In a neuromorphic computing system, the complex CMOS neuron circuits have been the bottleneck for efficient implementation of weighted sum operation. The phenomenon of metal-insulator-transition (MIT) in strongly correlated oxides, such as NbO_{2}, has shown the oscillation behavior in recent experiments. In this work, we propose using a MIT device to function as a compact oscillation neuron, achieving the same functionality as the CMOS neuron but occupying a much smaller area. Pt/NbO_{x}/Pt devices are fabricated, exhibiting the threshold switching I-V hysteresis. When the NbO_{x} device is connected with an external resistor (i.e., the synapse), the neuron membrane voltage starts a self-oscillation. We experimentally demonstrate that the oscillation frequency is proportional to the conductance of the synapse, showing its feasibility for integrating the weighted sum current. The switching speed measurement indicates that the oscillation frequency could achieve** **>33 MHz if parasitic capacitance can be eliminated.

Implementation of brain-inspired neural networks with conventional CPU/GPU platforms based on sequential von Neumann architecture is computationally expensive and power hungry.^{1} Alternative approaches, such as neuro-inspired architectures, have attracted great attention due to the tolerance to fault and error and massively parallel computation for speed-up.^{2,3} Resistive memory (RRAM) has been demonstrated to emulate the synapses in the neural network.^{4–6} Integration of RRAM into a crossbar array architecture can implement the weighted sum (i.e., vector-matrix multiplication) in a parallel fashion,^{7–9} accelerating the most time/energy-consuming operation in the neuro-inspired learning algorithms, as shown in Fig. 1(a). When an input vector is fed into the crossbar array, the weighted sum current (modulated by the weight or conductance of each RRAM synapse) will sink to the neuron node at the end of the column. The neuron node thus integrates this analog current and converts into spikes or digital outputs. Typically, a CMOS integrate-and-fire neuron circuit is needed to convert the analog current into spikes (essentially as an analog-to-digital converter). The counter further counts the number of spikes and converts them into digital bits. However, today's CMOS integrate-and-fire neuron typically requires tens of transistors, as shown in Fig. 1(b).^{10} Figure 2(a) shows the simulated waveform of the membrane voltage (V_{in}) and output spike (V_{spike}) for different weighted sum current values (6 *μ*A vs. 1 *μ*A). The number of output spikes is designed to be proportional to the amplitude of the input weighted sum current. Apparently, such a CMOS neuron is complex and occupies a much larger size than the column pitch of the crossbar array, thereby reducing the parallelism as the time-multiplexing is needed to sequentially read out all the weighted sum from the array.

The metal-Insulator-Transition (MIT) phenomenon has been observed in strongly correlated oxide devices such as VO_{2}^{11} and NbO_{2.}^{12} Recently, the MIT induced oscillation has been investigated for various applications.^{13–17} Design of the MIT device as a compact oscillation neuron in the RRAM array architectures and its advantages over the CMOS neuron, such as the area, latency, energy and leakage power, has been thoroughly investigated by circuit-level simulations.^{18} In this work, we experimentally demonstrate the compact oscillation neuron at the device-level using NbO_{x} in order to replace the CMOS neuron, as shown in Fig. 2(b). Due to the threshold switching I-V with hysteresis, the node voltage on the MIT device will oscillate and emulate the V_{in} node in the CMOS neuron, and the oscillation frequency is expected to be proportional to the weighted sum current.^{18} The switching speed measurement indicates that the oscillation frequency could achieve >33 MHz if parasitic capacitance can be eliminated.

Pt/NbO_{x}/Pt devices were fabricated in ASU NanoFab. The active device area (overlap region between top and bottom electrodes) is about 10 × 10 *μ*m^{2}. First, an e-beam evaporated Pt/Ti (25 nm/3 nm) bottom electrode was patterned by optical lithography techniques on a SiO_{2}/Si substrate (200 nm/500 *μ*m, respectively). A blanket NbO_{x} thin film (15 nm) was deposited by using reactive sputtering at 100 °C using an Nb target and an O_{2}/Ar gas mixture in the ratio of 1/10. The Pt (25 nm) electrode was formed on top of the NbO_{x} blanket layer by using e-beam evaporation with a subsequent optical lithography and lift-off process to define the perpendicular cross-point structure. The bottom electrode pads were exposed by optical lithography and wet etching of the NbO_{x} layer. A schematic of the Pt/NbO_{x}/Pt device is shown in the inset of Fig. 3.

A forming voltage of ∼3 V is needed to trigger the subsequent threshold switching. The ON/OFF ratio (R_{OFF}/R_{ON}) is about 50–100. Figure 3 shows the typical threshold switching I-V characteristics of the Pt/NbO_{x}/Pt devices. As the voltage was swept from 0 to 3 V with a current compliance of 1 mA, an abrupt increase in current was observed at about 1.9 V, called threshold voltage (V_{th}). While sweeping the voltage from 3 V to 0, the current switched to the OFF state at about 1.6 V, called hold voltage (V_{hold}). Similar behavior is also observed for the negative voltage sweeps (not shown), consistent with the nonpolar nature of insulation-metal-transition. The conduction mechanism in the NbO_{x} device is believed to be more filamentary in the ON state and more bulk-dominated in the OFF state.^{19,20} Therefore, it is observed that V_{th} and R_{ON} are insensitive to the device area, while R_{OFF} increases with the downscaling of the device size.^{13} However, these characteristics are subject to temperature changes. It was reported that R_{ON}, R_{OFF}, V_{hold}, and V_{th} decrease with higher temperature,^{21,22} where smaller R_{ON} and R_{OFF} can be attributed to a typical semiconducting behavior of the oxide. These resistance and voltage shifts will induce unwanted frequency deviations in the oscillation neuron, and thus, a compensation method for oscillation frequency may be required at the circuit level to remedy this issue. Nevertheless, the MIT phenomenon in NbO_{2} is much more thermally stable than that in VO_{2}, where the MIT phenomenon disappears above 67 °C.^{11}

X-ray Photoelectron Spectroscopy (XPS) is employed to characterize the stoichiometry and the binding energy of the NbO_{x} thin film. To avoid the effects of surface contamination, all the samples were surface etched for 4 nm using Ar^{+} sputtering in the XPS chamber before collecting the XPS information. Figure 4(a) shows the XPS spectrum of Nb3d in the NbO_{x} thin film. The fitting was performed using CasaXPS data processing software. The two peaks of the green fitting curve located at 205.5 eV and 208.3 eV correspond to NbO_{2} 3d_{5/2} and 3d_{3/2}, respectively, while the two peaks of the blue fitting curve located at 207.3 eV and 210.1 eV correspond to Nb_{2}O_{5} 3d_{5/2} and 3d_{3/2}, respectively, which indicates that both NbO_{2} and Nb_{2}O_{5} phases co-exist in the NbO_{x} thin film. It is known that NbO_{2} exhibits the MIT behavior, while Nb_{2}O_{5} may show the resistive switching.^{23} The O1s peak shows that the Nb-O bonds are located at ∼531 eV and other non-bridging oxygen bonds are located at ∼532.4 eV, as shown in Fig. 4(b).

To make the neuron node oscillate, we connect the NbO_{x} device with a load resistor (R_{L}) as synapse to demonstrate the oscillation neuron function, as shown in Fig. 5(a). The resistance of the load resistor is chosen in between NbO_{x} device's ON state (R_{ON}) and OFF state (R_{OFF}), and there is a parasitic capacitance (C) at the neuron node. When the voltage V_{DD} is applied, the membrane voltage on the capacitor will be charged because most of the voltage drop is on the NbO_{x} device (R_{OFF} > R_{L}). Once the voltage exceeds V_{th}, the NbO_{x} device switches to R_{ON}, and the capacitor starts discharging since the voltage drop on the NbO_{x} device becomes small (R_{ON} < R_{L}). Once the membrane voltage decreases below V_{hold}, the NbO_{x} device switches to R_{OFF}. This charging and discharging process repeats, and thus, the voltage of the neuron node oscillates between V_{hold} and V_{th}. From Ref. 18, the analytical solution of the charging time t_{rise} from V_{hold} to V_{th} can be expressed as

where R_{r} = R_{L}ǁR_{OFF}. Similarly, the discharging time t_{fall} from V_{th} to V_{hold} can be calculated as

where R_{f} = R_{L}ǁR_{ON}. If we assume R_{OFF} ≫ R_{L} ≫ R_{ON}, then R_{r} ≈ R_{L} and R_{f} ≈ R_{ON}, which makes t_{rise} proportional to R_{L} and t_{fall} to be a constant much smaller than t_{rise}. The ideal oscillation frequency f can be obtained by using Eq. (1)

where W_{L} = 1/R_{L} is the weight of the RRAM synapse. f is then proportional to W_{L}. Therefore, the oscillation frequency represents a weighted sum if the NbO_{x} device connected to all the RRAM synaptic weights in one column of the array. Figures 5(b)–5(d) show the measured oscillation frequency with different R_{L} values, i.e., different synaptic weights. A voltage pulse is applied to Channel 1 (CH1), and the node voltage is monitored on Channel 2 (CH2) using an oscilloscope. As the charging is through the load resistor and the discharging is through the NbO_{x} device at R_{ON}, the RC delay of the charging is larger than that of the discharging, which makes the voltage oscillation a triangular waveform. The oscillation frequencies are 2 MHz, 0.7 MHz, and 0.4 MHz with the different load resistance 3.6 kΩ, 11.5 kΩ, and 16.1 kΩ, respectively. This suggests that the oscillation frequency is proportional to the equivalent resistance of the column (i.e., weighted sum results) if the NbO_{x} neuron can be connected to the crossbar array. In our experiments, the oscillation frequency is limited by the parasitic capacitance (C_{1}=573 pF estimated) in the testing setup as the resistor is externally connected to the pad of the NbO_{x} device.

In order to explore the intrinsic switching speed of the NbO_{x} device, a voltage pulse with a high and low waveform is employed. The high pulse is to test the off-to-on speed, and the low pulse is to test the on-to-off speed. The measurement setup is schematically shown Fig. 6(a). There is a sudden increase in current, when time reaches the off-to-on switching time. To reduce the parasitic capacitance effect, CH2 of the oscilloscope is directly connected in the device and the input impedance of CH2 is set to 50 Ω. Figure 6(b) shows that the device will not turn on at 1.8 V. The device switches to the ON state at 2.0 V, and the off-to-on switching speed is around 33 ns, as shown in Fig. 6(c). Figures 6(d) and 6(e) show that the switching speed does not obviously change when increasing the pulse amplitude from 2.0 V to 2.4 V, indicating that the intrinsic switching speed is ∼33 ns, and thus, the oscillation frequency could achieve >33 MHz if parasitic capacitance can be eliminated.

Using the above parameters, we performed SPICE simulations of the oscillation neuron based on our developed Verilog-A behavior model of the NbO_{x} device to find out the feasible range of synaptic weights (1/R_{L}) for oscillation. As shown in Fig. 7, the SPICE simulation result shows good consistency with the measured oscillation frequencies in Figs. 5(b)–5(d), and its deviation from the ideal frequency estimation [Eq. (3)] is also observed, which is due to noticeable t_{fall}. Overall, the results suggest that there is a limited weight range for oscillation and larger frequency deviation occurs when the weight approaches either ON or OFF states of NbO_{x}. To support a wider weight range, we need a larger ON/OFF ratio of NbO_{x}, possibly by downscaling of the device size to reduce the off-state leakage or a more advanced device engineering by stacking a tunneling layer.^{24} It is estimated that at least an ON/OFF ratio of 1000 is required to support a 128 × 128 array.^{18} Compared to the CMOS neuron, the compact oscillation neuron can potentially achieve a >12.5X area and a >5X energy reduction as suggested in Ref. 18 if the NbO_{x} device characteristics can be improved with a larger ON/OFF ratio of 1000 and smaller operating voltages (V_{hold} and V_{th} <1 V).

In summary, an oscillation neuron using the NbO_{x} device is experimentally demonstrated with a synapse (load resistor). By varying the load resistance, the oscillation frequency is proportional to the synaptic conductance, showing the feasibility for integrating the weighted sum. The intrinsic switching speed of the NbO_{x} device is ∼33 ns, indicating that the oscillation frequency could achieve >33 MHz if the parasitic capacitance can be eliminated. This work reports a potential building block for the neuromorphic system.

This work was supported by NSF-CCF-1552687 and NSF-ECCS-1701565.

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