A Study of Noise Impact on the Stability of Electrostatic MEMS

Abstract

Noise induced motions are a significant source of uncertainty in the response of micro-electro-mechanical systems (MEMS). This is particularly the case for electrostatic MEMS where electrical and mechanical sources contribute to noise and can result in sudden and drastic loss of stability. This paper investigates the effects of noise processes on the stability of electrostatic MEMS via a lumped-mass model that accounts for uncertainty in mass, mechanical restoring force, bias voltage, and AC voltage amplitude. We evaluated the stationary probability density function (PDF) of the resonator response and its basins of attraction in the presence noise and compared them to that those obtained under deterministic excitations only. We found that the presence of noise was most significant in the vicinity of resonance. Even low noise intensity levels caused stochastic jumps between co-existing orbits away from bifurcation points. Moderate noise intensity levels were found to destroy the basins of attraction of the larger orbits. Higher noise intensity levels were found to destroy the basins of attraction of smaller orbits, dominate the dynamic response, and occasionally lead to pull-in. The probabilities of pull-in of the resonator under different noise intensity level are calculated, which are sensitive to the initial conditions.

Nonlinear stochastic dynamics of an array of coupled micromechanical oscillators

“…Remarkably, there are only a few papers in the literature pertaining to stochastic modeling and analysis of nonlinear micro/nano‐oscillators. The vast majority of these research efforts relate to low‐dimensional (typically single‐DOF) systems, for which an analytical or numerical solution treatment is tractable 24–28 . The few papers referring to large arrays of coupled micro/nano‐beams modeled as high‐dimensional multi‐DOF systems rely on significant simplifications and approximations that reduce, unavoidably, the accuracy degree of the stochastic response estimates.…”

“…The vast majority of these research efforts relate to low-dimensional (typically single-DOF) systems, for which an analytical or numerical solution treatment is tractable. [24][25][26][27][28] The few papers referring to large arrays of coupled micro/nano-beams modeled as high-dimensional multi-DOF systems rely on significant simplifications and approximations that reduce, unavoidably, the accuracy degree of the stochastic response estimates. Indicatively, a moments equations solution approach was used by Ramakrishnan and Balachandran 29 for determining the stochastic response of an array of microcantilevers under the assumption of weak coupling.…”

Highly Sensitive Self-Actuated Zinc Oxide Resonant Microcantilever Humidity Sensor

“…Notably, no input actuation voltage was required for the measurement in both conditions, that is, the cantilever “self-actuates”. This behavior is attributed to the cantilever’s relatively low total thickness (∼250 nm) and corresponding low mass, which makes it susceptible to mechanical-thermal noise (Brownian motion), which is imparted from the surrounding fluid (gas or liquid). − The molecular agitation or random movement of the fluid particles (air), because of their inherent thermal energy, results in collisions with the cantilever structure and its subsequent vibration at its natural resonance frequency. This vibration is represented as noise, which in statistical mechanics is expressed as where k B is the Boltzmann constant, T is the absolute temperature, B is the bandwidth of the measurement, k is the cantilever spring constant (stiffness), f 0 is the resonant frequency, and Q is the quality factor.…”