Study on the noise-induced stochastic fluctuation in a $NbO_x$ -based locally active memristor and its application to probabilistic computing

Abstract

$NbO_x$-based memristor is a locally active memristor that shows voltage threshold switching due to the thermally-activated conduction mechanism and insulator-to-metal transition at high temperatures of $NbO_x$ dielectric thin film. Due to the threshold switching property, oscillator circuits can be easily implemented when connected to serial resistance. Ideally, $NbO_x$ generates oscillations of a certain period, however recently, many complex oscillating phenomena such as chaotic oscillation and neuronal spikes have been reported. In this study, in addition to the above non-ideal oscillating phenomena, it was first observed through experiments that a new type of oscillation named stochastic oscillation occurs in $NbO_x$-based memristors. The stochastic oscillation is probabilistic and random. Since analysis on the non-ideal and complex dynamical phenomenon of stochastic oscillation has not been previously reported, a model that can sufficiently explain such a new type of oscillation was developed through an experimental and theoretical approach to the interaction of physical dynamics based on this $NbO_x$ system. Stochastic oscillation was modeled as the Ornstein-Uhlenbeck (OU) process, including noise in temperature and voltage, and the effect of device parameters on the stochastic oscillation distribution was explained. Subsequently, the oscillation probability was calculated analytically based on the boundary condition of oscillation generation with the temperature threshold derived from the experiment and simulation, and it explained a sigmoid-like distribution that closely matches the oscillation probability distribution in the experiment. In addition, the probabilistic computing system was constructed by extracting the experimentally obtained stochastic oscillation characteristics of the $NbO_x$ device. The feasibility of using the stochastic oscillation in $NbO_x$ memristors as a probabilistic computing unit (pBit) was confirmed through problem-solving integer factorization and finding the minimum energy configuration in the Hopfield network.