Programmable memristors with two-dimensional nanofluidic channels

Abstract

Nanofluidic memristors, obtained by confining aqueous salt electrolyte within nanoscale channels, offer low energy consumption and the ability to mimic biological learning. Theoretically, four different types of memristors are possible, differentiated by their hysteresis loop direction. Here, we show that by varying electrolyte composition, pH, applied voltage frequency, channel material and height, all four memristor types can emerge in nanofluidic systems. We observed two hitherto unidentified memristor types in 2D nanochannels and investigated their molecular origins. A minimal mathematical model incorporating ion-ion interactions, surface charge, and channel entrance depletion successfully reproduces the observed memristive behaviors. We further investigate the impact of temperature on ionic mobility and memristors characteristics. In this work, we show that the channels display both volatile and non-volatile memory, including short-term depression akin to synapses, with signal recovery over time. These results suggest that nanofluidic devices may enable new neuromorphic architectures for pattern recognition and adaptive information processing.

Fig. 1. Different memristor styles in nanochannels.

a Schematic of the device with 2D nanochannels composed of top, bottom, and spacer layers. The stack of these three layers rests over a microhole in a silicon nitride (SiN_x) membrane. The top and bottom layers used here are either hBN or MoS₂, and the spacer is graphene. An alternating voltage is applied across two Ag/AgCl electrodes in electrolyte solutions across the nanochannel. b Scanning electron microscopy (SEM) and c Atomic force microscopy (AFM) images of the spacers with a width of 130 nm and a height of 1.2 nm. d–g Electrical characterization of memristive behavior showing typical current–voltage characteristic curves observed in hBN channels, where either self-crossing (d and f) or non-self-crossing (e and g) memristor effects occur depending on the experimental conditions. The color codes of the IV curves show how they either cross (d and f) or tangentially touch (e and g) when meeting around 0 V. Current–voltage curves of (d) M1: crossing 1 memristor, the conductance decreases at positive polarity and increases at negative polarity. e M2: saturation memristor, the conductance decreases at both positive and negative high polarities. f M3: crossing 2 memristors, the conductance increases at positive polarity and decreases at negative polarity. g M4: Wien memristor, the conductance increases at both positive and negative high voltages. All the curves were obtained in a hBN device (h = 2 nm). Different electrolytes were used to obtain the corresponding loop styles: d AlCl₃ 1 M, e AlCl₃ 0.1 M, f AlCl₃ 0.01 M, and g KCl 3 M.

Fig. 2. 3D diagram and principal component analysis depicting memristive phenomena under various conditions.

The different memristor loop styles obtained from several a, b hBN, and c MoS₂ devices. The x, y, and z axes represent the salt type, salt concentration, and the nanochannel height, respectively. MoS₂ devices showed crossing 2-type (M3) memristor at low salt concentrations and for thick channels; Wien-type (M4) memristor at high concentration and thin channels; saturation-type (M2) mainly with trivalent aluminum chloride (or at very low concentrations of monovalent, where the memory is mixed with the capacitive effects). a, b The hBN devices showed crossing behavior at high concentration, particularly for multivalent cations. The existence of two crossing types, one at low and the other at high concentrations, occurs in several devices, which is attributed to charge inversion (discussed in Fig. 3); this effect is not seen in MoS₂ devices. The saturation style is limited to a certain concentration range of aluminum salts and MnCl₂. d PCA analysis of the measured devices (hBN, MoS₂) that reduces the dimensionality from 5 dimensions (salt type, valency, concentration, channel height, and channel material) to two principal components (PC1 and PC2) to enhance the visualization of clustering patterns and underlying phenomena.

Fig. 3. Mechanisms of the four memristive styles.

Type I (a, b) self-crossing and Type II (c, d) non-self-crossing memristive systems. a Crossing 2 (M3) memristor exhibits rectification (>1) at low salt concentrations due to variation of influx and outflux of cations in 2D nanochannels, resulting in enrichment or depletion depending on voltage polarity. b Crossing 1 (M1) memristor shows rectification (<1) at high salt concentrations, primarily with divalent and trivalent salts, leading to surface charge inversion (SCI) and anion-dominated current transport with variation of their influx and outflux due to the channel entrance asymmetry. c Saturation (M2) memristor loop features anion-selective nanochannels due to the SCI of the channel walls by bivalent Mn²⁺ or Al³⁺ ions. Initially, the ion concentrations at the nanochannel entrance are similar to the bulk, but within the channel, the anion concentration is higher, and the free cation concentration is reduced. At low voltages or high frequencies, ion movement in the nanochannels is proportional to the applied voltage, resulting in an ohmic response. Applying high voltages and low frequencies results in variation of influx and outflux of cations and the anions across the negative surface charge of the 2D nanochannels, and thus enrichment and depletion zones at the entrance of the nanochannels. This concentration difference leads to a force opposing the electric force, and thus the resultant force to move ions (and observe conduction across the nanochannel) becomes negligible, resulting in the stabilization of the current and the decrease of conductance with further increase of voltage. This is the limiting current zone. d Wien (M4) memristor loop shows high resistance at low voltages due to non-conductive Bjerrum pairs and transitioning to a low-resistance state with dissociation at high voltages.

Fig. 4. Temperature effect on type II non-self-crossing memristors.

a Current–voltage curves showcasing the Wien-type memory (M4) with a hBN device (h = 2 nm, HCl 1 M). c Current–voltage curves showcasing the Saturation-type (M2) memristor with a hBN device (h = 1 nm, AlCl₃ 0.5 M). Normalized area variation vs. temperature for b saturation type (M2) and d Wien-type (M4) memristors display contrasting effects with temperature. Normalization is done by dividing the loop area by the highest value of absolute conductance (${∣I∣}_{\max }/V_{\max }$).

Fig. 5. Simulation of four memristive loops using a minimal model.

a Schematic illustrating the various parameters used in the differential equations governing ion interactions inside the nanofluidic channel (See Supplementary Section 1). These include the adsorption (α_A, β_B) and desorption ($l_A,l_B$) rates of anions and cations to the wall charges, the ion–ion interaction term (${\delta }_0\left[f\right]$), and channel entrance depletion parameter ($\gamma$). Under an external forcing function $f\left(t\right)$, cations and anions migrate in opposite directions from two reservoirs with different concentrations ($c_r$ and $c_l$), reflecting the asymmetric entrance of the nanochannel. b–e and their insets show the corresponding current–voltage and conductance-voltage curves, respectively, obtained using the equations in the Supplementary Section 1 by varying the interaction parameters. This results in four distinct memory effects (M1–M4). The specific parameters used for each plot are indicated within the figure panels.

Fig. 6. Volatile and non-volatile memory.

a Excitatory action in a MoS₂ device (h = 0.7 nm, 1 M KCl) demonstrating a Wien-type memory (M4). The retained memory after applying a positive potential pulse of 1 V is partially erased and then completely erased after relaxation at 0 V for 1 min and 5 min, respectively, transitioning the system from low-resistance state (LRS) to high resistance state (HRS). The reading voltage is 500 mV. b Excitatory action in a hBN device (h = 0.7 nm, AlCl₃ 10 mM) demonstrating saturation-type memory (M2) after a 20-min relaxation at 0 V, read at 1 V. c Inhibitory action in a hBN device (h = 2 nm, AlCl₃ 1 M) demonstrating a crossing 1 type memory (M1) after a writing pulse of 0.8 V, read at 50 mV. Residual long-term memory persists, as the conductance does not return to its original value. d Inhibitory action in a hBN device (h = 1.4 nm, 3 M KCl) showing Wien-type memory (M4). The device is relaxed at 0 V and read at 1 V. The current magnitude variation relative to its equilibrium value is plotted against relaxation time in semi-log coordinates (inset). This case is the opposite of (b). e Non-volatile memory in MoS₂ device (h = 0.7 nm, 0.01 M KCl), showing a crossing 2 type memory (M3). The retained memory after a positive pulse of 0.12 V is not erased after relaxation at 0 V for 5 min. The reading voltage is 30 mV. f Non-volatile memory in a MoS₂ device (h = 0.7 nm, 0.1 M KCl), showing a crossing 2 type memory (M3). The retained memory after a positive pulse of 0.2 V is not erased after relaxation at 0 V for ~3 days. The reading and erasing voltages are −20 mV and −200 mV, respectively. g Coexistence of short- and long-term memory in a MoS₂ device (h = 0.7 nm, 0.01 M KCl), showing a crossing 2 type memory (M3). Varying writing pulse durations lead to both short (<20 s) and long-term memories. Reading is done at −0.03 V, whereas writing is done with +0.1 V pulses. h Coexistence of short- and long-term memory in a hBN device (h = 0.7 nm, CaCl₂ 0.3 M), showing a crossing 1 type memory (M1). Varying writing pulse duration leads to both short (<60 s) and long-term memories; however, the short-term memory was predominant compared to (g). Read at 0.03 V, written at −1 V.

Fig. 7. Nanochannels mimic biological ion channels and synapses.

a Schematic of the short-term depression in biological synapses and artificial nanochannels. The left panel shows two consecutive action potentials (AP₁ and AP₂) triggering neurotransmitter release from vesicles within the presynaptic nerve terminal, subsequently generating excitatory postsynaptic potentials (EPSPs) in the postsynaptic neuron. The amplitude of the second EPSP is affected by the relaxation time between the subsequent action potentials. The right panel shows the mechanism of the short-term depression in 2D nanochannels, where the potential difference obtained after application of subsequent constant currents is related to the relaxation time between the currents. When the current is applied, the polyelectrolyte is formed, and its dissociation to Bjerrum pairs, similar to the initial conditions, necessitates a sufficiently long relaxation time. b EPSP variation in nanochannels under a constant current of 200 nA for 30 s separated by different relaxation times (0.25 s, 5 s, 60 s, and 1200 s), simulating short-term depression observed in postsynaptic neurons. c Quantification of short-term depression by the ratio of the second EPSP peak (A2) to the first EPSP peak (A1), with varying relaxation times between excitations.