Randomly assembled networks of nanowires (NWs) can display complex memristive behaviors and are promising candidates for use as memory and computing elements in neuromorphic applications due to device fault tolerance and ease of fabrication. This study investigated resistive switching (RS) in two-dimensional, self-assembled silver sulfide (Ag2S) NW networks first experimentally and then theoretically using a previously reported stochastic RS model. The simulated switching behavior in these networks showed good correlation with experimental results. We also demonstrated fault-tolerance of a small NW network that retained RS property despite being severely damaged. Finally, we investigated information entropy in NW networks and showed unusual dynamics during switching as a result of self-organization of the memristive elements. The results of this work provide insights toward physical implementation of randomly assembled RS NW networks for reservoir and neuromorphic computing research.

Artificial neural networks (ANNs) today represent one of the most successful bioinspired technologies capable of performing a broad range of complex information processing tasks such as classification and regression.1,2 Conventionally, ANNs are implemented as software programs executed on silicon-based hardware systems that are highly sensitive to manufacturing defects and bear significant architectural limitations. Bioinspired hardware may provide useful alternatives. Unlike biological brains, conventional computing architectures spatially separate information storage and processing modules, which sets an upper boundary on the volume of information that can be processed. This limitation is generally referred to as the von Neumann bottleneck.3 

Neuromorphic hardware based on memristive components promises to overcome the von Neumann bottleneck via unification of data storage and information processing functions.4 The memristor was first introduced theoretically by Leon Chua in 1971 based on symmetry considerations as the fourth fundamental passive circuit element along with resistor, capacitor, and inductor.5 Memristors are resistive-switching devices with a simple two-terminal architecture and play the role of data storage using nonlinear hysteresis within changing resistance values.6,7 From a circuit point of view, the relationship between magnetic flux and electric charge defines memristance, and it depends on a time-dependent state variable. This time-dependency of the state variable is the fingerprint of a nonlinear memristor compared to a linear resistor and provides the system's memory.8 In 2008, a thin film TiO2 memristor was produced and characterized at HP laboratories,9 successfully establishing a concrete theoretical description of previous experimental results on RS mechanisms and memory.10–12 Due to their ability to approximate neuronal synaptic functions, memristors have been recognized as promising candidates for the fabrication of bioinspired neuromorphic systems.13 Although CMOS architectures have benefited from embedded crossbar memristor configurations, the realization of artificial neural networks of sufficient size14,15 with 2D crossbar assays in ordered architectures will come at a high manufacturing cost and require complex control electronics.4 Therefore, the future neuromorphic applications will likely be based on memristive devices with random configurations that may approximate some aspects of brain structure and that function with low energy and operational cost.

There has been considerable progress toward harnessing RS for in-memory computation. Recently, O'Callaghan et al. established an effective medium theory for Ag-based NW structures and networks. They studied the sheet resistance of disordered networks compared to regular ordered networks.16 Transition metal oxide NW networks were tested as memristive systems and showed RS behaviors while using materials such as NiO, TiO2, ZnO, and CuOx.17–20 In another study, Milano et al.21 developed a memristive reservoir with self-assembled Ag NWs with the crossbar configuration showing computing capability in spatio-temporal pattern recognition and time series prediction. Manning et al. and Li et al. studied RS of Ag@TiO2 core-shell single NW and NW networks.22,23 Gimzewski and colleagues also reported diverse research on self-organized complex networks, their electrical properties, and computational applications of silver iodide and silver selenide NW.24–29 It has been demonstrated that Ag-Ag2S-Ag nano-junctions displayed stable switching behavior by Gubicza et al.30 The effect of Joule heating (i.e., resistive heating) on single Ag2S NW memristance was also studied.31 However, the previous studies on chalcogenide RS systems such as Ag2S NW networks have not provided detailed microscopic image-based analysis nor a simulation model for the specific, stochastic NW network configuration. There has been no study investigating the electrical characteristics of different types of NW networks in terms of electrodes' point contact or surface contact, symmetry, or asymmetry of the experimental setup. Moreover, there has been a lack of detailed comparison between stochastic simulation model32 results of a non core-shell structure of Ag2S NW device networks and correlated experimental results.

In this work, we studied devices composed of random memristive networks of Ag2S NWs forming nonlinear switches along the length of the wires and at the junctions. These networks offer structural advantages compared to thin film crossbar arrays due to the simplicity of fabrication and resistance to physical damage. The NWs were produced based on previous studies which utilized inexpensive solution-processing techniques without the need for high temperature deposition or vacuum equipment and in which 2D random network structures were produced by drop-casting using nanomaterials synthesized and stored in solution.33,34 Compared to previous reports on memristor architectures that relied on metal deposition and lithographic processes, our manufacturing approach is inexpensive, rapid, and does not require cleanroom facilities or nanolithography equipment.

Two different types of Ag2S NW devices were studied in this work. In the first type, a small NW network with a visually countable number of wires was produced with characteristic asymmetry of the experimental setup. In this case, the asymmetry was created using differential contact area of the counter electrodes. In this device, a Pt/Ir probe installed on a nano-manipulator (Kleindiek, GmbH) served as one electrode to make a point contact, whereas silver paint contacting the wires served as a second electrode. An accurate image-based analysis under an optical microscope was performed to count and reconstruct the network for simulation within the stochastic memristor model.32 In the second type of device, we examined symmetric experimental setups using silver electrodes on both sides and studied RS in a larger and more complex network of NWs.

The stochastic ion drift RON RS model of individual Ag2S NWs32 is a modification of ionic drift models first introduced by Strukov et al.9 Compared to other models, the resistance of the ON state is taken as a stochastic parameter, whereas the overall resistivity of the device is a percolation probability function of metallic silver concentration in the Ag2S NW. The laws of percolation theory are shown to explain changes in resistivity of the highly conductive state during characterization of Ag2S NW. In the physical experiment, the current of a single Ag2S NW under changing voltage bias exhibited partially stochastic behavior, which was also reproduced by the model. In this article, the generality of the model is extended by showing agreement with different Ag2S NW structures. We simulate the behavior of two different sizes of 2D random interconnected Ag2S NW networks.

Shannon information entropy of memristive circuits is of a great interest as it provides clues to thermodynamic interpretation of complex circuits. The dynamics of information entropy has been previously studied for tree and hierarchical circuit configurations.35 It has been shown that these circuits exhibited tendencies for self-organization at each node upon DC voltage stimulation. On the other hand, random networks studied in this work exhibited similar self-organization behavior due to the emergence of switching between major current pathways. To the best of our knowledge, our study is the first reported visualization proof of entropy reduction as a result of self-organization in random memristive networks.

Therefore, this work explored nonlinear RS behavior of NW networks and compared them with simulation results. Moreover, detailed physical mechanisms, temporal evolution and deformation, and circuit entropy are investigated. Simulations of the temporal evolution of RS phenomena in the equivalent NW circuit under DC bias show a reduction in Shannon entropy that resulted in the development of highly conducting channels. Despite overall physical entropy increases, the evolution of highly conductive channels in the network led to a reduction of information entropy because of self-organization. Functional plasticity of the system is also studied. These systems are demonstrated both experimentally and through simulation to study their application for neuromorphic hardware with low-power consumption. The approach described here allows for the possibility of manufacturing high-density three-dimensional (3D) integrated circuits that could more closely mimic the complex network topologies of neuronal circuits in the brain.36 

Fabrication, characterization, and modeling of wires and networks studied here have been explained in detail recently.32 Based on the method reported by Andres et al.,37 high aspect ratio (AR) Ag NWs are synthesized through a modified one-pot polyol-mediated synthetic procedure in our laboratory. Measured from scanning electron microscopy (SEM) and transmission electron microscopy (TEM) characterizations, the mean length and diameter of Ag NWs are about 53 μm and 128 nm, respectively. The sulfurization process is performed by ultrasonic dispersion of sulfur powder (S) in the Ag NW-EtOH suspension (based on the stoichiometric ratio of Ag and S) at ∼60° C for around 5 min to modify Ag NWs into Ag2S NWs.38,39 The average length and diameter of the Ag2S NWs are about 25 μm and 135 nm, respectively.

To develop the simulation model of stochastic drift RON memristor, we considered the morphology of the Ag2S NWs based on SEM, TEM, and x-ray diffraction (XRD) spectra results besides the stochasticity we observed from electrical measurements of Ag2S NWs as reported previously.32 In particular, we described a model with stochastic resistance of the ON state parameter, RON, that is not a constant but rather a function of the volume fraction of reduced silver atoms in the Ag2S NW volume.32 Two modified software programs were also used to simulate the experimental configuration. Based on our previous work, first the percolator software,40 simulates random networks and nanojunctions between Ag2S NWs. The self-assembled circuit and network can be generated based on different materials, geometries, distribution, multiplatform generation, curation, analysis of random conductive networks, as well as the electrodes which yield reliable electrical contacts in a 2D and 3D collision engine. Second, CircuitSymphony41 simulates the resulting circuit with a custom-made electronic behavior simulator after analyzing the connectivity graph formed by the collision of wires. To fit the experimental data with the simulation model, the Optuna Python library42 was used to optimize the parameters; thereby the simulated current-voltage (I-V) curves are drawn.

This section describes measuring and simulating two-terminal devices made of small networks of Ag2S NWs with a limited number of wires that can be duplicated manually as the exact same structure for simulation. The experimental setup was straightforward as shown in Fig. 1. After casting a droplet of Ag2S NWs with concentration that was controlled to deliberately make a network with megaohm resistance onto the plasma-etched glass-slide substrate, a random network of NWs was formed after solvent evaporated. Then, a thin layer of Ag paint was deposited on one side of a copper tape while in contact with Ag NWs as part of the two-electrode setup. To make a point contact, a Pt/Ir microprobe of 100 μm diameter was installed on a nanomanipulator (Kleindiek MM3A) which was fixed on the XY-stage of an optical microscope (Nikon Optiphot 100). The 80/20 Pt/Ir microprobe was electrochemically etched and fabricated with a modified method described by Zhang et al.43 and Khan et al.44 In such a configuration, the Ag paint electrode and the microprobe's tip form an asymmetric two-electrode setup.

FIG. 1.

Schematic drawing of the experimental setup for performing the electrical measurements on a small Ag2S NW network in a low concentration drop-cast between Pt/Ir microprobe with a Kleindiek nanomanipulator and Ag paint electrodes; the inset shows a microscopic image of a small Ag2S NW network circuit.

FIG. 1.

Schematic drawing of the experimental setup for performing the electrical measurements on a small Ag2S NW network in a low concentration drop-cast between Pt/Ir microprobe with a Kleindiek nanomanipulator and Ag paint electrodes; the inset shows a microscopic image of a small Ag2S NW network circuit.

Close modal

Figure 2(a) shows the optical microscope image of the experimental setup in the inset of Fig. 1. The simulated small Ag2S NWs network with the electrical contact points in the percolator40 software which uses the same size and geometry of NWs from experiments is depicted in Fig. 2(b). After analyzing the connectivity and contact points, they were mapped to a standard circuit diagram in the CircuitSymphony41 electronic simulator, as shown in Fig. 2(c).

FIG. 2.

(a) Optical microscope image of the experimental setup for performing I-V measurements of small random Ag2S networks between Ag paint electrode and Pt/Ir microprobe. (b) Simulated connectivity graph network in percolator software. (c) Memristive circuit in CircuitSymphony constructed from the connectivity graph in (b). (d) Experiment I-V characteristics of the Ag2S memristor obtained by applying positive and negative bias voltages in 3 V pulses with sweep rate. The inset shows a typical I-V curve of the same network when the bias is swept between positive and negative in each turn. (e) Input voltage (dotted lines) and output current (solid lines) vs time. (f) Simulated I-V characteristics of the Ag2S memristor obtained by applying positive and negative bias voltages. (g) Simulated input voltage (dotted lines) and output current (solid lines) vs time.

FIG. 2.

(a) Optical microscope image of the experimental setup for performing I-V measurements of small random Ag2S networks between Ag paint electrode and Pt/Ir microprobe. (b) Simulated connectivity graph network in percolator software. (c) Memristive circuit in CircuitSymphony constructed from the connectivity graph in (b). (d) Experiment I-V characteristics of the Ag2S memristor obtained by applying positive and negative bias voltages in 3 V pulses with sweep rate. The inset shows a typical I-V curve of the same network when the bias is swept between positive and negative in each turn. (e) Input voltage (dotted lines) and output current (solid lines) vs time. (f) Simulated I-V characteristics of the Ag2S memristor obtained by applying positive and negative bias voltages. (g) Simulated input voltage (dotted lines) and output current (solid lines) vs time.

Close modal

The physical mechanism of the system is based on electrochemical metallization11,45,46 and electromigration of polymorphs of Ag2S that exist in a narrow temperature range. Under voltage bias ionically insulating acanthite Ag2S-α transforms into ionically conductive argentite Ag2S-β phase that facilitates growth of conducting filaments and is responsible for RS.47 In this work, positive bias (+3 V) was applied to the Ag paint electrode, and the Pt/Ir microprobe was grounded. At the Ag paint electrode, the positive bias induced oxidation of Ag atoms and produced Ag+ ion, and the ions migrated from the Ag anode to the Pt/Ir cathode. Across the insulating Ag2S NWs layer, the reduction of Ag+ to Ag created an ionic bridge between two electrodes through some NW pathways and formed the metallic filament, which turned the device ON during the SET process. By switching the polarity to negative bias (−3 V), oxidation and reduction occurred in the filament and Ag electrode, respectively, leading the system to an OFF state during the RESET process, as demonstrated in Fig. 2(d). The ON state was volatile with a current of about 80 nA and tended to switch OFF very quickly, which is why there is a minimal RESET transition at negative bias.

In the simulation, a network similar to the experiment setup was created in the percolator40 software and sent to CircuitSymphony41 to approximate the electronic circuit, and finally define memristive elements with the stochastic drift RON memristor model. The I-V curve and current-voltage versus time pulse behavior were obtained, based on the simulated parameters, as in Fig. 2(e). Since our experimental setup is not symmetric and we have different electrode types on each side, in the simulation we aligned 80% of the nanowires in one direction and 20% in the other direction to account for the asymmetric electrodes. The proof-of-concept simulation results using the stochastic RON model show similar behavior [Fig. 2(f)] to that observed in the experiment [Fig. 2(d)]. We repeated this mapping for several random, small networks and observed the same trend.

Stochastic current characteristics can also be caused by geometric changes in the network. Under constant voltage bias, a small network of Ag2S NWs undergoes significant changes (i.e., wire deformation) that can be observed in an optical microscope. In Fig. 3(a), 5 V DC voltage bias was applied to the small Ag2S network with a limited number of NWs for 20 s between the Pt/Ir microprobe tip (− terminal) and the Ag paint (+ terminal) while the structural changes in the network were recorded on a camera. Under the influence of the electric field, some parts of Ag2S NWs converted to argentite Ag2S-β phase, which permitted the migration of Ag+ ions from the Ag paint shore to the tip of the Pt/Ir microprobe tip. This migration of the Ag+ ions and expansion of the argentite Ag2S-β phase pathways deform the shape of the network first near the microprobe tip.47 As shown in Fig. 3(a), expansion of the wire leads to multiple effects such as 3D bending [marked with green (planar) and yellow (lift-off from the plane of the glass-slide substrate)] and also detachment of one of the pathways (red arrow). Despite significant deformation, the Ag2S NW network retained the RS property shown in Fig. 3(b), where it was stimulated with a single 20 s long triangular voltage pulse as depicted in the inset of Fig. 3(b).

FIG. 3.

(a) Reconfiguration of a small fault-tolerant Ag2S NW network under the influence of electric current and subsequent measurement of the I-V characteristics: (a) time-lapse of the deformation of the Ag2S NW network under constant DC bias of +5 V on the Ag paint shore. Over a period of 13 s, the Y-shaped structure, formed by two wires, connected to Pt/Ir tip and Ag paint, evolved into a new structure. Due to electromigration, wire 1 broke into two parts near the intersection with one part being fused with wire 2 and undergoing bending near the intersection which was followed by a detachment from the lower part of wire 2 at 10 s. Finally, the junction of wire 1 and half of wire 2 starts to bend upward away from the surface of the glass-slide substrate. (b) Despite severe deformation, the remaining structure preserved RS behavior, which was confirmed with an I-V curve obtained with a single 20 s long triangular pulse of 5 V. All scale bars are 10 μm long.

FIG. 3.

(a) Reconfiguration of a small fault-tolerant Ag2S NW network under the influence of electric current and subsequent measurement of the I-V characteristics: (a) time-lapse of the deformation of the Ag2S NW network under constant DC bias of +5 V on the Ag paint shore. Over a period of 13 s, the Y-shaped structure, formed by two wires, connected to Pt/Ir tip and Ag paint, evolved into a new structure. Due to electromigration, wire 1 broke into two parts near the intersection with one part being fused with wire 2 and undergoing bending near the intersection which was followed by a detachment from the lower part of wire 2 at 10 s. Finally, the junction of wire 1 and half of wire 2 starts to bend upward away from the surface of the glass-slide substrate. (b) Despite severe deformation, the remaining structure preserved RS behavior, which was confirmed with an I-V curve obtained with a single 20 s long triangular pulse of 5 V. All scale bars are 10 μm long.

Close modal

Temporal information entropy of a circuit provides a convenient method to estimate complexity of a circuit at any given time. Pershin et al.48 used circuit entropy to show self-organization of ordered memristive networks and applications to solve complex NP-hard problems with them. In this work, we simulated self-organization of conducting channels in randomly assembled Ag/Ag2S/Ag NWs that were modeled with a conventional RS model.9 Despite the continuous nature of the model, the current exhibits irregular changes even under DC bias, as shown in Fig. 4. This is attributed to different switching times of different memristive wires. The approach and parameters for simulating memristive switching in Ag2S NWs were adapted from a previous study.32 

FIG. 4.

Simulation of the temporal evolution of a memristive nanowire network between voltage input and current output marked with boxes. DC input voltage was applied to input at 0.1 V. The network in the first frame is the initial network in time zero. Thicker lines denote memristive Ag2S NWs, and thickness of the wire is proportional to the magnitude of current going through a wire. Output currents and circuit entropy based on the conductivities of each element are measured.

FIG. 4.

Simulation of the temporal evolution of a memristive nanowire network between voltage input and current output marked with boxes. DC input voltage was applied to input at 0.1 V. The network in the first frame is the initial network in time zero. Thicker lines denote memristive Ag2S NWs, and thickness of the wire is proportional to the magnitude of current going through a wire. Output currents and circuit entropy based on the conductivities of each element are measured.

Close modal

The network was stimulated with a DC bias where the input voltage was set to 0.1 V for 50 s, and all memristors were set to intermediate magnitude of memristance, i.e., RON+ROFF2. Hence, the circuit entropy aids the visual interpretation of the process, equivalent to the amount of information needed to describe the distribution of currents in the circuit. There are multiple ways that the information content of a system can be defined. For example, algorithmic complexity is defined as the length of the shortest program, written in any predefined programming language, that completely describes the distribution of the currents in a circuit.49 However, this approach is computationally inefficient since it requires a guarantee that there is no other, more efficient algorithm. Thus, here we use von Neumann entropy, a derivative of Shannon entropy50 to calculate the entropy S of a circuit with resistive elements, as shown in Eq. (1).

In Eq. (1), the value of ρij is defined between a pair of nodes ni and nj connected by an edge eij in the graph and is proportional to the absolute value of current going through the edge divided by the sum of absolute values of currents going through each edge. If the edge does not exist, then the value of ρij is set to 1. Mathematically, ρij is the density matrix of the graph and is defined as ρij=|Iij|i,j|Iij|, where ρij=1 when either Iij=0 or i,j|Iij|=0,

S=i,jnρijlog(ρij).
(1)

Initially, the current in the network is small and roughly equal in each wire of the network. Thus, the amount of information needed to describe such a system of evenly distributed current among the small components of the network is high; hence the thickness of all connections is relatively similar in Fig. 4 at time 0 s. As time progresses, memristors in the network are switched, and new, better-defined paths are created within the network, requiring less information to describe such a system as exhibited by the entropy plot. For example, at the time step of 6 s, a conducting pathway connecting input and output starts to be visible. While the current in both channels instantly increased, the entropy underwent an instantaneous decrease. Finally, approaching 12 s, the memristor pathway turns into a major path of least resistance, and the current rapidly jumped in the output channel. Notice the thickness of the channels in Fig. 4 at 50 s which shows the maximum current flow inside the network. Interestingly, the switching behavior in the circuit correlates with abrupt falls in entropy which is depicted by the circuit entropy plot. The behavior in this NW electronic circuit initiated by constant DC electric field stimulation is quite complex. As we will show in the next section, this complexity can be harnessed for neuromorphic computation. Entropy reduction due to self-organization of the current pathways in random nanowires can be helpful in developing brain-like nonequilibrium neuromorphic computers.

Figure 5(a) shows the experimental setup for the electrical measurement of larger networks of Ag2S NWs between two Ag electrodes drawn with the Ag paint. A plasma-etched glass-slide substrate is used as the insulator substrate, and two pieces of copper tape connect the electrodes to the source/monitor unit (Agilent E5272A) through the electric field isolated box (HP 16058A test fixture). In this experiment, since we collected the laboratory measurements without a microprobe and optical microscope, we ran the experiment inside the HP 16058A test fixture box to be isolated from environmental noise, as shown in Fig. 5(b). The gap between Ag electrodes is on the order of tens of micrometers. A droplet of Ag2S NW (2 ∼ 4 μl) suspension was placed with a pipet (Eppendorf) in the gap area between the electrodes. After the evaporation of ethanol solvent, a randomly interconnected network of Ag2S NWs was formed, as the inset of Fig. 5(a) shows.

FIG. 5.

(a) Schematic drawing of the experimental setup for performing electrical measurements on Ag2S NW networks between two Ag paint electrodes; the inset shows a microscopic image of a large Ag2S NW network. (b) hp 16058A Test fixture box.

FIG. 5.

(a) Schematic drawing of the experimental setup for performing electrical measurements on Ag2S NW networks between two Ag paint electrodes; the inset shows a microscopic image of a large Ag2S NW network. (b) hp 16058A Test fixture box.

Close modal

Figures 6(a) and 6(b) compare the experimental electrical characteristics to the computational data of Ag2S memristor networks between two Ag paint electrodes simulated with our stochastic model. The measurements contain ten consecutives positive (0–5 V) and negative (0 to −5 V) sweeps. It can be inferred from the inset of Fig. 6(a), that by applying the positive pulses, the network turns ON, and the current increases by the SET process until saturation, but by switching the polarity, the system changes again to the OFF state and eventually turns ON when it is saturated. Therefore, the SET process occurs for both polarities. Because both electrodes are Ag, the plot is symmetric. The proof-of-concept simulation in Fig. 6(b) shows the same result when we simulated the same setup according to our experimental parameters including the materials, size of the wires and gap, and Ag-Ag electrodes based on the stochastic drift RON memristor model.

FIG. 6.

Curves of current (solid) and voltage (dotted) vs. time: (a) Experiment. (b) Simulation. The insets show I-V characteristics of the Ag2S NWs network memristor by applying positive and negative bias voltages, respectively, with a voltage sweep range of 0–5 V: (a) Experiment. (b) Simulation. (c) Endurance performance cycling test at a readout voltage of 3 V for 50 cycles with an interval of 0.001 s. The inset shows the I-V curve of the Ag2S memristor for 50 successive cycles with a pulse interval of 0.001 s and a microscopic image of the NW network between two Ag electrodes. The legend shows the order of the cycles in rainbow colors, which is started with red (cycle 1) and ended with the violet (cycle 50). (d) Endurance performance cycling test at a readout voltage of 3 V for 50 cycles with an interval of 5 s. The inset shows the I-V curve of the Ag2S memristor for 50 successive cycles with a pulse interval of 5 s.

FIG. 6.

Curves of current (solid) and voltage (dotted) vs. time: (a) Experiment. (b) Simulation. The insets show I-V characteristics of the Ag2S NWs network memristor by applying positive and negative bias voltages, respectively, with a voltage sweep range of 0–5 V: (a) Experiment. (b) Simulation. (c) Endurance performance cycling test at a readout voltage of 3 V for 50 cycles with an interval of 0.001 s. The inset shows the I-V curve of the Ag2S memristor for 50 successive cycles with a pulse interval of 0.001 s and a microscopic image of the NW network between two Ag electrodes. The legend shows the order of the cycles in rainbow colors, which is started with red (cycle 1) and ended with the violet (cycle 50). (d) Endurance performance cycling test at a readout voltage of 3 V for 50 cycles with an interval of 5 s. The inset shows the I-V curve of the Ag2S memristor for 50 successive cycles with a pulse interval of 5 s.

Close modal

1. Plasticity of the Ag2S NW complex network

The described network of Ag2S NWs between two Ag paint electrodes that act as a drift memristor shows plasticity, the ability to rewire based on recent activity, which is one of the essential characteristics of biological brains. Neuroplasticity is typically defined as adjusting connection strength, wiring, and/or rewiring between neurons associated with memory and learning processes such as training, knowledge, or experiences that make changes in the neuron-synapse structures.51,52 When the biological brain receives external input signals through a combination of thermal, optical, and chemical receptors, the signal moves through the interconnected neuronal synapses, and memory processes ensue.53 By increasing the frequency of excitation pulses, strengthening of signal transmission between neurons causing long-lasting memory.54 

According to prior work by Wang et al.52 and Ohno et al.,55 in ionic drift memristor models, one of the expected characteristics is short-term plasticity (STP), in which the application of the paired pulses to synapses influences postsynaptic responses based on the frequency of applied pulses.56 This STP characteristic mimics the STP of biological systems. By increasing the number of pulses, an increase or decrease will be induced in the next conduction responses based on the frequency of the applied voltage (or the interval time between consecutive pulses). Here, we show that our randomly assembled networks of Ag2S NWs emulate the STP characteristics. The inset of Fig. 6(c) reports the RS behavior over 50 successive cycles in Ag2S networks sandwiched between two Ag paint electrodes (Fig. 5), as the microscope image shows in the inset. The sweep cycle has been applied from 0 V→5 V→0 V→−5 V→0 V to form the I-V curve. Data presented in Fig. 6(c) were collected using a time interval of 0.001 s, while Fig. 6(d) shows results using a 5 s time interval (as one example of a short interval time, 1 ms, and one example 5000 times longer interval time, 5 s). In both cases, the network memristor is initially in the HRS, and by applying a positive sweep from 0 to 5 V, the memristor turns ON and switches to the LRS. In the negative sweeps, the system switches from the HRS to the LRS as well. It can be observed in Figs. 6(c) and 6(d) that when the frequency is high (time interval of 0.001 s), the device conductance increases from the device steady state (initial conductance), as seen in the rising order of the loops in the inset of Fig. 6(c) or the decreasing of the resistance (from 32 to 27 MΩ in HRS and from 27 to 23 MΩ in LRS) in Fig. 6(c). In contrast, the longer interval time (5 s) in Fig. 6(d) shows that pinched hysteresis curves are still observed, but that there is no increment in the order of loops in the inset of Fig. 6(d) and all the loops are overlapping. The lower frequency of the applied pulses provided sufficient relaxation time between pulses such that no cumulative decrease in resistance is carried between individual stimulation pulses. Hence, the overall resistance of HRS and LRS in Fig. 6(d) is greater than in the short interval time plot [Fig. 6(c)]. Therefore, random networks of Ag2S NWs show STP characteristics. Figures 6(c) and 6(d) also examine the reliability of the fabricated device by studying the endurance performance of Ag2S memristor for these two interval times acquired by 50 full sweep cycles (read voltage of 3 V). They reveal that the device maintained its memristive behavior over such cycling. This is evidence of the device's uniform and stable electrical operation between LRS and HRS during the SET and RESET processes over 50 cycles.

Furthermore, we performed memory retention measurements with the Ag2S network by applying pulse bias input as initial stimulation (learning) and relaxation for a period of time (forgetting) by two different methods. Here, for the initial stimulation process, the frequency was 50 Hz, and ten pulses were applied to the device with an amplitude (height of pulse peaks), pulse width (time between the rising and falling edges of a single pulse), and pulse interval of 5 V, 0.8 s, and 0.2 s, respectively. In the first test, widths and intervals were constant, and spontaneous relaxation occurred while the voltage amplitude decreased to 2 V. Then, another ten pulses were applied with 5 V amplitude to repeat stimulation, as shown in Fig. 7(a). The current output trend (red) indicates that the current increased gradually until reaching the maximum current around 40 nA during the potentiation of synaptic activity (learning). Then, by reducing the input voltage to 2 V, the output current dropped to less than 10 nA representing depression of synaptic activity (forgetting). By applying a 5 V input bias again, the system repeated potentiation (relearning) while fewer pulses are required to reach the initial current. This means that the number of relearning pulses for memory retention was decreased during the third phase of measurements.57 

FIG. 7.

Periodic input pulses to indicate learning and forgetting synaptic behavior, (a) I-V curves collected from ten 5 V, ten 2 V, and ten 5 V pulses. (b) I-V curves collected from ten pulses with 0.8 s width and 0.2 s interval time followed by ten pulses with 0.2 s width and 0.8 s intervals time. (c) Non-linear transmission characteristic of the Ag2S memristor at 100 positive bias voltage. The legend shows the order of the cycles in rainbow colors, which begins with red (cycle 1) and ends with violet (cycle 100). (d) Synaptic weight motion of saturation with pulse amplitude 5 V and constant width and interval, the inset shows the current decay between each pair of pulses. The decay is caused by the combined capacitance of the measurement device and NW network wiring.

FIG. 7.

Periodic input pulses to indicate learning and forgetting synaptic behavior, (a) I-V curves collected from ten 5 V, ten 2 V, and ten 5 V pulses. (b) I-V curves collected from ten pulses with 0.8 s width and 0.2 s interval time followed by ten pulses with 0.2 s width and 0.8 s intervals time. (c) Non-linear transmission characteristic of the Ag2S memristor at 100 positive bias voltage. The legend shows the order of the cycles in rainbow colors, which begins with red (cycle 1) and ends with violet (cycle 100). (d) Synaptic weight motion of saturation with pulse amplitude 5 V and constant width and interval, the inset shows the current decay between each pair of pulses. The decay is caused by the combined capacitance of the measurement device and NW network wiring.

Close modal

In the second method, the forgetting or depression of synapses is illustrated by keeping the bias input amplitude constant at 5 V and narrowing the pulse width and widening the pulse interval. As shown in Fig. 7(b), during the first ten pulses, the pulse width and intervals were 0.8 and 0.2 s, respectively (ratio of 4). The pulse width was then adjusted to 0.2 s, and the pulse interval was switched to 0.8 s in the next ten pulses (ratio of 0.25). At the end of the first ten (wide) pulses, the conductance is at its maximum value. Saturation of the current peaks show the existence of complete pathways of metallic filaments between the Ag electrodes; by narrowing the pulse width, the conductance decreases as a result of the destruction of the ion bridges formed between electrodes, which is similar behavior to current depression and the forgetting process. In addition, a saturation state can be obtained when continuous pulses stimulate the device with constant pulse amplitude, width, and interval, as is demonstrated in Figs. 7(c) and 7(d). Also, it is notable in the inset of Fig. 7(d) that a current decay is observable during the interval between two subsequent pulses, which may demonstrate some volatile character in the device. The cumulative result of parasitic capacitance in the system, as the rising time of charging capacity in the depletion layer in the interface with the electrode and RS material, or slow diffusion of Ag atoms between each pulse after removing potentiation.58 These observable behaviors of the Ag2S NW networks can emulate the paired-pulse facilitation (PPF) phenomenon in biosynapses. PPF implies that the second postsynaptic response is higher than the first one during two successive stimulation pulses. Based on these results, random networks of self-assembled Ag2S NWs may be suitable candidates to be embedded in 3D nanocomposites and to form neuromorphic systems in next generation, bioinspired electronic hardware.

This work investigated RS in two different types of devices made of randomly assembled Ag2S NW networks. The devices exhibited stochastic memristive behavior, resistance to physical damage, and informational self-assembly characteristics. These systems were analyzed both experimentally and through simulation for their application for neuromorphic hardware. We considered the symmetry aspects of the experimental setup based on the point and surface contact of opposite electrodes.

Fabrication of RS devices in this study did not require cleanroom facilities or lithographic processes. Thus, the system is a network of multiple synapses and therefore is not restricted to a single synapse function as in memristor crossbar arrays. To analyze the dynamics, we simulated a small Ag2S NW network with a previously reported stochastic RS memristor model. The validity of the model was confirmed via fitting its parameters to experimental data, therefore suggesting that the resistance observed in the memristors' ON state is not a constant but rather a function of the volume fraction of reduced silver ions in the Ag2S matrix that changes stochastically over time due to spontaneous redox processes.

Also, we showed that our systems exhibited several crucial synaptic functions, such as learning, forgetting, PPF, and STP. These properties are useful for many types of bioinspired information processing algorithms. In addition, we showed the robustness and fault-tolerance of switching behavior of the network of NWs after physical damage. Also, for the first time, entropy reduction in random RS NW networks was shown to be a result of self-organization of current pathways.

The self-assembled nanodevices and device networks described here are the first steps toward three-dimensional randomly self-assembled nanocomposite memristor networks for neuromorphic computing applications. Such materials represent promising candidates for a new generation of designless neuromorphic hardware. A critical issue yet to be resolved involves interfacing such memristive device networks with multielectrode arrays such that finer grained substrates of the networks' electrical behaviors can be simultaneously and continuously read and routed for bioinspired computational tasks.

We thank Dr. Lorenz Lechner (Kleindiek Nanotechnik GmbH) for providing a MM3A nanomanipulator. The authors acknowledge financial support for this project from the U.S. National Science Foundation Grant (No. NSF-CISE-CCF 1748459) to T.H.L.

The authors have no conflicts to disclose.

All data that support the findings of this study are included within the article.

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