Stochastic Effects on the Dynamics of the Resonant Structure of a Lorentz Force MEMS Magnetometer

Abstract

Resonance features of slender mechanical parts of Lorentz force MEMS magnetometers are affected by the (weakly) coupled thermo-electro-magneto-mechanical multi-physics governing their dynamics. We recently showed that reduced-order models for such parts can be written in the form of the Duffing equation, whose nonlinear term stems from the mechanical constraint on the vibrations and is affected by the driving voltage. As some device performance indices vary proportionally to the amplitude of oscillations at resonance, an optimization of the operational conditions may lead to extremely slender, imperfection-sensitive movable structures. In this work, we investigate the effects of imperfections on the mechanical response of a single-axis magnetometer. At the microscopic length-scale, imperfections are given in terms of uncertainties in the values of the over-etch depth and of the Young’s modulus of the vibrating polycrystalline silicon film. Their effects on the nonlinear structural dynamics are investigated through a Monte Carlo analysis, to show how the output of real devices can be scattered around the reference response trend.