electrodes.

**Figure 1.** Nanochannel membrane structure. (**A**) Optical image of a silicon nanofluidic membrane, presenting electrode pads with exposed conductive polysilicon. (**B**) SEM micrograph, showing the array of nanochannel inlets. (**C**,**D**,**E**) Vertical cross-section image (SEM) obtained along the length of nanochannel, showing the membrane fabrication at different stages. Micrographs were color-enhanced for clarity of visualization. (**C**) Thermally grown SiO2 layer (~175 nm, blue); (**D**) Low-pressure chemical vapor deposition (LPCVD)-deposited poly-Si layer (~121 nm, red); (**E**) Plasma-enhanced-CVD deposited SiC coating (~64 nm, gray). Images **C**, **D**, and **E** do not picture the same membrane location.

## *3.2. Solid–Liquid Interface, SiO2 vs SiC*

To evaluate SiC properties as a gate dielectric in contact with ionic solutions, we compared its insulation performance to SiO2, which is a broadly used gate dielectric in solid electronics [63]. SiO2 and other metal oxides, such as alumina and hafnium dioxide, owe their success to their high dielectric constants that allow for low leakage currents. Even though these materials excel in solid electronic manufacturing, they either lack biocompatibility or chemical inertness and durability in aqueous environments [50].

Leakage current measurements (Figure 2A) performed with our membranes did not show substantial di fferences between SiO2 and SiC, except for 3 V. However, the steep increase in leakage observed for SiC between 2 and 3 V, emphasized by the electrolytic solution environment, suggests that the molecular arrangemen<sup>t</sup> in the dielectric layer is not ideal [64]. The literature on gate dielectric leakage in ionic solutions is scarce, and the available models for a solid-state field-e ffect transistor (FET) are unable to account for the e ffect of the electrolyte solution environment. In aqueous solutions, currents in the order of μA were measured for electric fields as low as 0.5 MV cm<sup>−</sup><sup>1</sup> (Figure 2A). In contrast, for solid-state FET, currents in the order of magnitude of μA are only expected for electric fields greater than 15 and 2 MV cm<sup>−</sup><sup>1</sup> for SiO2 and SiC, respectively. High leakage currents are usually attributed to the formation of conductive filaments within the oxide, whereby electrons are trapped and form clusters within defects in the material. When clusters are at tunneling distance, a conductive path can form, leading to high leakage currents [65,66]. The proportional increase in leakage currents at increasing ionic strength of the solution, previously reported by this group [39], provides further support for this phenomenon.

**Figure 2.** Leakage current and cyclic voltammetry. ( **A**) Comparison of gate leakage current for SiO2 and silicon carbide (SiC) dielectric. (**B**) Cyclic voltammetry comparison between SiO2 and SiC.

In the voltage range between −2 and 2 V, SiC and SiO2 exhibited similar values of leakage currents. Thus, to closer investigate di fferences in performances, we used cyclic voltammetry (CV). As compared to SiO2-coated membranes, lower currents were measured for SiC at each applied voltage (Figure 2B). Interestingly, we observed a non-linear proportional relationship between voltage and current for both materials. SiC exhibited a steep increase in current for voltages higher than 1 V in absolute value. This suggested that for small applied voltages, no faradaic currents occurred, and the material behaved almost as an ideal capacitor. For voltages above ± 1 V, electrochemical reactions between the surface groups (C, SiO−) and reactive species in the electrolyte solution (Cl<sup>−</sup>, HO−) led to increased currents.

In contrast, the significant current increase observed for the leakage currents (Figure 2A) for voltages over 2 V was likely related to material deterioration and conductive filament formation. The asymmetry between results obtained with positive and negative voltages provided further support for this theory. Higher currents for negative applied voltages were observed in both measurements. For negative voltages, positive species were attracted to the surface. The percolation model suggests that in the presence of strong electrostatic attraction, protons can di ffuse in the insulator, starting a percolating path that can lead to the formation of a conductive filament [65]. Instead, for positive potentials, proton repulsion may cause a reversible interruption of the conductive filament, e ffectively decreasing leakage [67]. Additionally, the di fference in hysteresis between the two CV profiles (Figure 2B) was suggestive of di fferences in surface charge accumulation between the two materials. A thinner CV profile usually correlates with low charge accumulation. Collectively, the results showed that SiC su ffered lower leakage currents in the −2 V to 2 V range, exhibiting better insulation performance than SiO2.

## *3.3. Electrochemical Characterization: Conductance*

To further investigate the surface properties of SiC, we performed conductance measurements of SiC-coated membranes in the ionic concentration range between 1 μM and 100 mM. We employed a custom fixture [39] that allowed us to limit wetting to the nanochannel part of the membrane. The results are shown in Figure 3A. At high ionic strengths (>10−<sup>4</sup> M), conductance measurements displayed a linear dependence on the ionic strength. In these conditions, the Debye length was significantly smaller than the size of nanochannels. Accordingly, the results were consistent with the bulk electrolyte conductance (red dashed line in Figure 3A). In contrast, at low ionic strengths (≤10−<sup>4</sup> M), we observed a plateau in conductance (in the log-log scale). This occurred when the Debye length approached the nanochannel dimension, and the excess of counter-ions balanced the surface charge, reaching channel electroneutrality [68]. Here, as it directly related to the conductance, the surface charge could be calculated by fitting the results to the equation [69]:

$$\frac{I}{V} = 2F\mu \sqrt{\left(\frac{\Sigma}{2}\right)^2 + c\_0^2} \frac{wh}{I} \tag{1}$$

In Equation (1), F, μ, and Σ are the Faraday's constant, ionic mobility, and the volume charge density, respectively. Further, *c*0 is the solution molarity, and w, h, and l are the nanochannels' width, height, and length, respectively. Using the relation *zF* Σ = <sup>−</sup>2σ*s*/*h*, we obtained a surface charge value of σs = 1.81 μC/m2, which was consistent with the previously reported data for SiC surfaces [70]. Our SiC coating exhibited a surface charge orders of magnitude smaller than SiO2 (1–100 mC/m2) [71], which correlated with better performance in electrostatic gating control. In fact, chemically reactive surfaces act as charge bu ffers. An externally applied electric field is quickly compensated by protonation or deprotonation of reactive groups on the surface, limiting charge rearrangemen<sup>t</sup> in the electrical double layer (EDL) [72]. Thus, to minimize surface charge, materials are often artificially treated [28].

**Figure 3.** Electrochemical measurements. ( **A**) Measured transmembrane ionic conductance. (**B**) Schematic of the electric double layer and relative model. (1) Inner Helmholtz plane; (2) Outer Helmholtz plane; (3) Di ffuse layer; (4) Solvated ion; (5) Specifically adsorbed ion; (6) Molecules of the electrolyte solvent. ( **C**) Fitted resistance of charge transfer (Rct) of SiO2-coated membranes versus SiC-coated membranes. ( **D**) Fitted double-layer capacitance (Cdl) of SiO2-coated membranes versus SiC-coated membranes.

## *3.4. Electrochemical Characterization: Electrochemical Impedance Spectroscopy*

To investigate dielectric/liquid interface properties with the application of an external voltage, we performed electrochemical impedance spectroscopy (EIS) measurements. Specifically, we compared the resistance to charge transfer and the double layer capacitance at di fferent gate voltages. A comparative assessment was conducted using SiC- and SiO2-coated chips. Figure 3B shows a schematics of the electrical double layer (EDL), which described the ionic distribution that occurres at the solid–liquid interface of a charged surface to maintain local electroneutrality. The EDL is usually described by that Grahame model, which identifies three main layers consisting of 1) non-hydrated ions adsorbed to the surface, ii) hydrated immobile ions, iii) free moving hydrated ions [73]. The first and second layers of immobile ions are often referred to as the Stern layer. The EDL region is modeled by a series of capacitors, referred to as double-layer capacitance (CEDL), where the Stern layer (~0.2 nm) [74] corresponds to the most significant contribution. As current can flow across the interface upon application of a DC potential, a resistive path is considered in parallel to the capacitance. This is usually referred to as a charge-transfer resistance (Rct). Rct can vary substantially depending on the material ability to exchange electrons with the electrolyte solution. Upon application of an external DC potential, if electrons cannot be easily exchanged, an overpotential builds up at the interface. In non-polarizable materials, such as Ag/AgCl, small Rct permits high currents. In contrast, polarizable materials present high Rct, and the current exchange is limited.

By fitting our EIS measurements to the model described above (Figure 3B), we calculated Rct and CEDL for both a SiO2- and a SiC-coated membrane at di fferent gate voltages (VG) applied (Figure 3C,D). Depending on the applied potential, SiC showed an Rct 1.5 to 8 times bigger than SiO2 (Figure 3C). Interestingly, both materials showed a clear dependence of Rct with the applied voltage. SiO2 exhibited a monotonic increase of Rct with the applied voltage, where more positive voltages resulted in higher Rct. In contrast, SiC showed a decrease in Rct proportional to the absolute value of the applied voltage. We attributed these phenomena to the di fference in surface charge between SiO2 and SiC. In fact, a higher number of available SiO− sites on the SiO2 surface allowed for increased electron exchange.

CEDL did not exhibit a correlation with the applied gate voltage for either material (Figure 3D). Moreover, we unexpectedly found six times higher CEDL for SiC with respect to SiO2. As CEDL mainly depends on the surface area and EDL thickness, our results could be explained in the context of the material porosity [75]. By presenting a larger surface area, pores displayed increased capacity. Overall, the low surface charge exposed by SiC and the high resistance to charge transfer qualified SiC as a polarizable interface suitable for electrostatic gating.

## *3.5. Mechanism of Analyte Flow Control through Electrostatic Gating*

Nanofluidic systems present high surface to volume ratios. In light of this, charged species di ffusing in nanoconfinement exhibit unique behaviors [76,77]. Electrostatic, steric, and hydrodynamic interactions with the nanochannel walls influence local molecular concentration and e ffective di ffusivity. Depending on solution properties, such as ionic strength, pH, and surface charge density, the EDL can extend from a fraction to hundreds of nm in the fluid. Both SiC and SiO2 surface expose native silanol groups, resulting in a net negative surface charge at pH 7.4 [78]. In proximity to the surface, charged species redistribute to reach electroneutrality [73]. While counter-ions concentration increases, co-ions are depleted following distribution with a characteristic dimension equal to the Debye length.

Once solution properties are defined, the surface charge is the only parameter that has a significant effect on the distribution of charges in the fluid. Thus, nanochannel charge-selectivity can be altered by controlling the channel surface charge. An applied di fference in potential between a buried gate electrode and an electrode in solution creates an overpotential at the surface. We employed this strategy to modulate the di ffusive transport of analytes through our nanofluidic membrane. With no applied voltage, molecules di ffused through the channel unperturbed. By applying a negative gate potential, the transmembrane transport of co-ions was substantially reduced.

## *3.6. In Vitro Release Modulation of Methotrexate*

To investigate the e ffectiveness of electrostatic gating on controlling trans-membrane transport of a small charged analyte, we performed an in vitro di ffusion study using methotrexate. Methotrexate has a molecular weight of 454 Da and is a good representative of small molecules (<900 Da) therapeutics, which accounts for the majority of pharmaceuticals [79]. Clinically, methotrexate is used as a chemotherapeutic agen<sup>t</sup> for the treatment of various cancers, as well as in the managemen<sup>t</sup> of rheumatoid arthritis [33].

Figure 4A shows the normalized release rates for four consecutive cycles alternating between passive and active phases. During the passive phases, negatively charged molecules (−2q for methotrexate) di ffused trough the nanochannels freely, largely una ffected by the low native charge of the SiC surfaces. When a negative voltage was applied (−3 V), an increase in negative surface charge repelled methotrexate molecules, reducing their release. The four alternation cycles between passive and active phases demonstrated that electrostatic gating allowed for repeatability of release modulation.

**Figure 4.** Electrostatically controlled release of methotrexate. ( **A**) The normalized release rate of methotrexate for four cycles between free di ffusion (Passive) and gated di ffusion (Active). (**B**) Release rates grouped by phase typology (\*\* *p* ≤ 0.01).

We observed a statistically significant (\*\* *p* ≤ 0.01) di fference in release rate between active and passive phases, whereby the applied potential −3 V yielded a decrease in the release rate of ~35%. During the passive phase, an average release rate of 10 μg/day was obtained, which was consistent with daily doses used to treat rheumatoid arthritis in pre-clinical testing [80]. Other small molecule therapeutics, including glucocorticoids [81], hormone therapeutics [82], and antivirals [83], present effective daily doses in the order of micrograms. This indicates that the current membrane architecture could, in principle, be adopted for various therapeutic applications. However, further testing with di fferent pharmaceutical agents is warranted.

## *3.7. In Vitro Controlled Release of Quantum Dots*

To assess the ability of our membrane to modulate the release rate of larger molecules, we performed an in vitro release study with quantum dots. Quantum dots possess broad applicability in bioengineering, including imaging [84], theranostics [85], cell labeling for in vivo tracking [86], tissue staining [87]. They have also been investigated as biomarkers for cancer detection and for targeted drug delivery [35]. Figure 5A shows the normalized release rate of each phase, where passive (0 V) and active phases (−1.5 V) were alternated over three cycles.

The application of the negative gate potential drastically reduced the release of quantum dots from the membrane. Subsequent cycles demonstrated consistent and reproducible release rate reduction, suggesting that the membrane and the gating performance were consistent over time. A statistically significant di fference (\*\*\*\* *p* ≤ 0.0001) in the release between active and passive phases (84%) was observed (Figure 5B). When compared to methotrexate, quantum dots clearly showed a more e ffective electrostatic modulation, which could be attributed to higher particle charge and lower ionic strength of the solution. Specifically, the high exposed charge is due to the carboxylic functionalization, where several groups result in a negative net charge that ranges from −5 to −15 depending on pH and

ionic strength [41]. Moreover, the low ionic strength solution (0.01 × PBS) has a Debye length 10 times greater than the 1 × PBS. These two properties contribute to enhance the electrostatic interactions between the wall and the solute. Thus, the application of the gate potential resulted in increased efficacy of release modulation.

**Figure 5.** Electrostatically controlled release of quantum dots. (**A**) The normalized release rate of quantum dots for three cycles between free diffusion (Passive) and gated diffusion (Active). (**B**) Release rates grouped by phase typology (\*\*\*\* *p* ≤ 0.0001).

## *3.8. Considerations on Electrostatic Gating Performance*

To achieve efficient devices for tunable molecular diffusion via electrostatic gating, various parameters need to be optimized. Of utmost importance is the choice of dielectric material to insulate the buried gate electrode. In this study, we investigated SiC as it conciliates the need for low leakage currents, with a dielectric constant similar to SiO2 (4.4–4.9) [88], and offers chemical inertness in aqueous solutions [48]. Moreover, SiC offers a low native charge; therefore, it minimizes unwanted non-linearities connected to the buffer capacity of strongly charged surfaces [72].

Further, efficient electrostatic flow modulation is strictly connected to the nanochannel size to the Debye length ratio (*h*/λ). Our membrane was designed for medical applications, where the ionic strength and pH were bound to physiological values. Our future investigations focus on manufacturing membranes with smaller nanochannels to be able, in principle, to completely stop analyte diffusion. Finally, as flow control trough electrostatic gating is mainly based on coulombic interactions, analytes that expose high surface charges are more suitable for gate modulation. Therefore, drug encapsulation with highly charged polymers can significantly improve administration control of small analytes.
