Electromechanical memcapacitive neurons for energy-efficient spiking neural networks

TL;DR

A comprehensive analysis is performed showing that several spiking types observed in biological neurons can be implemented with the leaky memcapacitor, and their use will simplify the creation of spiking neural networks.

Abstract

In this article, we introduce a new nanoscale electromechanical device -- a leaky memcapacitor -- and show that it may be useful for the hardware implementation of spiking neurons. The leaky memcapacitor is a movable-plate capacitor that becomes quite conductive when the plates come close to each other. The equivalent circuit of the leaky memcapacitor involves a memcapacitive and memristive system connected in parallel. In the leaky memcapacitor, the resistance and capacitance depend on the same internal state variable, which is the displacement of the movable plate. We have performed a comprehensive analysis showing that several spiking types observed in biological neurons can be implemented with the leaky memcapacitor. Significant attention is paid to the dynamic properties of the model. As in leaky memcapacitors the capacitive and leaking resistive functionalities are implemented naturally within the same device structure, their use will simplify the creation of spiking neural networks.

Figures (17)

• Figure 1: (a) An electromechanical leaky memcapacitor connected to a voltage source through a resistor. (b) The equivalent electronic circuit of the leaky memcapacitor: a memcapacitive system, C$_\textnormal{M}$, and memristive system, R$_\textnormal{M}$, connected in parallel. Both systems depend on the same internal state variable $x$.
• Figure 2: (a) Resistance as a function of the displacement of the top plate (Eq. (\ref{['eq:MemR']})). (b) Potential energy as a function of the displacement of the top membrane (Eq. (\ref{['eq:pot']})). The insets present a zoomed-in contact region. The dashed line refers to $x_c$.
• Figure 3: The response to a step-like voltage applied at $t=0$: starting from zero initial conditions ($x=0$, $q=0$), the circuit transits to (a), (b) a periodic spiking regime or (c) static regime. These plots were obtained using (a) $V=8.0829$, (b) $V=15.0111$, and (c) $V=7.8520$. In the top pannels, The black dashed line refers to $d$ and the brown one refers to $x_c$.
• Figure 4: (a) An overall picture: the fixed points and attractors depending on the applied voltage $V$. The phase diagrams at (b) $V=7.0437$ (the sink and limit cycle case in (a)), (c) $V=7.9674$ (the limit cycle case in (a)) and (d) $V=15.5000$ (the sink case on the right of the limit cycle one in (a)). In (b) the phase space is divided into two parts by the flow lines towards the saddle, as depicted with a dashed line. The semi-transparent gray thick line represents the limit cycle. The saddle, the sink, and the spiral source are labeled by black arrows, and the yellow star inside the limit cycle is located at the spiral source. The blue arrows in (b) and the orange arrows in (d) depict the shift direction of the three fixed points as $V$ increases. In (d), vector fields are added in small blue arrows to help show the fixed points. The initial conditions of the solutions are set discretely along the edge, as well as around the spiral source. In (b)-(d), the evolution time $t$ was 0.05.
• Figure 5: (a) Spike frequency as a function of $V$, and (b) Fourier transform of $V_C$ as a function of $V$. The dashed lines, from left to right, refer to $V_1$, $V_1'$ and $V_2$, respectively. Here, $P_1$ is the single-sided amplitude of the Fourier transform. In these calculations, to keep the system close to the limit cycle, the initial condition was selected as $x_0=6.6000$ and $q_0=2.0207$. The evolution time $t$ was 1.5, and we skipped the initial transient interval. (c)-(e) Steady-state oscillations at (c) $V=7.0183$ (regime I), (d) $V=11.5470$ (regime II) and (e) $V=15.0561$ (regime III). In (c)-(e), the black dashed line refers to $d$ and the brown one refers to $x_c$.