Stochastic Dynamics of Diffusive Memristor Blocks for Neuromorphic Computing

TL;DR

The work investigates the stochastic dynamics of a three-memristor neuromorphic block that models synaptic convergence among spiking neurons. It combines hardware experiments with a mesoscopic stochastic charge-transport model to map how input voltages $V_1$ and $V_2$ drive spiking patterns across the memristor trio and analyzes spike statistics via $CV_1$ and $CV_2$. Key contributions include identifying distinct spiking-regime regions on the $(V_1,V_2)$ plane, demonstrating computation-like functions such as pattern-based classification, comparators, and Boolean operations (AND/OR) implemented by the block, and validating these findings with experimental measurements that highlight filament nonstationarity as a source of variability. The results provide a pathway to universal, low-power neuromorphic computation blocks and offer a platform for exploring neural variability in hardware-inspired systems, with implications for bridging analogue and digital computing in neuromorphic architectures.

Abstract

Biological systems use neural circuits to integrate input information and produce outputs. Synaptic convergence, where multiple neurons converge their inputs onto a single downstream neuron, is common in natural neural circuits. However, understanding specific computations performed by such neural blocks and implementating them in hardware requires further research. This work focuses on synaptic convergence in a simplified circuit of three spiking artificial neurons based on diffusive memristors. Numerical modelling and experiments reveal input voltage combinations that enable targeted activation of spiking for specific neuron configurations. We analyse the statistical characteristics of spiking patterns and interpret them from a computational perspective. The numerical simulations match experimental measurements. Our findings contribute to development of universal functional blocks for neuromorphic systems.

Figures (7)

• Figure 1: (a) Synaptic convergence involving three neurons. (b) The neuromorphic block modeling the synaptic convergence: each artificial neuron consists of a diffusive memristor $R_{M_{i}}$ in series to a load resistor $R_{i}$ and in parallel to a capacitor $C_{i}$ ($i = 1,2,3$). External input voltages $V_{1}$ and $V_{2}$ are applied to the neuromorphic circuits mimicking Neuron 1 and Neuron 2 shown in the middle panel, respectively. The artificial neuron involving the memristor $R_{M_{3}}$ correspond to the post-synaptic Neuron 3 depicted in the middle panel. (c) The electrochemical potential profile U(x) of the diffusive memristor used in simulation ushakov2021role.
• Figure 2: The fabrication of each diffusive memristor occurred via magnetron sputtering deposition and UV photolithography techniques. Bottom electrodes of 5 nm Ti / 45 nm Au were deposited onto SiO2/Si wafers followed by a switching layer of 50 nm SiOx:Ag before top electrodes of thicknesses 5 nm Ti / 120 nm Au.
• Figure 3: Experimentally measured voltage oscillations for memristive device $M_{3}$ at voltages $V_{1}$ = 1.2 V and $V_{2}$ = 3.0 V. To receive the classification of 'spiking', the amplitude of oscillations in two or more of the ON periods must be $>$ 0 V and at least $10\%$ higher than the baseline noise level observed during OFF periods (indicated by orange threshold line). In addition to this single ON period example, the device meets this criteria in each other ON period, and is thus deemed to be spiking.
• Figure 4: Spiking in the second memristor $V_{M_{2}}(t)$ (a) is realized in the conductance $1/R_{M_{2}}(t)$ (b) where the local maxima meets the spiking criteria by exceeding the threshold $0.1$ (given by the orange horizontal line). This example is observed for parameters $V_1= 100$, $V_2=300$ and $2k_{B}\eta_{i} = 10^{-5}$.
• Figure 5: Areas of existence for various spiking patterns on the parameter plane $(V_1,V_2)$, calculated numerically for (a) $2k_{B}\eta_{i} = 10^{-5}$, (b) $2k_{B}\eta_{i} = 10^{-4}$, and (c) $2k_{B}\eta_{i} = 10^{-3}$. Different patterns are indicated by different colors. The corresponding $(CV_{1},CV_{2})$ values for (d)-(f) show that as noise-induced spiking dominates, the values of $(CV_{1},CV_{2})$ increase. We show $(CV_{1},CV_{2})$ values for memristor $R_{M_1}$ when $(1)$, $(1,3)$ and $(1,2,3)$-spiking occur.