Stochastic switching and squeeze of hysteresis window in nonlinear responses of silicon nitride membrane nanoelectromechanical resonators

TL;DR

This study investigates how white noise influences the nonlinear dynamics of silicon nitride membrane resonators, revealing stochastic switching, hysteresis window squeezing, and bifurcation shifts, with implications for nanomechanical device control.

Contribution

It demonstrates noise-induced effects on hysteresis and bifurcation in nanomechanical resonators, including stochastic switching and hysteresis squeezing, supported by experimental and theoretical analysis.

Findings

Switching between bistable states is noise-dependent and follows Kramer's law.

White noise causes hysteresis window squeezing and shifts bifurcation points.

Switching rate and activation energy are sensitive to hysteresis width and driving force.

Abstract

In this work, we present the effects of stochastic force generated by white noise on the nonlinear dynamics of a circular silicon nitride membrane. By tuning the membrane to the Duffing nonlinear region, detected signals switching between low- and high- amplitudes have been observed. They are generated by noise-assisted random jumps between bistable states at room temperature and exhibit high sensitivity to the driving frequency. Through artificially heating different mechanical vibration modes by external input of white noise, the switching rate exhibits exponential dependence on the effective temperature and follows with Kramer's law. Furthermore, both the measured switching rate and activation energy exhibit sensitivity to the width of the hysteresis window in nonlinear response and the driving force, which is in qualitative agreement with the theoretical descriptions. Besides, white noise-induced hysteresis window squeezing and bifurcation point shifting have also been observed, which are attributed to the stochastic force modulation of the spring constant of the membrane. These studies are essential for the generation and manipulation of stochastic switching effects, paving the way to explore new functions based on probability distributions in nanomechanical resonators.