Single Silicon Neuron Device Enabling Neuronal Oscillation and Stochastic Dynamics

In this work, we report a fully CMOS-compatible single silicon neuron device, by exploiting interlinked positive and negative feedback loops. The neuron device exhibits the key features of leaky integrate-and-fire functionality and can produce neuronal oscillations that resemble biological oscillations. The stochastic nature and analog input-sensitivity of the feedback switching dynamics are observed in the device. Moreover, the neuronal oscillations of the two-terminal device do not require any power supplied by external bias lines.

neurons plays a key role in providing accuracy in noisy and probabilistic signal processing. Some studies proposed neuron devices to emulate biological systems [13]- [19]. However, spike responses were not from biomimetic feedback dynamics. In addition, their stochastic neuronal functionalities arose from the variations in the fabrication processes [16]. Meanwhile, some simple relaxation oscillator circuits are well known for their spiking capabilities [20]- [22]; external bias voltages are indispensable for three-terminal structures to operate these circuits. Despite some recent works on other device stacks that can also mimick the performance of a neuron, the NbO 2 -based material stacks are still challenging for practical devices and systems [23], [24].
Thyristor-random access memories (T-RAMs), which employ p-n-p-n structures, provide positive feedback loop [25]- [27]. Nevertheless, T-RAMs have also three-terminal structures which are not suitable for artificial neuron. In this study, we introduce a single two-terminal silicon neuron device with oscillatory and stochastic neuronal dynamics by using interlinked positive and negative feedback loops.

II. EXPERIMENTAL
The single silicon neuron device was fabricated from a p-type (100)-oriented SOI wafer with resistivity 18-22 · cm, using fully CMOS processes (Fig. 1). The n-doped regions were formed by a conventional n-well process with a doping concentration of ∼10 17 cm −3 . The doping concentration of the p-doped regions was ∼10 18 cm −3 . A poly-Si gate with a physical length of 2.5 μm was formed by low-pressure chemical vapor deposition onto the SiO 2 gate oxide layer. Also, heavily doped p + drain and n + source regions (∼10 20 cm −3 ) were created by masked ion implantations. Conventional Ti/TiN/Al/TiN metal stacks were used to contact the drain, source, and gate regions.

III. RESULTS AND DISCUSSION
The single silicon neuron device consists of a p + -n-pn + diode with connected drain and gate terminals, resistors (R 1 and R 2 ), and a parasitic capacitance from the output node V out to the ground ( Fig. 2(a)). The resistance R 1 sets a compliance current to generate interlinked positive and negative feedback loops. The diode generates the positive and negative feedback loops. And the resistance R 2 converts the signals from interlinked positive and negative feedback loops into voltage spikes. The two-terminal design allows the device to function as a threshold switch for neuron oscillations [28].
The measured I − V characteristics are shown in Fig. 2(b). When the voltage (V DD ) is swept from 0 to 3 V in medium mode (HP 4155C), an abrupt increase in current, which corresponds to the latch-up state, is observed at a certain  voltage (V latch-up ) because of the generation of a positive feedback loop. During the reverse bias sweep, the formation of a negative feedback loop triggers an abrupt decrease in current at a certain voltage (V latch-down ), i.e., the latch-down state. These interlinked positive and negative feedback loops, which correspond to the mutual interactions between the latch-up and latch-down states, generate neuronal oscillations.
The oscillatory neuronal behaviors were characterized, as shown in Fig. 2(c). After the integration of a certain period of input voltage (V in ), the neuron device generated an output signal (i.e., the device fired) when a membrane potential crossed the firing threshold. The firing event was enabled by the positive feedback loop (Fig. 2, (b) and (c), curve 1). As the device reached the latch-up state, because of the firing event, the voltage across the resistors increased suddenly. As V in was constant, the immediate voltage across the device decreased, driving the device back into the latchdown state. After reaching the firing threshold, the device was automatically reset to the initial state, enabled by the negative feedback loop (Fig. 2, (b) and (c), curves 2 and 3).
Energy band diagrams illustrate the leaky integrate-and-fire dynamics (Fig. 2(d) to 2(f)). The n-and p-doped regions, which act as the membranes, create potential wells for charge-carrier accumulation, thereby allowing the device to integrate presynaptic signals. In addition, the recombination of the accumulated charge carriers in the potential wells allows the integrated input signal to decay, which corresponds to the leaky membrane potential. When input voltages are applied to the neuron devices, holes can accumulate at the potential well of the p-doped region or recombine if there is no input (Fig. 2(d)), i.e., leaky integration. During the leaky integration, the accumulation of holes lowers the height of the potential barrier formed at the p-doped region, thereby allowing the electrons in the n + source to accumulate at the n-doped region and flow toward the p + drain. The accumulation of electrons also encourages the injection of more holes.
The mutual interaction between the potential barriers and charge carriers produces the positive feedback loop, which leads to the diode in the latch-up state. If the threshold is reached by the accumulation of the charge carriers in the potential wells, the positive feedback loop is activated, and the neuron fires (Fig. 2(e)). Until the neuron fires, the voltage across the device in the latch-up state decreases because of the resistors, thus triggering the negative feedback loop. This drives the device back into the latch-down state after an effective refractory period (Figs. 2, (b) and (c), curve 2), thereby resetting the initial threshold ( Fig. 2(f)).
The neuron spiking behaviors with oscillatory neuronal dynamics were investigated by applying diverse input signals (Fig. 3). When V in was below 2.3 V, no oscillations were generated. The conditions for oscillation had to be satisfied: Here, R latch-down is the resistance of the single silicon neuron device in the latch-down state and R latch-up is the resistance of the device in the latch-up state. When a pulse amplitude of 2.3 V is fed into the input, neuronal oscillations with integrate-and-fire functionalities are observed ( Fig. 3(a)). The integrate-and-fire dynamics were enabled by the generation of the positive feedback loop in the device, which is similar to the ion channels in biological neurons. Moreover, the device was automatically reset to the initial state after the firing event because the output spike triggered the negative feedback loop. The positive and negative feedback loops could create multiple consecutive spike events, i.e., neuronal oscillations. The number of spike events within a defined time interval can be tuned by adjusting the input amplitude. As V in changed from 2.3 to 3.1 V, the tuning linearity of the spike events was observed ( Fig. 3(b)). The modulation of the input signals allows a tunable integration time in the neuronal oscillations.
The leaky integrate-and-fire functionality was demonstrated by applying consecutive pulses to the input node (Fig. 3(c)). An input voltage of 0 V between consecutive pulses resulted in the recombination of the accumulated charge carriers in the potential wells, enabling leaky integration. After the arrival of five pulses into the neuron device, the membrane potential reached the threshold and the neuron device fired. The spike response of the analog or mixed signals in the artificial neuron was one of the most important neuronal functionalities for analog computation in neural networks [29]. Analog tuning in the artificial neurons is implemented by the modulation of the neuronal oscillation frequency when a sinusoidal waveform is applied to the input node ( Fig. 3(d)). Although the sinusoidal input signals exceeded the stimulation threshold, the amplitudes of the individual spikes were nearly constant. The neuronal oscillatory dynamics by analog or mixed signals allowed our device to implement biologically plausible leaky integrate-and-fire neurons.
The single two-terminal silicon neuron device exhibits a lower energy value of ∼719 pJ/spike and occupies a smaller area, compared to CMOS-based neurons devices that use complex circuits including source followers, inverters, reset circuits, and current-to-voltage converters [34]- [37]. The two-terminal configuration in our device enables the leaky integrate-and-fire functions without external applied voltages, whereas three-terminal configuration in CMOS-based neurons devices does not. As the resistors cannot affect the whole device scalability, it is expected that the scaled device allows sub-1-V operation and sub-pJ energy consumption.
The neuronal activity in biological systems exhibited complex stochastic behaviors owing to the noisy, irregular, and unreliable molecular mechanisms [30]- [32]. Stochastic operation plays a key role in complex computational tasks in neuronal networks; an example would be the Bayesian inference, performed by stochastic neuronal populations [33]. The capability of the spike response from the analog inputs to the device (Fig. 3(d)) enabled stochastic firing responses for developed neuronal networks. In addition, stochastic feedback switching dynamics were inherent in the device because of the accumulation and recombination of charge carriers in the potential wells by the Shockley-Read-Hall generation and recombination or band-to-band tunneling, which are probabilistic processes. Thus, the native physics of the single silicon neuron device could realize stochastic behaviors for neuronal computation.
The inherent stochasticity of the single silicon neuron device led to a distribution of inter-spike intervals, defined as the time difference between consecutive spikes in multiple leaky integrate-and-fire cycles (Fig. 4(a)). Our device shows approximately symmetrical distributions of inter-spike intervals. Nevertheless, as the amplitude of the input DC voltage varied from 2.3 to 3.1 V, the inter-spike intervals around the mean response of consecutive spikes decreased. Variations were also observed in the frequency responses of the leaky integrateand-fire neurons (Fig. 4(b)). While the mean firing rate of the consecutive spikes could be modulated from 61.0 to 210.5 Hz by increasing the magnitude of the input signal from 2.3 to 3.1 V, the consistency of the spike amplitudes and stochasticity of the frequency responses were retained. Fig. 4(c) shows that the variability of the action potential duration was not dependent on the magnitude of the input stimulus. It indicates that the interlinked positive and negative feedback loops in the device bore a resemblance to the feedback mechanism in biological cells. The effective refractory period over the range of the input signal exhibited irregularity and skewed distribution, as shown in Fig. 4(d).

IV. CONCLUSION
In summary, inspired by the interlinked positive and negative feedback loops in biological cells, the leaky integrate-andfire functionalities with oscillatory and stochastic dynamics were demonstrated in a single silicon neuron device. Moreover, our two-terminal device produces neuronal oscillations without power supplied by external bias lines. The capability of analog input-sensitive neuronal behaviors with oscillatory and stochastic dynamics can open up possibilities to revolutionize the entire neuromorphic hardware technology.