Introduction

A primary challenge hindering the large-scale commercialization of memristive1 technologies is their inconsistent switching behaviors, commonly termed device-to-device and cycle-to-cycle variability. In the most technologically advanced resistive random access memories (ReRAMs), such as electrochemical metallization (ECM)2 and valence change mechanism (VCM)3 devices, the switching typically occurs due to the growth or dissociation of a conductive filament. The conductivity of a filament, which is a nanoscale structure made up of cations in ECM devices and anions in VCM devices, is greatly influenced by the arrangement of atoms that cannot be precisely controlled. Thus, the variation in response in such devices can be attributed to the stochastic nature of filament formation. Currently, it seems very difficult or even impossible to eliminate this in the existing solid-state technology.

In the present work, we utilize the advantages of the liquid phase material system, which consists of two EGaIn:sodium hydroxide solution interfaces contained within a narrow tube, as an alternative to a solid phase material architecture. In fact, liquid-state memristors have recently attracted increasing attention4,5. But what makes liquid memristors different? Unlike in the solid phase, atoms and molecules within a liquid are more mobile. Consequently, large ensembles of atoms/molecules of the same type undergo on-average uniform interactions with other species in the surrounding liquid, resulting in a homogeneous collective response. As a result, an important distinction between our EGaIn liquid metal device and conventional memristors lies in the bulk switching mechanism, which provides an extra level of cycle-to-cycle and device-to-device averaging. Although the structure of our devices is very different from that of biological synapses, they both operate on nearly the same time scale likely because they both rely on liquid. Therefore, our EGaIn memristive devices may be relevant to several important applications such as neuroprosthetics6 and brain-computer interfaces.

In addition to various nanofluidic, liquid-based, and hydrogel-based ionic memristors7,8,9, liquid metals (LMs), including eutectic gallium indium (EGaIn) and gallium indium tin (Galinstan), have attracted interest for building memristors, generally via one of three approaches. In the first, LMs were used as flexible metal contacts on one side of a dielectric thin film (e.g., polymer10, metal organic framework11, inorganic oxide12, or self-assembled monolayer13,14,15) on a solid metal substrate. In this metal-insulator-metal (MIM) configuration, applied voltage drives Ga ions from the LM through the dielectric to form conductive nanofilaments, resulting in bipolar nonvolatile memristance. An advantage of using LM as one of the metal contacts is its native flexibility, enabling devices to operate under significant mechanical deformations11,15. An interesting extension of the first approach is an LM-based system where the switching occurs through a piezo-acoustic effect16. A second approach harvested the solid gallium oxide layer from the surface of the LM to form the central dielectric material in an MIM sandwich. To do so, Xu et al. printed the 2.5−3.5 nm thick Ga2O3 LM coating onto an n+-Si solid surface17. Upon the addition of a Pt top contact, the MIM device displayed bipolar memristive switching, attributed to oxygen vacancy migration through Ga2O3. The third approach, which is most similar to our work presented herein, utilizes one or more LM volumes interfacing an aqueous electrolyte. Koo et al. demonstrated that bipolar memristance could be achieved with two EGaIn volumes separated by a bi-layer arrangement of acidic (PAA, pH  ~ 3) and basic (PEI, pH  ~ 10) aqueous hydrogels18. Bipolar memristance was attributed to the asymmetric gel arrangement that enabled nonvolatile oxide growth at the PAA interface (stable switching from the low resistance state, LRS, to the high resistance state, HRS) under positive voltages (3−5 V) and volatile oxide growth at the PEI interface under negative voltages (−1 V). Recent works19,20 have also shown that liquid metal EGaIn interfacing aqueous electrolytes at controlled pH levels enables programmable, voltage-dependent changes in device impedance, offering pathways for building physical neural networks for signal and flexible random access memory for information storage.

Herein, we demonstrate that a symmetric, all-liquid configuration of EGaIn/electrolyte/EGaIn exhibits volatile memristance through voltage-controlled electrochemical oxidation and reduction that occurs alternatively at the two EGaIn-electrolyte interfaces. Our devices are volatile in the standard sense used for memory technologies: the stored information is lost when the applied voltage is removed. Under an appropriate applied voltage, however, our devices can persistently store Boolean information. The use of a fully liquid system ensures atomically smooth interfaces (on average), while the electrochemical mechanism of resistive switching occurs uniformly, in a spatially distributed manner across the interface, which provides repeatable switching characteristics on biological time scales (milliseconds), low cycle-to-cycle performance variation, and device longevity (weeks). Reliable switching voltages and memory states enable consistent changes in the device conductance state, which are leveraged to demonstrate logic gate functionality.

Results and discussion

I−V curves and switching mechanism

The schematic diagram of an EGaIn tube memristor is shown in Fig. 1a (for the fabrication details, see the Methods section). The I−V characteristics recorded using a source-measure unit (Fig. 1b) are consistently reproducible and free of noise, see Fig. 1c–e. These I−V curves are classified as unipolar and binary as, within the hysteresis window, our devices support only two stable resistance states for any given applied voltage. This is in contrast to conventional ReRAM cells, whose resistance can be tuned continuously. The switching is characterized by two voltage thresholds, Voff ≈ 0.3−0.5 V and Von ≈ 0.1 −0.2 V, with a hysteresis interval between Von and Voff. Although the shape of I−V curves is somewhat similar to that of solid-state diffusive memristors21,22, we emphasize an important difference: the direction around the loops is clockwise in our devices. This indicates that our devices start in a lower resistance state (LRS = on) and switch to a higher resistance state (HRS = off) when the voltage eclipses Voff. In the reverse direction, a return to the lower resistance state occurs when voltage reaches Von.

Fig. 1: Schematics of a tube memristor and its response recorded using a source measure unit (SMU).
Fig. 1: Schematics of a tube memristor and its response recorded using a source measure unit (SMU).
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a EGaIn tube memristor is composed of two external copper electrodes inserted into a plastic tube. The electrodes' surfaces facing each other are covered with EGaIn and are separated by 3M NaOH solution. b Measurement setup. c–e Representative examples of current–voltage curves. The recording in (c) was obtained using the voltage ramp, γ, of 0.09 V/s. f Temporal current response to a constant voltage level, V0. “V0 = 0.6 V → 0.2 V” indicates the measurement at V0 = 0.2 V was performed after the device was switched to its off state by applying V0 = 0.6 V.

Within these devices, all switching operations take place entirely in the liquid segment, which consists of two EGaIn-coated copper (Cu) electrodes separated by a NaOH aqueous solution. In the absence of EGaIn deposited onto the copper electrodes, the current–voltage response measured between a Cu/NaOH/Cu device shows significantly smaller current, no strong oxidation or reduction potentials (Fig. S3a (SI)), and it lacks pinched I−V hysteresis. However, replacing the copper electrodes with gold-plated brass versions maintains the same I−V behaviors (Fig. S3b) observed in Fig. 1. These comparisons confirm that the liquid EGaIn/NaOH interfaces are responsible for the pinched, hysteretic I−V response that allows this tube-style device to function as a memristor.

These pinched, hysteretic I−V features, including the values of Voff and Von, are maintained across a range of sweep rates of the applied voltage (Fig. 1d). At higher sweep rates, the I−V traces no longer pinch at zero due to the presence of significant capacitive charging currents. Varying the amplitude of the sweep confirms that the hysteresis requires the applied voltage to surpass Voff (Fig. 1e). We emphasize that a slight increase in the hysteresis size with frequency in Fig. 1d is consistent with memristor theory in general (see Sec. S3 of the SI).

Figure 1f shows the measured current through an EGaIn memristive device to different applied dc voltages. An important aspect of these responses is the power-law relaxation, suggesting a potential fractional-order effect23, similar to the behavior described by the Curie-von Schweidler law in capacitors24,25. Moreover, impedance measurements discussed below confirm the presence of pseudo-capacitance at intermediate frequencies (~10−1000 Hz). Nevertheless, in this work, we primarily concentrate on memristive phenomena, postponing the exploration of capacitive effects for subsequent investigations. Beyond their transient dynamics, these curves provide insight into the stability of the on and off states at specific potentials. For example, the V0 = 0.3 V curve in Fig. 1f (shown in blue) exhibits an abrupt transition at t ≈ 600 s from the on to the off state, indicating that the on state (at V0 = 0.3 V) is metastable, while the off state, recorded at V0= 0.4 V after increasing from V0 = 0.3 V and at V0 = 0.2 V upon returning from V0 = 0.6 V, is stable. A metastable on state will be associated with local minima in the Landau free energy in our model of EGaIn memristors (in the Memristive model section below).

Prior works describe the reversible electrochemical oxidation and reduction of EGaIn in basic solutions26,27,28. Therefore, we hypothesized the symmetric, voltage-dependent resistive switching exhibited by an EGaIn tube memristor stems from the combination of opposite electrochemical activities of the two separate EGaIn/NaOH interfaces. Thus, we performed half-cell measurements on single EGaIn/NaOH interfaces to better understand the individual responses of a single interface at both positive and negative applied potentials. Figure 2a shows a representative I−V relationship obtained using a 3-electrode setup for a single EGaIn volume (~20 μL) surrounded by 1 M NaOH electrolyte. Figure S5(a) (SI) compares this response to the hysteretic I−V response of an EGaIn half-cell containing 3 M NaOH concentration. Figure 2b and Fig. S5(b) (SI) show how the voltage scan rate affects the I−V relationship for 1 and 3 M NaOH, respectively. Details of this measurement method are provided in the Methods section.

Fig. 2: Half-cell EGaIn/NaOH current–voltage relationships.
Fig. 2: Half-cell EGaIn/NaOH current–voltage relationships.
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a I−V response measured in 1 M NaOH using a scan rate of 50 mV/s. The open circuit voltage (VOC) and passivating potential (VP) are denoted by the dashed lines. The five different oxidation regions observed at positive potentials are shown. b Representative examples of half-cell I−V curves in 3 M NaOH at varying scan rates.

These half-cell I−V recordings agree well with previous measurements made on EGaIn in NaOH at similar conditions27,28 and they share some of the same features as the whole-cell memristor presented in Fig. 1. For a single EGaIn/NaOH interface, the open circuit potential, Voc, defined where measured quasi-static current is zero when returning EGaIn from a fully-reduced state, occurs at a potential near −1.5 V vs. an Ag/AgCl reference electrode saturated in 3 M KCl (Fig. 2a). For dV/dt > 0 and VOC < V < −1.41 V, the measured current increases roughly linearly with voltage. In this oxidizing region27,28, the increase in current corresponds to the electrochemical oxidation of Ga by hydroxide (OH−) groups in the solution, which produces water-soluble gallate [\({Ga(OH)}_{4}^{-}\)] ions. The anodic current exhibits a local oxidation peak at a potential of −1.44 to −1.41 V, termed the passivation potential, VP27,28. The stability of the location of VP across different scan rates indicates quasi-reversibility of the reaction.

When V > VP (i.e., the passivation regime), the measured current falls sharply due to the formation of an insulating anodic film, likely composed of water-soluble gallium oxyhydroxide (GaOOH) or GaO3Hy (y < 3) facilitated by the adsorption of gallate ions27,28. At potentials near −1.35 to −1.39 V, the interface enters the transpassive regime where electrostatic attraction of OH− anions leads to solubilization of the GaOOH to the soluble Ga(OH4)− form. This corresponds to a slight rise in the measured current. At around −1.25 V, the current slope again becomes linear with voltage, signifying the onset of steady-state oxidation in which Ga(OH)3 is formed. Depending on the potential scan rate and the NaOH concentration (Fig. S5, SI), a local peak is observed at potentials between −1 and −0.8 V, marking the transition to a partial-repassivation region.

During the reverse sweep (dV/dt < 0) at positive overpotentials (V > VOC), the current takes a different path: it remains lower than that measured for dV/dt > 0 across the same potential range. The arrows in Fig. 2(a) differentiate the paths of the I−V relationship during forward and reverse sweeps. This hysteresis is due to the retention of the Ga(OH)3 oxide layer on the surface that keeps the interface in a state of higher resistance. As V approaches VOC during the reverse sweep, the interface exhibits either a re-oxidation peak (at low scan rates ≤100 mV/s) or a reduction peak (for scan rates >100 mV/s) at a potential between −1.42 and −1.5 V (Fig. 2a). This is likely a result of the finite diffusivity of oxidized species leaving (or staying) at the interface, which causes either re-oxidation or reduction, respectively, to occur.

At negative overpotentials (where V < VOC; the unshaded region in Fig. 2a), the EGaIn interface remains in a reduced state where current increases quadratically with increasing overpotential. Moreover, we observed bubble formation (presumably H2 gas27,28)—especially for the 3 M NaOH case—on the surface of the EGaIn at sufficiently negative overpotentials and slow sweep rates, which created significant noise in the measured current of the half-cell configuration (Fig. 2b). More broadly, measurements in 3 M NaOH produced larger oxidation and reductive currents than those in 1 M NaOH (Fig. S5, SI). Additionally, VP occurs at −1.45 V in 3 M NaOH, versus appearing at −1.42 V for 1 M NaOH. In both concentrations, sweep rates above ~100 mV/s induced significant capacitive charging currents.

These data reveal key similarities and differences between the I−V relationships of a single EGaIn/NaOH interface half-cell (Fig. 2) and of a tube memristor consisting of two EGaIn/NaOH interfaces (Fig. 1). For V > Voc and dV/dt > 0, both the whole cell device (Fig. 1c) and the half-cell EGaIn/NaOH interface (Fig. 2, in the regions labeled oxidizing, passivation, transpassive, and steady-state oxidation) exhibit local current maxima (corresponding to Voff and Vp, respectively), followed by sharp decreases in current that flatten and then increase again at higher potentials. Both systems local current peaks at voltages more positive than Voc, followed by a sharp reduction in current magnitude, a flattened current regime, and then a successive rise with continued increases in voltage. The shape of the I−V hysteresis at positive overpotentials (V > Voc) for each system is similar too; both exhibit lower net currents during the reverse sweep (dV/dt < 0) at positive potentials (provided the previous maximum potential exceeded passivation potential) and a small local current peak at a potential (Von) located slightly above Voc.

However, their responses are starkly different for V<Voc: The asymmetric half-cell exhibits an I−V relationship at negative potentials that is governed by the reduced state of EGaIn. Meanwhile, the tube memristor has a second EGaIn/NaOH interface (EGaIn2) that undergoes electrochemical oxidation with increasing negative overpotentials, causing its I−V response at negative potentials to mirror that measured at positive potentials. Also, the half-cell device measurement covers a wider potential range than that used on the full device. Therefore, not all features of the response shown in Fig. 2 are observed in the recordings in Fig. 1(c). Moreover, the relative voltages at which the various I−V features occur are significantly higher in the whole-cell device due to the additional electrochemical impedance contributed by the second EGaIn/NaOH interface. As a result, the passivation peak occurs at an overpotential of ΔV ≡ V − Voc ≈ 0.05−0.10 V for the half-cell, versus current showing a sharp decline at a switching voltage of ΔV ≈ 0.3−0.5 V, depending on the device and NaOH concentration. The former potential difference represents the overpotential across a single EGaIn/NaOH interface, while the latter reflects the difference in overpotentials across both half-cell interfaces in the whole-cell memristor.

These comparisons reveal that an EGaIn tube memristor exhibits symmetric and hysteretic I−V relationships as a result of alternating electrochemical responses at the two EGaIn surfaces, which occur at opposite voltage polarities. For V > 0, the EGaIn interface (EGaIn1) attached to the source electrode of the voltage supply undergoes electrochemical oxidation, according to the responses seen in Fig. 2. Meanwhile, the EGaIn interface (EGaIn2) attached to the ground electrode of the voltage supply, which feels a net negative voltage difference compared to the NaOH, at a positive supply potential is held in a non-oxidizing state (unshaded region of Fig. 2a). This behavior reverses when V < 0: EGaIn1 is now held at in a non-oxidizing state, while EGaIn2 exhibits electrochemical oxidation and reduction according to the amplitude of the applied voltage. Thus, Voff defined for the whole-cell memristor corresponds directly to VP from the half-cell recordings.

The cycle-to-cycle reproducibility (Fig. 1 and Fig. S11, SI) indicates that the electrochemical state of each EGaIn/NaOH interface is sufficiently reversible. Thus, while the I−V data in Fig. 2 shows only oxidative currents at positive voltage, the devices are able to sufficiently reset even under positive-only applied potentials (Fig. S4, SI). Thus, the oxidized EGaIn/NaOH surface appears to “reversibly reset” its electrochemical state, provided the applied voltage is reduced below ∣Von∣ during a given sweep.

The switching potentials in the whole cell memristor occur at different nominal values than the half-cell system because the two liquid metal interfaces are coupled via the conductive NaOH electrolyte, which causes the total applied voltage between the source and ground to be dynamically divided across EGaIn1 and EGaIn2. This specific behavior was directly observed by inserting a pseudo-reference electrode into the NaOH solution between EGaIn1 and EGaIn2 (Fig. 3a). Here, a multi-channel data acquisition system was used to supply a 4 V, 80 mV/s triangular voltage waveform [V(t)] to a 10 kΩ resistor wired in series with a tube-memristor. Both the voltage at EGaIn1 (VM) and the potential at the middle electrode (VN) were recorded (Fig. 3b). During first quarter of the cycle (V > 0 and dV/dt > 0), VM and VN increase with increasing voltage. However, VM undergoes a sharp rise that occurs as it surpasses ~0.33 V. VN exhibits a much smaller decrease. The magnitudes and directions of these responses signify that EGaIn1, which experiences a voltage roughly equal to VM − VN undergoes an increase in effective resistance. Meanwhile, the small dip in VN, is due to the fact that the resistance of EGaIn2 is now a smaller portion of the total resistance of the device. At negative potentials as ∣V∣ increases, both VM and VN exhibit sharp increases in their respective values when ∣VM∣ ≈ 0.33 V. This shared response indicates that EGaIn2 undergoes a marked increase in resistance, causing both VM and VN to increase.

Fig. 3: Three-terminal measurements of a tube memristor.
Fig. 3: Three-terminal measurements of a tube memristor.
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a The measurement setup. To distinguish the separate contributions of the two electrodes to the signal, a sewing needle (acting as a pseudo-reference electrode) was inserted into the center of the tube. The measurements were performed using a multifunctional data acquisition unit (MDAQ) that was used to apply the driving signal V(t) and read the response signals VM and VN. The arrow’s orientation shows if a signal is an input or an output. b Measured response to a triangular waveform (shown in the inset). Here, \({V}_{N}^{* }\) represents the needle voltage that has been adjusted by the open circuit needle voltage (approximately 1.17 V).

Device impedance

Electrical impedance spectroscopy (EIS) measurements were performed on whole-cell EGaIn tube memristors to quantify changes in device impedance at various dc biases. The corresponding I−V curve of one representative device is shown in Fig. 4a. Figure 4b, c shows how the impedance magnitude (top) and phase (bottom) of this same device vary with frequency for both forward and reverse bias sweeps from between 0 and +0.7 V. The impedance spectra reveal that the tube memristor is not simply a resistive device, but includes psuedo-capacitance and sometimes inductive components in its responses. Figure S8 (SI) provides Nyquist representations of these same data, which are similar to those obtained on single EGaIn interfaces at positive potentials relative to VOC by Hillaire et al.28. However, our measurements combine changes in impedance at both EGaIn interfaces.

Fig. 4: Electrical impedance spectroscopy measurements of a whole-cell EGaIn tube memristor.
Fig. 4: Electrical impedance spectroscopy measurements of a whole-cell EGaIn tube memristor.
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a I−V relationships from 2 consecutive cycles (sweep rate: 50 mV/s) for a device containing 3 M NaOH. Electrical impedance magnitude (top) and phase (bottom) versus frequency during sequential voltage increases (b) and decreases (c) between 0 and  + 0.7 V. d Equivalent circuit used to fit the EIS data. e Low-frequency resistance (R2) versus voltage during quasi-state forward and reverse sweeps.

Similar to the I−V relationships, which show that dc current returns to zero as the voltage completes a full half-cycle, the EIS data show reversible changes in the impedance spectra. At DC potentials very close to 0 V, EIS measurements reveal the presence of two different resistor–capacitor (RC) pairs (see the two separate dips in phase angle versus frequency). However, at non-zero dc voltages, the memristors exhibit only a single RC time constant and are well approximated (Fig. S9, SI) by the equivalent circuit shown in Fig. 4d. In this simplified circuit model, a constant phase element (CPE, or psuedocapacitance) and R2 are used to describe the electrochemical state of the EGaIn/NaOH interface, while R1 represents the ionic resistance of the NaOH solution. For this particular device, R1 is ~130 Ω. More generally, R1 is expected to increase with increasing tube length, decreasing tube diameter, or decreasing NaOH concentration. The larger-valued R2 parameter determines the low-frequency, or quasi-static, resistance of the device that affects the dc I−V relationship.

A nonlinear least-squares fitting routine (see Methods) was used to extract estimates for R2 versus the dc bias (Fig. 4e). Matching the trend of the low-frequency impedance magnitude shown in Fig. 4b, c, these data show that R2 exhibits a hysteretic path with changes in voltage. Apart from the increase in R2 observed between V = 0 and V = 0.1V, R2 steadily decreases from ~10 kΩ to <1 kΩ with increasing voltage until reaching V = Voff ≈ 0.5 V, where the memristor switches from on to off. At this location, R2 sharply rises to ~5 kΩ. Further increases in V cause R2 to again reduce below 2 kΩ. Subsequently, decreasing the dc bias below +0.7 V causes the value of R2 to increase steadily above 8 kΩ by V = 0.4 V, where it remains until falling back to the starting value of 2 kΩ for V < 0.05 V. This hysteretic path identifies the net resistance of the device as voltage changes and quantifies how much R2 changes as each EGaIn interface undergoes electrochemical oxidation and reduction. For this device, a maximum Roff/Ron resistance ratio of 8−10 occurs at a voltage just below Voff. Given the symmetry of the I−V curves, similar changes in device resistance are found at negative potentials too. Fitting the EIS spectra also revealed that the constant phase element changes hysteretically with voltage; details of this pseudo-capacitive switching and memory will be discussed in a separate publication.

To understand the time constants associated with the switching process, square voltage pulses were used on a resistor-memristor circuit (refer to Fig. 5a). As depicted in Fig. 5b, when the pulse amplitude is less than Voff, the voltage across the memristor closely mimics the form of the input voltage, with the exception of a minor decaying tail. When the applied voltage exceeds Voff, a shoulder-like step appears, somewhat similar in shape to the 0.7 anomaly in quantum point contacts (but, definitely, of a different origin)29, followed by a region where the voltage rises gradually (refer to Fig. 5c for a detailed structure). Similarly, as the voltage drops to zero, there is a shoulder-like drop followed by a non-exponential extended tail (refer to Fig. 5d for a detailed structure). These rising (falling) shoulder-like steps correspond to the creation (dissolution) of the oxide film at the liquid metal surface.

Fig. 5: Pulse control of EGaIn memristive devices.
Fig. 5: Pulse control of EGaIn memristive devices.
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a The measurement setup (R = 10 kΩ). b Response to a stepwise voltage that is lower/higher than the switching threshold. Response to positive (c) and negative (d) voltage pulses for various chosen pulse durations. e, f Response to voltage pulse sequences. In c and d, the orange curves were obtained using fixed time increments of 10 ms and 20 ms, respectively.

To determine the reset time (the transition from on to off), we altered the duration of a high-amplitude pulse, followed by the hold voltage, as shown in the inset of Fig. 5c. According to our measurements, the reset time is approximately 25 ms, and can be reduced to below 20 ms by using a higher amplitude voltage pulse (refer to Fig. 5e). As shown in Fig. 5f, the set time is relatively longer, approximately 150 ms. We emphasize that the measurements in Fig. 5c, d correlate the points for maximum curvature (in the “shoulder” regions) with the transitions between states on and off.

Memristive model

Existing memristive models, including the VTEAM30 and others, do not capture the binary nature of the I−V characteristics of the EGaIn memristive devices. We propose a phenomenological model inspired by concepts from the Landau phase transition theory31. Consider a free energy

$$F(x,{V}_{M})=\frac{1}{2}a{x}^{2}+\frac{1}{4}b{x}^{4}+\kappa (| {V}_{M}| -{V}_{0})x,$$
(1)

where a < 0, b > 0, κ > 0, and V0 > 0 are constants, VM is the applied device voltage, and x is the order parameter. When ∣VM∣ = V0, the free energy in Eq. (1) exhibits a \({{\mathbb{Z}}}_{2}\) symmetry, indicating that there exist two equivalent phases, corresponding to the on and off memristive states, within the hysteresis region. This symmetry breaks down when ∣VM∣ deviates from V0, favoring one of the states. As the deviation continues to rise, a bifurcation is induced, resulting in only one energy minimum remaining (on or off state). Illustrative examples of F(x, VM) are presented in Fig. S1 of the SI.

We model the dynamic switching behavior as a relaxation process, dx/dt ~ − Γ ∂F(x, VM)/∂x, where Γ is the relaxation rate that may depend on the voltage. Substituting Eq. (1), one obtains the equation of motion

$$\frac{{{{\rm{d}}}}x}{{{{\rm{d}}}}t}=-\Gamma (-x+b{x}^{3}+\kappa (| {V}_{M}| -{V}_{0})),$$
(2)

where some of the constants were re-normalized. Additionally, the memristive response is described by a generalized Ohm’s law

$$I=({G}_{on}({V}_{M}){f}_{on}(x)+{G}_{off}({V}_{M})(1-{f}_{on}(x))){V}_{M},$$
(3)

where fon(x) ∈ [0, 1] is a function that describes the contribution of the on-state conductivity Gon to the total conductivity at a particular value of the order parameter x. It is important to recognize that this model accommodates transient states beyond binary. Nevertheless, the system internally stabilizes into a binary state under zero or a finite constant voltage. Overall, Eqs. (2) and (3) describe a voltage-controlled first-order memristive system1. See SI for additional information on the model, including expressions for its coefficients and an example of I−V curve.

In-memory computing

Neuromorphic and reservoir computing, access devices, and hardware security are among the most-studied applications for volatile memristors32,33. In contrast, we present experimental evidence of in-memory computing using our EGaIn memristive devices. Their inherent bi-stable states make them quite suitable for storing Boolean data. Traditional memristive devices have been shown to be well-suited for implementing material implication logic gates34. Moreover, volatile memristor emulators (with diffusive memristor hysteresis) were used to demonstrate material implication logic gates and their inverse35.

Next, we demonstrate that EGaIn memristive elements are suited to realize AND and OR logic gate In this demonstration, we associate the off state of one memristor with Boolean 0, while the on state of the same memristor with Boolean 1. For this purpose, we built the circuit shown in Fig. 6a. A multifunctional data acquisition unit (MDAQ) was used to apply and read voltages. The circuit includes a relay to induce the interaction of two memristors, M1 and M2. The experiment implementing the truth table of AND (Fig. 6b) consisted of three phases: initialization, interaction, and reading (Fig. 6c–f). In the initialization phase, the relay was open, and the states of the memristors were individually programmed by applying (or not applying) a voltage pulse of 1.8 V for 200 ms at t = 3 s and then maintaining a holding voltage of 1.2 V. The amplitude and duration of the pulse were chosen so that the memristors exposed to it switch to the off state. Consistent with Fig. 5c, the voltage across each memristor subjected to the programming pulse converges to a high stable final value, indicating it is in the off state (Boolean 0) or, otherwise, low stable final value, indicating the on state (Boolean 1).

Fig. 6: Demonstration of AND gate.
Fig. 6: Demonstration of AND gate.
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a Circuit schematics (R1 = R2 = 10 kΩ, R3 = 3.3 kΩ). b The truth table of AND. c–f An experimental demonstration of AND gate.

In the interaction phase, the relay is closed and a positive voltage pulse of 1.6 V is applied to M2 (through R2) for 200 ms at t = 5.2 s, while the holding voltage is continuously applied to M1 (through R1). Within this setup, the pulse-induced switching of M2 is controlled by the state of M1. If M1 is on, the voltage across M2 is reduced so that the transition of M2 from on to off is blocked (as the voltage across M2 stays below the threshold Voff). In contrast, when M1 is off, the switching of M2 from on to off is allowed (as the voltage across M2 exceeds the threshold Voff). Figure 6c–f shows that M1’s state remains unchanged throughout the interaction phase. In panels (c) and (d) of Fig. 6, M2 ends up in the off state, given that it started off. When you examine Fig. 6d, M2 switches to off due to M1 being off. Conversely, in Fig. 6e, M2 stays on because M1 is on.

In the reading phase, the relay is opened and the states of M1 and M2 are evaluated in terms of memristor voltages, VM,1 and VM,2, which are recorded in response to the same holding voltage. Using the state of M2 as the output of the logic gate, it is evident that this experiment reproduces the logic table of AND. Referring to Fig. 6c–f, the truth table for the AND gate can be read by linking the high voltage level of VM,2 to Boolean 0, and the low voltage level to Boolean 1, as previously discussed. Thus, the output of the AND gate produces a Boolean 1 only when both memristors are on (Boolean 1).

To realize the OR gate, we employed the experimental setup depicted in Fig. 6a, with the sole change being the use of a negative amplitude for VM,2 during the interaction phase. As demonstrated in Fig. S6 (Supplementary Information), the final state for M2 corresponds to the functionality of the OR gate.

Accelerated and decelerated switching

Additionally, we investigated how EGaIn memristive devices behave when connected in series and parallel circuits (Fig. S7(c) and (d) of SI). Using these circuits, we observed two notable phenomena: accelerated (simultaneous) and decelerated (time delayed) switching36, both of which stem from the voltage-divider effect. In the circuit of series-connected memristors subjected to a triangular voltage, the initial switching of one memristor decreases the voltage drop occurring across the other, as the resistance of the first memristor increases. This causes the second memristor to switch at a notably higher voltage, note two peaks at V > 0 in Fig. S7(e) of SI. In contrast, for memristors connected in parallel, the first switching event raises the voltage drop across the second memristor, leading to (almost) simultaneous switching of both memristors (a single peak at V > 0 in Fig. S7(e), SI).

Reproducibility

Devices exhibited good reproducibility, endurance, and stability. The data provided in Fig. S10 (SI) aimed to show to the reader that nine different devices exhibit quantitatively similar metrics of switching and exhibit reasonable stability over time (~25−42 days). Figure S11 shows the results of 1000 resistive-switching cycles using stepwise changes in applied potential.

The behaviors of the EGaIn tube memristor introduced herein demonstrate that voltage-dependent oxidation and reduction at a molecularly smooth liquid interface yield reliable resistive switching, both between devices and across activation cycles and time. These are important criteria for enabling memristive technologies in signal processing or brain-inspired computing circuitry. Unlike the localized formation of conductive filaments in solid-state memristors that results in highly stochastic device operation, EGaIn devices exhibit voltage-driven changes in resistance, and without requiring an initial forming step, via spatially distributed electrochemical oxidation and reduction reactions occurring across the EGaIn:NaOH liquid interface. The associated reaction-diffusion kinetics that control the rates of gallium oxidation and reduction cause resistive switching to occur at similar speeds to many biological sensory and communication processes. Moreover, the recorded values of ∣Voff∣ and ∣Von∣ are well below 1 V, which makes EGaIn-based devices comparable to many solid-state devices, such as those based on transition metal oxides37. However, the relatively low values of on and off resistance (<10 kΩ, Fig. 4e) increase power consumption in EGaIn tube memristors. We expect that shrinking the characteristic device size, as governed by the EGaIn:NaOH interfacial area, will increase nominal resistance and reduce power dissipation. In addition, future works should investigate ways to achieve non-volatile memory storage, characterize the intrinsic fractional capacitance exhibited at intermediate frequencies, and explore their rich nonlinear properties in adaptive signal processing applications (e.g., physical reservoir computing).

Conclusion

In this work, we have realized EGaIn-based memristive devices that exhibit distinct switching behavior, characterized by i) unipolar operation, ii) binary resistance states, iii) volatility, and iv) an on state that remains stable at V = 0. Our EGaIn devices most closely resemble diffusive memristors21, with the key difference that, in diffusive memristors, the off state is the stable state at V = 0. Although the structure and physical mechanisms of our devices are very different from those employed by biological synapses, they both operate on similar millisecond time scales. These similarities likely emerge from the fact that our system utilizes ion transport and diffusion-limited oxidation/reduction processes in a liquid environment, similar to the aqueous electrolyte environments in cells. A neuromorphic device that operates on similar timescales as biological signaling events could enable real-time temporal processing of biological signals, which could potentially be applied in biomedical devices, including wearable or implantable technologies. We anticipate that operational voltages could be lowered via interface or material engineering and/or device scaling; however, this remains a subject for future investigation.

Methods

Device fabrication

To make a device, we employed polyvinyl chloride (PVC) tubing approximately 22 mm long, with an internal diameter of 1/16 inch (1.5875 mm) and an external diameter of 1/8 in. (3.175 mm) (Grainger Part No. 4EGY3). First, a 10 AWG copper electrode was inserted ~6 mm deep into the tube. With the tube oriented vertically and the copper electrode pointing downward, a syringe filled approximately two-thirds of the empty tube volume with 3 M NaOH. A separate syringe was then used to inject EGaIn liquid metal (Indalloy® 300E (78.6Ga/21.4In), Indium Corporation) close to the copper electrode, in an amount equating to approximately 1–2 mm of tube length. Subsequently, the tube was topped with NaOH and a second electrode was inserted 6 mm deep into the tube. Gentle tapping allowed a portion of EGaIn to transfer to the second electrode. We made sure that there were no trapped bubbles in the device at all. Some devices were exposed to sonication (with a Central Machinery 2.5 l ultrasonic cleaner), which contributed to lowering and achieving more consistent switching thresholds.

It was observed that small bubbles developed over time have no to little effect on the device characteristics. However, the performance of the device declines when a bubble completely obstructs the tube’s cross-section. In these cases, performance might be restored by eliminating the bubble through opening. To prevent or minimize bubble formation, we tried to keep the applied voltage to the device below 0.8 V. In these circumstances, the devices were observed to operate reliably for long durations (several weeks, see Fig. S10 in the SI). However, testing was not conducted continuously. Figure S11 (SI) shows an excellent switching capability of our devices subjected to 1000 switching cycles.

Several earlier studies26,27,28,38 employed a 1 M concentration of NaOH as standard when performing experiments with EGaIn. We began with 1 M devices in our tests, but found that devices with a 3 M NaOH concentration exhibited a more consistent response. Consequently, we have opted for the 3 M concentration in our main experiments, especially since these devices demonstrated a significantly clearer transition from off to on in their current-voltage curves.

Electrical measurements

The I−V curves presented in this article were obtained using the Keithley 236 source measurement unit (SMU). In our experiments, the SMU was used to apply a voltage and record the current while limiting it to a predefined maximum (compliance) value, typically 1 mA. This value was not attained in most measurements. Additionally, we utilized the SMU to observe the device’s behavior at a fixed level of voltage.

The MDAQ, model Keysight U2542A, was used to apply and measure voltage. The MDAQ was programmed using a custom code to deliver a time-dependent voltage (e.g., voltage pulses) to small memristive circuits, as described in this article. Several MDAQ input channels were employed to record the voltage at the nodes of interest. In Boolean logic experiments shown in Fig. 6, the relay was activated by the MDAQ unit. As depicted in Fig. 6a, a wire runs from the MDAQ to the relay coil, which is responsible for engaging the relay. A script on a PC produced the sequence of signals controlling the EGaIn devices and the relay.

In the experiment illustrated in Fig. 3, a stainless steel needle was used, and it was cleaned with IPA before insertion.

Electrochemical measurements

Half-cell cyclic voltammetry (I−V) recordings at single EGaIn/NaOH interfaces were performed in a 3-electrode electrochemical cell that was controlled by a Biologic SP300. Simulating the EGaIn volume and arrangement in the tube-memristor, a ~20 μL volume of EGaIn droplet supported by a copper rod was submerged into NaOH solution. The copper rod was insulated such that only EGaIn made contact with the surrounding electrolyte. This represented the working electrode for the system. The reference and counter electrodes consisted of Ag/AgCl in 3 M KCl and Pt, respectively. Measurements were controlled using Biologic EC-Labs software.

Electrical impedance measurements and supplementary cyclic voltammetry measurements on whole-cell tube memristors were performed using a Biologic SP200 Potentiostat using a two-electrode configuration in which the device leads were connected directly to the copper rods supporting the two EGaIn interfaces within the tube. EIS measurements were performed using a 10 mV sinusoidal AC voltage across the frequency range 100 kHz and 100 mHz. Measurements were controlled using Biologic EC-Labs software. Estimates of equivalent circuit parameters (as defined in Fig. 4d) were obtained from raw EIS data through a custom MATLAB script that employed a bounded, nonlinear least-squares fitting routine.

All measurements were performed at ambient conditions.