Stochastic Effects on the Dynamics of a Resonant MEMS Magnetometer: A Monte Carlo Investigation

Abstract

In the design of Lorentz force MEMS magnetometers, the coupled thermo-electro-magneto-mechanical fields governing the dynamics of the relevant compliant structures can be appropriately exploited to enhance their performances. In recent works, we showed that reduced-order models for the dynamics of the said movable structures can be recast in the form of theDuffingequation, where nonlinear terms arise from the multi-physics governing the problem. As stochastic effects may play a role due to the micrometric dimensions of the device, an investigation of the link between the statistics of sensor imperfections and output is here carried out. The said imperfections at the microscopic length-scale are modeled in terms of:overetch thickness, assumed to feature a uniform distribution in a proper interval matching available experimental data; and elastic properties of the vibrating polycrystalline silicon film, as obtained through a numerical homogenization procedure over a representative film volume. To get insights into the effects of the parameters governing the nonlinear dynamics of the resonant structure, a Monte Carlo analysis is adopted. In the design of Lorentz force MEMS magnetometers, the coupled thermo-electro-magneto-mechanical fields governing the dynamics of the relevant compliant structures can be appropriately exploited to enhance their performances. In recent works, we showed that reduced-order models for the dynamics of the said movable structures can be recast in the form of theDuffingequation, where nonlinear terms arise from the multi-physics governing the problem. As stochastic effects may play a role due to the micrometric dimensions of the device, an investigation of the link between the statistics of sensor imperfections and output is here carried out. The said imperfections at the microscopic length-scale are modeled in terms of:overetch thickness, assumed to feature a uniform distribution in a proper interval matching available experimental data; and elastic properties of the vibrating polycrystalline silicon film, as obtained through a numerical homogenization procedure over a representative film volume. To get insights into the effects of the parameters governing the nonlinear dynamics of the resonant structure, a Monte Carlo analysis is adopted.