Configurable NbOx Memristors as Artificial Synapses or Neurons Achieved by Regulating the Forming Compliance Current for the Spiking Neural Network

For the first time, a configurable NbOx memristor is achieved that can be configured as an artificial synapse or neuron after fabrication by controlling the forming compliance current (FCC). When the FCC ≤ 2 mA, the memristors exhibit the resistive‐switching (RS) property, enabling multiple types of synaptic plasticity, including short‐term potentiation, paired‐pulse facilitation, short‐term memory, and long‐term memory. When the FCC ≥ 3 mA, the memristors can be electroformed and exhibit the threshold switching (TS) property with excellent endurance (>1012), thus achieving various biological neuron characteristics, such as threshold‐triggering, strength‐modulation of spike frequency, and leaky integrate‐and‐fire. This enables the successful implementation of a spiking Pavlov's dog that employs the spikes as information carrier by connecting an RS NbOx memristor as artificial synapse and a TS memristor as artificial neuron in series. Furthermore, a fully NbOx memristors‐based single‐layer spiking neural network is simulated. It is first found that, due to the forgetting property of synapse, the recognition accuracy for the Modified National Institute of Standards and Technology handwritten digits is increased from 85.49% to 91.45%. This study provides a solid foundation for the development of neuromorphic machines based on the principles of the human brain.

neuromorphic computing. [13][14][15][16] Recently, multiple types of biological synaptic plasticity are realized by using resistiveswitching (RS) memristors, [17][18][19] and various biological neuronal functions have been achieved based on threshold-switching (TS) memristors. [20][21][22] However, most of the reported memristors exhibit only RS or TS properties. If the switching properties of a memristor can be configured after the fabrication, the fabrication process of neuromorphic chip will be greatly simplified and the integration scale greatly enhanced. Due to the abundance of chemical valence states of niobium (Nb), NbO x memristors can exhibit both RS and TS properties by controlling the oxygen contents. [19,[23][24][25][26] Thus, it is highly possible to enable the simultaneous realization of various synaptic plasticity and neuronal functions in a single NbO x memristor. For example, Liu et al. demonstrated a Pt/NbO 2 /Pt device for TS property and a Pt/Nb 2 O 5 /Pt device for RS and obtained a hybrid characteristic by connecting these two devices in series. [27] Luo et al. reported a 3D TiN/TiO 2 /NbO x /Pt device with RS and TS property before and after the forming process. [28] Although the reported devices exhibit the characteristics of RS and TS property, they do not possess the synaptic behaviors or neuronal properties.
In this work, a NbO x memristor with the structure of Ti/W/NbO x /Nb/Pt can be configured as the artificial synapse or artificial neuron by regulating compliance current during the forming process (forming compliance current (FCC)). The memristors have excellent consistency, low forming voltage (≈4.2 V), and good endurance (>10 12 ). When the FCC ≤ 2 mA, the memristors exhibit multiple types of biological synaptic plasticity, including short-term potentiation (STP), paired-pulse facilitation (PPF), short-term memory (STM), and long-term memory (LTM). Meanwhile, when the FCC ≥ 3 mA, the memristors show various biological neuronal behaviors, such as threshold-triggering, strength-modulation of spike frequency, leaky integrate-and-fire (LIF), and refractory period. Based on the artificial synapses and neurons implemented by the configurable NbO x memristors, employing the spikes as information carrier, a spiking Pavlov's dog was successfully implemented in hardware and a fully connected single-layer SNN was set up to recognize the Modified National Institute of Standards and Technology (MNIST) handwritten digits with the recognition accuracy of 91.45% by simulation, thus providing a solid foundation for the realization of neuromorphic machines.

Characterization of NbO x Memristors
As shown in Figure 1a,b, the memristors were fabricated on SiO 2 /Si wafer, employing a via-hole (≈10 µm) structure of

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Ti/W/NbO x /Nb/Pt crossbar. The cross-section transmission electron microscope (TEM) images of the memristor are shown in Figure 1c and Figure S1a in the Supporting Information. The as-deposited NbO x is amorphous as determined by the electron diffraction pattern (see Figure S1d, Supporting Information).
As shown in Figure 1d, when the FCC ≤ 2 mA, the currents of the NbO x memristors have large hysteresis windows without abrupt change during the forming process, exhibiting RS property, thus the devices are configured as artificial synapses whose conductance can be modulated by applied voltage pulses. Meanwhile, when the FCC ≥ 3 mA, the currents of the memristors change abruptly and the memristors are electroformed, showing the TS property, thus the devices are configured as the artificial neurons that can generate oscillating spikes under proper driven current or voltage. As shown in the inset of Figure 1d, the forming voltages of eight devices (FCC ≥ 3 mA) are all distributed around 4.2 V, indicating the good consistency of forming process.

Synaptic Plasticity of the Configured Artificial Synapse
As shown in Figure 2a and Figure S2a-c in the Supporting Information, when the device is configured as the artificial synapse with the FCC ≤ 2 mA, the backward current of the memristor gradually decreases and forward current gradually increases as the cycle number of the positive DC voltage sweeps increased, thus the hysteresis window gradually decreases, suggesting that the conductance of the memristor can be gradually modulated under voltage pulses. Then, the devices were measured under different voltage pulses as shown in the inset of Figure 2b. Under 30 positive voltage pulses (4.5 V/0.1 s set, 0.5 V/0.1 s read, I CC = 2 mA, the set compliance current during pulse measurement), the conductance of the memristors gradually decreases, and under 30 negative voltage pulses (−4.0 V/0.1 s reset, 0.5 V/0.1 s read, I CC = 2 mA), the conductance gradually increases to the initial highest conductance state. The conductance of the memristor can be repeatedly increased or decreased by applying positive or negative pulse trains, thus successfully simulating the depression and potentiation plasticity of biological synapse. The variations in the conductance of different synaptic devices are shown in Figure S2d in the Supporting Information, indicating that the configured artificial synapses have good consistency.
To construct an SNN, multiple types of synaptic plasticity, including STP, PPF, STM, and LTM [29,30] are emulated by using the configured artificial synapses. As shown in Figure 2c, when a single presynaptic voltage pulse (4.5 V/0.1 s, I CC = 2 mA) is applied, a sharp increase in current (excitatory postsynaptic current, EPSC) is observed, but then the EPSC rapidly drops back to its initial value after the removal of the applied voltage pulse, thus realizing the STP. When two paired voltage pulses (4.5 V/0.1 s, interval of 0.5 s, I CC = 2 mA) are applied, the EPSC of the second voltage pulse (A2) is higher than that of the first pulse (A1), hence the device exhibits the PPF with the strength A2/A1 of 1.7 ( Figure 2d). As shown in Figure 3, the transition from STM to LTM can be achieved by applying consecutive voltage pulses. When a few pulses (−4.0 V/0.2 s, I CC = 2 mA) www.advelectronicmat.de applied, the conductance of artificial synapse quickly decreases to its initial state after the removal of the applied pulse(s), which is the forgetting property of the artificial synapse. The good endurance of the forgetting property is shown in Figure S3 in the Supporting Information. With the number of applied pulses increased, the conductance gradually increases and remains at high level for long time after removal of applied pulses (see Figure 3a), indicating that the transition from STM to LTM is successfully achieved. More details on retention time of synaptic weights are shown in Figure S4 in the Supporting Information.
In order to accurately describe the forgetting property of the configured artificial synapses, the relation between the relaxation time constant (τ) that evaluates the forgetting speed of the artificial synapse and synaptic weight (G) can be obtained by fitting the retention curve with the modified Kohlrausch equation, [31] expressed by where G(t) and G 0 are the synaptic weights retained at the time of t and at the stabilized state, respectively, and A is the preexponential factor. As shown in Figure 3b, with the number of pulses increased, the τ gradually increases, suggesting that the synaptic weight can be maintained at high level for long time.

Artificial Neuron Achieved by the NbO x Memristor
When the FCC is set at 5 mA, the as-fabricated NbO x memristors were electroformed and successfully configured as TS memristor as shown in Figure S5 in the Supporting Information. The compliance current during pulse measurement (I CC ) is set to 1 mA. Figure S6 in the Supporting Information shows a distinct region of negative differential resistance during DC current sweeping after forming process. The forming processes of 15 devices are shown in Figure S7 in the Supporting Information, illustrating that the devices have good consistency of device-to-device variation. The current-voltage (I-V) curves of 50 DC voltage sweeps after forming process were characterized as shown in Figure 4a. The I-V curves of different sweeps nearly overlap with each other, and V th changes slightly with the cycles while the V hold is fixed, indicating the good cycle-to-cycle variation. As shown in Figure S8 in the Supporting Information, after 10 4 back-and-forth DC voltage sweeps, the I-V curves of NbO x memristor after forming process nearly show no change, and through the oscillation test shown in the inset in Figure S9a in the Supporting Information, the memristor operated at least 10 12 times in 10 6 s, proving that the devices have good endurance. Thanks to the TS characteristics of NbO x memristors, an artificial neuron (leaky integrate-and-fire neuron) is realized as shown in the inset of Figure 4b. When an input voltage (V in ) of 6 V is applied, output spikes can be obtained at V C (V O ) as shown by the blue (red) curve in Figure 4b. When the V in is below 4.0 V, the no output spikes are observed. After the V in increased to 4.5 V, output spikes are generated at V C (V O ), resembling to the threshold-triggering properties of biological neurons [32] (see Figure 4c). When the V in is increased from 4.5 to 8.0 V, the frequency of output spikes at V C (V O ) is linearly increased, which bears a resemblance to the strength modulation of spike frequency of biological neurons, i.e., the output spike frequency of neurons increases with the increase of input stimulation. [33,34] The endurance of the strength modulation of the spike frequency function of the NbO x neurons is shown in Figure S10 in the Supporting Information. The LIF model of a single neuron greatly simplifies the neural activity to a combination of two mechanisms: "integrate" and "fire," which catches the primary properties of biological neurons. An LIF neuron can be achieved by using the TS NbO x memristor. When the voltage pulses with constant amplitude (8 V/0.03 s, interval of 0.02 s) are applied, the capacitor (C) will be charged, and the voltage at V C is gradually accumulated (integrate or summation) as shown by the blue curve in Figure 4d. When the voltage at V C reaches the V th of NbO x memristor, the resistance state of the memristor changes from the high resistance state (HRS) to the low resistance state (LRS), and thus a spike is generated at V O (fire). When outputting a spike, the TS NbO x memristor is in the LRS, so the C cannot be charged (refractory period). When the V in is removed, the charge on C will gradually leak through the resistor (R m ) (leaky). Thus, an LIF neuron is obtained, whose behavior is similar to that of biological neurons. The relationship between the spikes firing frequency of the LIF neuron and amplitude/duration of the input voltage pulse is shown in Figures S11 and S12 in the Supporting

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Information, respectively. With the increase of amplitude/duration of the input voltage pulse, the spiking frequency gradually increases. Therefore, an artificial neuron based on the configurable NbO x memristor is successfully constructed for the SNN.

Spiking Pavlov's Dog
The associative learning, an important type of learning process generally existing in biology, refers to that two stimuli happen very close and finally form a connection in the brain, such as the famous classical conditioning Pavlov's dog experiment [35] as shown in Figure 5a. Here, the Pavlov's dog experiment is successfully implemented by the configurable NbO x memristors as artificial synapse and neuron (see Figure 5c) with the learning and testing conditions illustrated in Figure 5b. As shown in Figure 5d, before learning, the RS NbO x memristor (artificial synapse) was in HRS, and V O had no spikes output when 6 V voltage pulse as input. After the artificial synapse was trained by using 30 voltage pulses (−4 V/0.2 s, I CC = 2 mA), the artificial synapse is in LRS, and when the voltage pulse (6 V, I CC = 2 mA) is used as input again, spikes can be generated by the TS NbO x memristor (artificial neuron) at the V O (see Figure 5e), thus realizing the associative learning.

Working Mechanism of the Configurable NbO x Memristors
The conductance of NbO x can be modulated by the ratio of Nb/O (the lower the Nb/O, the worse the conductivity of NbO x ). [36] The possible working mechanism of NbO x memristor is shown in Figure 6a,b. When FCC ≤ 2 mA, we can see that the devices cannot be electroformed from the I-V curves (Figures 1d and 2a), and there is no change in the TE of device before and after voltage sweep (see Figure S13a, Supporting Information). Therefore, we can safely conclude that the drift of oxygen vacancies in NbO x under the electric field leads to the change of its resistance state due to the change of Nb/O ratio, [28] thus realizing the artificial synapses. When FCC ≥ 3 mA, the device is electroformed with an abrupt current change (see Figure 1d) and a distinct "black spot" appears on the TE of device (see Figure S13b, Supporting Information), proving that a NbO 2 conductive filament (CF) is formed locally in NbO x due to the high temperature during the electroforming process, results in the abrupt change of the resistance state as illustrated in Figure 6c,d. The NbO 2 filament undergoes the Mott insulator-metal transition under applied voltage and is switched between the insulator phase (i.e., HRS) and metal phase (i.e., LRS), [37] thus enabling the realization of the oscillating neurons.
To verify the working mechanism of the NbO x memristors, the reduction of synaptic weight for the NbO x synapse and variation of I-V curves for the NbO x TS memristor under different temperatures were measured as shown in Figure 7. As shown in Figure 7a, the higher the temperature is, the worse the memory of the NbO x synapses. This is consistent with the fact that the speed of oxygen vacancy migration in the NbO x increased with the temperature increased. Therefore, the realization of the synaptic plasticity is mainly attributed to the oxygen vacancy migration in the NbO x . As shown in Figure 7b, the resistance of HRS and LRS decreases and the memory window (V th −V hold ) shrunk with the temperature increased. The resistance of Mott memristor depends on the temperature with an abrupt change at the transition temperature, therefore, with the ambient temperature rising, the resistance of HRS and LRS decreases, and the required Joule heat generated from the applied voltage to reach the transition temperature of NbO 2 decreases, thus the I-V curve of the NbO x TS memristors shifts to the left. In sum, the temperature-related study reveals that the synaptic memory properties of configured artificial synapse is attributed to the drift of oxygen vacancies in NbO x under the electric field, and the threshold switching property of the electroformed NbO x memristors results from the locally formed NbO 2 CF, enabling the various neuronal functions of TS NbO x memristors.

SNN based on the Configurable NbO x Memristors
Recently, Pickett and Williams developed a coupled electrothermal physical model to accurately describe the steady-state  www.advelectronicmat.de I-V relationships and dynamic switching features observed in nanoscale NbO 2 . [38] Based on the work, the neuron behavior of the NbO x memristors was modeled using SPICE. The modeling process and parameters we used are shown in Equations (S1)-(S5) and Table S1 in the Supporting Information. As shown in Figure S14 in the Supporting Information, the simulated I-V curve fits well with the experimentally measured data, thus providing a guarantee for the construction of NbO x memristor-based SNN.
A single-layer fully connected SNN can be achieved for the MNIST handwritten digit recognition by using the synapse array based on RS NbO x memristors and neurons based on TS NbO x memristors as shown in Figure 8a (more details are referred to the Note S1, Supporting Information). The synapse array is trained offline using 900 MNIST handwritten digits by Python simulator and the training results are shown in Figure S15 in the Supporting Information. The trained positive and negative synaptic weights in hardware are achieved by additional amplifiers (conversion circuits) and the neurons are constructed by connecting a TS memristor with a capacitor and a resistor as shown in Figure 8a. The simulated recognition accuracy of MNIST handwritten digits gradually increases as the number of training epoch increases (see Figure 8c). After 100 epochs, the recognition accuracy can reach 85.49%, assuming that synaptic weights do not change over time during training, i.e., without synaptic forgetting training. Considering that NbO x memristors  www.advelectronicmat.de used as artificial synapses have the forgetting property, the simulated recognition accuracy is revealed to be increased to 91.45% after 100 epochs, i.e., synaptic forgetting training (see Figure 8c). The increase of recognition accuracy is attributed to that the synaptic array quickly forgets unimportant weights, thus making larger weights more important. As a result, the recognition accuracy of SNN is significantly increased when the forgetting characteristics of synapses is considered in the SNN. Figure 8d shows the relationship between recognition accuracy and degradation of synaptic weights over time. Assuming that all synaptic weights degenerate over time at the same rate after the training, when the synaptic weights lost 50%, the recognition accuracy of SNN with/without forgetting property does not change, but when the synaptic weights lost 90%, the recognition accuracy of SNN with the forgetting property dramatically decreases. The simulation results demonstrate that the introduction of the forgetting property can greatly improve the recognition accuracy, at the same time degrade the stability of the SNN over time.

Conclusion
In conclusion, the functions of biological synapse and neuron are realized by controlling FCC of the memristor with the structure of Ti/W/NbO x /Nb/Pt. The memristors have good consistency and low forming voltages. When FCC ≤ 2 mA, the memristors exhibit multiple types of biological synaptic plasticity, including STP, PPF, STM, and LTM. Meanwhile, when the FCC ≥ 3 mA, the memristors show various biological neuronal behaviors, including threshold triggering, strengthmodulated spike frequency, and LIF property. Based on the artificial synapses and neurons implemented by the NbO x memristors, the Pavlov's dog experiment was successfully realized and an SNN was set up to recognize the MNIST handwritten digits with the recognition accuracy of 91.45%, hence, providing a solid foundation for the realization of neuromorphic machines.

Experimental Section
Device Fabrication: The fabrication process was as follows. First, the Ti/W (≈10 nm/80 nm) bottom electrode (BE) was deposited by a radio frequency magnetron sputterer and then patterned by using the lift-off process. After that, the Al 2 O 3 (≈30 nm) as isolation layer was prepared and patterned. Finally, the NbO x (≈50 nm) as switching layer, and Nb/Pt (≈50 nm/100 nm) as top electrode (TE) were also sputtered and then patterned by using the lift-off process. The detailed parameters of magnetron sputtering for each layer are as listed in Table 1.
Measurement: All the electrical measurements were conducted in air at room temperature by an Agilent 4155C semiconductor parameter analyzer and a Keysight B2901A precision source/measure unit. The DC bias was applied to the TE while the BE was grounded.
SNN Simulation: The single-layer fully connected SNN for the handwritten digit recognition was built in Python based on experimental results using SpikingJelly. [39] The synapse array was trained offline using surrogate gradient method. The simulated SNN was composed of 784 input, 7840 synapses, and 10 output neurons which corresponded to 10 handwritten digits (from 0 to 9). TS NbO x devices were used as LIF neurons of SNN where the parameters were extracted from experimental data. The main parameters of the LIF neuron used in the simulation are V th (1.2 V), V hold (0.8 V), and neuronal membrane potential decay time constant (τ = 100). Surrogate gradient method was used to train the neural network online. Here, the relaxation time constant τ synapse = 35. 7840*2 RS NbO x devices could be used to store synaptic weights in hardware. The probability of spikes could be calculated in each time step by comparing the spiking frequency with the length of the simulation time step. The higher the frequency was, the greater the probability of spiking at each time step. The index of the most frequently spiking neuron was taken as a prediction result. Other parameters used in this simulation were batch size = 100, timesteps = 200, SNN learning rate = 1e-3, and training epoch = 100.

Supporting Information
Supporting Information is available from the Wiley Online Library or from the author.