Gate-Tunable Ionothermoelectric Cooling in a Solid-State Nanopore

Abstract

Efficient heat dissipation at the nanoscale remains a major challenge for high-performance microelectronics. Here, we demonstrate a proof-of-concept approach for ionothermoelectric cooling, the ionic analogue of the Peltier effect, using gate-tunable solid-state nanopores integrated with nanoscale thermocouples. By integrating a nanoscale thermocouple directly adjacent to a gate-tunable solid-state nanopore, we quantitatively map local thermal responses driven by voltage-induced ion transport. We show that ionic heating scales with input power and varies with the ion species, revealing a dependence on the intrinsic heat of transport. Under salt concentration gradients, we observe ionic cooling, a fluidic analogue of the Peltier effect, arising from directional cation transport through negatively charged nanopores. This effect is further enhanced via electrostatic gating, which modulates the pore wall surface potential to tune the permselectivity. Under optimal gating, the system exhibits reversible transitions between heating and cooling regimes with temperature drops exceeding 2 K. Although modest compared to electronic Peltier devices, this effect establishes a viable mechanism for active, electrically tunable thermal management in nanofluidic systems. Given that water-based flow cooling already outperforms solid-state thermoelectrics by orders of magnitude, incorporating ionothermoelectric cooling can further enhance heat-pumping efficiency in micro- and nanofluidic architectures, thereby establishing a scalable on-chip ionic refrigeration strategy for next-generation semiconductor thermal control.

Introduction

Continuous device scaling has pushed the integrated circuit technology for the sub-3 nm node, , while More-than-Moore strategies such as three-dimensional monolithic stacking have transformed chip architecture and functional density. In parallel, the rise of artificial-intelligence workloads and data-centric applications has driven a surge in computation and memory traffic across hyperscale data centers. − This relentless escalation in on-chip switching activity concentrates heat in ever-smaller volumes, making energy dissipation a crucial bottleneck to further performance scaling. , For example, air-cooled heat sinks, ubiquitous in present servers, are already approaching their thermodynamic limits at power densities >100 W cm^–2. , Whereas state-of-the-art facilities, therefore, rely increasingly on liquid cooling, a fundamental mismatch persists between nanoscale thermal hotspots and millimeter-scale fluidic channels, leading to inefficient thermal coupling, consuming vast quantities of water and thereby raising environmental concerns.

Active on-chip cooling via fluid flow offers a compelling route toward thermally sustainable microelectronics. Advanced semiconductor technologies have enabled the monolithic integration of micro- and nanoscale fluidic channels beneath wafers, facilitating codesigned architectures for efficient thermal regulation. − Laminar flow within these miniaturized conduits enables precise thermal control and low interfacial resistance, outperforming conventional indirect cooling strategies.

Here, we introduce an alternative and complementary approach that harnesses ionic heat transport through nanofluidic channels, drawing conceptual parallels to thermoelectric effects in solids. Analogous to the Peltier effect, where directional transport of charge carriers in a solid induces localized heating or cooling, we demonstrate that field-effect-controlled ion transport in a nanopore, which inherently carries both electrical charge and enthalpy, can generate directed thermal fluxes when driven through permselective nanopores. This ionothermoelectric phenomenon enables active heat modulation in fluidic systems (Figure ), offering potential synergy with microchannel-based convective cooling schemes for the thermal management of next-generation high-power-density processors.

1.

Schematic illustration of gate-controlled ionothermoelectric cooling in a nanopore. A gate voltage tunes the surface potential of the nanopore wall, electrostatically excluding co-ions (anions, shown in blue) and enriching counterions (cations, shown in red) near the interface (image not to scale). The resulting permselective ion flux drives directional heat transport, transferring thermal energy across the membrane and thereby realizing an ionic analogue of Peltier cooling.

Results and Discussion

To probe the thermal response of field-gated ionic transport, we formed a gate-all-around nanopore , in a 70 nm thick SiN _x /SiO₂ membrane with a nanoscale Au/Pt thermocouple adjacent to the Au gate electrode (Figure a–c, see also Figures S1–S4). The field-effect transistor-like nanofluidic architecture − allows the modulation of pore wall surface potential via the applied gate voltage V _g under given Debye screening effects, , proven effective for tuning molecular translocation, ionic rectification, in-pore chemical reactions, , and even permselectivity. , Meanwhile, the thermocouple generates a thermovoltage V _th in μV, which we calibrate to the local temperature T _pore = 5.9 V _th + T ₀, where T ₀ = 293 K (Figure S5). , Embedding the thermocouple at the edge of a pristine nanopore has been previously shown to enable accurate local temperature measurement with errors below 5% (Figure S6). Due to the presence of the gate electrode, however, the thermal sensor needs to be positioned approximately 100 nm away from the nanopore center, slightly compromising the accuracy in estimating the in-pore temperature. Quantitatively, this design reduces the temperature sensitivity by 67% compared to a directly coupled configuration (Figures S7 and S8), a trade-off we find acceptable for resolving ion-transport-mediated local heat dissipation.

2.

Negligible gating effects on in-pore ionic heat dissipation at a high slat concentration. (a) Schematic model of a thermocouple-embedded gate-all-around nanopore. Ionic current I _ion through the pore is measured under the applied transmembrane V _b and gate voltage V _g. (b) False-colored optical image showing a square SiN _x /SiO₂ membrane with four metal lines comprising the gate electrode and nanothermocouple. (c) False-colored scanning electron micrograph displaying the structure of the gate-all-around nanopore with the embedded thermocouple. (d) Ionic current I _ion through a 70 nm thermocouple-embedded gate-all-around nanopore in 1.4 M NaCl, plotted as a function of transmembrane voltage V _b. Blue and red traces indicate forward and reverse voltage sweeps, respectively. The inset shows an equivalent circuit model comprising pore resistance R _pore and access resistance R _acc. (e) Corresponding nanopore temperature T _pore during voltage sweeps. The green curve is a quadratic fit. (f) Nanopore heating characteristics in 1.4 M NaCl under V _g = 0.8 V (green) and −0.8 V (purple). (g) T _pore plotted against the input power P = I _ion V _b. The dashed line is a linear fit. (h) The nanopore heating rate r _h deduced from the slopes in the linear T _pore versus P characteristics. The nanopore conductance G _pore is also shown.

Simultaneous measurements of the ionic current I _ion and T _pore were performed under varying transmembrane voltage V _b. T _pore is confirmed to respond rapidly against a change in the transmembrane voltage (Figure S9) for the small volume of water with low heat capacity involved in the local ionic heat dissipation, ensuring neglectable influence of thermal drift. In 1.4 M KCl, a 70 nm nanopore exhibited an ohmic I _ion–V _b behavior, yielding a conductance G _pore consistent with the Maxwell–Hall model (Figure d). , Meanwhile, T _pore demonstrated a nonlinear increase with |V _b|, suggestive of local Joule heating via the ion electromigration under the focused electric field at the nanopore (Figure e,f). − Plotting against the input power P = I _ion V _b, T _pore is shown to rise linearly defining a constant heating rate r _h (Figure g). Results are found as qualitatively the same in a 1 μm micropore, except for the lower r _h indicating less efficient ionic heating in larger pores (Figure S10).

The thermal system can be modeled as a Joule heat source at the pore center connected to the thermal resistance K _i of the surrounding salt water with heat capacity c _i (Figure e inset). Heat flow in the thermal circuit under an input power is described as

$$\frac{T_{\mathrm{pore}}-T_0}{P}=\frac{1}{tc+1/K}$$ 1

where K and c are the combined K _i and c _i, respectively. Since t = 0 at a steady state, the equation reduces to KP = T _pore – T ₀, which is consistent with r _h P = T _pore in Figure g. Assuming a constant thermal conductivity λ of the electrolyte solution, K is approximated by LS ^–1λ^–1, with L ∼ 2d _pore and S ∼ πd _pore ²/4, predicting a ∼10-fold higher K for the 70 nm nanopore than the 1 μm micropore. This explains the larger Joule heating rate in the smaller pore (r _h = 8.5 and 3.9 K/μW for 70 nm and 1 μm pores, respectively), with the error ascribed in part to the difference in the relative contributions of the access resistance (Figure S10), i.e., the resistance components outside the pores, for the two pores of different aspect ratio structures.

Gating effects on ionic Joule heat dissipation are revealed to be negligible. This is shown by the I _ion– and T _pore–V _b characteristics remaining almost unchanged under V _g = ±0.8 V (Figure f, see also Figure S11). The result is consistent with the strong electrostatic screening in the high salt concentration solution that spatially confines the electric field at the pore wall to the subnanometer level. The resulting little contribution of the counterion conduction on the net ionic flux gives a constant nanopore conductance and heating rate irrespective of V _g (Figure h).

To explore how ionic species influence the ionic Joule heat dissipation, we examined a series of mono- and multivalent electrolytes: LiCl, NaCl, KCl, RbCl, CsCl, CaCl₂, MnCl₂, and AlCl₃. I _ion–V _b characteristics in 2 M solutions reveal a variation in G _pore reflecting the differing bulk solution conductivity of the salt solutions containing different cations of distinct mobilities (Figure a, see also Figures S12 and S13 for results with all types of salts). Meanwhile, although one might expect heating efficiency r _h to be independent of electrolyte composition, given that salt water thermal conductivity λ is presumed to be constant, our measurements revealed a non-negligible salt dependence (Figure b, see also Figure S14 for T _pore plotted as a function of I _ion). Since r _h ^–1 ∼ λ according to the thermal circuit, this suggests a change in the effective thermal conductivity by the inclusion of ions in water.

3.

Ionic contribution to heat dissipation in a nanopore. (a) I _ion–V _b characteristics of a 70 nm thermocouple-embedded nanopore measured in 2 M solutions of different salts: LiCl (blue), KCl (orange), RbCl (red), CaCl₂ (green), and AlCl₃ (purple). (b) Corresponding nanopore temperature T _pore during voltage sweeps in each salt solution. Color coding follows panel a. (c) Plots of inverse heating rate r _h ^–1 against the heat of transport of ions Q _ion. Data are shown for the salts whose Q _ion values are available in the literature. Dashed line is a linear fit. (d) A model used for the thermal analysis consisting of a nanopore in a SiO₂ (sky blue) /SiN _x (yellow) membrane of 70 nm thickness. (e) Temperature distribution around the nanopore by local Joule heating under transmembrane voltage of 0.9 V in 2 M NaCl. (f) Temperature distributions around the self-heated nanopore under 0.9 V in 2 M NaCl with different specific heat capacity C _w of water. The plots are superimposed with each other, manifesting the negligible influence of the solution heat capacity on the heat dissipation at steady states. (g) Temperature distributions at the self-heated nanopore under different salt concentrations at 0.9 V. (h) Nanopore temperature at z = 0 in panel d plotted as a function of the salt concentration c _NaCl. The gray line is a linear fit. (i) The nanopore temperature at 0.9 V in 2 M NaCl with varying liquid thermal conductivity λ_w. The gray line is a linear fit.

The capability of ions as carriers of enthalpies in aqueous solutions is described by the heat of transport Q _ion. Assuming no electrostatic screening by ion–ion interactions, Q _ion is given as Q _ion = τq ²/8πεr, where q, ε, and r are the charge, the dielectric constant, and the radius of ions, respectively, while τ represents the temperature dependence of ε. Indeed, heating rates in the equimolar solutions of different salts are found to scale with Q _ion as r _h ^–1 ∼ Q _ion (Figure c), suggesting the profound influence of ionic drift on the heat dissipation at the self-heated nanopores (only Q _ion available in the literature is considered).

We conducted finite element simulations incorporating the coupled Poisson–Nernst–Planck, Navier–Stokes, and thermal transport equations to elucidate the origin of the observed ion-dependent heating behavior (Figure d, see also Figures S15 and S16). , These analyses confirmed that Joule heating, derived from diffusive ion transport via the focused electric field in the viscous media, is highly localized near the nanopore (Figure e). Meanwhile, while the pore conductance is estimated to increase linearly with NaCl concentration, consistent with σ = ec _NaCl(μ_Na + μ_Cl), where μ_Na,Cl is the mobility of Na⁺ and Cl^–, the specific heat capacity of the solution is found to cause no notable change in the temperature distribution around the nanopore (Figure f). Moreover, when the thermal conductivity λ_w of the electrolyte was held constant, the simulated heating rate remained unchanged across a range of c _NaCl values examined (Figure g,h). Changing λ_w from 0.56 W/mK, on the other hand, alters the local heating efficiency as r _h ^–1 ∼ λ_w (Figure i, see also Figure S17). These results support the accuracy of the thermal circuit model in Figure e, corroborating the notable roles of ion transport in the experimentally observed variations in r _h.

Direct evidence of ion-mediated heat transport emerged under salt gradients across permselective nanopores (Figure a,b). Diluting the salt water expands the electrostatic potential distributions by the surface charges on the membrane surface to render charge-selective ion transport in the pore. , This is seen as an increase in the open circuit voltage V _off in the I _ion–V _b curves upon decreasing the ion concentration c _cis at the cis side (Figure a). More quantitatively, V _off under the salinity gradients is given as V _off = V _red + V _dif (Figure c), where V _red and V _dif are the redox voltage at the electrode and the transmembrane electric potential difference generated by the diffusive ion transport, respectively (V _red is estimated as shown in Figures S18 and S19). Here, V _dif is nearly zero in a nonpermselective nanopore, as diffusion of the equivalent amounts of anions and cations induces negligible voltage. On the contrary, selective ion transport through the pore provides finite diffusion potential reflecting the permselectivity as denoted by the Nernst equation, V _dif = S _ion(k _B T/e) ln­(a _cis/a _trans), where S _ion is the coefficient defining the magnitude of permselectivity with S _ion = +1 and −1 for the case of perfect cation and anion selectivity and 0 for nonselective transport. Assuming the ion activity at the cis and trans, a _cis,trans, to be approximated as c _cis and c _trans, V _dif is obtained by subtracting V _red, which decreased to below 0 V with decreasing c _cis (Figure d). It indicates the cation-selective transport in the nanopore, consistent with the negative native charges on the SiO₂ membrane surface causing Coulombic repulsion of anions at the orifice to hinder their translocation.

4.

Ionic refrigeration in a nanopore under salinity gradients. (a) I _ion–V _b characteristics of a 70 nm thermocouple-embedded nanopore under transmembrane salinity gradients. The salt concentration on the cis side (c _cis) was varied from 1.4 M (red) to 0.00014 M (orange), while the trans side (c _trans) was held constant at 1.4 M. The salinity ratio r _ion = c _trans/c _cis defines the gradient strength. (b) Corresponding changes in nanopore temperature (T _pore) recorded simultaneously with I _ion. Color coding matches panel a. (c) Close view showing the open circuit voltage derived from the redox (V _red) and diffusion voltage (V _dif) under a 10⁴-fold salinity difference. (d)V _dif–r _ion dependence suggesting cation selectivity of the nanopore. (e) Plot of input power P versus T _pore under varying salinity gradients. Joule heating dominates at positive V _b, whereas at large r _ion, Peltier cooling at negative V _b leads to net refrigeration, with T _pore dropping below ambient at c _cis = 0.0014 M.

The permselectivity induces ionic current rectification. Under positive transmembrane voltage, high concentration Na⁺ flows from the trans to cis side, resulting in a high G _pore. In contrast, at negative voltage, the Cl^– flux is impeded by electrostatic repulsion from the negatively charged membrane surface. Consequently, the nanopore admits only dilute Na⁺ flux, thereby suppressing I _ion. No matter the rectifying behavior, the Joule heat becomes smaller as the ionic conductance is lowered with decreasing c _cis, giving rise to weaker changes in T _pore under the V _b scans (Figure b). Notably, meanwhile, it exhibits refrigeration at r _ion larger than 10⁴, where T _pore falls below ambient temperature under negative V _b, highlighting the predominant role of ionic heat of transport (Figure e). This active cooling is attributed to enhanced cation selectivity at low c _cis, which promotes the Na⁺-selective transport-mediated unidirectional heat flow, i.e., an ionic analogue of the Peltier effect, to outweigh its contribution over the counteracting Joule heating.

Because permselectivity is essential for enabling ion-driven thermoelectric effects, a refrigeration behavior is absent in larger pores where selectivity is minimal. For instance, in a 1 μm-diameter micropore, imposing a salt concentration gradient results in pronounced ionic current rectification, including signatures of negative differential resistance (Figure S20), arising from electroosmotic flow-induced modulation of local ion concentrations. Although the current–voltage characteristics superficially resemble those observed in nanopores, no signs of ionic cooling are detected, attributed to the negligible permselectivity in the micrometer-scale conduit, where the electric double layer is too thin relative to the pore size to exert significant electrostatic control over ion transport (Figures S20 and S21).

The gating effect offers a powerful means for the active control of ionothermoelectric transport, particularly under low ionic strength conditions where counterion transport is highly sensitive to surface potential modulation by the gate voltage. With a 10⁴-fold salinity gradient, the intrinsic negative surface charge of the nanopore in the absence of gating renders it cation-selective, leading to weak cooling at negative transmembrane bias via Na⁺-dominated transport. Applying a negative gate voltage enhances this cation selectivity, as demonstrated by the V _off shifting to more negative values (Figure S22), modestly increasing the cooling efficiency as V _g is tuned from −0.4 to −0.8 V (Figure a). In contrast, a positive V _g inverts the wall potential, modulating the permselectivity. At V _g = +0.4 V, the opposing effects of ionothermoelectric cooling and Joule heating approximately cancel, resulting in a negligible net temperature change. Increasing the V _g to +0.8 V further modulates the surface potential toward anion selectivity and ultimately reverses the thermal response from heating to cooling. Meanwhile, the local temperature exhibits distinct responses to positive and negative V _g reflecting the differing contributions of sodium and chloride counterions due to their intrinsic differences in heat of transport (3.5 versus 0.5 kJ/mol) and diffusivity (1.3 × 10^–9 versus 2.0 × 10^–9 m²/s).

5.

Field-effect modulation of ionic heat dissipation in a nanopore. (a, b) Temperature variations ΔT _pore with respect to room temperature in response to V _g modulation in a 70 nm nanopore under positive (a) and negative (b) transmembrane voltage. The gate bias dynamically alters the ionic heating profile depending on the direction of ion transport. (c, d) ΔT _pore–V _b characteristics at r _ion = 10⁴ (c) and 10³ (d) under V _g = +0.8 V (green) and −0.8 V (purple). T _pos,neg denotes the temperature at V _b = 1.4 and −1.4 V, respectively. (e) Plots of T _pos,neg as a function of V _g. Blue and red regions denote nanopore cooling and heating via the V _g-derived permselective ion transport.

Because the majority carrier switches polarity with the direction of V _b, the gating effect is reversed under positive bias (Figure b): ionic heating is amplified by negative V _g, while positive V _g enhances cooling. This gate-controlled thermoelectric response is more pronounced in dilute electrolytes. At a salinity ratio of r _ion = 10⁴, applying ±0.8 V to the gate electrode effectively switches the thermal response from heating to cooling (Figure c). In contrast, under a reduced salinity gradient (r _ion = 10³), the gating effect is attenuated: while negative V _g still induces notable cooling at negative bias, it has minimal impact on Joule heating at positive V _b (Figure d, see also Figure S23).

To highlight these effects, we plotted the nanopore temperature at V _b = +1.4 V (T _pos) and −1.4 V (T _neg) as a function of the gate voltage (Figure e). Sign changes in T _pos and T _neg mark the transition between heating and cooling driven by permselectivity inversion. Noticeably, at r _ion = 10⁴ and V _g = −0.8 V, T _neg exceeds −2 K (Figure S24), nearly 3 times greater than the corresponding value at r _ion = 10³ (we note that this T _neg underestimates the actual temperature inside the nanopore by approximately 70%, anticipating local refrigeration by more than 3 K). These results establish that ion-driven heat transport can be actively and reversibly modulated via electrostatic gating, providing a programmable platform for nanoscale thermal control.

Conclusions

This study demonstrates that ionic heat transport in nanopores is not merely a passive consequence of Joule heating but a controllable phenomenon with functional relevance for nanoscale thermal management. Under an applied bias, each ion drags a certain amount of heat along with its charge. Thus, directional ion flow can carry away the enthalpy from the nanopore region. In a nonselective pore, cations and anions migrate in opposite directions, and their transported heats cancel out, yielding no net cooling. By contrast, a permselective pore passes almost only one type of ion so that ionic enthalpy is carried predominantly in one direction, pumping heat out of the nanopore and lowering its local temperature. This mechanism is the ionic analogue of the Peltier effect, where the voltage-driven counterion flux extracts enthalpy from the pore and releases that heat on the far side, producing a localized cooling effect. The gate electrode in this study actively tunes the permselectivity by modulating the surface charge. As a result, the thermal response is reversible and gate-controllable. This cooling is highly localized to the nanoscale vicinity of the pore since the region of enthalpy removal is confined to the tiny nanopore and immediate fluid around it. However, energy is fully conserved since the extracted heat is expelled into the surrounding environment or downstream fluid by the ion flow. In other words, the electrical work performed on the ions drives a heat current from the nanopore to the external reservoirs. So while the nanopore cools, an equivalent amount of heat is dissipated to warm the bulk solution. Importantly, any Joule heating from the ionic current occurs in parallel and tends to heat the pore. As such, net cooling is observed only when the enthalpy carried away by the selective ion flux outweighs local Joule heating.

Previous studies have shown voltage-controlled ionic rectification using confined nanopore systems. For instance, nanopore electrode arrays via a cation-exchange overlayer and top electrode achieved a voltage-switched diode behavior by electrochemical gating. Attoliter-scale encapsulated nanopores demonstrated rectification arising from ion migration under strong confinement. In contrast, the present gate-tunable solid-state nanopore integrates direct electrostatic gating within a single-pore platform, unifying active charge modulation with nanoscale confinement. This architecture allows the dynamic inversion of ionic permselectivity and extends the rectification concept to controllable ionothermoelectric cooling, a functionality beyond purely electrical gating.

Permselectivity and ionic conductance in a nanopore are found to be important factors affecting the efficiency of ionothermoelectric cooling. Without ion selectivity, anions and cations pass through a conduit under the applied voltage. As heat is carried in opposite directions by the migrating ions, it causes a negligible temperature difference across the membrane. On the contrary, the unidirectional flux of anions or cations in a permselective pore pumps heat via the voltage-driven ion transport to induce ionic cooling. In this work, refrigeration occurred under a large salinity difference, leveraging the depressed ion concentration around the pore that augmented the Coulombic co-ion repulsion from the charged wall surface to render stronger ion selectivity. The fact that r _ion of 10⁴ allowed a more pronounced decrease in T _pore than with r _ion = 10³ manifests this mechanism, where the former condition rendered stronger permselectivity to enable more efficient heat pumping by the selective ion transport. Meanwhile, although excessive dilution of salt solutions serves to further enhance the selectivity, it also entails ion depression, thereby weakening the ionic cooling effect (Figure S25). Besides these contributions, ionic Joule heating counteracts the ionic Peltier effect, complicating the energy dissipation phenomenon in nanopores.

These findings bridge the gap between thermal and ionic transport in nanoscale systems, highlighting the potential for ionothermoelectrics, a field that may complement electronic thermoelectricity in soft, aqueous, or biological environments. As the mechanism stems primarily from the selective ion transport, it can, in principle, be implemented not only in silicon nitrides but also in a wide range of membrane materials provided that their surface charge density is sufficiently high to impart strong permselectivity to nanopores. While demonstrating large-area cooling using multinanopore membranes remains an essential step toward practical implementation, the full compatibility of solid-state nanopores with semiconductor fabrication technologies promises the ion-mediated heat modulation to be harnessed for enhancing cooling efficiency in micro/nanochannel systems integrated for the on-chip thermal management.

Methods

Fabrication of Thermocouple-Embedded Nanopores

A 4 in. Si wafer with 50 nm thick SiN _x layers coated on the surfaces was diced into 25 × 25 mm chips with a dicer. Microelectrodes were patterned on the chips by photolithography with the AZ5206-E photoresist followed by metal deposition by radio frequency magnetron sputtering. As a result, Au microelectrodes were formed by sonication in N,N-dimethylformamide (DMF) for lift-off. A nanowire was delineated by electron beam lithography with the ZEP520A electron beam resist, whose one end was overlapped with one of the microelectrodes. Subsequently, Pt was deposited by the sputtering and lifted off in DMF. The same process was carried out to create the Au nanowire, whose position was aligned with respect to a lithography-defined marker to form a point contact with the Pt nanowire. After the nanowire thermocouple was formed, a circle was patterned at the vicinity of the point contact by the electron beam lithography with ZEP520A. After development, the residual resist layer was used as a mask to drill a pore in the SiN _x membrane by reactive ion etching. Finally, the top surface was coated with 20 nm thick SiO₂ by chemical vapor deposition.

Fabrication of Thermocouple-Embedded Gate-All-Around Nanopores

Most of the fabrication processes are the same as those for fabricating thermocouple-embedded nanopores. One difference lies in the second EB lithography to form a Au nanowire. To form a gate electrode, a rectangular pattern was drawn along with the nanowire. By this, a Au gate electrode and a nanowire were created simultaneously by depositing Au and lift-off in DMF. Furthermore, to drill a pore through the Au/SiN _x layer by EB lithography and reactive ion etching, the etching time was adjusted to be longer than that for creating SiN _x nanopores.

Flow Cell Integration

The nanopore chips were sealed with flow cells made of polydimethylsiloxane (PDMS). The cells were composed of 15 × 15 × 10 mm blocks with a microfluidic channel patterned on one side of the surfaces. To form the cells, a mold was fabricated by creating I-shaped patterns on a Si wafer by photolithography with an SU-8 photoresist. Sylgard 184 was poured on the mold placed on a Petri dish and cured in an oven at 90 °C for 9 h. The blocks were cut out with a surgical knife. In each block, three holes were punched to inject salt solutions as well as to place a Ag/AgCl rod for ionic current measurements. For sealing, the PDMS block and the nanopore chip were exposed to oxygen plasma for surface activation. Subsequently, they were put together for bonding. This process was repeated once again to seal the chip from both sides.

Simultaneous Measurement of Ionic Current and Nanopore Temperature Measurements under Gate Voltage

The nanopore chip was mounted on a sample holder. Metal pins were contacted by the microelectrode pads on the chip. Two of the pins connected to the Au/Pt nanowire thermocouple were wired to a Keithley 2182A nanovoltmeter (Keithley) for the nanopore temperature measurements, while one connected to the gate electrode was wired to a picoammeter-source unit Keithley 6487 (Keithley) for the application of the gate voltage. Meanwhile, salt solutions were poured into the pore by injecting through one of the three holes in each of the two PDMS cells using a pipet. After that, Ag/AgCl rods were placed at both sides. Transmembrane voltage was applied to one of the rods, and the resulting ionic current was measured through the other rod using another Keithley 6487. The thermovoltage and ionic current were recorded simultaneously under the transmembrane voltage ramps, and the gate voltage was controlled through GPIB with a program coded in Visual Basic.

Thermocouple Calibration

The thermovoltage V _th at the thermocouple was measured under substrate heating with an electrical heater to a constant temperature using a temperature controller. The relationship between V _th (in μV) and the substrate temperature T _s gives an equation T _s = 5.9V _th + T ₀ for converting the thermovoltage to the local temperature at the point contact, where T ₀ = 293 K is the ambient temperature.

Redox Potential Measurement

I _ion–V _b characteristic measurements were performed on a 3 μm micropore in a 50 nm thick SiN _x membrane with the cis and trans compartments filled with NaCl solutions of salt concentrations c _cis and c _trans. Specifically, c _trans was kept at 1.4 M while changing c _cis from 1.4 to 0.000014 M. The redox potential was obtained from the open circuit voltage at the zero current intersections in the I _ion–V _b curves.

Finite Element Analysis

To model the temperature distribution within a nanopore under applied cross-membrane voltage, we employed finite element simulations based on heat transfer equations incorporating Joule heating. The steady-state heat equation was defined separately for (eq ) solids and (eq ) fluids as follows:

$$\mathrm{\nabla }·(\kappa \mathrm{\nabla }T)+J·E=0$$ 2

$$\mathrm{\nabla }·(\kappa \mathrm{\nabla }T)+J·E={\rho }_{\mathrm{d}}{C}_{\mathrm{p}}u·\mathrm{\nabla }T$$ 3

where J and E are the current density and electric field, respectively. Here, κ is the thermal conductivity, T is the temperature, ρ_d is the fluid density, C _p is the specific heat capacity, and u is the velocity field of the fluid. The current density J was determined from the steady-state continuity equation. Assuming Ohm’s law, the current density was linked to the electric field by J = σE, with σ being the electrical conductivity given by σ = (μ_ac_a + μ_cc_c)F, where μ_a = 7.9 × 10^–8 m² V^–1 s^–1 and μ_c = 5.194 m² V^–1 s^–1 are the mobilities of Cl^– and Na⁺, respectively, while F is the Faraday constant. The steady-state spatial distributions of anions and cations (n _a, n _c) were computed by using the Nernst–Planck equation. The electric field E was solved using the nonlinear Poisson–Boltzmann equation considering the temperature-dependent permittivity of water as ε_w = (249 – 0.790T + 7.30 × 10^–4 T ²)­ε₀, with ε₀ being the vacuum permittivity. Electroosmotic flow was modeled by solving the incompressible Navier–Stokes equation. All equations were simultaneously solved using the COMSOL Multiphysics 6.3 software package (COMSOL Inc., Stockholm, Sweden).

The data sets generated and/or analyzed during the current study are available from the corresponding authors on reasonable request.

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acsnano.5c13339.

• Fabrication flowchart and SEM images of thermocouple-embedded nanopores with and without gate electrodes; evaluation of errors in the local temperature assessments; measurements of leakage current through gate electrodes; finite element analyses of temperature distributions around Joule heated nanopores; and reproducibility of field-effect-controlled ionothermoelectric cooling (PDF)

All authors discussed the data and reviewed the manuscript.

The authors declare no competing financial interest.