A resistive random-access memory (RRAM)-based neural network has been extensively studied as a promising solution to overcome the von Neumann bottleneck faced in conventional artificial intelligence (AI) hardware^[1-4]. As inspired by a biological neural network, an artificial neural network consists of synaptic and neuronal devices. In order to improve speed and power efficiency, the RRAM crossbar array, which can significantly accelerate the vector-matrix multiplication, has been developed to implement artificial synapses^[5-8]. On the other hand, a neuronal device is needed at the end of each crossbar bit line (BL) to convert the weighted sum current of the analog RRAM synapses into spikes to transmit information to the next layer of neurons. Here integrate-and-fire neurons built with CMOS circuits are typically employed^[9]. However, such complex CMOS neurons would occupy a much larger footprint than the BL pitch of the crossbar array, which causes serious column pitch matching problem^{[10, 11]}.

Recently, a compact oscillation neuron based on a metal–insulator transition (MIT) threshold switching (TS) device was proposed as a more scalable artificial neuron^[12-16]. Compared to the CMOS neuron, an oscillation neuron has the benefits of small size and simple circuit structure, which is appealing for large-scale neuromorphic system applications. However, the on/off ratio of a typical MIT TS device is small (~10²), which cannot be used for a large RRAM crossbar array (e.g., 12 × 1 array)^[15]. Moreover, the high operation voltage of the MIT TS device may disturb the weights of the RRAM synapses and also increase the power consumption^[16]. Alternatively, TS devices based on electrochemical metallization (ECM) filaments have attracted considerable attention due to their simple structure, large on/off ratio, and low operation voltage^[17-23]. However, the uniformity of typical ECM TS devices is relatively poor, which may affect the accuracy of artificial neural networks. More recently, we have developed a high-uniformity HfO₂-based TS device with patterned Ag nanodots (NDs) as the high-performance selector, which shows low leakage current (< 1 pA), high on/off ratio (> 10⁸), and high endurance (> 10⁸ cycles)^[24].

In this work, we further implement an oscillation neuron using the HfO₂/Ag NDs TS device. This neuron exhibits self-oscillation behavior at low applied voltage (1 V), where the oscillation frequency increases with the applied voltage and decreases with the load resistance. In addition, it can work with a large RRAM crossbar array (> 128 × 128) owing to the high on/off ratio (> 10⁸) of Ag NDs TS device. Moreover, in the neural network simulation, a high recognition accuracy (loss < 1%) can be achieved by using this oscillation neuron because of its high uniformity.

Fig. 1(a) illustrates the schematic diagram of a simple artificial neural network. When the input voltages are applied to the crossbar synaptic array, the weighted sum currents are integrated by the neurons at the end of each column (BL) and trigger output spike firing when they reach the neuron thresholds. The circuit implementation of the oscillation neuron based on the TS device is shown in Fig. 1(b). The load resistance (R_L) represents the RRAM synaptic weight connected in series with the TS device. Also, C_L is the load capacitance including parallel capacitance and parasitic capacitance at the neuron node. Initially, the TS device is in the off state (R_off). When applying an input voltage pulse (V_in), the voltage mainly drops on the TS device since R_off > R_L, and C_L starts to charge. When V_in is larger than the threshold voltage of the TS device V_th, it turns to the on state (R_on), and then C_L starts to discharge since the voltage drop on the TS device is reduced (R_on < R_L). Once the voltage drop on the TS device is below the hold voltage of TS device V_hold, it switches back to R_off, ready for the next firing event. In this way, the TS device switches on and off between R_on and R_off, and the neuron outputs oscillation signal. If R_L is chosen to satisfy R_off > > R_L > > R_on, the ideal oscillation frequency f can be described as^[13]:

$ f=1/\left[{R}_{\rm L}{C}_{\rm L}\times {\rm{log}}\left(\frac{{V}_{\rm{hold}}-{V}_{\rm{in}}}{{V}_{\rm{th}}-{V}_{\rm{in}}}\right)\right]. $  (1)

Eq. (1) shows a one-to-one correspondence between f and R_L at a certain C_L and V_in. Therefore, the oscillation frequency can be used to represent the weight of the RRAM synapse accurately.

In this study, we demonstrate the oscillation neuron using the Ag NDs TS device based on ECM filaments. The devices were fabricated with a cell size of 10 × 10 μm². The bottom electrode was patterned by photolithography and deposited by sputtering of 5 nm Ti and 50 nm Pt. An 8 nm thick HfO₂ dielectric was deposited by atomic layer deposition (ALD) at 250 °C. The Ag NDs with diameters of 50 nm were patterned by e-beam lithography (EBL) and deposited by sputtering. A 40 nm-thick Pt was deposited as the top electrode. The transmission electron microscope (TEM) image of the Ag NDs TS device is shown in Fig. 2(a). Fig. 2(b) exhibits the schematic illustration of the threshold switching process in the device. In the initial state, there is no conductive filament in the dielectric layer, and the device is in the high-resistance state (HRS). When applying a voltage (V_appl) larger than V_th, the electric field is locally enhanced in the areas with Ag NDs, so the Ag atoms are easier to be ionized as the ion source (Ag → Ag⁺ + e⁻) for diffusing toward the bottom electrode, which leads to the formation of metallic filaments and turns the device to a low-resistance state (LRS). In this device, the Ag filaments are thin and unstable due to the small amount of Ag ions. Spontaneous rupture of the filaments occurs immediately when V_appl goes below V_hold, which turns the device back to HRS. In this process, the Ag atoms form clusters on the trace of filaments. Owing to the highly ordered Ag NDs, Ag filaments tend to form at the same positions and the formed filaments would have similar morphology, in different operation cycles or different devices. Fig. 2(c) shows the typical current–voltage (I–V) curve of the Ag NDs TS device under voltage sweeps between 0 and 1 V. This device exhibits a low leakage current less than 1 pA and large selectivity over 10⁸. The V_th and V_hold of Ag NDs TS device are 0.6 and 0.2 V, respectively, which are carefully tuned to work with the RRAM synapse. In order to evaluate the uniformity of the Ag NDs TS device, the distributions of V_th and V_hold are analyzed, and the cumulative probability of V_th and V_hold is shown in Fig. 2(d). The coefficient of variation is defined as C_V = σ/μ to evaluate the variation, where μ and σ are the mean and standard deviation, respectively. This Ag NDs TS device exhibits excellent uniformity (C_V < 10%) compared to other TS devices based on ECM filaments ^[24]. The endurance test of the Ag NDs TS device is shown in Fig. 2(e). In this measurement, the device is repeatedly turned on with SET pulses of V_set = 1 V and t_set = 10 μs, and then relaxed to the off state, which is read with a small pulse of V_read = 0.1 V and t_read = 10 μs. The on-state current (I_on) is limited to 10 μA. It is found that the Ag NDs TS device exhibits a high endurance of over 10⁸ cycles. To implement an oscillation neuron, we connect the Ag NDs TS device in parallel with a load capacitance (C_L) and then in series with a load resistor (R_L) following the circuit configuration in Fig. 1(b). Fig. 2(f) shows the measured oscillation waveform of the neuron when R_L = 50 kΩ, C_L = 750 pF and V_in = 1 V. The test result shows that this oscillation neuron can output a continuous oscillation signal, when V_in, R_L and C_L are fixed. In addition, the Ag NDs TS oscillation neuron shows a certain time delay before its stable oscillation, which leads to a higher V_out in the first peak. It is owing to the turn-on delay time of the TS device^[24]. The higher first peak may have an adverse effect on the synaptic weight precision by distorting the oscillation waveform, which can be minimized by further improving the TS device switching speed.

More systematic studies on the oscillation neuron characteristics are performed as shown in Fig. 3. Fig. 3(a) shows the oscillation waveforms at different input pulse voltages when R_L = 50 kΩ and C_L = 750 pF. The oscillation frequencies are 31.6, 40.2, 46.9 and 51.4 kHz for V_in = 1, 1.2, 1.4, and 1.6 V, respectively. It is found that the oscillation frequency increases as a function of the pulse amplitude of V_in as described in Eq. (1), and shows good consistency with the simulation results, as shown in Fig. 3(b). Similarly, Fig. 3(c) shows the oscillation waveforms of the Ag NDs TS devices with different R_L values (i.e., different synaptic weights) when V_in = 1.2 V and C_L = 750 pF. The oscillation frequencies are 40.2, 30.5, 26.1 and 16.8 kHz for R_L = 50, 80, 100 and 150 kΩ, respectively. The oscillation frequency decreases as R_L increases, as shown in Fig. 3(d). The test results indicate that this Ag NDs TS oscillation neuron exhibits self-oscillation behavior, and the output oscillation frequency can be used to sense the weight of the RRAM synapse accurately when the neuron is connected to the crossbar array.

Based on experimentally derived device data, a model of the RRAM crossbar array is developed to evaluate synaptic weights of different array sizes. Then SIPCE simulation is used to investigate the relationship between the oscillation frequency and the RRAM crossbar array size. In order to simplify the simulation process, the resistance RRAM device is fixed at an intermediate resistance state (R_L = 500 kΩ), and V_in is applied to all the word lines (WLs) in parallel. The results are shown in Fig. 4. If the on/off ratio of the TS device is less than 100, only a limited range of the weighted sum could meet the criterion for oscillation (R_off > R_L > R_on). It means that the oscillation neuron can only be used for small crossbar arrays (< 16 × 16). With the increase of on/off ratio, the oscillation neuron can work with a wider range of load resistance. Therefore, the weighted sum in a larger RRAM crossbar array can be successfully identified by distinguishable oscillation frequency. As in the case of our present Ag NDs TS device with on/off ratio > 10⁸, it can work with a large RRAM crossbar array of size > 128 × 128.

In order to investigate the impact of TS device variation on the oscillation neuron, the oscillation frequency distribution with different C_V under the same experimental conditions is shown in Fig. 5(a). The uniformity of the TS device deteriorates with the increase of C_V, which leads to a large variation of the oscillation frequency under the same load condition. Fig. 5(b) shows the oscillation frequency distribution of different R_L with different TS devices. Compared with the Ag thin film device (C_V ~ 30%)^[23], the output frequency distribution of the Ag NDs TS neuron (C_V ~ 7%) is more concentrated. Therefore, the oscillation neuron based on the Ag NDs TS device can achieve higher accuracy for neuromorphic computing.

In order to further analyze the impact of the TS device’s uniformity on the artificial neural network, a multi-layer perceptron (MLP) of 784 × 200 × 10 is simulated to classify the handwritten digits in the Modified National Institute of Standards and Technology (MNIST) dataset, as shown in Fig. 6(a)^[25]. The simulation results displayed in Fig. 6(b) indicate that the increase in C_V leads to a dramatic degradation of the recognition accuracy, especially when C_V > 15%. Therefore, the oscillation neuron based on the high uniformity Ag NDs TS device developed in this work is beneficial to reduce the network accuracy loss.

In conclusion, we have demonstrated a reliable oscillation neuron using the low-variability Ag NDs TS device for high-performance neuromorphic computing. This neuron exhibits self-oscillation behavior at low applied voltages down to 1 V. A systematic study on the oscillation characteristics reveals that the oscillation frequency increases with the applied voltage and also the synaptic conductance connected as the load resistor. The high uniformity and large on/off ratio of the Ag NDs TS device enable the oscillation neuron to reduce the neural network accuracy loss (< 1%) and make it applicable to a large-scale RRAM crossbar array (> 128 × 128). The developed oscillation neuron hence has great potential for future neuromorphic system applications.

This work was supported in part by China Key Research and Development Program (2016YFA0201800), and the National Natural Science Foundation of China (91964104, 61974081).